Interest Rates and Budget Deficits: A Study of the Advanced Economies (Routledge Studies in the Modern World Economy, 1)

INTEREST RATES AND BUDGET DEFICITS Does fear of higher inflation lead to higher interest rates? For the past decade, rising interest rates have dominated economic headlines. It now seems that the persistently low rates of the 1970s have given way to persistently high rates in the 1980s and 1990s. Interest Rates and Budget Deficits explores this phenomenon and discusses various aspects of interest rates across a range of developed countries. In particular, the authors examine: • the relationship between high budget deficits, debts and high interest rates; • the role of inflation expectations and the Fisher hypothesis; • empirical evidence from eleven advanced economies: Australia, Belgium, Canada, France, Germany, Italy, Japan, the Netherlands, Sweden, the U.K. and the U.S.A. Kanhaya L.Gupta and Bakhtiar Moazzami challenge a number of widely held conceptions, and their analysis produces some surprising results. It shows, above all, that cross-country generalizations about interest rate behaviour can be misleading and that factors specific to individual countries are still of vital importance. Kanhaya L.Gupta is Professor of Economics at the University of Alberta. Bakhtiar Moazzami is Associate Professor at Lakehead University. Both have published widely in the fields of macroeconomics and monetary policy.

ROUTLEDGE STUDIES IN THE MODERN WORLD ECONOMY 1 INTEREST RATES AND BUDGET DEFICITS A Study of the Advanced Economies Kanhaya L.Gupta and Bakhtiar Moazzami 2 WORLD TRADE AFTER THE URUGUAY ROUND Prospects and Policy Options for the Twenty-first Century Edited by Harald Sander and András Inotai 3 THE FLOW ANALYSIS OF LABOUR MARKETS International perspectives Edited by Ronald Schettkat

INTEREST RATES AND BUDGET DEFICITS A study of the advanced economies

Kanhaya L.Gupta and Bakhtiar Moazzami

London and New York

First published 1996 by Routledge 11 New Fetter Lane, London EC4P 4EE This edition published in the Taylor & Francis e-Library, 2005. “ To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to http://www.ebookstore.tandf.co.uk/.” Simultaneously published in the USA and Canada by Routledge 29 West 35th Street, New York, NY 10001 © 1996 Kanhaya L.Gupta and Bakhtiar Moazzami All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. Library of Congress Cataloging in Publication Data A catalogue record for this book has been requested. ISBN 0-203-98434-X Master e-book ISBN

ISBN 0-415-10135-2 (Print Edition) ISSN 1359-7965 (Print Edition)

To Pat, Lew and Neda

CONTENTS List of figures

vii

List of tables

xi

Acknowledgements

xvi

1 INTRODUCTION

1

2 PROBLEMS OF MEASURING EX-ANTE REAL INTEREST RATES

4

3 ESTIMATES AND BEHAVIOUR OF EX-ANTE REAL INTEREST RATES

8

4 INTEREST RATES, INFLATION AND TAXES

59

5 ON THE EXOGENEITY OF THE REAL INTEREST RATE

84

6 BUDGET DEFICITS AND INTEREST RATES: THEORY

131

7 BUDGET DEFICITS AND INTEREST RATES: THE EVIDENCE

139

8 SOME LESSONS

216

Notes

219

Select bibliography

222

Index

228

FIGURES 3.1

Short-term pre-tax ex-ante real interest rates

10

3.2

Pre-tax short-term real rates: survey method

21

3.3

Medium-term pre-tax ex-ante real interest rates

25

3.4

Real rates as index-linked bonds

31

3.5 Nominal, pre- and post-tax real short-term rates

34

3.6 Nominal, pre-and post-tax real medium-term rates

39

3.7

After-tax short-term real rate: survey method

43

5.1

Responses of the ex-ante short-term real interest rates to innovations: Australia

94

5.2

Responses of the ex-ante short-term real interest rates to innovations: Belgium

96

5.3

Responses of the ex-ante short-term real interest rates to innovations: Canada

98

5.4

Responses of the ex-ante short-term real interest rates to innovations: France

101

5.5

Responses of the ex-ante short-term real interest rates to innovations: Germany

104

5.6

Responses of the ex-ante short-term real interest rates to innovations: Italy

106

5.7

Responses of the ex-ante short-term real interest rates to innovations: Japan

109

5.8

Responses of the ex-ante short-term real interest rates to innovations: the Netherlands

112

5.9

Responses of the ex-ante short-term real interest rates to innovations: Sweden

114

5.10 Responses of the ex-ante short-term real interest rates to innovations: U.K.

116

5.11 Responses of the ex-ante short-term real interest rates to innovations: U.S.A.

119

7.1

140

Ex-ante real (short) rate and budget deficit

7.2 Ex-ante medium rate and budget deficit

151

7.3

Actual, fitted and conditional forecast of short-run interest rate: 166 Australia

7.4

Actual, fitted and conditional forecast of medium-term interest rate: Australia

7.5

Actual, fitted and conditional forecast of short-run interest rate: 170 Belgium

7.6

Actual, fitted and conditional forecast of medium-term interest rate: Belgium

7.7

Actual, fitted and conditional forecast of short-run interest rate: 174 Canada

7.8

Actual, fitted and conditional forecast of medium-term interest rate: Canada

7.9

Actual, fitted and conditional forecast of short-run interest rate: 178 France

7.10 Actual, fitted and conditional forecast of medium-term interest rate: France

166

170

174

178

7.11 Actual, fitted and conditional forecast of short-run interest rate: 181 Germany 7.12 Actual, fitted and conditional forecast of medium-term interest rate: Germany

182

7.13 Actual, fitted and conditional forecast of short-run interest rate: 186 Italy 7.14 Actual, fitted and conditional forecast of medium-term interest rate: Italy

186

7.15 Actual, fitted and conditional forecast of short-run interest rate: 190 Japan 7.16 Actual, fitted and conditional forecast of medium-term interest rate: Japan

190

7.17 Actual, fitted and conditional forecast of short-run interest rate: 194 the Netherlands 7.18 Actual, fitted and conditional forecast of medium-term interest rate: the Netherlands

194

7.19 Actual, fitted and conditional forecast of short-run interest rate: 198 Sweden 7.20 Actual, fitted and conditional forecast of medium-term interest rate: Sweden

198

7.21 Actual, fitted and conditional forecast of short-run interest rate: 202 U.K. 7.22 Actual, fitted and conditional forecast of medium-term interest rate: U.K.

203

7.23 Actual, fitted and conditional forecast of short-run interest rate (real actual federal deficits): U.S.A.

208

7.24 Actual, fitted and conditional forecast of medium-term interest rate (real actual federal deficits): U.S.A.

208

7.25 Actual, fitted and conditional forecast of short-run interest rate (real national income deficits): U.S.A.

209

7.26 Actual, fitted and conditional forecast of medium-term interest rate (real national income deficit): U.S.A.

209

TABLES 3.1

Mean and standard deviation of pre-tax ex-ante real short-term interest rates: auto and Mishkin estimates

16

3.2 Data used for nominal medium-term interest rates

22

3.3

Mean and standard deviation of pre-tax ex-ante real mediumterm interest rates

23

3.4

Short-term and medium-term pre-tax ex-ante real interest rates for 1990:4

30

3.5

Mean and standard deviation of post-tax ex-ante real short-term interest rates: auto and Mishkin estimates

32

3.6

Mean and standard deviation of post-tax ex-ante real mediumterm interest rates: auto and Mishkin estimates

33

3.7

Correlations between nominal and ex-ante real interest rates

43

3.8

Testing for unit root based on equation (4)

50

3.9

Maximum likelihood estimate of model (8) (ex-ante real shortterm rates)

53

3.10 Testing for unit root based on equation (4)

54

3.11 Unit root test: allowing for one-time break

55

3.12 Maximum likelihood estimate of model (8) (ex-ante real medium 56 rates) 4.1

Testing for unit root short-run nominal interest rates

64

4.2

Unit root test: allowing for one-time break short-run nominal interest rates

65

4.3

Testing for unit root short-run inflationary expectations (Mishkin 65 method)

4.4

Unit root test: allowing for one-time break short-run inflationary 66 expectations

4.5

Summary results of stationarity tests

67

4.6

Fisher hypothesis using short-term interest rates

68

4.7 Fisher hypothesis using post-tax short-term interest rates

71

4.8

Testing for unit root medium-run nominal interest rates

74

4.9

Unit root test: allowing for one-time break medium-term nominal 75 interest rates

4.10 Testing for unit root medium-run inflationary expectations

75

4.11 Unit root test: allowing for one-time break short-run inflationary 76 expectations 4.12 Summary results of stationarity tests

76

4.13 Fisher hypothesis using pre-tax medium-term interest rates

78

4.14 Fisher hypothesis using post-tax medium-term interest rates

82

5.1

Granger causality test of the ex-ante real short-term interest rate

90

5.2

Proportions of forecast error K quarters ahead, produced by each 92 innovation (Australia: 1969:3–1990:4)

5.3

Proportions of forecast error K quarters ahead, produced by each 95 innovation (Belgium: 1969:3–1990:4)

5.4

Proportions of forecast error K quarters ahead, produced by each 97 innovation (Canada: 1969:3–1990:4)

5.5

Proportions of forecast error K quarters ahead, produced by each innovation (France: 1969:3–1990:4)

100

5.6

Proportions of forecast error K quarters ahead, produced by each innovation (Germany: 1969:3–1990:4)

102

5.7

Proportions of forecast error K quarters ahead, produced by each innovation (Italy: 1969:3–1990:4)

105

5.8

Proportions of forecast error K quarters ahead, produced by each innovation (Japan: 1969:3–1990:4)

107

5.9

Proportions of forecast error K quarters ahead, produced by each innovation (Netherlands: 1969:3–1990:4)

110

5.10 Proportions of forecast error K quarters ahead, produced by each innovation (Sweden: 1969:3–1990:4)

112

5.11 Proportions of forecast error K quarters ahead, produced by each innovation (U.K.: 1969:3–1990:4)

115

5.12 Proportions of forecast error K quarters ahead, produced by each innovation (U.S.A.: 1969:3–1990:4)

117

5.13 Granger causality test of the ex-ante real medium-term interest rate

121

5.14 Granger causality tests of exogeneity of ex-ante real rates (1969:3–1990:4)

128

5.15 Existence of a causal relationship between real rate and money supply (1969:3–1990:4)

129

5.16 Existence of a causal relationship between real output and real interest rates (1969:3–1990:4)

129

5.17 Existence of a causal relationship between real rate and expected rate of inflation

130

7.1

164

Instrumental variable estimation: Australia

7.2

Mean values of actual, fitted and conditional forecast of interest 167 rates in Australia

7.3

Instrumental variable estimation: Belgium

7.4

Mean values of actual, fitted and conditional forecast of interest 171 rates in Belgium

7.5

Instrumental variable estimation: Canada

7.6

Mean values of actual, fitted and conditional forecast of interest 175 rates in Canada

7.7

Instrumental variable estimation: France

7.8

Mean values of actual, fitted and conditional forecast of interest 179 rates in France

7.9

Instrumental variable estimation: Germany

168

172

176

180

7.10 Mean values of actual, fitted and conditional forecast of interest 182 rates in Germany 7.11 Instrumental variable estimation: Italy

183

7.12 Mean values of actual, fitted and conditional forecast of interest 185 rates in Italy 7.13 Decomposition of the variance of money supply in Italy

187

7.14 Instrumental variable estimation: Japan

188

7.15 Mean values of actual, fitted and conditional forecast of interest 191 rates in Japan 7.16 Instrumental variable estimation: the Netherlands

192

7.17 Mean values of actual, fitted and conditional forecast of interest 195 rates in the Netherlands

7.18 Instrumental variable estimation: Sweden

196

7.19 Mean values of actual, fitted and conditional forecast of interest 199 rates in Sweden 7.20 Instrumental variable estimation: U.K.

200

7.21 Decomposition of the variance of money supply in the U.K.

202

7.22 Mean values of actual, fitted and conditional forecast of interest 204 rates in the U.K. 7.23 Instrumental variable estimation: U.S.A.

205

7.24 Decomposition of the variance of money supply in the U.S.A.

207

7.25 Mean values of actual, fitted and conditional forecast of interest 210 rates in the U.S.A. 7.26 Impact of deficits on short-run interest rates

211

7.27 Impact of deficits on medium-term interest rates

213

7.28 Impacts of money, inflation and trade balance on short-run interest rates

214

7.29 Impacts of money, inflation and trade balance on medium-term 214 interest rates

ACKNOWLEDGEMENTS We would like to express our sincere thanks to the anonymous reader at Routledge for very constructive criticisms and suggestions. The sequencing of the chapters is in no small measure due to the suggestions of the referee. Our thanks also go to Charlene Hill for her excellent typing of numerous drafts. We would like to acknowledge the permission granted by the editor of Public Finance for using the material in our paper, ‘Dynamic Specification and the Long-run Effect of Budget Deficits on Interest Rates’, Public Finance, XXXXVI/No. 2/1991. Finally, we would like to thank Dr V.Tanzi for supplying the data on tax rates for the U.S.A.

1 INTRODUCTION The behaviour of nominal and real interest rates in the developed countries over the last several decades has been the subject of considerable scrutiny and debate. But in spite of the various controversies surrounding this issue, it is rather strange that most of the empirical literature in this area has been confined to the U.S.A. Our aim in this study is to fill this gap to some extent. However, we would like to add that the aim is not only to extend the coverage to more countries, but also to suggest, what we hope, are better ways of answering the questions to be explored. At a more specific level, we plan to ask some of the same kinds of questions which have been asked over the last decade or so about the behaviour of real interest rates. And we do that for a sample of eleven developed countries. Thus we ask: (a) How should we measure the ex-ante real interest rates, given that they are generally not observable in most countries? (b) Do the measured rates remain constant over time? (c) Do they tend to be equal across the countries? If so, does the equality hold only in the long run? (d) Does the Fisher hypothesis hold in all countries and in all time periods covered? Once again, does the validity of this hypothesis depend on whether we are dealing with the long term only? (e) Do the real rates tend to be exogenous in a world characterized by a certain set of variables? (f) Do budget deficits matter in determining the intertemporal behaviour of the real rates? Do they account for the persistently high rates in the 1980s and persistently lower rates in the 1970s? Would the rates have behaved differently if the time path of the deficits had been different? (g) Is the answer to one or more of the above questions sensitive to the particular time period covered or to how the real rates are generated or the type of the interest rate used? Of course, there are other questions one could ask. But given the number of the countries covered in our sample, we confine ourselves to a manageable set of questions. In order to assist the reader in the reading of our work, we offer a brief summary of the chapters to follow.

Interest rates and budget deficits

2

Chapter 2. The first major problem about the subject under consideration is that the variable of our inquiry, namely the ex-ante real interest rate, is not directly observable except in the case of index-linked bonds. This means that some proxy must be found. This chapter discusses alternate means of generating them, including the advantages and disadvantages of each method. It also discusses the problems with the real rates obtained from index-linked bonds. Since the real rates used in economic decision making are often post-tax rates, we also comment upon them. Chapter 3. The estimation methods discussed in the last chapter are used to present estimates of the ex-ante real interest rates for the eleven countries. The interest rates covered are both short term and medium term. These estimates are then used to examine their intertemporal behaviour. For example, were the estimated rates higher during the 1980s than during the 1970s, as is commonly believed? Did their variability differ between different decades? Do the estimates indicate any significant structural breaks? These rates are further used to examine questions about the international linkages and the equality of the rates across the countries. But before doing that, the chapter presents extensive evidence on the time series properties of the estimated rates. Then using a model which is a combination of Mishkin (1984) and Wickens and Breusch (1988), we test three hypotheses: first, whether the rates are linked internationally; second, whether this linkage is full or partial; and, third, whether the rates are equal internationally. An interesting aspect of the methodology used is that it allows us to test both the long-run and the short-run relationship as well as to allow us to estimate the speed of adjustment of the estimated rates to their long-run equilibrium values. Chapter 4. This chapter deals with one of the most important hypotheses in monetary economics, namely, the Fisher hypothesis. A distinctive feature of the evidence presented is that it is also based on the methodology used in Chapter 3. In other words, we are able to distinguish between the long-run validity of the hypothesis versus the short-run verification. Chapter 5. Here we explore the question first discussed in detail by Litterman and Weiss (1985), namely, the question about the exogeneity of real interest rates. This is done using the Granger causality test and the innovation accounting technique. We first test the null hypothesis that the real rate is exogenous relative to a universe that includes money, real output and expected inflation. Then, as an additional test of exogeneity of the real rates, we decompose their variance into components explained by orthogonalized innovations in money, real output and expected inflation. Chapter 6. From the properties of the real rates, in this chapter we turn to what is arguably the most talked about and controversial policy issue in the literature on interest rates. We are, of course, referring to the role of budget deficits. It has been suggested that in order to appropriately discriminate between the competing paradigms on this issue, we must be able to distinguish between the effects of permanent vis-à-vis transitory changes in budget deficits (Bernheim, 1989). In this chapter we propose a model which allows us to achieve this goal without the necessity to generate such proxies and thus enables us to distinguish between the competing paradigms. Chapter 7. This chapter provides the most extensive evidence to date on the role of budget deficits on interest rates. This is done in three stages. First, we look at the descriptive evidence on deficits and the estimated rates and check whether the data display any regularities which require explanation. Second, we provide a very brief

Introduction

3

survey of the existing evidence. Finally, we estimate the model of Chapter 6 and also employ the innovation accounting technique used in Chapter 5. An interesting feature of these results is the simulations done to trace the time path of the estimated rates if the deficit is set equal to zero over the time horizon under consideration. Chapter 8. Since the evidence is very extensive, no attempt is made in the final chapter to summarize the results. That is done in each chapter individually. However, we simply try to gather together some broad lessons which emerge from our findings and the use of the methodology employed.

2 PROBLEMS OF MEASURING EX-ANTE REAL INTEREST RATES It was pointed out in Chapter 1 that the relevant interest rates for economic decision making are the post-tax ex-ante real interest rates. Leaving aside the question of taxes for the moment, even the estimation of pre-tax ex-ante real interest rates poses problems because they are not directly observable in general. Even for the index-linked bonds, where such rates are directly observable, there are serious difficulties, as discussed below. This chapter briefly describes the various approaches to the estimation of such rates in the literature and the approaches used by us. ALTERNATE METHODS OF ESTIMATING EX-ANTE REAL INTEREST RATES For ease of discussion, we distinguish four approaches: 1 direct estimates from index-linked bonds; 2 survey method based on direct estimates of inflation expectations; 3 standard method using current and/or past rates of inflation to estimate inflation expectations; and 4 the rational expectations approach. Since the four methods of estimation are relatively well known, our discussion is brief. Clearly, the most attractive solution would be if we could directly observe such rates. In principle, yields on index-linked bonds could provide such a measure. But, unfortunately, as, for example, Wormell (1985), has pointed out there is no commonly agreed method for calculating the real yields on such bonds, and the yields published by brokers and newspapers tend to differ widely. This happens because of the differences in the assumptions made about expected inflation. Generally, two approaches are used to formulate such expectation: either that inflation would continue at a constant rate, starting from a certain date, or that it will continue at a level equal to the average of some recent period. Both assumptions have disadvantages. Therefore, brokers tend to publish yields based on a range of retail price index changes and let the users choose what they like. The result, according to Wormell is that, ‘the yields on index-linked stocks have swung widely since their introduction. This volatility has been a result of not changes in real returns in the economy, but of other, more technical reasons’ (p. 101). Thus, it is clear that even if we had such estimates available for all of the countries in our sample, they would not necessarily provide an accurate measure of the ex-ante real interest rates. But a more practical limitation for us is that such rates are available only for the U.K. and those

Problems of measuring ex-ante real interest rates

5

too only since March 1981. However, just for the sake of comparison with alternate estimates, we would use the available information on these rates in the next chapter. A rather popular method for estimating ex-ante real interest rates, whether pre- or post-tax, in the United States has been based on the use of survey data on inflation expectations. Of course, once data on expected inflation is given, the rest of the calculations are not that difficult. The main question when this method is used is whether the survey data represent unbiased measure of the inflation expectations, i.e., whether they are consistent with the rational expectations hypothesis. Existing empirical evidence suggests that the survey data on inflation expectations are not an unbiased measure of expected inflation. (See, for example, Baghestani (1992), among others.) In fact, in a recent study, Lahiri and Zaporowski go on to conclude that, the expected inflation series resulting from the rationally expected real rate model supports the hypothesis of unbiasedness. However, the original data does not support the unbiasedness property. Since the Livingston series typically underestimates the true market expectations, the use of this data to compute real interest rates will tend to overestimate actual exante real interest rates. (1988, p. 310) The estimates reported in the next chapter support this conclusion. Quite apart from the use of survey data as being the most appropriate measure of expected inflation, like the yields on index-linked bonds, here we also face a practical problem. Such survey data are available for very few countries in our sample. Consequently, given the shortcomings of using such data, as discussed above, and the lack of such data for most of the countries in our sample, we would only provide evidence for the U.S.A. in the next chapter just to highlight the differences with respect to alternate estimates. This takes us to what we call the standard method. This method constructs proxies for expected inflation, based on current and/or past inflation rates. There is no commonly agreed-upon formula, so that there are various alternatives, for example, the adaptive procedure, the extrapolative procedure, a mixture of the two and so on (see, for example, Cukierman (1977) and Lovell (1986), among others). But regardless of the scheme used, the starting point for the estimates is the Fisher equation, which in its approximate form is given by (1) where R represents the ex-ante real interest rate, NI the nominal interest rate, and PE the expected rate of inflation, which an investor expects to prevail over the holding period. In order to estimate PE, we use the autoregressive approach. This approach is somewhat different when used for the short- and medium-term ex-ante real interest rates. Since estimates for both rates are reported in the next chapter, the differences in the method used are explained below. Our procedure closely follows that of Blanchard and Summers (1984). For the short rate, we use rolling autoregressive forecasts, for one quarter ahead, reestimating the equation on the basis of the last twenty quarters, using six lags of inflation.

Interest rates and budget deficits

6

We also tried eight lags and twenty-four quarters, but the results were neither better nor different. When we used four quarter lags of inflation, the results were decidedly inferior. The medium rates pose a somewhat different problem because the maturity period of medium-term securities is more than a quarter. Therefore, medium ex-ante real interest rates are constructed by (2)

where

and

are the real and the nominal rates on bonds of maturity j and

is the mean nominal PEt,t+k is the forecasts of inflation in period t+k, as, of time t. rate of interest over the period examined. It is important to note that although the forecasts of inflation are generated by the same formula as for the short rate, in this case forecasts are generated over the life of the bond and not one period ahead only. It is clear that the estimates of the ex-ante real interest rates generated by the above method are sensitive to the estimates of PE. The autoregressive procedure used for estimating expected inflation has been criticized on many grounds, the most important being that economic agents may formulate their price expectations on the basis of more information than the current and past behaviour of inflation alone. This suggests the need for an approach which completely avoids the use of expected inflation in the measurement of ex-ante real interest rates. Such an approach has been proposed by Mishkin (1984). This approach exploits the hypothesis of rational expectations to generate a series on the ex-ante real interest rate and then the series on the expected rate of inflation is derived as a by-product by using equation (1). This approach can be briefly described as follows: Define the ex-post real interest rate as (3) when EPR is the ex-post real interest rate and is the actual rate of inflation. The ex-ante real interest rate is then given by (4) where E is the expectations operator. Combining equations (3) and (4) we get (5) where (6) Invoking the assumption of rational expectations for future inflation, we have

Problems of measuring ex-ante real interest rates

7

(7) where Z is the set of all available information at time t (for simplicity, time subscripts have been omitted in the above equations except (2)). Mishkin (1984) proposes that the best linear prediction of E(EPR) given X be used as an estimate of the ex-ante real interest rate, where X is a subset of the information set Z which is observed and which is assumed to be correlated with E(EPR). In other words the projection equation for ex-ante real interest rate is (8) where v is the projection equation error. Substituting (8) into (5) we get (9) The estimated ex-ante real interest rates are the predicted value from equation (9): (10) We can immediately see that by using the values of EPR and equation (1), we can get (11) where PÊ is the estimated value of expected inflation by Mishkin’s method. The estimates of expected inflation from (11) and the autoregressive scheme are used to examine the Fisher hypothesis and the Mundell-Tobin effect. PRE-TAX VERSUS POST-TAX EX-ANTE REAL INTEREST RATES As mentioned above, the relevant interest rates for economic decision are the post-tax exante real interest rates. This means that we must have information on how the nominal interest incomes are treated for tax purposes. In the case of the index-linked bonds, the added problem of how the inflation premium is taxed must be considered. For the other three methods, we must have time series data on the marginal rate of tax on interest income. Given the different treatment of interest income in different countries, preparation of such data are well beyond the scope of such a study. However, some time series data for the U.S.A. and some summary data for a number of other countries are available. These data are used to provide estimates of the post-tax ex-ante real interest rates wherever possible.

3 ESTIMATES AND BEHAVIOUR OF EXANTE REAL INTEREST RATES This chapter presents the estimates of the ex-ante real interest rates for the eleven countries included in this study. This is done, wherever possible, using the four procedures discussed in the last chapter. While the estimates for the pre-tax interest rates are presented for all of the countries included, the post-tax are presented only for a subset of the sample, because of the unavailability of the tax rate data. The rates included are both short and medium term. The estimated rates are used to shed light on two specific issues: first, whether the observed nominal interest rates have served as a reliable proxy or a signalling device for the behaviour of the ex-ante real interest rates, and second, whether they have been equal across the countries. THE ESTIMATES OF THE SHORT-TERM PRE-TAX EX-ANTE REAL INTEREST RATES In order to estimate the short-term pre-tax ex-ante real interest rates, we need a measure of the nominal interest rate and of the price index. Since there is no consensus on what constitutes ‘the’ short-term interest rate or ‘the’ price index, the usual practice in singlecountry studies is to use alternate measures of both variables and check whether the resulting estimates of the ex-ante real interest rates are sensitive to the alternate measures. Such an approach is not feasible for this study for two reasons. First, given the large number of countries included in our sample, the sheer size of the exercise would constrain such an approach. Second, and even more important, in order to render the results comparable, we need data which to a considerable degree are comparable, which is not possible for too many of the alternatives. Consequently, we use the three-month treasury bill rate as a measure of the short-term nominal interest rate for Canada, the Netherlands, the U.K. and the U.S.A. For the other countries, the short-term rate is represented by the money market rate. For the price index, we use the consumer price index. The data used are quarterly and generally cover the period from 1967:2 to 1990:4. The period prior to 1967:2 was used up in calculating the expected rates of inflation so that estimates of the ex-ante real interest rates for that period cannot be provided, unless data on the price index are available since 1957 which is not the case. Since most of the discussion in this chapter and the subsequent chapters is based on the estimates derived by using the standard method and the rational expectations hypothesis, we start by presenting estimates using these methods. The specific standard method used was described in Chapter 2. But some further details of the rational expectations hypothesis are required before we can present the estimates. In order to

Estimates and behaviour of ex-ante real interest rates

9

implement the rational expectations or the Mishkin approach, we need to specify the variables in the information subset X. The variables finally selected were the current nominal interest rate, three lagged values of actual inflation, time, time squared, time cubed and time raised to the power four. We also tried more lagged values of inflation and both higher and lower degree polynomials in time. But the results, using Akaike’s Final Prediction Error criterion showed that our preferred selection of the variables was the best. Therefore, the ex-ante real interest rates by the Mishkin method are the fitted values from the regressions of the ex-post real rates on information, as defined above, at the beginning of the period. The series on expected inflation by this method can be obtained by using equation (11) in Chapter 2. In the tables and the figures that follow, we have used certain notations. The shortterm pre-tax ex-ante real interest rates estimated by the autoregressive and the Mishkin approaches are denoted by RAUT and RHMISHK, respectively, and the expected inflation rates by PH and PMISHK, respectively. The short-term nominal interest rate is denoted by NI. The two estimates of the short-term pre-tax ex-ante real interest rates are given in Figure 3.1, while their means and standard deviations are given in Table 3.1. Looking at Figure 3.1, its first striking feature is the very close similarity between the two estimates for each of the eleven countries. This inference is further confirmed from the data in Table 3.1. The means and the standard deviations for the different periods for each country are very close, many a time virtually identical. This close correspondence between the two estimates is quite remarkable when we consider how different are the two estimation procedures. This should provide us considerable confidence in our estimates, because clearly they are not very sensitive to these two alternate estimation procedures. We now turn to a detailed discussion of these estimates, both ove time for each country and across countries for a comparative analysis, paying particular attention to the 1980s. In a study involving as large a number of countries as this one, it is always problematic to decide how to organize the discussion. Since the behaviour of ex-ante real interest rates in each country is of interest in its own right, quite apart from how it relates to that in the other countries, we have organized our analysis on a country-by-country

Interest rates and budget deficits

10

Figure 3.1 Short-term pre-tax ex-ante real interest rates r

Estimates and behaviour of ex-ante real interest rates

11

Interest rates and budget deficits

12

basis and draw comparative conclusions wherever appropriate. In the case of Australia, the short-term pre-tax ex-ante real interest rate has increased systematically over the four sub-periods. We can see from Table 3.1 that it was the lowest in the 1960s and the highest in the second half of the 1980s, being over twice the mean rate in the 1970s. The behaviour in the 1980s is also interesting in that the rate increased from the early to the late 1980s. The increase

Estimates and behaviour of ex-ante real interest rates

13

in the mean rate of nearly 860 basis points between the 1960s and the 1980s is quite remarkable. It is important to note that along with this increase, their variability also increased, although this increase was more marked from the 1960s to the 1970s than from the 1970s to the 1980s. In fact, the decline in the variability in the late 1980s compared to the early 1980s is noteworthy, considering that the real rate increased. This positive relationship between increases in the

Interest rates and budget deficits

14

real rate and in variability in the earlier periods, followed by a negative relationship in the later period suggest that the role of uncertainty may not have been symmetrical during the 1980s. This issue is explored in more detail later on. It is clear from Figure 3.1 that these averages mask important variations within each period. It is thus important to look more deeply into the 1980s. Using the autoregressive estimates, we find

Estimates and behaviour of ex-ante real interest rates

15

that the real rate in 1990:4 was 10.36 per cent as against 10.67 per cent in 1980:1, hardly any change. The estimates seem to reveal a number of fundamental breakpoints. For example, in 1983:1, then in 1988:1, after which the real rate continued to rise until 1989:3 and then started to decline. But the rate still remained very high. A comparison with the other countries is also revealing. Thus, we find that during the 1980s Australia had the highest real rate and also the greatest variability among the countries covered here. For example, compared to the U.S.A., the real rate was almost 500 basis points higher. This comparison is all the more revealing when we note that the Australian real rate was higher by only 150 basis points in 1980:1, but this difference in 1990:4 had shot up to 422 basis points, almost three times as much. A further comparison with the non-European countries, that is, Canada, Japan and the U.S.A., shows that the general trend towards lower short-term real rates was similar, though less pronounced. In short, Australian short-term pre-tax ex-ante real rates are characterized by high and variable levels and show a recent tendency towards declining, a tendency shared by many of the other countries in the sample. The two estimates for Belgium again reveal an identical pattern. From Table 3.1, the mean short-term real rate was 2.89 in the 1960s, rising to 4.09 in the 1970s and then to 6.2 per cent in the late 1980s. It is interesting to note that unlike Australia, the mean real rate in Belgium declined from the early to the late 1980s. But like Australia, these rising mean rates are not accompanied by increasing volatility. In fact, the value of the standard deviation in the 1980s is hardly different from that in the 1960s, but lower than that in the 1970s. Thus, in the case of Belgium, increased real rates in the 1980s have been accompanied by reduced volatility. This again points to a potential role for uncertainty, though the direction of causality is no longer as transparent as in the case of Australia.

Interest rates and budget deficits

16

Table 3.1 Mean and standard deviation of pre-tax ex-ante real short-term interest rates: auto and Mishkin estimates* Country

1967:3– 1990:4 Me an

Aus tralia Belgium

8.93

1967:3– 1969:4

1970:1– 1979:4

1980:1– 1984:4

1985:1–1990:4

St. dev.

Me an

St. dev.

M ean

St. dev.

M ean

St. dev.

M ean

St. dev.

4.1

3.88

0.75

6.28

2.24

11.63

2.81

13.22

2.20

(9.00) (4.1) (3.75) (0.66) (6.39) (2.17) (11.50) (2.50) (13.44) (2.25) 5.47

2.67

2.89

1.73

4.09

2.23

8.53

1.86

6.28

1.14

(5.44) (2.60) (2.86) (1.39) (4.05) (2.16) (8.64) (1.50) (6.17) (1.08) Canada

7.41

3.18

5.39

1.07

5.21

2.19

10.86

2.63

9.06

1.82

(7.39) (3.17) (5.24) (0.81) (5.19) (2.15) (10.87) (2.70) (9.07) (1.66) France

7.53

2.39

5.92

1.76

6.20

1.89

10.53

1.87

7.93

0.95

(7.52) (2.42) (5.90) (1.64) (6.13) (1.89) (10.73) (1.67) (7.84) (0.89) Germany 5.07

2.42

2.84

1.80

4.74

2.56

6.89

2.20

5.03

1.47

(5.06) (2.30) (2.77) (1.48) (4.75) (2.38) (7.00) (2.01) (4.93) (1.36) Italy

9.01

3.86

3.32

0.60

7.40

2.85

13.96

1.97

10.54

0.97

(9.15) (3.86) (3.18) (0.37) (7.47) (3.03) (13.94) (1.53) (10.43) (0.89) Japan

5.38

1.89

5.22

1.13

5.15

2.17

6.56

1.68

4.86

1.45

(5.36) (1.65) (5.01) (0.65) (5.15) (2.01) (6.50) (1.23) (4.87) (1.06) Nether lands Sweden

5.18

2.83

4.10

1.89

4.20

3.44

6.79

2.19

5.98

1.35

(5.09) (2.78) (3.62) (1.64) (3.98) (3.20) (7.16) (2.20) (5.85) (1.20) 7.00

3.22

5.47

1.31

4.38

2.27

9.58

1.78

9.82

1.67

(6.93) (3.21) (5.03) (0.94) (4.25) (2.12) (9.89) (1.32) (9.71) (1.59) U.K.

7.64

2.81

6.14

0.79

5.83

2.44

9.16

1.98

10.02

1.92

(7.66) (2.60) (5.51) (0.43) (5.90) (2.08) (9.39) (1.53) (10.04) (1.40) U.S.A.

5.97

2.26

4.78

0.63

4.53

1.25

9.19

2.03

6.11

1.00

(5.90) (2.24) (4.46) (0.51) (4.47) (1.32) (9.14) (1.85) (6.11) (0.81) *The figures in parentheses are those based on Mishkin procedure.

Figure 3.1 reveals considerable variation during each sub-period. Thus, there seems to be a sudden break in 1979:3 when the real rate jumped from 4.78 per cent in the previous

Estimates and behaviour of ex-ante real interest rates

17

quarter to 8.2 per cent in 1979:3. The rates remained relatively high until 1983:1 and then went down to 5.9 per cent in the next quarter. During the last two years of the 1980s, we see a pattern somewhat different from Australia, in that the rate continuously rises from 1988:4 to 1990:1 and then declines and rises, alternately. A look at the figures for France, Germany and the Netherlands shows a close correspondence between the four towards the last four years of the 1980s. It is also interesting to note that the estimates for France and Germany suggest a breakpoint in 1979:3 and those for the Netherlands a quarter later. Use of monthly data may reveal a closer correspondence between the timing of this breakpoint. What is thus clear is that in the case of Belgium, the short-term ex-ante real rate did not remain constant over the period, but it did not show the same increasing volatility with rising levels as was the case with the Australian rate. According to Table 3.1, the mean short-term pre-tax ex-ante real rate in Canada remained virtually constant from the 1960s to the 1970s and then increased by almost 467 basis points in the 1980s. In this respect, Canadian experience is different from Australia and Belgium in the earlier periods, but shares the same characteristic in the 1980s. But if we look at the two sub-periods of the 1980s, Canada’s experience is more like that of Belgium than Australia. However, when we turn to the volatility of these mean rates, the results are even more different. The first interesting part of these estimates is that although the mean rate hardly changes between the 1960s and the 1970s, the standard deviation almost doubles, suggesting much greater volatility in the 1970s. On the other hand, when the mean rate nearly doubles from the 1970s to the 1980s, the variability hardly changes. The value of the standard deviation increases only marginally from 2.19 to 2.37. The pattern of the French short-term real rate seems to mirror the Canadian experience. From Table 3.1, the mean rate remains virtually constant from the 1960s to the 1970s, although, unlike Canada, it rises marginally rather than falls in the second period. But in the 1980s, it increases by about 290 basis points, whereas the corresponding increase in Canada was greater. But unlike any of the other three countries discussed so far, in this case the variability remains almost constant until the mid-1980s, declining sharply thereafter. It is also interesting to note that the mean rate in the 1980s was higher than that for members of the G-7 or for the European countries, the rate for the two being 8.53 and 8.57 per cent, respectively. Compared to the U.S.A., the French rates were higher in each period. Turning to the behaviour in the 1980s, there is a sharp jump in 1979:4, then again a breakpoint in 1981:2. During 1988 it varied between a very narrow range of around 6.75 per cent. In 1989 it moved closer to 8 per cent and then in 1990 to 9 per cent. Thus, in the case of France, short-term pre-tax real rates have remained far from constant during the 1980s and relative to a number of the OECD countries have tended to be on the high side. The behaviour of the short-term real rates in the 1980s is quite different from that of the other countries in the sample, except to some extent for Japan. The real rate varied from a low of 2.87 per cent to a high of 11.09 per cent during the 1980s. But this maximum occurred in 1981:3. From Table 3.1, it is clear that the mean short-term real rate for Germany increased right from the 1960s to the mid-1980s, the increase being almost 215 basis points from the 1970s to the mid-1980s. But from the mid- to the late 1980s, the mean rate showed a

Interest rates and budget deficits

18

sharp decline, being equal to 186 basis points. Thus, Germany’s experience during the 1980s parallels that of Belgium, Canada and France, even though the absolute rates in Germany were much lower than in the other three countries. In terms of the volatility, Germany’s experience corresponds to that of Belgium, first suggesting a positive and then a negative relationship between changes in real rate and the level of variability. The behaviour of the short-term real rates in Germany in the 1980s is quite different from that of the other countries in the sample, except to some extent for Japan. The real rate varied from a low of 2.87 per cent to a high of 11.09 per cent during the 1980s. But this maximum occurred in 1981:3. For most of the rest of the decade, the real rate remained at or well below 5 per cent and went as high as 8 per cent in 1990:3, then declining to 7.5 per cent in 1990:4. A comparison with the other countries in the sample is most revealing. In the 1960s, Germany had the lowest mean pre-tax ex-ante real short-term rate, but by the 1970s, this was no longer the case, although it still was one of the lowest. But Germany again regained this distinction in the 1980s if we exclude Japan, although even Japan’s rate was only marginally lower, a mere 25 basis points. An even more remarkable aspect of the estimates for Germany vis-à-vis the other countries in the sample is that Germany experienced, excluding Japan, by far the smallest increase in the real rate from the 1970s to the 1980s, a mere 113 basis points. A comparison with the U.S.A. is also revealing. From the mean rates given in Table 3.1, the U.S. estimate for the 1980s exceeds the German estimate by 165 basis points. But if we consider the last five quarters, we find that the U.S. real rates have declined while German rates have moved up with the result that unlike the mean for the whole decade, the German real rate in the last three quarters of 1990 were higher than those of the U.S.A. On the whole though, during most of the period covered, Germany experienced rather low short-term rates accompanied by low and declining variability. Only in the late 1980s did the rates show a tendency to catch up with those in many of the other countries. For Italy, the real rate of interest went up from a low of 3.32 per cent in the 1960s to 7.40 per cent in the 1970s and then again to 12.09 per cent in the 1980s. Thus, Italy experienced almost the highest increases in the two periods in the entire sample. What is more, the mean rate in the 1960s was among the lowest, but by the 1970s it had become the highest among the eleven countries and, with the exception of Australia, the same being the case in the 1980s. This behaviour is even more strikingly different if we compare it to the U.S.A. Thus, in the 1960s, the U.S. real rate exceeded that of Italy by about 146 basis points, but by the 1970s the Italian rate exceeded the U.S. rate by almost double the amount, 187 basis points, and in the 1980s this gap increased to 457 basis points. It should be noted, however, that in the second half of the 1980s, the Italian shortterm rate, though still the highest in the sample (except for Australia), had nevertheless gone down considerably compared to the mid-1980s, by almost 340 basis points. In terms of the variability of the real rate, Italy also displays a distinctly different pattern. In the 1960s, Italy experienced the lowest standard deviation in its short-term real rate, but by the 1970s this had not only gone up by a factor of almost five, but had also become the largest in the sample, if we exclude the Netherlands. But in the 1980s, although, as already pointed out, the real rate again increased sharply, its variability declined considerably, being close to those of the other members of the G-7. Relative to the other countries in the sample, Italy thus presents one of the most important exceptions and it

Estimates and behaviour of ex-ante real interest rates

19

would be interesting to examine in the subsequent chapters the reasons for this distinctive experience. Turning to the experience during the 1980s, we can see from Figure 3.1 that the high mean rate for the 1980s masks considerable variations. For example, during this period, the rate ranged from a maximum of 17.65 per cent in 1981:2 to a low of 8.84 per cent in 1987:1, thus suggesting a breakpoint during the latter quarter. After reaching the peak in 1981:2, the real rate has shown a marked tendency to decline, although during 1989 and 1990 it has tended to stabilize around 11 per cent, except for the last quarter when it went down by over 100 basis points. Thus, while the rate peaked in the early 1980s and has shown a steady decline since, it has nevertheless tended to remain at a relatively high level, most often equalling or exceeding 10 per cent. These kind of high real rates during the 1980s have not been the experience of most of the members of the G-7 or for that matter of the other countries in the sample. In terms of the mean real rates of interest reported in Table 3.1, Japan stands out as the most unique case. The mean rate seems to have remained virtually constant over the 1960s and the 1970s, rising in the first half of the 1980s and then going down in the second half. It is also distinguished by the fact that the mean rate remained at the lower level of about 5 per cent. While in the 1960s, this rate was nowhere near the lowest rates experienced by the other countries, for example only 2.84 per cent for Germany, nevertheless by the 1970s it had become one of the lower ones and by the 1980s it was the lowest. A comparison with the U.S.A. is revealing here. Thus, while in the 1960s and the 1970s, the U.S. mean real rate was lower than that of Japan by about 55 basis points, in the 1980s the difference had turned the other way, with the U.S. mean real rate exceeding the Japanese rate by as much as 200 basis points. In terms of the volatility of the mean rates, Japan’s experience is more like Belgium and Germany, namely, a decline in volatility accompanied by an increase in the real rate. These mean rates, however, give an exaggerated view of the constancy of the pre-tax short-term ex-ante real rates in Japan, as can be easily verified from Figure 3.1. A number of turning points can be identified; for example, some of the possible breakpoints are 1974:4 and 1980:1. Since 1981:1 the real rate has tended to be relatively lower, until 1990. During 1990, the rate moved between 6 and 7.6 per cent. A comparison of Figure 3.1 for Japan and for the U.S.A. shows a certain correspondence between the temporal behaviour of the short-term real rates in the two countries, but the Japanese rates appear to be more volatile and the turning points not always the same. The mean real rate for the Netherlands remained almost constant from the 1960s to the 1970s, although it became much more volatile in the 1970s. In the 1980s, on the other hand, while the real rate increased by nearly 50 per cent, the volatility was reduced by half. With the exception of Germany and Japan, the Netherlands had the lowest mean real rate in the 1980s. It was considerably below the average for the G-7 and the European countries by about 200 basis points. A look at Figure 3.1 shows lack of constancy of the real rate over time, although it can also be seen that the degree of variability is considerably less marked during the 1980s compared to the earlier periods. A comparison of Figure 3.1 for the Netherlands and Sweden shows considerable correspondence between the behaviour of the real rates in the two countries, particularly in the 1980s, including an increase in the real rate in the last quarter of 1990, a feature not shared by any other country in the sample.

Interest rates and budget deficits

20

For Sweden the mean real rate declined by about 110 basis points from the 1960s to the 1970s but then rose by 533 basis points in the 1980s over the 1970s, suggesting one of the highest increases in the sample. Sweden is one of the three countries in the sample, besides Australia and the U.K., in which the mean real rate increased and the volatility declined from the first half of the 1980s to the second half. The variability of the real rate, however, displays a reverse pattern. It increased when the rate went down but went down when the real rate increased, thus mirroring the experience of the Netherlands as noted above. In absolute terms, the mean rate in the 1980s was above the mean for the G-7 and for the European countries. Looking at Figure 3.1 for Sweden, once again it would seem that the real rate has not remained constant over time. The real rate shows a tendency to increase towards the end of the period. The mean real rate for the U.K., although it went down in the 1970s compared to the 1960s, nevertheless became quite volatile with the standard deviation having increased by almost three times. Like many of the other countries in the sample, the mean rate in the 1980s increased sharply over the 1970s, but was accompanied by reduced volatility. As mentioned above, the U.K., unlike most other countries in the sample, experienced an increase in the real rate in the second half of the 1980s. A comparison of Figure 3.1 for the U.K. and the U.S.A. shows a much greater correspondence between the behaviour of the short-term real rate in the two countries in the 1980s than in the earlier periods, but in absolute value the U.K. rates have tended to exceed the U.S. rates by about 200 basis points, thus suggesting considerable independent variation. The estimates for the U.S.A. confirm the findings of Cumby and Mishkin (1985) and others for the 1970s and early 1980s, namely that the real rates were substantially lower in the 1970s than in the 1980s. Our estimates extend the findings for the 1980s and suggest that the rates were substantially higher and more volatile not only for the early 1980s but for the entire decade, with the real rate exceeding by as much as 300 basis points over the mean rate for the 1970s and the standard deviation being nearly twice as much. But it should be noted that the real rate in the second half of the 1980s was almost 300 basis points lower than in the first half with greatly reduced volatility. An interesting feature of the estimates for the U.S.A. is that unlike most of the members of the G-7, the mean volatility of the real rate increases over the entire sample period, in spite of the fact that the U.S.A. did not by any means experience the highest increase in mean real rate from the 1970s to the 1980s. In fact, the mean rate in the 1980s was still one of the lowest in the sample and with the exception of Germany and Japan, the lowest in the G-7 countries. This would seem to suggest a certain lack of correspondence between the behaviour of the pre-tax short-term real rates in the U.S.A. and that of the other countries. Figure 3.1 for the U.S.A. also confirms two other findings by Cumby and Mishkin (1985) and others, namely possible structural breaks in the early parts of the last quarters of 1979 and 1982. Our estimates also suggest a possible break in early 1982. It is well known that the structural breaks of October 1979 and October 1982 also coincided with monetary policy regime changes in the U.S.A. As Bonser-Neal (1990) has pointed out, some of the break-off points we have identified above for Canada, Germany and the U.K., also seemed to coincide with policy regime changes in those countries. The question whether there is a causal and predictable relationship between policy regime changes and changes in real rates is an important one and will be pursued in the following

Estimates and behaviour of ex-ante real interest rates

21

chapters. Suffice it to say here that the structural breakpoints noted in the above discussion call for an explanation, one which may be due to policy regime changes, but may be due to other factors also, say uncertainty. The role of these and other factors is considered later on. The above discussion has been based on the estimates derived from the standard procedure and the rational expectations hypothesis. Before we turn to a general summary of these estimates, a brief word is in order about the use of survey data on inflation expectations for calculating ex-ante real interest rates, as discussed in Chapter 2. Because of the biasedness of such survey forecasts, as pointed out in Chapter 2 and also because of the lack of suitable data for many of the countries in the sample, we only report some estimates for the U.S.A. just to illustrate the difference between the three types of estimates. The survey data on expected inflation was taken from Lahiri et al. (1988) which is itself based on an inflation expectations survey by the American Statistical Association and the National Bureau of Economic Research (ASA/NBER) of the implicit GNP price deflator. They explain that in order to use the information in the probability distribution reported by the ASA/ NBER survey, we must match the forecast span of the distribution with the nominal interest rates of identical length maturity. This was

Figure 3.2 Pre-tax short-term real rates: survey method done by using the method described by them. The secondary market treasury bill yields were used as the nominal interest rate. The estimates by the three methods are shown in Figure 3.2. Because of the data limitations, the period covered for this comparison is from 1969:4 to 1986:3. The autoregressive and the rational expectations hypothesis estimates of the pre-tax short-term real ex-ante interest rates are virtually identical. But the estimates based on the survey data are systematically lower, a conclusion which confirms the findings of many other studies, which report that the survey estimates of expected inflation systematically overestimate the actual expected inflation.

Interest rates and budget deficits

22

Concentrating on the general discussion above, it is possible to conclude that for virtually all of the countries in the sample, the pre-tax short-term real ex-ante interest rates behaved differently in the three decades, and within the 1980s the behaviour was quite distinct, with the rates being generally lower in the second half than in the first. It is also clear that while the general movement across the countries is in the same direction, there are wide quantitative differences between them in virtually all time periods; thus, for example, the pre-tax short-term real rate ranged from a low of 4.85 per cent for Japan to a high of 13.22 per cent for Australia in the second half of the 1980s.

Table 3.2 Data used for nominal medium-term interest rates* Country

Data

Australia

1970–90, Australian Government Security, 5 years’ maturity or Commonwealth Government bond, maturity 5 years

Belgium

1965–69, Central Government Bond, 10 or more years’ maturity 1970–90, Central Government Bond in secondary market, 10 or more years’ maturity

Canada

1965–90, Federal Government Bonds, 3–5 years’ maturity, in secondary market

France

1965–69, Bonds guaranteed by government and similar issues, 10 or more years’ maturity 1970–90, Public sector bond in secondary market, 10 or more years’ maturity

Germany

1965–69, Public sector bond (outstanding bond) 1970–90, 3–7 years Public sector bond in secondary market

Italy

1965–90, ‘Crediop’ bonds on Treasury Account, 5 years’ average maturity

Japan

1965–90, Central Government Bond, 7 years’ average maturity 1970–90, Central Government Bond in secondary market, 7 years’ average maturity

Netherlands

1965–90, Central Government Bond, 5–8 years’ maturity

Sweden

1965–69, Effective yield on short-term Central Government Bond 1970–90, 5 years Central Government Bond in secondary market

U.K.

1965–90, Government Bond rate, 5 years’ maturity

U.S.A.

1965–69, 3–5 years U.S. Government notes and bond rate 1970–90, 5 years U.S. Government notes and bond rate in secondary market

*For calculating expected inflation, the following maturities were assumed: Australia (20 quarters), Belgium (40 quarters), Canada (20 quarters), France (40 quarters), Germany (20 quarters), Italy (20 quarters), Japan (28 quarters), the Netherlands (32 quarters), Sweden (20 quarters), the U.K. (20 quarters) and the U.S.A. (20 quarters).

Estimates and behaviour of ex-ante real interest rates

23

Table 3.3 Mean and standard deviation of pre-tax ex-ante real medium-term interest rates* Country

Australia Belgium

1967:2– 1990:4 Mean

St. dev.

8.50a

St. dev.

Mean

St. dev.

3.28

5.19b

1.60

11.35

1.35

11.28

0.78

(7.58)

(1.63)

(6.54)

(0.60)

(9.86)

(0.88)

(7.07)

(1.16)

7.92

2.20

7.07

1.14

10.82

0.93

9.15

0.73

c

9.01 6.78

Italy

9.53 (8.59)

Japan

5.71 (5.09)

Netherlands

6.76 (6.41)

Sweden

8.12 (7.80)

U.K.

8.32 (7.77)

U.S.A.

7.12 (6.81)

6.95

(1.35) (7.14) 3.38

d

6.85

(1.76) (7.82) 1.17

(6.61)

5.51

(2.11) (5.73) 2.11

(8.15) Germany

(4.29) (2.37) 2.30

(7.40) France

1985:1– 1990:4

Mean

5.64

6.13

(2.56) (6.59) 1.35

5.34

(1.08) (5.53) 1.33

6.11

(1.36) (5.94) 2.13

5.93

(1.90) (5.89) 2.08

6.92

(1.79) (6.98) 2.29

5.16

(2.00) (5.27)

St. dev.

1980:1– 1984:4

St. dev.

7.61

Mean

1975:1– 1979:4 Mean

(7.01) Canada

1967:2– 1974:4

0.83

(3.20) (5.74) 0.83

6.44

(0.88) (6.10) 0.48

8.17

(1.11) (7.91) 1.08

5.97

(1.00) (5.55) 1.31

9.36

(1.07) (8.48) 0.95

6.01

(0.59) (4.45) 1.03

6.13

(0.83) (5.39) 0.76

7.14

(0.65) (6.76) 1.60

7.48

(1.61) (6.50) 0.69

6.00

(0.83) (5.65)

(0.54) (10.47) (1.51) (11.17) (0.76) 1.27

10.67

1.59

8.74

0.84

(1.05)

(9.87)

(2.07)

(8.58)

(0.91)

0.71

12.08

1.15

9.98

0.79

(6.62)

(0.99)

(0.59) (10.42) (1.26) 0.97

7.61

1.05

6.54

1.06

(1.08)

(7.47)

(1.21)

(6.07)

(1.30)

1.37

14.39

2.52

10.02

1.09

(8.14)

(1.31)

(0.59) (12.37) (2.52) 1.48

6.96

0.91

4.90

1.23

(1.27)

(5.75)

(0.33)

(4.69)

(1.23)

1.04

8.28

1.17

6.87

0.95

(0.83)

(7.99)

(1.33)

(6.54)

(1.15)

0.62

9.98

1.08

10.22

1.27

(0.52)

(9.32)

(0.52)

(9.86)

(1.22)

2.14

10.19

1.55

9.27

1.23

(1.71)

(8.84)

(1.43)

(6.94)

(0.98)

0.87

10.55

1.69

7.71

1.05

(1.02)

(9.69)

(1.49)

(7.38)

(0.87)

*The figures in parentheses are based on Mishkin estimates, (a) The period is from 1971:4 to 1990:4. (c) The period is from 1971:4 to 1990:4. (b) The period is from 1971:4 to 1979:4. (d) The period is from 1969:4 to 1990:4.

Interest rates and budget deficits

24

THE ESTIMATES OF THE MEDIUM-TERM PRE-TAX EX-ANTE REAL INTEREST RATES Given the importance of long-term ex-ante real interest rates in economic decision making, particularly those relating to business, it would be useful to provide estimates of such rates. But as already discussed in Chapter 2, this is quite difficult regardless of which of the three methods (excluding the survey method, of course) we use. As a compromise we present estimates for the medium-term rates which in our case implies returns on bonds of three to five years’ maturity. Since the autoregressive method provides the most reliable estimates, the discussion will be based on the estimates using this procedure. However, for the sake of comparison, estimates using Mishkin’s method and the returns from the index-linked bonds for the U.K. are also presented. The data on the nominal medium-term interest rates as well as the other variables were again collected from the various issues of the OECD Financial Statistics. The exact details of the interest rate series used are given in Table 3.2. The period covered is not the same as for the short-term rates in some cases because of the unavailability of the relevant data. The means and the standard errors of the estimated values of the pre-tax medium-term ex-ante interest rates, based on the autoregressive and Mishkin procedures, are given in Table 3.3. We note that for all countries in our sample, except for Australia, the autoregressive estimates were obtained for the post-1967 period. Due to data limitations, the Mishkin estimates for Australia, France, Belgium and Japan could be obtained for the post-1971 period. For other countries, the Mishkin estimates cover the 1967:1–1990:4 period. Before analysing these estimates in detail, a word is in order about the relative magnitudes of the two estimates. A comparison with Table 3.1 shows that the two estimates are not as close as those for the short-term rates. However, with the exception of a few cases, the two estimates are still relatively close. But more importantly, the general inference suggested by the two estimates is the same. For example, both estimates suggest that for the U.S.A. the rate was higher in the early 1970s than in the late 1970s and further that it was higher in the first half of the 1980s than in the second half. The following discussion is based on the autoregressive estimates. The results of Table 3.3 confirm the findings about the ex-ante real short-term rates, namely, that the medium-term real rates were higher in the 1980s compared to the 1960s and 1970s. It is interesting to note though, that the rates in the second half of the 1980s were somewhat lower than in the first half. A notable exception is Germany where the rate has remained relatively stable, as also reported by Blanchard and Summers (1984) for the period earlier than 1984:2. However, across the countries there was considerable variation. Thus, in the second half of the 1980s, the mean real medium-term interest rate in Australia was as high as 11.28 per cent while in Japan it was only 4.90 per cent. The mean rate was 8.86 per cent in Europe and 7.71 per cent in the U.S.A. during the same period. A comparison between Japan and the U.S.A. shows that the U.S. rate exceeded the Japanese rate by as much as 281 basis points in the 1985–90 period. But in terms of the variability of these mean rates, we observe a different pattern. By the second half of the 1980s not only had the degree of variability been reduced in all but two cases, Japan

Estimates and behaviour of ex-ante real interest rates

25

and Sweden, but also it had become relatively uniform across the countries. Thus the value of the standard deviation varied from a high of 1.27 to a low of 0.73. As expected, these mean rates mask important intertemporal differences as can be readily ascertained from Figure 3.3. A detailed country-by-country comparison, along the lines of that done for the pre-tax ex-ante short-term real interest rate, would reveal important intra- and inter-country differences. This is left as an exercise for the reader. But a comparison of the short- and medium-term pre-tax

Figure 3.3 Medium-term pre-tax exante real interest rates

Interest rates and budget deficits

26

ex-ante real rates for the latest period in the sample, namely 1990:4, is instructive. The relevant information is given in Table 3.4. This table reveals a number of important characteristics of the most recent experience. First, the lowest medium-term real rate was experienced by Japan, followed by the U.S.A., and in contrast the rest of the countries experienced relatively high rates. Thus, the mean rate for Europe was 9.93 per cent as against a rate of only 5.97

per cent for Japan and 6.90 per cent for the U.S.A. A comparison of Canada, the U.K. and the U.S.A. is also striking. Thus, while the rates for Canada and the U.K. are virtually the same, they both exceed the U.S. rate by over 250 basis points, thus suggesting considerable scope for independent movement of the domestic rates. It is also important

Estimates and behaviour of ex-ante real interest rates

27

to point out that over time there has been a fundamental change in the relative positions of these countries.

Thus, Blanchard and Summers (1984) reported that in 1984:2 the U.S.A. had the highest real medium-term rate in a sample of six countries, but our Table 3.4 shows that by 1990:4, the U.S.A. had one of the lowest rates among these countries. The second characteristic of this table is the behaviour of the medium rates relative to that of the short rate. For six of the countries in our sample and for 1984:2 Blanchard and Summers (1984) reported that the medium-

Interest rates and budget deficits

28

term real rates were at least as high as the short-term real rates. It is interesting to note that the same cannot be said for 1990:4. In particular, this is no longer the case for Japan and the U.K., although it still holds true for the other four countries, namely France, Canada, Italy and the U.S.A. For the other five countries in our sample, the medium-term real rate exceeds the short-term real rate in Australia, Belgium and the Netherlands, but not in Canada and

Estimates and behaviour of ex-ante real interest rates

29

Sweden. A comparison of Canada and the U.S.A. is particularly revealing. Thus, in Canada the medium-term rate falls short of the short-term rate by almost 100 basis points, whereas it exceeds by 76 basis points in the U.S.A., thus suggesting a difference of 176 basis points. These differences clearly suggest, further, that just as in the case of the short-term real rate, the countries in our sample do not display identical behaviour with respect to the medium rate either.

Interest rates and budget deficits

30

Table 3.4 Short-term and medium-term pre-tax exante real interest rates for 1990:4 Country

Short rate

Medium rate

Australia

10.35

12.21

Belgium

7.07

9.98

Canada

10.37

9.34

France

9.02

10.57

Germany

7.48

8.47

Italy

9.69

10.56

Japan

7.04

5.97

Netherlands

8.20

8.43

Sweden

12.00

11.74

U.K.

11.92

9.75

6.14

6.90

U.S.A.

As mentioned in Chapter 2, rates of return on index-linked bonds can be used as a direct measure of ex-ante real interest rates, although there are serious shortcomings of such data. For our sample of countries, such data are available only for the U.K. The yields on the index-linked bonds cannot be compared with those estimated by other methods because of the differences in maturity, assumptions about the future rate of inflation and so on. However the information that we have since 1981 leads to similar

Estimates and behaviour of ex-ante real interest rates

31

Figure 3.4 Real rates as index-linked bonds conclusions. For example, if we consider index-linked bonds of over 5 years’ maturity, we find that the mean real yield was 3.64 per cent during the late 1980s as against the mean of 3.006 during the early 1980s. The standard deviation, on the other hand, was 0.33 and 1.29 for the two periods, respectively, suggesting greater volatility during the earlier period. If we consider the real yields, assuming a 5 and 10 per cent constant rate of inflation, on index-linked bonds of 5 or less years’ maturity estimated by our autoregressive scheme, we find that while the later estimates are much higher, the general behaviour of the three sets of estimates is quite similar. These estimates are shown in Figure 3.4. The data in this figure represent the average gross redemption yield in the last week of each quarter and were collected from the Financial Times. But these rates can vary widely. Thus, according to the Financial Times, 14/15 November 1992, the average gross redemption yield on index-linked bonds of up to 5 years’ maturity, assuming a 5 per cent rate of inflation, varied between a low of 2.25 per cent and a high of 5.06 per cent, a difference of over 124 per cent. If the assumption about expected inflation is changed to 10 per cent, this difference rises to 182 per cent. Thus, the reported ex-ante yields on index-linked bonds need to be treated with extreme caution as indicators of actual ex-ante real interest rates. ESTIMATES OF POST-TAX EX-ANTE REAL INTEREST RATES Given the importance of after-tax real interest rates in economic decision making, this section presents some estimates for such rates. The basic requirement in calculating such rates is the data on marginal tax rates on interest income. Unfortunately such data are not easy to obtain. We have only two sets of data at our disposal. The first is the time series data for the U.S.A. supplied by Tanzi. And the second is the average data for the period 1971–81, as given in Tanzi (1984) for eight countries. The use of the average data poses

Interest rates and budget deficits

32

two problems. One is that it masks intertemporal variations even for the period 1971–81. But the other and more serious problem is that it implies assuming that the tax rates were the same in the other periods covered in the study, a not very plausible assumption. But given the enormity of the task involved in the calculation of tax rates for such a large number of countries, we must make do with what we have, but keeping in mind these limitations while interpreting the reported estimates. This said, the estimated post-tax exante real short-term and medium-term rates are given in Tables 3.5 and 3.6, respectively. In order to bring out the comparison between the nominal, the pre-tax and the post-tax real interest rates, we have plotted them in Figure 3.5 for the short-term, based on the

Table 3.5 Mean and standard deviation of post-tax ex-ante real short-term interest rates: auto and Mishkin estimates* Country

Canada France Germany Italy Japan Netherlands U.K. U.S.A.

1967:3– 1990:4

1967:3– 1969:4

1970:1– 1979:4

1980:1– 1984:4

1985:1– 1990:4

Mean

St. dev.

Mean

St. dev.

Mean

St. dev.

Mean

St. dev.

Mean

St. dev.

6.06

2.69

4.46

0.93

4.15

1.83

8.93

2.15

7.55

1.54

(6.04)

(2.67)

(4.29)

(0.66)

(4.13)

(1.78)

(8.93)

(2.22)

(7.55)

(1.38)

4.42

1.53

3.61

1.11

3.42

1.17

6.15

1.22

5.06

0.60

(4.44)

(1.53)

(3.60)

(0.98)

(3.37)

(1.13)

(6.36)

(1.02)

(4.97)

(0.53)

3.04

1.59

1.67

1.24

2.71

1.71

4.18

1.40

3.22

0.95

(3.03)

(1.46)

(1.59)

(0.94)

(2.72)

(1.51)

(4.29)

(1.20)

(3.11)

(0.83)

5.65

2.53

2.14

0.44

4.23

1.75

8.66

1.39

6.98

0.65

(5.63)

(2.48)

(1.99)

(0.21)

(4.31)

(1.81)

(8.63)

(0.97)

(6.86)

(0.53)

4.91

1.76

4.76

1.10

4.65

2.00

6.02

1.56

4.49

1.34

(4.89)

(1.49)

(4.55)

(0.59)

(4.65)

(1.83)

(5.97)

(1.10)

(4.51)

(0.95)

3.73

2.24

2.86

1.56

2.85

2.70

4.94

1.63

4.55

1.07

(3.64)

(2.18)

(2.46)

(1.30)

(2.64)

(2.44)

(5.30)

(1.63)

(4.42)

(0.89)

5.25

2.23

4.45

0.67

3.69

1.94

6.36

1.42

7.28

1.43

(5.27)

(1.97)

(3.81)

(0.27)

(3.76)

(1.42)

(6.58)

(0.96)

(7.29)

(0.89)

4.26

1.69

3.60

0.51

3.15

1.02

6.62

1.55

4.42

0.72

(4.19)

(1.66)

(3.30)

(0.48)

(3.10)

(1.07)

(6.57)

(1.34)

(4.40)

(0.54)

*The figures in parentheses are those based on Mishkin procedure.

Estimates and behaviour of ex-ante real interest rates

33

Table 3.6 Mean and standard deviation of post-tax ex-ante real medium-term interest rates: auto and Mishkin estimates* Country

Canada France

a

Germany Italy Japan

b

Netherlands U.K. U.S.A.

1967:2– 1990:4

1967:2– 1974:4

1975:1– 1979:4

1980:1– 1984:4

1985:1– 1990:4

Mean

St. dev.

Mean

St. dev.

Mean

St. dev.

Mean

St. dev.

Mean

St. dev.

6.22

1.94

4.49

0.73

5.15

1.11

8.77

1.28

7.23

0.72

(6.02)

(1.76)

(4.71)

(0.73)

(4.81)

(0.88)

(7.97)

(1.75)

(7.08)

(0.80)

a

a

5.85

1.43

b

3.99

0.46

4.65

0.53

7.15

0.77

6.78

0.60

(4.45)

(1.06)

(4.76)

(0.68)

(4.39)

(0.46)

(5.55)

(0.85)

(3.42)

(0.72)

4.19

0.76

4.21

0.71

3.57

0.67

4.65

0.67

4.29

0.66

(4.02)

(0.89)

(4.40)

(0.56)

(3.15)

(0.70)

(4.51)

(0.81)

(3.83)

(0.90)

5.95

2.30

3.77

1.30

5.35

1.13

8.96

1.76

6.74

0.79

(5.01)

(1.48)

(4.23)

(0.75)

(4.46)

(0.42)

(6.94)

(1.74)

(4.85)

(1.11)

5.24

1.34

4.75

1.08

5.47

1.41

6.40

0.87

4.53

1.15

(4.60)

(1.01)

(5.01)

(0.53)

(3.91)

(1.18)

(5.19)

(0.32)

(4.32)

(1.15)

4.95

1.08

4.38

0.86

4.34

0.93

6.08

0.86

5.25

0.74

(4.60)

(1.11)

(4.21)

(0.62)

(3.59)

(0.68)

(5.79)

(1.00)

(4.92)

(0.93)

5.78

1.69

4.85

1.19

4.71

1.90

7.13

1.16

6.75

0.99

(5.23)

(1.45)

(4.91)

(1.15)

(3.73)

(1.38)

(5.78)

(1.02)

(6.43)

(0.73)

5.17

1.77

3.69

0.56

4.20

0.66

7.71

1.40

5.77

0.82

(4.87)

(1.46)

(3.79)

(0.62)

(3.85)

(0.77)

(6.86)

(1.13)

(5.44)

(0.64)

*The figures in parentheses are those based on Mishkin estimates. (a) The period is from 1971:4 to 1990:4. (b) The period is from 1969:4 to 1990:4.

Interest rates and budget deficits

34

Figure 3.5 Nominal, pre- and post-tax real short-term rates Mishkin method, and in Figure 3.6 for the medium-term using the autoregressive method. To get some idea whether the use of the average tax rate for the period 1971–81 for the entire period makes any significant difference, we have plotted the after-tax real ex-ante short-term interest rates for the U.S.A. using three methods in Figure 3.7. In these figures RTMISH and RTAUT represent the post-tax estimates by the Mishkin and autoregressive methods, respectively.

Estimates and behaviour of ex-ante real interest rates

35

Before turning to a detailed comparative analysis of these estimates, it is best to deal with the U.S. evidence first, because of the additional evidence we have on this one country. Figures 3.5 to 3.7 for the U.S.A. show clearly that the post-tax estimates of real ex-ante short-term rate are sensitive to the two alternate tax rates used in these estimates. However, the general direction of the estimates based on the autoregressive and Mishkin methods is fairly similar. An interesting feature of Figure 3.7 is that the post-tax shortterm real rate in the U.S.A. was negative for a good part of the period if measured using the survey data on inflation expectations, an inference not supported by the other two estimates. This brings into serious question whether the use of the survey method is really appropriate. We now consider the results in Tables 3.5 and 3.6 in greater detail. The short-term as well as the medium-term after-tax rates were positive for all the countries in each of the sub-periods. Like the pre-tax rates, the post-tax rates were also lower in the second half of the 1980s compared to the first half. And they were the lowest in the 1970s. While no attempt is made to carry out the same detailed inter-country comparison of these rates, nevertheless a look at Figures 3.5 and 3.6 is instructive. Each graph shows three rates: the nominal rate, the pre-tax real ex-ante rate and the after-tax real ex-ante rate. Ignoring for the moment the lines representing the nominal rate, it can be seen that neither of the two rates was negative at any time included in the sample. However, the pre-tax and post-tax rate differences are not necessarily the same for each of the eight countries. Consider the more extreme cases. In Japan, the difference between the two rates was minimal, presumably reflecting low tax rates. On the other hand, this difference was quite marked for France and Italy. It is also interesting to note that, except for Japan, the difference between the pre- and post-tax rates varied considerably over the period in most of the countries, suggesting that pre-tax ex-ante real interest rates may not always be an accurate guide to the behaviour of the corresponding post-tax rates; this holds true both with respect to the level as well as the variability of the rates.

Interest rates and budget deficits

36

Estimates and behaviour of ex-ante real interest rates

37

Interest rates and budget deficits

38

Estimates and behaviour of ex-ante real interest rates

39

Figure 3.6 Nominal, pre- and post-tax real medium-term rates THE ROLE OF NOMINAL INTEREST RATES AS A SIGNAL FOR THE BEHAVIOUR OF EX-ANTE REAL INTEREST RATES One way to get insight into the process generating ex-ante real interest rates is to see the extent to which nominal interest rates serve

Interest rates and budget deficits

40

as a guide to the behaviour of the unobserved expected real interest rates. We can get some idea about this issue by looking at the simple correlations between the nominal interest rates and the ex-ante real interest rates given in Table 3.7 and their temporal behaviour in Figures 3.5 and 3.6. Not unexpectedly, the correlations and the movements of the post-tax real rates and the nominal interest rates

Estimates and behaviour of ex-ante real interest rates

41

are not as close as those of the pre-tax real rates and the nominal rates. Concentrating on the pre-tax rates only, the results are quite striking. It would seem that, with few exceptions, the two rates have moved closely so that movements in nominal rates have served as a reliable signal for the movements in the expected real rates. The most

Interest rates and budget deficits

42

important exception is Japan in the 1960s until the mid-1970s, when the correlation was in fact negative. This is not surprising, because during this period the medium rates were highly regulated. France and the U.S.A. also provide some interesting exceptions. Thus, in France, the correlation was in fact negative. Again, this is not surprising, because during this period the medium rates were highly

Estimates and behaviour of ex-ante real interest rates

43

Figure 3.7 After-tax short-term real rate: survey method Table 3.7 Correlations between nominal and exante real interest rates Short-term rate Country

r

(NI,RHMISHK)

r

Medium-term rate

(NI,RTMISHK)

r

(NI,RAUT)

r

(NI,RTAUT)a

Australia 1967:3–1990:4

0.99

0.96

1967:3–1969:4

0.99

1970:1–1979:4

0.98

0.88

1980:1–1984:4

0.99

0.91

1985:1–1990:4

0.99

0.88

1967:3–1990:4

0.97

0.86

1967:3–1969:4

0.99

0.57

1970:1–1979:4

0.97

0.79

1980:1–1984:4

0.99

0.93

1985:1–1990:4

0.99

0.71

Belgium

Canada 1967:3–1990:4

0.98

0.98

0.97

0.95

Interest rates and budget deficits

44

1967:3–1969:4

0.99

0.98

0.74

0.64

1970:1–1979:4

0.99

0.98

0.96

0.94

1980:1–1984:4

0.99

0.99

0.97

0.95

1985:1–1990:4

0.99

0.99

0.97

0.96

Short-term rate Country

r

(NI,RHMISHK)

r

Medium-term rate

(NI,RTMISHK)

r

(NI,RAUT)

r

(NI,RTAUT)a

France 1967:3–1990:4

0.96

0.90

0.89

0.52

1967:3–1969:4

0.99

0.98

0.90

0.59

1970:1–1979:4

0.99

0.96

0.85

0.90

1980:1–1984:4

0.98

0.94

0.95

0.81

1985:1–1990:4

0.98

0.95

0.96

0.26

1967:3–1990:4

0.98

0.96

0.89

0.72

1967:3–1969:4

0.95

0.93

0.90

0.74

1970:1–1979:4

0.99

0.98

0.85

0.65

1980:1–1984:4

0.99

0.98

0.95

0.88

1985:1–1990:4

0.99

0.97

0.96

0.91

1967:3–1990:4

0.97

0.94

0.92

0.81

1967:3–1969:4

0.95

0.82

0.18

0.12

1970:1–1979:4

0.99

0.99

0.74

0.58

1980:1–1984:4

0.95

0.87

0.98

0.96

1985:1–1990:4

0.98

0.94

0.84

0.66

1967:3–1990:4

0.94

0.92

0.64

0.60

1967:3–1969:4

0.98

0.97

−0.47

−0.57

1970:1–1979:4

0.99

0.99

0.81

0.79

1980:1–1984:4

0.99

0.98

0.73

0.89

1985:1–1990:4

0.95

0.94

0.94

0.92

0.97

0.95

0.83

0.72

Germany

Italy

Japan

Netherlands 1967:3–1990:4

Estimates and behaviour of ex-ante real interest rates

45

1967:3–1969:4

0.99

0.97

0.81

0.70

1970:1–1979:4

0.99

0.99

0.71

0.62

1980:1–1984:4

0.99

0.98

0.96

0.93

1985:1–1990:4

0.99

0.99

0.92

0.87

Sweden 1967:3–1990:4

0.99

0.95

1967:3–1969:4

0.98

0.65

1970:1–1979:4

0.99

0.76

1980:1–1984:4

0.96

0.87

1985:1–1990:4

0.99

0.98

U.K. 1967:3–1990:4

0.93

0.87

0.78

0.64

1967:3–1969:4

0.95

0.87

0.87

0.76

1970:1–1979:4

0.99

0.97

0.69

0.57

1980:1–1984:4

0.98

0.96

0.89

0.80

1985:1–1990:4

0.98

0.96

0.89

0.83

1967:3–1990:4

0.97

0.95

0.95

0.91

1967:3–1969:4

0.95

0.91

0.68

0.44

1970:1–1979:4

0.98

0.98

0.86

0.74

1980:1–1984:4

0.97

0.94

0.85

0.76

1985:1–1990:4

0.95

0.81

0.97

0.95

U.S.A.

(a) Time periods as specified in Table 3.6.

regulated. France and the U.S.A. also provide some interesting exceptions. Thus, in France, the correlation is 0.66 in the period 1966–76 for the medium rate, which jumped to 0.92 during 1980:1 to 1984:4, but then went down to 0.67 in the latter half of the 1980s. For the U.S.A., just like France, the correlation was lower during the late 1960s and early 1970s, but then showed a continuous increase going as high as 0.97 during the second half of the 1980s.

Interest rates and budget deficits

46

STATISTICAL BEHAVIOUR OF EX-ANTE REAL INTEREST RATES Before proceeding to estimation and testing of the long-run relationships about the behaviour of ex-ante real interest rates, we have to examine the univariate statistical properties of these series. More specifically, we need to examine whether ex-ante real interest rates tend to revert back to some long-term equilibrium path following a shock or whether they tend to follow a random walk process. If real rates follow random walk the effect of temporary shocks such as an oil price increase or a change in the conduct of monetary policy (such as the change in the Federal Reserve operating procedure in October 1979) will be permanent. If real rates do not follow a random walk process these shocks will have a temporary effect on these rates, and after a long period of time they revert back to their long-run equilibrium value. The standard econometric theory is based on the assumption that the underlying economic time series are stationary with constant unconditional mean and variance over time. This implies that shocks will generate transitory fluctuations around a relatively stable trend path. If economic time series are non-stationary, a regression of one against another can result in spurious results. In this case, ordinary least squares does not yield a consistent parameter estimator and the Gauss-Markov theorem does not hold.1 Over the last century, most economic variables have experienced significant shifts in their mean and variance so that their first two moments can no longer be characterized as being constant. This phenomenon has resulted in a series of studies on stationary and spurious regressions.2 The seminal study by Nelson and Plosser (1982) found that most macroeconomic variables behave like random walks. The Nelson and Plosser study was followed by a series of empirical studies which basically confirmed the original findings.3 Most of these studies employ the unit root tests introduced by Dickey and Fuller.4 The problems of estimation and statistical inference in the presence of non-stationary variables are discussed by Phillips (1986), Granger and Newbold (1974), Nelson and Kang (1981), and Nelson and Plosser (1982). There seem to be two basic reasons for an overwhelming support for the hypothesis that most macroeconomic variables appear to be random walks, or at least appear to have random walk components rather than being trend reverting. First, small sample size used in estimation and testing for the presence of unit root or non-stationarity in a series. It is entirely possible that economic variables behave like a random walk with growing mean and variance within a small time interval. As time lapses, however, the variables may revert to their long-run equilibrium path.5 Second, even when long time series are available, the presence of a structural break or shift in a series can make it appear to be non-stationary using standard tests when, in fact, it is stationary. The influential study by Perron (1989) shows that the standard tests of unit root hypothesis cannot reject the unit root hypothesis if the true data-generating mechanism is that of stationary fluctuations around a trend function which contains a one-time break. Perron derived test statistics which allow for the presence of breaks in the series, applied them to the data set used by Nelson and Plosser and found that most macroeconomic time series are not characterized

Estimates and behaviour of ex-ante real interest rates

47

by the presence of a unit root and their fluctuations are indeed stationary around a deterministic trend function. In what follows, we first discuss the unit root testing procedures and then apply them to the ex-ante real rate series derived in the previous sections. TESTING THE ORDER OF INTEGRATION OF ECONOMIC TIME SERIES In order to estimate and test the equality of real rates across different countries, we first have to examine the order of integration of the real rate series. For this purpose, we proceed as follows. Assume that the real rate series Yt can be described by the following data generating process: (1) where ut is a well behaved random disturbance, and T is a time trend. Equation (1) tests two possible hypotheses concerning the behaviour of the variable Yt. First, Yt has been growing over time because it has a positive trend (β1>0), but would be stationary after detrending (ρ<1). In this case, the variable Yt can be used in regression analysis and standard econometric theory applies. The second possibility is that Yt has been growing because it follows a random walk with a positive drift (β1=0, α0>0 and ρ=1). In this case, the presence of Yt in standard regressions can produce spurious results.6 If ρ=1, the variable Yt is said to contain a unit root. Yt is said to be integrated of order 1 if it has a unit root, but becomes stationary if differenced once. If Yt is integrated of order 1, its variance increases over time. Dickey and Fuller (1979) considered the problem of testing for the presence of unit root in the time series Yt by testing the null hypothesis of H0: ρ=1 versus the alternative hypothesis of stationarity around a deterministic trend; i.e., H1: ρ<1. To test the null hypothesis, one can rewrite equation (1) as: (2) where H0: ρ=1 is equivalent to H0: θ=0. The test is carried out by calculating ordinary tstatistics for θ. However, this statistic does not have the standard distribution. The critical values based on simulation are tabulated and given in Fuller (1976). McKinnon (1991) used Monte Carlo methods and estimated response surfaces for several tests of unit root, which allows critical values to be read off for any sample size.7 It should be mentioned that the testing procedure and the critical values used depend on the assumptions made concerning the parameters α0 and β1. If a time series follows equation (1), under the null hypothesis of unit root, it can be written as: (3)

Interest rates and budget deficits

48

As discussed by Dolado et al. (1990), if the unit root process Yt contains a linear trend (β1≠0) or a drift (α0≠0), its variability, using equation (3), can be shown to be dominated by a quadratic or linear trend which converges to constants. As several authors have shown (see West (1988) and Hylleberg and Mizon (1989)), only when the process does not contain a drift and linear trend (α0=β1=0), it converges to a non-standard distribution. When β1≠0 (or α0≠0 with β1=0), the test statistic is asymptotically distributed as N (0, 1). This implies that in order to test for the presence of unit root, one can follow the following testing procedure. First, estimate model (2) and use t-statistic on θ to test the null hypothesis of unit root using critical values given in Fuller (1976, p. 373). Second, if the null is not rejected, test for the significance of the trend under the null using the Φ3 distribution tabulated in Dickey and Fuller (1981, p. 1063). If the trend is significant, then test for the presence of unit root using the standard normal distribution. Third, if the trend is not significant, estimate (2) without trend and test for the unit root using the critical values given in Fuller (1976). Fourth, if the null is not rejected, test for the significance of the constant term under the null hypothesis (β1=0 and θ=0) using the Φ2 distribution tabulated in Dickey and Fuller (1981, p. 1063). If the constant term is significant, test again for a unit root using standard normal distribution. Finally, if the constant term is not significant, estimate (2) without trend and constant and test for the unit root using the Dickey-Fuller distribution. The above testing strategy assumes that the error term of equation (2) is white noise. In general, equation (2) can be augmented by first differences of Yt to ensure that the residuals are white noise. In general, equation (2) can be modified as: (4) where k is large enough to ensure that ut is white noise. Tests based on the augmented equation (4) are known as ‘Augmented Dickey-Fuller’ statistics. The critical values and testing strategy are the same as those discussed above. So far we have discussed the problem of testing for unit root without allowing for the presence of a structural break in the level or in the slope of the trend function. Perron (1989) showed that standard tests cannot reject the unit root hypothesis if the true data generating mechanism are that of stationary fluctuations around a trend function which contains a one-time break. He developed and tabulated the critical values for test statistics which allow us to distinguish the unit root hypothesis from that of a stationary series around a trend which has a single break. TESTING FOR THE PRESENCE OF UNIT ROOT IN EX-ANTE SHORT-TERM REAL INTEREST RATES The presence of unit root in ex-ante real interest rates has important macroeconomic implications. Under this hypothesis, which gives rise to stochastic trends as opposed to deterministic trends, random shocks to real interest rates have permanent effects and

Estimates and behaviour of ex-ante real interest rates

49

fluctuations are not short-run or transitory around a long-run equilibrium path, but one of a permanent nature. This runs counter to the prevailing economic theory that suggests that, in the long run, equilibrium real interest rates should equate individuals’ marginal time preferences with the marginal physical productivity of capital. It is usually assumed that individuals prefer current consumption to future consumption and therefore have positive time preference.8 This implies that they want to be rewarded for postponing their present consumption, that is, to save, at least equal to their marginal time preference. Investors, on the other hand, are willing to pay a reward, in the form of interest payments, to induce individuals to forgo present resources that allow them to increase their capital stock. The rate of interest that they are prepared to offer depends on the marginal productivity of capital. Therefore, the long-run equilibrium real rate is the rate that equates saving and investment. This implies that although real interest rates might be subject to short-run policy-induced fluctuations, in the long run they tend to return to an ‘equilibrium’ or ‘normal’ level based on the marginal productivity of capital. Of course, the marginal product of capital can be expected to change over time, thus making the detrended real rates stationary. Therefore, the question is whether the real interest rate can best be described by a random walk process or alternatively as a first-order autoregressive process, perhaps with trend. In examining the statistical properties of the ex-ante real interest rate series estimated in this chapter, we follow a two-step procedure. First, we test the null of non-stationarity versus the alternative of stationarity around a deterministic trend using the testing strategy outlined above. If the presence of the unit root cannot be rejected, we re-examine the series and allow for the possibility of a structural break using the Perron methodology described above. The only practical difficulty in estimating model (4) is the determination of the optimum lag values k. For this, we employed the Akaike Final Prediction Error (FPE) criterion. We start with testing the presence of unit root in the ex-ante real interest rate for Australia by estimating equation (4). The number of observations used in the regression was equal to 113. The optimum lag length on the first differenced terms was equal to one. The t-statistics on the lagged interest rate was equal to (−4.74) which is smaller than the critical value of (−3.45) reported by Fuller (1976). Therefore, the null hypothesis of nonstationarity can be rejected at 95 per cent confidence level. We also calculated the F-ratio of the random walk hypothesis, i.e., of the hypothesis that β1=0 and θ= 1. The value of the F-ratio with 2 and 111 degrees of freedom was equal to 11.35 which exceeds the critical value of 6.49 reported by Dickey and Fuller (1981). This result also leads us to reject the null of unit root at 5 per cent level. The result of applying the above procedure to the cases of Belgium, France, Japan, the Netherlands, Sweden and the U.K. were similar to that of Australia. To save space we summarize them in Table 3.8. In addition, Table 3.8 also includes the results for Canada, Germany, Italy and the U.S.A. The optimum lag length on the first differenced terms are given in parentheses. Table 3.8 shows that we can reject the null hypothesis of unit root versus the alternative of trend stationarity for Australia, Belgium, France, Japan, the Netherlands, Sweden and the U.K. For Canada, Germany, Italy and the U.S.A., we cannot reject the

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null hypothesis of non-stationarity. For these countries, the F-ratio of the test of the significance of trend was below the 5 per cent critical value of 6.49. Therefore, following the testing strategy outlined above, we estimated equation (4) without trend and tested for the presence of unit root using the critical values given in Fuller (1976). In this case, the null of non-stationarity was rejected at 95 per cent

Table 3.8 Testing for unit root based on equation (4) Country

ττ

[β1=0 and θ=0]

Australia (1)

−4.74

11.35

Belgium (1)

−3.64

6.65

Canada (3)

−2.89

4.21

France (1)

−3.52

6.52

Germany (1)

−3.20

5.13

Italy (1)

−2.11

2.48

Japan (2)

−4.39

9.72

Netherlands (1)

−4.59

10.56

Sweden (1)

−3.59

6.50

U.K. (1)

−4.01

8.05

U.S.A. (3)

−2.25

2.72

confidence interval only for Germany. For Canada, Italy and the U.S.A. we could not reject the null of non-stationarity against the alternatives of stationarity with trend, without trend, with or without a drift. After careful examination of these time series, we decided to reformulate our test and allow for both changes in the level and rate of growth of the series occurring between 1979 and 1981 using the specification (C) used by Perron (1989, equation 14). After allowing for the presence of break in the series, they no longer exhibited non-stationarity and the null hypothesis was rejected at 5 per cent level in all three countries. MODELLING AND TESTING THE EQUALITY OF EX-ANTE SHORT-RUN REAL RATES Using the estimates of the ex-ante real rates obtained by the Mishkin procedure, we want to test three hypotheses. First, whether the ex-ante real rates are linked internationally; second, whether this linkage is full or partial; and third, whether the ex-ante real rates are equal internationally. In carrying out the test procedure, we employ a methodology which allows us to distinguish the appropriateness of the above hypotheses in the short run and in the long run. In addition, we estimate the speed of adjustment of the ex-ante interest rates to their long-run equilibrium values.

Estimates and behaviour of ex-ante real interest rates

51

To test the above hypotheses, Mishkin (1984) considered the following model: (5) where and are ex-ante real rates in country m and the U.S.A., respectively. The above three hypotheses can be tested by testing the following null hypotheses: (1) H0: δm≠0; (2) H0: δm= 1; and (3) H0: δm=1; αm=0. Mishkin tested these hypotheses by estimating model (5) using an instrumental and the variable method to prevent the bias caused by a possible correlation of error term. Note that testing the above hypotheses using model (5) implies an instantaneous adjustment between the rates in the U.S.A. and other countries. Therefore, tests of the above hypotheses based on model (5) should be regarded as tests of instantaneous or short-run linkage and/or equality of ex-ante real rates. To allow for the presence of lags in the adjustment of ex-ante real rates in country m to changes in the rates in the U.S.A., we can rewrite model (5) as: (6) Estimating model (6), one can calculate the long-run response coefficient of ex-ante real rate in country m to the changes in the rates in the U.S.A. as follows: (7) The above hypotheses can then be tested by testing the restrictions on θm and αm. However, in order to test these hypotheses we need to estimate model (6), and calculate θm and its standard error. The above approach, however, is not computationally efficient because of the two-step procedure involved. Clearly, it would be better if we could find the estimate of θm and its standard error directly. This can be done by using an extended version of the transformation proposed by Wickens and Breusch (1988). Following them, we can transform model (6) as follows: (8)

Model (8) is in an error correction form popularized by Hendry (1986). Estimating model (8) allows for direct estimation of the long-run coefficient and testing of the long-run propositions. Moreover, the coefficient (1−Σ βi) measures the speed of adjustment towards the long-run equilibrium. If interested, the instantaneous (impact) or short-run effect is captured by the coefficient δ0. Note that the long-run steady-state equilibrium solution of model (8) is identical to model (5). Therefore, tests of the above three hypotheses can be conducted using the estimated coefficients of model (8).

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ESTIMATION AND RESULTS USING EX-ANTE REAL INTEREST RATES (MISHKIN PROCEDURE) Before proceeding to the estimation of model (8), three statistical problems should be addressed. The first issue deals with the problem of potential correlation between the variable, which appears in and the error term. To rectify this problem, we substituted it with its estimated value from the ordinary least squares regression of exante real U.S. rate on a constant, its past six lags and time trend raised to the power one, two and three. The second issue deals with the problem of non-linearity in the estimation of model (8). As it stands, model (8) is non-linear in coefficients and cannot be directly estimated without obtaining some estimates for the initial values of the parameters. To rectify this problem, we first estimate model (8) in an unrestricted form by allowing the individual variables in the error-correction term to appear as separate regressors. The third issue deals with the question of the optimum lag structure of model (8). For this, we allowed for a lag of up to three years on each variable and then subjected the unrestricted model to a series of F-tests along with the Akaike Final Prediction Error as the selection criterion. Having obtained the optimum lag structure, the unrestricted model was estimated to obtain the starting values for the non-linear maximum likelihood estimation of model (8). In estimating model (8), our diagnostic testing revealed that in the cases of Australia, Japan and the U.K., we require including a time trend among the explanatory variables to capture the linear trend present in the dependent variables. Also, for Sweden, we found evidence of a structural break and, therefore, estimated the equation with an intercept dummy which took zero up to 1981:1 and unity thereafter. To ensure the validity of the estimated results for drawing statistical inferences, the estimated equations were subjected to a series of diagnostic tests. The Lagrange multiplier test (Breusch and Godfrey, 1981) was used to test for the possibility of the presence of first-order autoregressive disturbances. This result, shown in the row labelled t(LM) in Table 3.9, suggests the absence of autocorrelation in the dynamic models. The LM test proposed by Engle (1982) was used to test the hypothesis that the errors follow a first-order ARCH model. Results indicated the absence of heteroscedasticity in the residuals. Having ensured that the estimated models are well specified, we can now turn to discussion of the results and testing of the above hypotheses. To save space, we do not report the estimated coefficients on the first differenced terms, except for the coefficient of the first differenced U.S. ex-ante real rate which captures the instantaneous or shortterm impact of change in the U.S. rate on the other rates. Table 3.9 shows that the adjustment coefficients are all highly significant. They have the correct signs and are relatively large, indicating short adjustment lags. The long-run coefficients are all positive and significantly greater than zero, indicating the presence of linkages between the ex-ante real interest rates in these countries. The hypothesis of complete linkage is tested by testing the null hypothesis that θm is equal to unity. T-test of this hypothesis is given in the row labelled T-test(H2). As indicated in Table 3.9 the null hypothesis of full linkage cannot be rejected at 95 per cent confidence interval for Belgium, Canada, France and the Netherlands. For Italy, the null cannot be rejected at 98 per cent and for Australia at 99 per cent confidence intervals. For

Estimates and behaviour of ex-ante real interest rates

53

Germany, Sweden, Japan and the U.K. the long-run coefficient is positive, but significantly less than unity. The equality of real rates was tested by testing the joint hypothesis of θm being equal to unity and the constant term being equal to zero employing the Wald chi-square (χ2) test. Results are given in the row labelled χ2(Wald). We can observe that the equality of ex-ante real rates as a long-run proposition cannot be rejected at 5 per cent level of significance only for Belgium. For Canada, the null hypothesis of equality cannot be rejected at 2.5 per cent level of significance. For all other countries, the equality of real rate hypothesis is rejected by the data. Finally, Table 3.9 presents the short-run or the impact effect. It can be seen that the short-run impact is positive and smaller than unity for all countries. However, the shortrun impact is significantly different from zero only in the case of Australia and Canada.

Table 3.9 Maximum likelihood estimate of model (8) (ex-ante real short-term rates)

Constant (1−Σβ) θ

Aust ralia

Belg ium

Can ada

Fra nce

Ger many

Italy

−0.84

−0.26

−0.05

0.44

0.46

−0.10

(2.02)

(1.14)

−0.50

Trend

U.K.

0.95

0.52

−0.46

(0.22) (2.32) (1.91) (0.39)

(4.11)

(1.20)

(2.54) (2.28)

−0.44

−0.14

−0.11

−0.28

−0.58

−0.32 −0.31

(6.85)

(7.24)

(2.52) (6.32) (5.52) (3.28)

(5.44)

(7.49)

(4.83) (5.33)

0.61

1.02

0.40

0.98

(2.83)

(8.92)

0.10

0.41

(0.88)

(1.30)

−0.01

–

1.35

−0.29 −0.30 1.00

0.60

1.80

0.61

0.11

(3.72)

(0.83)

0.05

–

0.72

0.07

0.02

0.12

(3.63) (0.72) (0.16) (0.82) –

–

–

–

(5.06) 2

Swe den

1.42

(3.72) (11.54) (4.85) (9.64) (4.65) (4.54) Short-term (δ0)

Japan Nethe rlands

0.36

0.45

(1.83) (3.07) 0.13

0.14

(1.37) (1.14) –

(2.60)

0.01 (3.56)

R

0.35

0.33

0.24

0.38

0.24

0.14

0.27

0.34

0.18

0.25

D.W.

2.04

2.04

1.90

2.00

1.98

1.83

1.89

1.98

2.07

1.99

t(LM)

0.49

0.78

0.75

0.37

0.25

0.92

0.10

0.03

1.40

0.11

T test(H2)

2.37

0.23

1.27

0.02

3.13

2.01

4.32

0.17

3.24

3.82

18.62

4.94

7.26

24.09

13.05

14.31

23.38

11.53

10.54

14.74

2

χ (Wald)

2

Critical values for χ at 5 per cent and 2.5 per cent level with two degrees of freedom are 5.99 and 7.38, respectively. Critical values for t-test at 5 per cent, 2 per cent and 1 per cent level are 1.96, 2.32 and 2.58, respectively.

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TESTING FOR THE PRESENCE OF UNIT ROOT IN EX-ANTE MEDIUM-TERM REAL INTEREST RATES In examining the statistical properties of the ex-ante real medium-term interest rate series, we follow the two-step procedure discussed on pages 52–4. First, we test the null of nonstationarity versus the alternative of stationarity around a deterministic trend using the testing strategy outlined on pages 52–3. If the presence of the unit root cannot be rejected, we re-examine the series and allow for the possibility of a structural break using Perron methodology. Again, as was the case with the short-term rates, the optimum lag values were determined based on the Akaike Final Prediction Error (FPE) criterion. To test the presence of unit root in the ex-ante medium-term real interest rates, we estimated equation (4). The number of observations used in the regressions was equal to 95. The critical value for the hypothesis of unit root based on Fuller (1976) is equal to (−3.45). The critical value of F-ratio for testing the null hypothesis (β1=0 and θ=0) reported by Dickey and Fuller (1981) is equal to 6.49. The results are given in Table 3.10. The optimum number of lags on the first differenced terms are given in parentheses. Table 3.10 shows that we can reject the null hypothesis of unit root against the alternative of trend stationarity for Japan, Sweden and the U.K. For the rest of the countries we cannot reject the null hypothesis of non-stationarity. For those countries, the F-ratio of the test of the significance of trend was below the 5 per cent critical

Table 3.10 Testing for unit root based on equation (4) Country

ττ

[β1=0 and θ=0]

Australia (1)

−2.37

3.22

Belgium (3)

−2.19

3.18

Canada (1)

−2.87

4.19

France (2)

−1.81

1.80

Germany (2)

−2.08

2.25

Italy (1)

−1.98

2.06

Japan (1)

−4.48

10.09

Netherlands (1)

−3.29

5.41

Sweden (1)

−3.73

7.11

U.K. (2)

−3.75

7.07

U.S.A. (1)

−2.11

2.31

value of 6.49. Therefore, following the testing strategy outlined above, we estimated equation (4) without trend and tested for the presence of unit root using the critical values given in Fuller (1976). In this case, the null of non-stationarity was rejected at the 5 per cent level only for the Netherlands and Germany. In the cases of the Netherlands and

Estimates and behaviour of ex-ante real interest rates

55

Germany, the estimated t-ratio on the coefficient θ was equal to (−3.16) and (−3.31), which is smaller than the critical value of (−2.89) reported by Fuller (1976). For Australia, Belgium, Canada, France, Italy and the U.S.A. we could not reject the null of non-stationarity against the alternatives of stationarity with trend, without trend, with or without a drift. Therefore, we need to examine these series individually. As is clear from Figure 3.6, in all of these countries the behaviour of ex-ante real medium rate has undergone a major break somewhere between 1979 and 1981. Therefore, as shown by Perron (1989), the standard tests of the unit root hypothesis against trend stationarity alternatives cannot reject the unit root hypothesis if the underlying series have undergone a break. After careful examination of these variables, it became apparent that all of them have undergone a change in their level and in their rate of growth between 1979 and 1981. Therefore, test of unit root was conducted employing the specification (C) used by Perron (1989, equation 14). The results are given in Table 3.11. Perron (1989) has provided tables of critical values based on simulations. Tables of critical values are organized on the ratio of pre-break sample size to total sample size which in the present case is between 0.5 and 0.6. Based on Table VI.6 reported by Perron, the critical values at 2.5, 5 and 10 per cent are equal to −4.53, −4.24 and −3.96, respectively. Comparing the t-statistics on θ with these critical values, we observe that the null of non-stationarity can be rejected

Table 3.11 Unit root test: allowing for one-time break Country

Breakpoint

θ

tθ

Australia (1)

1981:1

−0.69

−4.84

Belgium (0)

1980:1

−0.30

−4.09

Canada (4)

1980:4

−0.43

−4.23

France (0)

1981:1

−0.42

−4.47

Italy (0)

1981:1

−0.30

−4.05

U.S.A. (1)

1980:4

−0.55

−5.69

at 2.5 per cent for Australia and the U.S.A. For Canada and France, the null hypothesis can be rejected at 5 per cent, and for Belgium and Italy at 10 per cent level of significance. TESTING THE EQUALITY OF EX-ANTE MEDIUM REAL RATES To estimate model (8) using ex-ante real medium rates we followed a procedure similar to that used as for the short-term real rates. To prevent the potential simultaneity between the

variable, which appears in

and the error term, we substituted

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with its estimated value from the OLS regression of ex-ante real U.S. rate on a constant, its past eight lags and time trend raised to the power of one, two and three. As was discussed above, model (8) is non-linear in parameters and cannot be estimated without assigning some initial values for the parameters. To obtain estimates for the initial values of the parameters we first estimate model (8) in an unrestricted form by allowing the individual variables in the error-correction term to appear as separate regressors. Finally, the optimum lag structure of model (8) was determined based on a series of F-tests along with the Akaike Final Prediction Error. Having obtained the optimum lag structure, the unrestricted model was estimated to obtain the starting values for the non-linear maximum likelihood estimation of model (8). In estimating model (8), our initial diagnostic testing suggested that in the cases of Australia, Sweden and Canada, we needed to include a time trend among the explanatory

Table 3.12 Maximum likelihood estimate of model (8) (ex-ante real medium rates)

Constant (1−Σβ) θ

Aust ralia

Belg ium

Can ada

Fra nce

Ger many

Italy

Ja pan

Nethe rlands

Sw eden

U.K.

−0.09

0.85

0.93

1.33

1.17

0.65

2.39

2.26

2.05

4.01

(0.22) (2.69) (2.93) (2.97) (2.90) (1.28) (3.85)

(4.43)

(4.30) (5.14)

−0.51

−0.48

−0.43

−0.59

(5.01) (3.50) (4.13) (3.27) (3.02) (3.47) (5.10)

(4.87)

(5.48) (6.89)

0.62

−0.27 0.68

−0.43 0.43

−0.31 0.67

−0.19 0.07

−0.25 1.00

0.09

(4.75) (5.85) (3.55) (5.37) (0.42) (3.76) (0.65) Short-term (δ0) Trend

0.38

0.04

0.07

−0.05

0.04

0.02

(3.71) (0.74) (0.45) (1.33) (1.17) (0.47) (0.27) 0.04

–

(3.39) 2

0.03 0.02

–

–

–

–

0.25

0.34

−0.71 0.41

(2.58)

(3.53) (3.72)

−0.05

−0.05

(0.87)

(0.79) (2.12)

–

(3.54)

0.03

0.22 –

(3.64)

R

0.34

0.22

0.29

0.27

0.37

0.17

0.28

0.31

0.31

0.48

D.W.

2.06

2.06

1.98

1.93

1.87

2.06

2.01

2.03

1.83

1.98

t(LM)

0.94

0.38

0.32

0.35

0.62

0.97

0.46

0.27

0.81

0.03

T-test(H2)

2.94

2.72

4.74

2.60

5.45

0.05

6.21

7.61

6.81

5.33

14.64

9.06

23.84

10.78

31.15

7.21

38.59

59.86

48.50

33.57

2

χ (Wald)

2

Critical values for χ at 5 per cent and 2.5 per cent level with two degrees of freedom are 5.99 and 7.38, respectively. Critical values for t-test at 5 per cent, 2 per cent and 1 per cent level are 1.96, 2.32 and 2.58, respectively.

variables. To ensure the validity of the estimated results for drawing statistical inferences, the estimated equations were subjected to a series of diagnostic tests. The Lagrange multiplier test (Breusch and Godfrey, 1981) was used to test for the possibility

Estimates and behaviour of ex-ante real interest rates

57

of the presence of first-order autoregressive disturbances. This result shown in the row labelled t(LM) in Table 3.12 suggests the absence of autocorrelation in the dynamic models. The LM test proposed by Engle (1982) was used to test the hypothesis that the errors follow a first-order ARCH model. The results indicated the absence of heteroscedasticity in the residuals. Finally, a series of sequential Chow tests revealed that the estimated regressions do not exhibit any structural break. Having ensured that the estimated models are well specified, we can now turn to discussion of the results and testing of the above hypotheses. To save space, we do not report the estimated coefficients on the first differenced terms, except for the coefficient of the first differenced U.S. ex-ante real rate which captures the instantaneous or short-term impact of change in the U.S. rate on the other rates. Table 3.12 shows that the adjustment coefficients are all highly significant and have the correct signs indicating that the adjustment process is stable and convergent. The long-run coefficients are not significantly different from zero for Germany and Japan, suggesting the lack of linkage between their medium-term real rates and the U.S. rates. For all other countries, the long-run coefficients are positive and significantly greater than zero indicating the presence of positive and significant linkage between the mediumterm ex-ante real interest rates in these countries. The hypothesis of complete linkage is tested by testing the null hypothesis that θm is equal to unity. T-test of this hypothesis is given in the row labelled T-test(H2). As indicated in Table 3.12, the null hypothesis of full linkage cannot be rejected at 5 per cent level only for Italy. For Australia, Belgium, Canada, France, the Netherlands, Sweden and the U.K. the long-run coefficients are positive, but significantly less than unity. The equality of real rates was tested by testing the joint hypothesis of θm being equal to unity and the constant term being equal to zero employing the Wald chi-square test. The results are given in the row labelled χ2(Wald). We can observe that the equality of ex-ante real medium rates as a long-run proposition can be rejected at 5 per cent level for all countries in our study. Only in the case of Italy, the long-run equality hypothesis cannot be rejected at 2.5 per cent significance level. Finally, we can also read the short-run or the impact effect from Table 3.12. It can be seen that the short-run impacts are not significantly different from zero for all countries except for Australia and the U.K. For Australia and the U.K. the short-run effects are positive but significantly smaller than unity. CONCLUDING REMARKS On the basis of the estimates of the ex-ante real interest rates presented in this chapter, it is clear that the short-rates behaved differently in the three decades from the 1960s to the 1980s. The rates during the 1980s were relatively higher with the rates in the second half generally being lower than those in the first half. While the general movements across the countries was in the same direction, there were wide quantitative differences between them in virtually all the time periods. In most cases, the nominal interest rates provided a useful guide for the behaviour of the ex-ante real interest rates.

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Before examining the equality of real interest rates across different countries, the chapter presents extensive evidence on the time series properties of the estimated ex-ante rates. Then using a model which is a combination of Mishkin (1984) and Wickens and Breusch (1988), we examine the question of linkages between interest rates in different countries. The equality of real interest rates is then tested for both short-run and mediumrun interest rates. An interesting aspect of our testing methodology is that it allows for not only the long-run relationship but also for the short-run.

4 INTEREST RATES, INFLATION AND TAXES One of the most popular but controversial issues in the literature relating to interest rates is the relationship between expected inflation and interest rates. This relationship was first articulated by Fisher (1930) in a concrete form. Briefly, this states that in the long run, nominal interest rates will change one-for-one for a given change in expected inflation. This prediction, however, holds only when there are no taxes. This prediction is changed to a greater than unity effect once taxes on interest income are included (see Darby (1975) and Feldstein (1976)). There have been numerous attempts to test the Fisher effect.1 But still there is no general support for its validity either across time for a given country or across different countries for the given time period (Mishkin, 1984). While we do not expect to settle this issue, nevertheless we present the most extensive evidence on this hypothesis as yet available. This is done using the most recent techniques available for analysing time series data. THE MODEL AND THE METHODOLOGY The Fisher hypothesis postulates that in the long run a rise in the expected rate of inflation will lead to an equivalent rise in the nominal interest rate: (1) is the expected rate of inflation at time t, where it is the nominal interest rate at time t, Re is the ex-ante real rate of interest and ut is a stochastic disturbance term. If taxes are ignored, the Fisher hypothesis can be tested by testing whether the coefficient of the expected rate of inflation is identical to unity. Estimating the Fisher equation in the form presented in (1) suggests that we are continuously on the long-run steady-state equilibrium path and that there is no deviation from this long-run equilibrium path in the short run. A common characteristic of the estimated results reported for equation (1) is a low Durbin-Watson statistic which can be regarded as a manifestation of specification error due to the omission of the short-run dynamics. Most researchers have dealt with this problem by using the Cochrane-Orcutt procedure which corrects for the presence of firstorder autocorrelation in the disturbance term.2 Lucas (1980) in his examination of the Fisher hypothesis subjected the raw data to a filter that retained power at very low frequencies, while reducing power at high frequencies. In effect, he eliminated the short-run variations of the data to obtain new

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variables which reflected only the long-run tendencies of the data. Lothian (1985), on the other hand, computed the average rates of growth of each variable to minimize the effects of shorter-term fluctuations in the data. Summers (1983, 1986) used frequency domain time-series techniques that concentrate on low frequency co-movements in variables or, equivalently, long periodicity aspects of the data to test the long-run relationship hypothesized by the Fisher proposition. However, in using these transformations, all the information on the short-run dynamics is lost. To allow for the presence of lags in the adjustment of the nominal interest rate to changes in the expected inflation rate we re-specify equation (1) as: (2) Equation (2) can be regarded as the dynamic representation of the Fisher equation stated in (1). Under the assumption of no autocorrelation, model (2) can be estimated by ordinary least squares (OLS). The resulting estimates can be used to obtain the long-run response coefficient of the interest rate as: (3)

where θ is the long-run response coefficient of interest rate to changes in expected inflation. The validity of the Fisher hypothesis can be tested by testing the null hypothesis of H0: θ=1. As we discussed in Chapter 3, testing the above hypothesis based on the OLS estimates is computationally inefficient since we not only have to calculate the long-run coefficient θ, but also have to compute its standard error. The transformation introduced in Chapter 3 can be utilized to test the Fisher hypothesis. Following the same procedure as in Chapter 3, without imposing any restrictions, we can transform equation (2) as: (4) Equation (4) is in an error-correction form and shows that changes in the nominal interest rates in the short run are either due to short-term changes in the expected rate of inflation or are caused by deviations of the nominal rate from its long-run equilibrium relationship with the expected rate of inflation as postulated by the Fisher hypothesis. β0 measures the impact effect of changes in the expected rate of inflation on the nominal interest rate and θ measures the long-term response of the nominal interest rate to changes in the inflationary expectations. So far we have assumed that the ex-ante real interest rate is constant over time. Different authors have questioned the constancy of the ex-ante real rate and have allowed the real rate to vary over time by assuming that the ex-ante real rate follows a random walk process.3 In Chapter 3, we observed that in the sample period covered in this study the real interest rates do not follow a random walk process but rather are characterized by stationary processes along a time trend which in the cases of Canada, Italy and the U.S.A. has also undergone a structural break. The presence of time trend in the ex-ante real

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interest rate can be interpreted as representing factors that influence real rates but are not directly quantifiable, such as changes in production technology and marginal productivity of capital. Therefore, we model the ex-ante real interest rate in the so-called trend-dependent variation form similar to those introduced by Farley and Hinich (1970). We can, therefore, write the ex-ante real rate as: (5) where T is time trend, D is an intercept dummy, DT is a trend dummy equal to D*T, and ε is a stochastic disturbance term. Substituting (5) in (4) we have: (6)

Estimating equation (6), we can test both the short-term and the long-run impacts of changes in inflationary expectations on the nominal interest rates. FISHER EQUATION AND NON-STATIONARY VARIABLES So far we have assumed that all of the variables in (6) are stationary. If nominal interest rates and expected inflation rates contain unit roots, estimates of model (6) using standard techniques would produce spurious results unless these two variables are cointegrated. Two variables are called ‘cointegrated’ if there exist a linear combination of them which has a lower order of integration than do any of the two individual random variables (Stock, 1987). In Granger’s (1986, p. 215) notation, if Xt and Yt is a pair of series each of which is integrated of order one and there exists a constant θ such that (7) is integrated of order zero, then Xt and Yt are said to be cointegrated. Using Engle and Granger’s (1987) terminology, coefficient θ that reduces the order of integration of the system is referred to as a cointegrating coefficient. This cointegrating coefficient describes the long-run ‘equilibrium conditions’ to which Xt and Yt tend to return. The implication of this result for economic modelling is immediately apparent. The relationship (8) can be interpreted as a long-run or equilibrium relationship stemming from economic theory. Zt can then be thought of as measuring the extent to which the system is out of equilibrium. In Granger’s terms, it is an equilibrium error, with the terminology chosen to

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depict the fact that it describes the tendency of the system to move towards equilibrium values. Engle and Granger (1987) have further shown that if two series are each integrated of order one and cointegrated there always exists a generating mechanism called the error correction form, linking changes in Xt and Yt to their levels in the previous period plus lagged values for the first differences. What this means in practical terms is that if a longrun equilibrium relationship can be shown to hold for any series of economic variables, it is legitimate to interpret deviations from this equilibrium as adjustments to that steady state. The link goes both ways. Cointegrated variables must obey such a model and data generated by a valid error correction model (ECM) must be cointegrated. Engle and Granger proposed a two-step estimation procedure. In the first step the cointegrating vector is estimated by OLS and the extent of disequilibrium is captured by the residuals of the cointegrating regression. In the second step the full ECM is estimated, again by OLS, with the lagged residual of the cointegrating regression appearing among the explanatory variables. Stock (1987) showed that the OLS estimator of the cointegrating coefficient θ from regression of the long-run relationship in the first step of this two-step procedure is superconsistent in the sense that it converges in probability faster than T1–δ for any positive δ. This contrasts sharply with conventional asymptotic results in which the rate of convergence is T1/2. The least squares estimators of the parameters describing the short-run dynamics of the error correction model converge to limiting normal random variables at the usual rate, T1/2. An implication of the super-consistency result is that it is possible to misspecify the dynamic structure of model (2) when interest rates and inflationary expectations are nonstationary by omitting higher-order lags from the model or, in the case of the alternative formulation (4), by omitting differenced terms without affecting the consistency of the estimates of the long-run multipliers associated with the non-stationary variables. The contributions of the additional variables are asymptotically negligible. In general, however, such an estimator of θ will be biased in finite samples and this bias can be quite large as discussed by Banerjee et al. (1986) and Stock (1987). One source of bias is evident. Omitting the higher-order lags from model (2) or, in the case of the alternative formulation, the differenced terms results in error terms that may have significant finite sample correlation with the included variables. To reduce the small sample bias and to increase the efficiency of the estimated longrun coefficient it would be better to simultaneously estimate the long-run equilibrium relationship and the short-run dynamics in one step by estimating model (4) or (6) directly. Since transformation (4) is derived from model (2) without imposing any restrictions, there does not seem much point in using a two-step estimation procedure. The asymptotic distribution of the estimates would be the same. The long-run coefficient θ can be computed directly from the OLS estimators of the coefficients on the laggedlevel terms in the unconstrained ECM representation of model (4) or (6). In fact, due to the fast rate of convergence of estimators of the long-run coefficient θ, the short-run parameter estimators of the error correction model are asymptotically independent of the estimator of θ and their distribution is well approximated by the standard output of OLS packages.

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Stock (1987) examined a one-step non-linear least squares (NLS) estimator of the error correction models and compared them with the two-step OLS procedures proposed by Engle and Granger. Based on Stock’s findings, a one-step NLS estimator of model (4) or (6) is asymptotically equivalent to the two-step OLS estimator. Both the NLS and the two-step OLS estimators of the coefficients of the short-run variables have a limiting normal distribution, converging at rate T1/2. The NLS and two-step OLS estimators of the short-run dynamics are asymptotically independent of the respective estimators of the cointegrating coefficient θ. The one-step NLS estimator, however, might be more efficient since it utilizes information contained in the short-run dynamics of the model. In the next section, we employ this estimator when estimating the Fisher equation for countries for which nominal interest rate and inflationary expectations are either integrated of order one but cointegrated or are stationary. TESTING FOR THE PRESENCE OF UNIT ROOT IN NOMINAL SHORT-TERM INTEREST RATES AND INFLATIONARY EXPECTATIONS In examining the statistical properties of the nominal interest rates and inflationary expectations, we use the two-step testing procedure outlined on pages 52–4. First, we test the null hypothesis of non-stationarity against the alternatives of stationarity with or without trend using the testing strategy outlined on pages 52–3. If the unit root hypothesis cannot be rejected, we re-examine the series and allow for the possibility of a structural break using Perron methodology. Figure 3.5 shows the graph of the nominal short-term interest rate variables. It can be observed that nominal interest rates in all of the countries under study reached exceptionally high levels around 1974 and 1980:1974 coincides with the oil price shock and 1980 marks the era of new interest rate policies in most OECD countries.4 Therefore, in testing for the presence of unit root in interest rate series, we pay special attention to the possible change of behaviour of the series around these two data points. To test the presence of unit root in the nominal interest rates, we utilized the entire sample period of 1960:1 to 1990:4. After allowing for lags, the effective number of observations used was equal to 116. The critical values for the hypothesis of unit root against the alternatives of stationarity with and without trend (based on Fuller 1976) are equal to (−3.45) and (−2.89) for sample size of 100 and (−3.18) and (−2.93) for sample size of 50, respectively. The critical values of F-ratio for the null hypothesis of non-stationarity with zero coefficient on the trend variable using Dickey and Fuller (1981) is equal to 6.49 for sample size of 100 and 6.73 for sample size of 50. The results of the stationarity test for nominal interest rate series are given in Table 4.1. Again, as was discussed in Chapter 3, the optimum lag structure, reported in parentheses, was determined based on the Akaike Final Prediction Error. Table 4.1 shows that we can reject the null hypothesis of unit root against the alternative of trend stationarity at 5 per cent level of significance for Australia, Germany, Japan, the Netherlands, Sweden

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Table 4.1 Testing for unit root short-run nominal interest rates Country

ττ

Φ3

τµ

Australia (1)

−4.45

6.85

–

Belgium (1)

−3.35

5.63

−2.61

Canada (1)

−3.09

4.81

−2.19

France (1)

−3.19

5.17

−2.70

Germany (2)

−3.65

6.66

–

Italy (1)

−1.95

2.07

−1.70

Japan (4)

−4.06

8.35

–

Netherlands (1)

−4.29

9.23

–

Sweden (3)

−3.65

6.69

–

U.K. (1)

−3.68

6.82

–

U.S.A. (3)

−2.49

3.28

−2.30

Critical value

−3.45

6.49

−2.89

and the U.K. For France, Belgium, Canada, Italy and the U.S.A., we cannot reject the null hypothesis of non-stationarity against the alternatives of stationarity with trend, without trend, with or without a drift. Therefore, we re-examined these series individually and allowed for the presence of a change both in the level and in the slope of the nominal interest rates using the specification (C) employed by Perron. The results are given in Table 4.2. Comparing the t-ratios in Table 4.2 with the critical values reported by Perron we can observe that the null hypothesis of unit root in the short-run nominal interest rate series can be rejected at 5 per cent level of significance for Belgium and France. The unit root hypothesis cannot be rejected for Canada, Italy and the U.S. at 95 per cent confidence interval. However, the t-ratios are smaller than the 10 per cent critical value of (−3.96) and, therefore, the non-stationarity hypothesis can be rejected at 10 per cent level of significance. Table 4.3 shows the tests for the presence of unit root in the inflationary expectation series. Note that for inflationary expectations series, the sample period used, after allowing for lags, was from 1963:1 to 1990:4 which provides an effective sample size of 116. This table also shows that the null hypothesis of non-stationarity against the alternative of trend stationarity can be rejected only for Japan. Therefore, we decided to reformulate our unit root tests allowing for the presence of a structural break in the series. Examining the inflationary expectations closely, we observe that the series for Canada, the U.K. and the U.S.A can potentially be characterized by a trend function with a constant slope but with a change in its level around 1980. Therefore, test of the unit root was conducted employing the specification (A) used by Perron (1989). For other countries, namely Australia, Belgium, France, Germany, Italy, the

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Table 4.2 Unit root test: allowing for one-time break short-run nominal interest rates Country

Breakpoint

tθ

Belgium (1)

1980:4

−4.73

Canada (1)

1980:4

−3.88

France (1)

1980:4

−4.36

Italy (1)

1980:4

−3.87

U.S.A. (3)

1980:4

−4.03

Table 4.3 Testing for unit root short-run inflationary expectations (Mishkin method) Country

ττ

Φ3

τµ

Australia (1)

−1.41

2.49

−2.25

Belgium (2)

−1.86

1.90

−1.69

Canada (2)

−1.29

1.51

−1.78

France (3)

−1.53

1.39

−1.43

Germany (2)

−2.25

1.19

−2.27

Italy (0)

−1.11

0.84

−1.41

Japan (1)

−3.88

6.65

–

Netherlands (1)

−3.01

4.58

−2.42

Sweden (0)

−1.60

1.29

−1.59

U.K. (1)

−1.58

1.25

−2.05

U.S.A. (4)

−1.95

2.08

−2.05

Netherlands and Sweden, in addition to change in the level, we also allowed for the change in the slope of the series using the model (C) specification of Perron (1989). The results are given in Table 4.4. The critical values for model (A) at 2.5 per cent, 5 per cent and 10 per cent when the break occurred in 1974 are (−4.01), (−3.72) and (−3.44), respectively. For model (C), the critical values at 5 per cent and 10 per cent level of significance when the break occurs either at 1974 or 1980 are (−4.22) and (−3.95), respectively. Comparing the test statistics reported in Table 4.4 with the critical values reported above, we observe that the null hypothesis of unit

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Table 4.4 Unit root test: allowing for one-time break short-run inflationary expectations Breakpoint

Model (A) tθ

Model (C) tθ

Australia (1)

1974:2

–

−4.40

Belgium (2)

1974:2

–

−3.95

Canada (1)

1980:4

−4.71

–

Germany (1)

1980:4

–

−4.93

France (1)

1980:4

–

−3.97

Italy (1)

1980:4

–

−2.88

Netherlands (0)

1980:4

–

−5.57

Sweden (1)

1980:4

–

−4.53

U.K. (2)

1980:4

−4.06

–

U.S.A. (2)

1980:4

−3.96

–

Country

root in short-term inflationary expectations can be rejected at 5 per cent level of significance for Australia, Canada, Germany, the Netherlands, Sweden, the U.K. and the U.S.A. For Belgium and France the unit root hypothesis can be rejected at 10 per cent level. For Italy, the null hypothesis of non-stationarity cannot be rejected even at 10 per cent level of significance. Table 4.5 summarizes the results of stationarity tests for the nominal short-term interest rates and inflationary expectations. The table also shows that the null hypothesis of unit root can be rejected for both interest rates and inflationary expectations series for all countries except Italy. Therefore, to prevent any spurious results we treat both series for Italy as being non-stationary. Hence, before estimating the Fisher hypothesis for Italy, we examine whether the nominal interest rate and inflationary expectations series for Italy are cointegrated. The most popular tests for cointegration are conceptually and computationally quite simple (Davidson and McKinnon, 1993). If N time series yt=[Y1t…Ynt], each of which is integrated of degree one, are cointegrated, there exists a vector β such that Xt=[1yt]β is integrated of degree zero, i.e., is stationary. To implement the test using OLS the cointegration regression is run: (9) We then obtain the estimated error terms and test the null hypothesis that the estimated error contains a unit root by estimating the following regression: (10)

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Table 4.5 Summary results of stationarity tests Country

Interest rate

Inflationary expectations

Australia

Yes (5%)

Yes (5%)

Belgium

Yes (10%)

Yes (10%)

Canada

Yes (10%)

Yes (5%)

France

Yes (5%)

Yes (10%)

Germany

Yes (5%)

Yes (5%)

Italy

Yes (10%)

No

Japan

Yes (5%)

Yes (5%)

Netherlands

Yes (5%)

Yes (5%)

Sweden

Yes (5%)

Yes (10%)

U.K.

Yes (5%)

Yes (5%)

U.S.A.

Yes (10%)

Yes (5%)

Significance levels of the tests are in parentheses.

The null hypothesis of H0: ρ=0 should be rejected if the N time series are cointegrated. In some cases, as was pointed out by Engle and Yoo (1987), it makes sense to add a trend to the cointegrating regression. Inclusion of time trend to the cointegration regression can be justified on the grounds that the time series Y1 to Ynt may be expected to change systematically as well as stochastically over time. Thus, the constant term and the time trend capture the non-stochastic component of the series. If the cointegration regression includes a time trend, it is not necessary to include trend and also the constant term in equation (10) since these variables are orthogonal to εt–1.5 Using response surface regressions, Davidson and McKinnon (1993) have provided reasonably accurate critical values for the cointegration tests. Therefore, for testing whether the nominal interest rate and inflationary expectations for Italy are cointegrated, we first run the cointegration regression with time trend.6 The results are as follows: (11) Next, using the estimated residuals from the cointegration regression (11), we tested the null hypothesis of unit root using equation (10). The t-ratio on coefficient ρ was equal to (−4.53) which is smaller than the asymptotic critical value of (−3.34) reported by Davidson and McKinnon (1993).7 Therefore, the null hypothesis of non-cointegration can be rejected at 5 per cent level of significance.

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FISHER HYPOTHESIS: ESTIMATION AND RESULTS Having examined the statistical properties of the underlying variables in equation (6), we can proceed to estimating and testing the Fisher hypothesis. In estimating model (6), we allow for the possibility of structural break either in 1974 or in 1980 in the real interest rate series captured by the intercept terms. The data cover the period from 1963:1 to 1990:4. Estimation was performed using the non-linear least squares method. To ensure that estimated results are appropriate for making statistical inference, we subjected the results to a series of diagnostic testing. All regressions were tested for the presence of ARCH effect in the residuals. No ARCH effect

Table 4.6 Fisher hypothesis using short-term interest rates U.S.A. Canada Belgium Germany 1963– 1980– 1963– 1963– 1980– 1963– 1963– 1980– 1963– 1963– 1980– 1963– 79 90 90 79 90 90 79 90 90 79 90 90 Constant 0.55 (1.83) λ −0.19 (1.77) θ 1.96 (3.64) Dummy – (1980:4) Trend –

5.15 (2.00) −0.30 (1.58) 2.71 (2.64) –

DT

–

∆Πe

1.64 (5.18) 0.50 1.88 0.50 1.78 OK

−0.04 (1.91) 2.51 (2.52) 0.49 1.818 1.09 1.67 OK

–

0.94 (3.95) −0.41 (4.92) 2.19 (5.48) 8.32 (5.80) 0.003 (0.51) −0.07 (4.82) 2.18 (6.68) 0.55 1.87 1.11 2.98 NO

−0.04 (0.16) −0.03 (0.56) 2.06 (0.22) –

1.82 (2.54) −0.26 (2.50) 3.57 (4.69) –

0.67 (1.85) −0.32 (3.12) 2.01 (2.78) –

2.46 (3.67) −0.53 (3.82) 3.35 (10.24) –

–

0.10 (0.42) −0.15 (2.52) 3.76 (4.46) 0.95 (2.90) –

–

0.41 (1.05) 0.39 (3.97) 4.10 (4.11) –

1.01 (2.98) −0.28 (2.83) 4.60 (8.19) –

–

0.40 (1.53) −0.24 (3.54) 2.48 (3.58) 0.90 (2.51) –

–

–

0.38 (1.63) −0.34 (4.65) 4.12 (6.08) 0.97 (3.16) –

–

–

–

–

–

–

–

–

–

–

1.33 (2.72) 0.32 1.77 0.26 0.11 **

7.13 (7.71) 0.73 1.94 0.22 3.38 NO

3.79 (6.83) 0.46 1.85 0.15 3.28 NO

1.55 (3.19) 0.26 1.96 0.003 1.40 OK

3.03 (7.07) 0.59 2.00 0.21 7.19 NO

1.83 (5.82) 0.63 1.85 0.16 6.41 NO

1.90 (6.13) 0.43 1.97 0.40 4.61 NO

1.96 1.00 (5.61) (2.58) 0.30 0.30 R2 D.W. 2.02 2.03 T(LM) 0.66 0.46 t-test 2.13 3.11 OK at NO 99% T(LM) is the Lagrange multiplier test of the presence of first-order autocorrelation. **Original variable is insignificant. ***t-Statistic does not have standard distribution.

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Italy France U.K. Netherlands 1963– 1980– 1963– 1963– 1980– 1963– 1963– 1980– 1963– 1963– 1980– 1963– 79 90 90 79 90 90 79 90 90 79 90 90 Constant 0.24 (1.27) λ −0.24 (2.39) θ 3.31 (11.51) Dummy – (1980:4) Trend –

1.50 (1.66) −0.22 (2.04) 3.22 (5.79) –

DT ∆Πe

– 2.58 (6.63) 0.63 1.68 0.09 3.99 ***

R2 D.W. T(LM) t-test

– 3.24 (13.25) 0.80 1.87 0.15 8.03 ***

–

1963– 79 Constant λ θ Dummy (1980:4) Trend DT ∆Πe R2 D.W. T(LM)

0.20 (1.22) −0.23 (3.26) 3.43 (13.09) 1.34 (3.10) –

0.80 (3.88) −0.23 (4.36) 2.14 (6.28) –

1.09 (2.17) −0.17 (2.32) 3.70 (5.34) –

–

–

– – 3.03 3.24 (15.50) (10.04) 0.75 0.76 2.06 1.92 0.88 0.37 9.27 3.35 *** NO

Sweden 1980– 1963– 90 90

0.75 (1.58) −0.19 (2.33) 1.23 (1.19) –

2.73 (2.48) −0.42 (3.64) 2.87 (3.53) –

–

–

0.29 (0.64) −0.14 (1.87) 2.50 (1.87) 0.78 (1.75) –

– 2.20 (4.45) 0.34 1.83 0.78

– 3.09 (5.85) 0.64 2.21 1.12

– 2.71 (6.55) 0.40 2.04 0.65

– 4.51 (9.42) 0.82 2.00 0.38 3.90 NO

0.98 (4.53) −0.30 (5.25) 2.84 (12.72) 1.77 (5.64) −0.01 (2.29) – 3.68 (12.93) 0.77 2.10 −1.35 8.25 NO

1963– 79

0.45 (1.21) −0.13 (1.42) 1.92 (3.19) –

5.26 (4.92) −0.62 (4.97) 1.84 (10.95) –

–

–

– 2.50 (8.06) 0.64 1.85 1.44 1.53 OK

0.33 (1.13) −0.18 (2.47) 2.31 (3.37) 0.50 (1.34) –

−0.85 (0.84) 0.68 (4.39) 3.91 (4.20) –

0.97 (2.06) −0.19 (2.08) 3.31 (2.16) –

–

–

−0.79 (1.11) −0.50 (5.08) 4.24 (5.10) 3.09 (3.73) –

– – 2.40 2.41 (7.52) (10.82) 0.73 0.61 1.79 1.92 0.35 1.03 4.98 1.91 NO OK

– 2.24 (3.03) 0.32 1.96 0.12 3.13 NO

– 1.38 (1.58) 0.27 1.65 0.93 1.51 OK

– 1.87 (3.32) 0.27 2.02 0.24 3.90 NO

Australia 1980– 1963– 90 90

0.83 (1.56) −0.54 (3.98) 1.49 (1.72) –

3.89 (2.95) −0.29 (3.66) 0.77 (0.60) –

0.05 (1.82) – 5.63 (5.98) 0.58 1.98 0.21

– – 9.24 (12.08) 0.86 2.01 0.08

0.55 (1.27) −0.46 (5.58) 2.29 (4.96) 2.36 (3.65) 0.02 (2.10) – 7.83 (12.21) 0.70 1.98 0.26

1963– 79

Japan 1980– 90

1963– 90

0.15 (1.67) −0.07 (2.76) 2.59 (4.29) –

0.04 (0.28) −0.03 (0.98) 2.40 (3.13) –

0.11 (1.55) −0.04 (2.79) 2.64 (4.67) –

–

–

–

– 4.22 (44.10) 0.98 2.04 0.99

– 4.23 (58.89) 0.99 2.04 0.98

– 4.23 (64.15) 0.98 2.08 1.25

Interest rates and budget deficits t-test

0.22 **

2.29 NO

1.12 OK

0.56 OK

0.17 **

2.79 NO

70 2.63 NO

1.83 OK

2.90 NO

was found. Presence of first- to fourth-order autocorrelation was tested using the Lagrange multiplier test. No autocorrelation was detected. The results are given in Table 4.6. To save space, we have not reported the results for the first differenced terms except for ∆Πe which captures the impact effect of inflationary expectations on interest rates. This table also shows that the estimated Fisher equations for the entire sample period of 1963–90 exhibit a number of remarkable properties. First, the coefficient of adjustment, λ, is significantly different from zero for all countries signifying the fact that deviations of the nominal interest rates and inflationary expectations from their long-run equilibrium relationship for all countries have been partially corrected for in the short run. Second, the adjustment coefficients for all countries (except Japan) have been relatively high, pointing to the fast adjustment of nominal interest rates to changes in the inflationary expectations. Third, the estimated long-run coefficients of adjustment of nominal interest rates to inflationary expectations, θ, for all countries are significantly different from zero. Fisher hypothesis as a long-run proposition was tested by testing the null hypothesis of θ being equal to unity. The t-values for the Fisher hypothesis are reported in the row labelled ttest. Comparing the t-statistics with the 5 and 1 per cent critical value of 1.96 and 2.58 respectively, we observe the following. Fisher hypothesis is rejected for all countries except for the U.K. and Sweden at 95 per cent and for Belgium at 99 per cent confidence level. For Italy, the t-statistic on the longrun coefficient does not have standard distribution and therefore cannot be used for statistical inference. The rejection of the Fisher hypothesis during the 1963–90 period implies that, during that period, the short-run before-tax nominal interest rates for all countries, except for Belgium, the U.K. and Sweden, have been more than compensated for by the changes in the inflationary expectations, giving rise to increasing real rates in those countries during the 1960–90 period. Fourth, all of the estimated equations, except for Japan, show a significant increase in their intercept after 1980:4. This implies that the mean values of the real interest rates have significantly increased during the post-1980:4 period. Fifth, the short-run or the impact effect of changes in inflationary expectations on the nominal interest rates captured by the coefficient of ∆Πe is significantly different from zero for all countries. In fact, the size of the short-run effects are relatively high. The estimated results reported in Table 4.6 support the findings of Table 3.3 in that the mean value of the ex-ante real rates have increased significantly during the 1980s as compared to the 1960s and the 1970s. The above results are based on the entire time period covered. To see whether the hypothesis also held for the 1960s and the 1970s combined and for the 1980s we also estimated the model for the periods 1963:1 to 1979:4 and 1980:1 to 1990:4. These results are given in columns (1) and (2) of Table 4.6, respectively.

Interest rates, inflation and taxes

71

Concentrating on the t-test of the hypothesis of θ being equal to unity, we can see that, for the period 1963:1 to 1979:4, the Fisher hypothesis cannot be rejected for the U.S.A. (95 per cent), Belgium (99 per cent), the U.K. (95 per cent) and Australia (90 per cent). The coefficient is insignificant for Canada and Sweden. Finally, the hypothesis is rejected for France, Germany, Japan and the Netherlands. It should be noted, however, that the short-run effect of inflationary expectations on before-tax short-term nominal interest rates is highly significant for all countries. For the period 1980:1 to 1990:4, the Fisher hypothesis cannot be rejected for Japan (95 per cent), the Netherlands (95 per cent) and the U.S.A. (95 per cent). The coefficient is insignificant for Australia. And the hypothesis is rejected for Belgium, Canada, France, Germany, Italy, Sweden and the U.K. Once again, we should note the short-run significance of inflationary expectations for all countries. Thus, a comparison of the results for the two sub-periods with those for the whole period reveals considerable differences for some of the countries, though not for all. For Canada, France, Germany and Italy the hypothesis is rejected for all three periods. But such consistency is not observed for any of the other seven countries. It is interesting to note that the hypothesis is not rejected for the 1960s and 1970s combined for Australia,

Table 4.7 Fisher hypothesis using post-tax shortterm interest rates Japan U.S.A. Canada U.K. 1964:1– 1980– 1964– 1963– 1980– 1963– 1963– 1980– 1963– 1963– 1980– 1963– 1979:4 90 90 79 90 90 79 90 90 79 90 90 Constant

0.14 (1.67) −0.07 (2.76) 2.41 (4.29) –

0.04 (0.28) −0.03 (0.98) 2.23 (3.13) –

0.11 (1.55) −0.04 (2.79) 2.45 (4.67) –

0.44 (1.83) −0.19 (1.77) 1.48 (3.27) –

3.97 (2.00) −0.30 (1.58) 2.09 (2.64) –

Trend

–

–

–

–

–

DT

–

–

–

–

−0.03 (1.91) 1.93 (2.52) 0.49 1.81 1.09 1.89 1.37 OK

λ θ Dummy

DX

3.92 3.93 3.93 1.30 (44.11) (58.89) (64.15) (5.08) 0.98 0.99 0.98 0.50 R2 D.W. 2.04 2.04 2.08 1.88 t(LM) 0.99 0.98 1.25 0.50 F-test 6.30 2.99 7.66 1.13 t-test 2.51 1.73 2.76 1.01 OK NO OK H0: θ=1 OK* *99%.

0.71 (3.45) −0.41 (4.80) 1.69 (5.39) 6.42 (5.80) 0.003 (0.53) −0.06 (4.74) 1.70 (6.54) 0.56 1.87 1.11 4.88 2.21 OK*

−0.03 (0.16) −0.03 (0.56) 2.00 (0.22) –

1.54 (2.54) −0.26 (2.50) 3.03 (4.69) –

0.34 (1.21) −0.13 (1.42) 1.46 (3.19) –

3.99 (4.92) −0.62 (4.97) 1.39 (10.95) –

–

0.08 (0.42) −0.15 (2.52) 3.20 (4.46) 0.81 (2.90) –

–

–

0.25 (1.13) −0.10 (1.47) 1.76 (3.37) 0.38 (1.34) –

– –

–

–

–

–

–

1.12 (2.72) 0.32 1.77 0.26 0.01 0.11 –

6.06 (7.71) 0.73 1.94 0.22 9.89 3.14 NO

3.22 (6.83) 0.46 1.85 0.15 9.40 3.07 NO

1.90 (8.06) 0.64 1.85 1.44 1.00 1.00 OK

1.82 (7.52) 0.73 1.79 0.35 9.61 3.10 NO

1.84 (10.82) 0.61 1.92 1.03 2.12 1.46 OK

Interest rates and budget deficits

72

France Netherlands Germany Italy 1963– 1980– 1963– 1963– 1980– 1963– 1963– 1980– 1963– 1963– 1980– 1963– 79 90 90 79 90 90 79 90 90 79 90 90 Constant 0.53 (3.88) λ −0.23 (4.36) θ 1.43 (6.28) Dummy – Trend DT DX

–

– 2.17 (10.04) 0.76 R2 D.W. 1.92 t(LM) 0.37 F-test 3.65 t-test 1.91 H0: θ=1 OK

0.73 (2.17) −0.17 (2.32) 2.48 (5.34) – – – 3.02 (9.42) 0.82 2.00 0.38 10.17 3.19 NO

0.66 (4.53) −0.30 (5.25) 1.91 (12.72) 1.18 (5.64) −0.005 (2.29) – 2.46 (12.93) 0.77 2.10 1.35 36.64 6.05 NO

−0.66 (0.84) −0.68 (4.40) 3.01 (4.20) –

0.74 (2.06) −0.19 (2.08) 2.55 (2.16) –

0.30 (1.09) −0.40 (3.90) 2.69 (4.01) –

0.67 (2.98) −0.28 (2.83) 3.04 (8.19) –

–

−0.61 (1.11) −0.50 (5.08) 3.26 (5.10) 2.38 (3.73) –

– – 1.73 (3.03) 0.32 1.96 0.12 7.88 2.80 NO

0.17 (1.27) −0.24 (2.39) 2.32 (11.51) –

1.05 (1.66) −0.22 (2.04) 2.26 (5.79) –

–

0.28 (1.77) −0.35 (4.63) 2.69 (6.08) 0.64 (3.11) –

–

–

0.14 (1.22) −0.23 (3.26) 2.40 (13.09) 0.94 (3.10) –

–

– 1.06 (1.58) 0.27 1.65 0.93 1.72 1.31 YES

– 1.44 (3.32) 0.27 2.02 0.24 12.53 3.54 NO

– 0.66 (2.35) 0.30 2.03 0.46 6.34 2.52 OK*

– 1.21 (5.83) 0.63 1.85 0.16 30.21 5.50 NO

– 1.27 (5.92) 0.44 1.97 0.40 14.59 3.82 NO

– 2.27 (13.25) 0.80 1.87 0.15 42.81 6.54 NO

– 1.80 (6.63) 0.63 1.68 0.09 10.40 3.22 NO

– 2.13 (15.50) 0.75 2.06 0.88 58.39 7.64 NO

Belgium, the U.K. and the U.S.A., but is rejected for the first three countries for the 1980s, while for the U.S.A. it continues to be supported. Interestingly, the pattern is just the reverse for Japan and the Netherlands. Our findings would thus seem to suggest that the long-run validity of the Fisher hypothesis, as far as the short-term pre-tax nominal interest rates are concerned, is far from robust.

The above results did not allow for the effect of taxes on interest income. As pointed out above, once we introduce taxes on interestincome, the value of the Fisher coefficient changes. We tested for the implications of including taxes for our results. We did this by estimating the above model but by using the after-tax short-term nominal interest rates. But we encountered a serious problem in this part of the analysis. We do not have quarterly data on marginal tax rates for any of the countries and even the annual data are available for only Canada and the U.S.A. Consequently, we were obliged to use a constant average rate for all times for each country. Even these limited data were not available for Australia, Belgium and Sweden. A disadvantage of using these data is that basically we are not estimating another regression. All we are doing is scaling down the dependent variable, thus leaving all other coefficients and their t-statistics as those before introducing tax. The only things that are different are the size of the constant, the long-run coefficient and the impact coefficient. Be that as it may, the post-tax rate results are given in Table 4.7.

Interest rates, inflation and taxes

73

Once again, concentrating on the t-test of the hypothesis of θ being equal to unity, we can see that for the period 1963:1 to 1979:4, the hypothesis cannot be rejected for France, Germany, Japan, the U.K. and the U.S.A. The coefficient is insignificant for Canada and the hypothesis is rejected for the Netherlands. For Italy, the t-ratio does not have standard distribution. For the 1980s, the Fisher hypothesis cannot be rejected for Japan, the Netherlands and the U.S.A., all at the 95 per cent level, but is rejected for Canada, France, Germany and the U.K. For Italy, once again, the t-ratio does not have standard distribution. For the whole period, the Fisher hypothesis cannot be rejected for the Netherlands (95 per cent), the U.K. (95 per cent) and the U.S.A. (99 per cent), but is rejected for Canada, France, Germany, Italy, Japan and the Netherlands. We can carry out the same kind of comparison as we did above for the pre-tax interest rate results. Once again it is clear that the validity of the Fisher hypothesis varies, both across time and across the countries. FISHER HYPOTHESIS: MEDIUM-TERM INTEREST RATES Testing for the presence of unit root in nominal medium-term interest rates and inflationary expectations The analysis of the previous section was confined to short-term interest rates. However, the Fisher hypothesis is supposed to hold for financial assets of varying maturity, and therefore it is interesting to see whether such is also the case for our sample of countries. We examine this issue by concentrating on one representative asset, namely, the one examined in Chapter 3. That rate is the medium-term interest rate, as defined there. We carry out the analysis of these rates the same way as we did that for the short-term rates. So, we start, first, by examining the statistical properties of the medium-term nominal interest rates and inflationary expectations. Once again, we use the two-step testing procedure outlined on pages 52–4. Figure 3.6 shows the behaviour of nominal and real medium-term interest rates. It can be seen that the nominal interest rates in all of the countries in this study reached an exceptionally high level around 1980. Therefore, in testing for the presence of unit root in interest rate series, we pay special attention to the possible change of behaviour of the series around 1980. To test the presence of unit root in the nominal interest rates, we utilized the sample period of 1967:1 to 1990:4. After allowing for lags, the effective number of observations used was about 90. The critical values for the hypothesis of unit root against the alternatives of stationarity with and without trend based on Fuller (1976) are equal to (−3.45) and (−2.89) for sample size of 100 and (−3.18) and (−2.93) for sample size of 50, respectively. The critical values of F-ratio for the null hypothesis of non-stationarity with zero coefficient on the trend variable using Dickey and Fuller (1981) is equal to 6.49 for sample size of 100 and 6.73 for sample size of 50. The results of stationarity test for medium-term nominal interest rates are given in Table 4.8. Again, as we discussed in Chapter 3, the optimum lag structure, reported in parentheses, was determined on the basis of Akaike Final Prediction Error.

Interest rates and budget deficits

74

Table 4.8 shows that we can reject the null hypothesis of unit root against the alternative of trend stationarity at 5 per cent level of significance only for Germany and the U.K. and at 10 per cent level

Table 4.8 Testing for unit root medium-run nominal interest rates Country

ττ

Φ3

τµ

Australia (0)

−1.71

2.69

−2.27

Belgium (1)

−1.85

2.06

−2.04

Canada (2)

−1.85

1.93

−1.90

France (1)

−1.60

1.68

−1.82

Germany (4)

−3.05

4.66

−2.89

Italy (1)

−1.45

1.59

−1.76

Japan (4)

−3.30

5.48

−2.74

Netherlands (3)

−2.64

3.54

−2.68

Sweden (1)

−2.92

4.29

−1.71

U.K. (2)

−2.28

2.70

−2.94

U.S.A. (3)

−2.01

2.22

−2.06

Critical value (5%)

−3.45

6.49

−2.89

Critical value (10%)

−3.15

−2.58

of significance for Japan and the Netherlands. For Australia, Belgium, Canada, France, Italy, Sweden and the U.S.A., we cannot reject the null hypothesis of non-stationarity against the alternatives of stationarity with or without trend. Therefore, we re-examined these series individually and allowed for the presence of a change both in the level and in the slope of the nominal interest rates using the specification (C) employed by Perron. The results are given in Table 4.9. Comparing the t-ratios in Table 4.9 with the critical values reported by Perron we observe that the null hypothesis of unit root in the medium-run nominal interest rate series can be rejected at 5 per cent level of significance for Australia and the U.S.A., and at 10 per cent level of significance for Belgium, Canada, France and the U.K. The unit root hypothesis cannot be rejected for Italy and Sweden. Table 4.10 shows the tests for the presence of unit root in the inflationary expectation series. This table also shows that the null hypothesis of non-stationarity can be rejected at 5 per cent level of significance for Germany and Belgium and at 10 per cent level for Australia. For the rest of the countries, the null hypothesis of non-stationarity cannot be rejected. Therefore, we reformulated the unit root tests allowing for the presence of a structural break in the series. Examining the inflationary expectations closely, we observed that the series can potentially be characterized by a trend function with

Interest rates, inflation and taxes

75

Table 4.9 Unit root test: allowing for one-time break medium-term nominal interest rates Country

Breakpoint

tθ

Australia (3)

1980:4

−4.89

Belgium (1)

1980:4

−3.96

Canada (4)

1980:4

−3.95

France (3)

1980:4

−3.95

Italy (4)

1980:4

−3.42

Sweden (1)

1980:4

−3.78

U.S.A. (3)

1980:4

−4.35

Critical value (5%)

−4.24

Critical value (10%)

−3.96

Table 4.10 Testing for unit root medium-run inflationary expectations Country

ττ

Φ3

τµ

Australia (1)

−2.57

3.63

−2.67

Belgium (4)

−3.10

4.94

−3.08

Canada (4)

−1.97

2.22

−2.10

France (4)

−1.70

2.46

−2.04

Germany (4)

−3.68

6.93

–

Italy (2)

−1.06

2.48

−1.74

Japan (3)

−2.43

3.02

−1.69

Netherlands (4)

−2.97

4.59

−1.88

Sweden (3)

−1.69

2.45

−2.05

U.K. (4)

−2.04

2.68

−1.86

U.S.A. (3)

−2.30

2.82

−2.30

Critical value (5%)

−3.45

6.49

−2.89

Critical value (10%)

−3.15

−2.58

a change in both the slope and the intercept. Therefore, we employed model (C) specification of Perron (1989). The results are given in Table 4.11. Comparing the test statistics reported in Table 4.11 with the critical values, we observe that the null hypothesis of unit root in medium-term inflationary expectations can be

Interest rates and budget deficits

76

rejected at 5 per cent level of significance for Australia and at 10 per cent level of significance for Canada, France, Japan, the Netherlands, the U.K. and the U.S.A. For Italy and Sweden the unit root hypothesis cannot be rejected.

Table 4.11 Unit root test: allowing for one-time break short-run inflationary expectations Country

Breakpoint

Model (C) tθ

Australia (1)

1976:4

−4.69

Canada (4)

1980:4

−4.15

France (4)

1980:4

−3.97

Italy (2)

1980:4

−3.13

Japan (3)

1976:4

−4.11

Netherlands (4)

1980:4

−4.16

Sweden (3)

1976:4

−3.51

U.K. (4)

1976:4

−3.99

U.S.A. (3)

1980:4

−4.13

Critical value (5%)

−4.24

Critical value (10%)

−3.96

Table 4.12 Summary results of stationarity tests* Country

Interest rate

Inflationary expectations

Australia

Yest (5%)

Yes (5%)

Belgium

Yes (10%)

Yes (5%)

Canada

Yes (10%)

Yes (10%)

France

Yes (10%)

Yes (10%)

Germany

Yes (5%)

Yes (5%)

Italy

No

No

Japan

Yes (10%)

Yes (10%)

Netherlands

Yes (10%)

Yes (5%)

Sweden

No

No

U.K.

Yes (10%)

Yes (10%)

U.S.A.

Yes (5%)

Yes (10%)

*Significance levels of the tests are in parentheses.

Interest rates, inflation and taxes

77

Table 4.12 summarizes the results of stationarity tests for the nominal medium-term interest rates and inflationary expectations. This table also shows that the null hypothesis of unit root can be rejected for both interest rates and inflationary expectations series for all countries except for Italy and Sweden. Therefore, before estimating Fisher hypothesis for Italy and Sweden, we examine whether the nominal interest rate and inflationary expectations series for these countries are cointegrated. COINTEGRATION TEST FOR ITALY AND SWEDEN Following the procedure discussed on pages 75–6, we first estimated the cointegration regressions with and without time trend for both countries. Estimated cointegration regression for Italy is as follows:

Estimated cointegration regression for Sweden is as follows:

Next, using the estimated residuals from these cointegration regression, we tested the null hypothesis of unit root in the residuals. The t-ratios on coefficient ρ were smaller than the asymptotic critical values reported by Davidson and McKinnon (1993). Therefore, the null hypothesis of non-cointegration can be rejected at 5 per cent level of significance for both countries. FISHER HYPOTHESIS USING MEDIUM-TERM INTEREST RATES: ESTIMATION AND RESULTS Having examined the statistical properties of the underlying variables in equation (6), we can proceed to the estimation and testing of the Fisher hypothesis. In estimating model (6), we allow for the possibility of structural break in the early 1980s in the real interest rate series captured by the intercept terms. The data cover the period 1969:1 to 1990:4. Estimation was performed using the non-linear least squares method. The results using before-tax interest rates are given in Table 4.13. To ensure that estimated results are appropriate for making statistical inference, we subjected the results to a series of diagnostic testing. All regressions were tested for the presence of ARCH effect in the residuals. No ARCH effect was found. Presence of autocorrelation was tested using the Lagrange multiplier test. The row labelled t(LM) in Table 4.13 presents the results of the autocorrelation tests and shows the absence of autocorrelation in all estimated equations. The Fisher hypothesis is tested by testing the null hypothesis of the coefficient of θ being identical to unity. The

Interest rates and budget deficits

78

Table 4.13 Fisher hypothesis using pre-tax medium-term interest rates U.S.A. U.K. Canada Germany 1969:1– 1980:1– 1969– 1969– 1980– 1969– 1969– 1980– 1969– 1969– 1980– 1969– 1979:4 1990:4 1990:4 79 90 90 79 90 90 79 90 90 Constant

0.90 (1.23) −0.21 (1.50) 1.82 (1.99) –

2.86 (3.74) −0.45 (3.81) 2.15 (6.95) –

1.33 1.50 (3.62) (1.47) λ −0.38 −0.19 (4.57) (1.29) θ 2.26 1.01 (8.15) (1.88) Dummy 1.05 – (3.51) Trend – – – – DT – – – – ∆IIe 0.38 0.63 2.27 0.84 (2.01) (0.27) (1.45) (0.66) 0.28 0.47 0.32 0.24 R2 D.W. 1.91 2.05 2.05 2.03 t(LM) 0.83 0.32 0.65 0.82 t-test 0.89 3.72 4.54 0.02 OK NO NO OK H0: θ=1 **Original coefficient is insignificant.

3.59 (3.36) −0.41 (3.40) 1.13 (3.92) – – – 0.38 (0.27) 0.29 1.88 0.25 0.45 OK

2.18 (3.74) −0.30 (4.09) 1.00 (4.26) 0.48 (1.52) – – 0.61 (0.71) 0.22 1.95 0.63 0.01 OK

1.09 (1.38) −0.22 (1.65) 1.69 (2.68) –

6.16 (4.80) −0.70 (4.64) 1.38 (5.32) –

– – 1.59 (0.92) 0.45 1.98 0.26 1.10 OK

– – 0.80 (0.21) 0.42 2.01 1.07 1.46 OK

1.72 (3.32) −0.36 (3.58) 1.63 (4.90) 1.10 (2.76) – – 1.61 (0.76) 0.26 1.96 0.38 1.89 OK

2.05 (3.72) −0.28 (3.38) 0.40 (0.64) –

2.11 (2.37) −0.28 (1.96) 0.61 (0.50) –

– – 1.54 (0.91) 0.47 2.11 – 0.94 **

– – 3.04 (1.03) 0.27 1.99 – 0.32 **

1.82 (4.27) −0.28 (3.72) 0.87 (1.47) 0.15 (1.16) – – 2.78 (1.92) 0.32 2.04 – 0.22 **

France Belgium Sweden Australia 1969– 1980– 1969– 1969– 1980– 1969– 1969– 1980– 1969– 1969– 1980– 1969– 79 90 90 79 90 90 79 90 90 79 90 90 Constant 1.88 (2.69) λ −0.27 (2.46) θ 1.37 (7.11) Dummy –

3.51 (3.92) −0.40 (3.64) 1.60 (7.20) –

Trend DT ∆IIe

– – 3.71 (2.21) 0.45 2.07 0.61

R2 D.W. t(LM)

– – 2.35 (2.76) 0.57 1.81 0.63

1.16 (3.13) −0.20 (6.58) 1.68 (6.58) 0.51 (2.18) – – 3.41 (3.46) 0.32 2.01 0.34

0.76 (1.39) −0.12 (1.34) 1.40 (2.23) –

0.78 (1.49) −0.08 (1.33) 0.48 (0.24) –

– – 1.68 (1.86) 0.31 1.99 0.66

– – 1.49 (0.92) 0.43 2.19 1.29

0.36 (1.78) −0.04 (1.27) 0.91 (0.54) −0.02 (0.13) – – 0.73 (0.93) 0.29 2.05 1.02

1.57 (3.16) −0.27 (3.25) 1.54 (6.57) –

2.99 (3.05) −0.27 (3.02) 0.47 (1.06) –

– – 0.26 (0.49) 0.39 2.01 –

– – 1.18 (1.41) 0.33 2.00 –

1.34 (3.45) −0.22 (3.65) 1.21 (3.92) 0.69 (3.04) – – 0.93 (1.68) 0.28 1.94 –

0.59 (1.70) −0.14 (1.61) 1.38 (1.32) –

3.83 (2.50) 0.32 (3.28) 0.61 (0.68) –

– – 1.82 (1.22) 0.10 1.88 0.48

– – 1.41 (0.97) 0.22 1.93 0.25

0.60 (2.08) −0.16 (2.55) 1.92 (2.97) 0.81 (1.65) – – 2.40 (1.90) 0.14 1.95 0.27

Interest rates, inflation and taxes t-test H0: θ=1

1.92 OK

2.71 NO

2.67 NO

0.64 OK

0.26 **

0.05 **

Italy

Constant λ θ Dummy

2.30 NO

79

1.20 **

0.69 OK

Japan

0.36 **

0.43 **

1.42 OK

Netherlands

1969– 79

1980– 90

1969– 90

1969– 79

1980– 90

1969– 90

1969– 79

1980– 90

1969– 90

1.12

1.91

0.67

1.33

0.87

0.87

3.46

1.10

0.97

(2.29)

(2.84)

(2.59)

(2.56)

(1.72)

(3.11)

(3.06)

(1.89)

(2.72)

−0.18

−0.16

−0.11

−0.19

−0.17

−0.15

−0.47

−0.15

−0.14

(2.41)

(2.49)

(2.64)

(2.26)

(1.38)

(3.14)

(2.95)

(1.70)

(2.26)

1.59

0.95

1.45

0.33

1.29

0.68

0.27

1.20

0.51

(7.26)

(1.62)

(4.14)

(0.96)

(0.90)

(2.40)

(0.75)

(1.18)

(0.55)

–

–

0.26

–

–

–

–

–

0.04

(1.31)

(0.19)

Trend

–

–

–

–

–

–

–

–

–

DT

–

–

–

–

–

–

–

–

–

1.96

0.98

1.33

0.38

0.05

0.36

−0.14

1.38

0.10

(3.64)

(1.04)

(2.77)

(1.21)

(0.03)

(1.00)

(0.14)

(0.75)

(0.11)

R

0.56

0.36

0.32

0.54

0.26

0.26

0.26

0.34

0.21

D.W.

2.13

1.97

2.05

1.83

1.94

1.87

2.00

1.97

1.99

t(LM)

0.67

0.22

0.43

0.87

0.27

0.37

0.02

0.51

1.21

t-test

2.71

0.24

1.29

1.98

0.02

1.12

2.03

0.20

0.53

H0: θ=1

NO

OK*

OK

**

**

OK

**

**

**

e

∆II 2

row labelled t-test in Table 4.13 presents the results. This table also shows that the estimated Fisher equations exhibit a number of interesting properties. We discuss the results for the following different sub-periods. 1969:1 to 1979:4 period First, the coefficient of adjustment, λ, is significantly different from zero for Germany, France, the Netherlands, Japan, Italy and Sweden. For the U.S.A., the U.K., Canada, Belgium and Australia, the coefficient of adjustment is not significantly different from zero. Second, the estimated long-run coefficients of adjustment of medium-term nominal interest rates to inflationary expectations, θ, are significantly different from zero at 5 per cent level of significance for the U.S.A., Canada, France and Belgium. For the U.K., the

Interest rates and budget deficits

80

long-run coefficient is significantly different from zero at 10 per cent level of significance. For Sweden and Italy the long-run coefficients have large t-ratios. However, the distribution of the t-ratios for the long-run coefficients are not standard and cannot be used for making statistical inference. For Germany, Australia, Japan and the Netherlands the long-run coefficients are not statistically significant. Fisher hypothesis as a long-run proposition was tested by testing the null hypothesis of θ being equal to unity. The t-ratios for the Fisher hypothesis are reported in the row labelled t-test. Comparing the t-statistics with the 5 and 1 per cent critical value of 1.96 and 2.58 respectively, we observe that the Fisher hypothesis cannot be rejected for the U.S.A., the U.K., Canada, France and Belgium. For the rest of the countries, except for Sweden and Italy, the long-run coefficients are statistically insignificant. For Italy and Sweden, the numerical values of the long-run coefficients are close to unity. However, the t-ratio does not have the standard distribution and therefore cannot be used to make statistical inference concerning the validity of the Fisher hypothesis. The short-run impact of changes in inflationary expectations on the level of mediumterm interest rates are significant only for the U.S.A., France, Belgium and Italy. 1980:1 to 1990:4 period First, the coefficient of adjustment, λ, is significantly different from zero for all countries except for Belgium, the Netherlands and Japan. For the Netherlands, the coefficient of adjustment is significantly different from zero at 10 per cent level of significance. Moreover, the coefficients of adjustments are relatively high implying a very fast adjustment of medium-term interest rates to changes in inflationary expectations during the 1980s. Second, the estimated long-run coefficients of adjustment of medium-term nominal interest rates to inflationary expectations, θ, are significantly different from zero at 5 per cent level of significance for the U.S.A., the U.K., Canada and France. For Sweden and Italy the t-ratios on the long-run coefficients do not have standard distribution and cannot be used for making statistical inference. For Germany, Australia, Japan, the Netherlands and Belgium the long-run coefficients are not statistically significant. Fisher hypothesis as a long-run proposition was tested by testing the null hypothesis of θ being equal to unity for those countries with significant long-run coefficients. The Fisher hypothesis cannot be rejected for the U.K. and Canada. For the U.S.A., and France, the long-run coefficients are significantly greater than unity. The short-run impact of changes in inflationary expectations on the level of mediumterm interest rates are significant only for France. Comparing the estimated equations for the two periods of the 1970s and 1980s, we observe that the estimated intercept terms for the period of the 1980s are numerically larger than the 1970s, implying higher real rates in the 1980s. 1969:1 to 1990:4 period First, the coefficient of adjustment, λ, is significantly different from zero for all countries except for Belgium. Moreover, the coefficients of adjustments are relatively high,

Interest rates, inflation and taxes

81

implying a very fast adjustment of medium-term interest rates to changes in inflationary expectations during the 1969–90 period. Second, the estimated long-run coefficients of adjustment of medium-term nominal interest rates to inflationary expectations, θ, are significantly different from zero at 5 per cent level of significance for Australia, Japan, the U.S.A., the U.K., Canada and France. For Sweden and Italy, the t-ratios on the long-run coefficients are large. However, they do not have standard distribution and cannot be used for making statistical inference. For Germany, Belgium and the Netherlands the long-run coefficients are not statistically significant. Fisher hypothesis as a long-run proposition was tested by testing the null hypothesis of θ being equal to unity for those countries with significant long-run coefficients. The Fisher hypothesis cannot be rejected for the U.K., Canada, Australia and Japan. For the U.S.A. and France, the long-run coefficients are significantly greater than unity. The short-run impact of changes in inflationary expectations on the level of mediumterm interest rates are significant only for Germany, France and Australia. The dummy variable which captures the effect of a rise in real rates during the 1980s is significantly different from zero for the U.S.A., Canada, France and Sweden. This implies that the mean value of real interest rates have significantly increased during the post-1980:4 period for these countries. We also tested the validity of the Fisher hypothesis in the presence of taxes in this case. But given the limitations of the data on tax rates discussed before, the same observations we made about the short-term interest rates apply in this case too. The results for the post-tax rates are given in Table 4.14. We just concentrate on the coefficient θ and test whether it was equal to unity. Very briefly, we can observe the following. For the period 1969:1 to 1979:4, the Fisher hypothesis cannot be rejected for any of the countries. However, for the period 1980:1 to 1990:4, such unambiguous results are available only for Canada, France and the U.K. The hypothesis is clearly rejected for the U.S.A. and the long-run coefficients are statistically insignificant for Germany, Japan and the Netherlands. For Italy, although numerically the coefficient is close to unity, its tvalue cannot be determined with precision. For the entire period 1963:1 to 1990:4, the hypothesis cannot be rejected for Canada, France, Japan and the U.K. It is again rejected for the U.S.A. For Germany and the Netherlands the long-run coefficients are insignificant and Italy shows the same result, namely, a coefficient of approximate unity but an imprecise t-value. The results for this section suggest the same conclusion as those for the short-term interest rates, namely, that regardless of the maturity of the asset involved, the Fisher hypothesis is not robust, both across time and across countries. At the same time, a comparison of the two sets of results also shows that the validity of the Fisher hypothesis is sensitive to the term to maturity of the asset being considered. Thus, for example, for the pre-tax short-term interest rates, we rejected the hypothesis for a number of countries, but such was not the case with respect to the pre-tax medium-term interest rate.

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Table 4.14 Fisher hypothesis using post-tax medium-term interest rates Italy Japan Canada Germany 1969– 1980– 1969– 1969– 1980– 1969– 1969– 1980– 1969– 1969– 1980– 1969– 79 90 90 79 90 90 79 90 90 79 90 90 Constant 0.79 (2.29) λ −0.18 (2.41) θ 1.12 (7.26) Dummy –

1.34 (2.84) −0.16 (2.49) 0.67 (1.62) –

0.47 1.24 (2.59) (2.56) −0.11 −0.19 (2.64) (2.26) 1.02 0.30 (4.14) (0.96) 0.18 – (1.31) Trend – – – – DT – – – – DX 1.36 0.69 0.93 0.35 (3.64) (1.04) (2.77) (1.21) 0.56 0.36 0.32 0.54 R2 D.W. 2.13 1.97 2.05 1.83 t(LM) 0.67 0.22 0.43 0.87 F-test 0.58 0.65 0.04 4.84 t-test 0.76 0.81 0.06 2.19 OK OK OK ** ** Original coefficient is insignificant.

0.81 (1.72) −0.17 (1.38) 1.20 (0.90) –

0.81 (3.11) −0.15 (3.14) 0.63 (2.40) –

0.93 (1.38) −0.22 (1.65) 1.44 (2.68) –

5.24 (4.80) −0.70 (4.64) 1.17 (5.32) –

– – 0.05 (0.03) 0.26 1.94 0.27 0.02 0.15 **

– – 0.34 (1.00) 0.26 1.87 0.37 1.92 1.39 OK

– – 1.35 (0.92) 0.45 1.98 0.26 0.68 0.82 OK

– – 0.68 (0.21) 0.42 2.01 1.07 0.61 0.78 OK

1.46 (3.31) −0.36 (3.58) 1.39 (4.90) 0.94 (2.76) – – 1.37 (0.76) 0.26 1.96 0.38 1.87 1.37 OK

1.35 (3.72) −0.28 (3.38) 0.26 (0.63) –

1.39 (2.37) −0.28 (1.96) 0.40 (0.50) –

– – 1.02 (0.91) 0.47 2.11 – 3.09 1.76 **

– – 2.01 (1.03) 0.27 1.99 – 0.55 0.74 **

1.20 (4.27) −0.28 (3.72) 0.57 (1.48) 0.10 (1.16) – – 1.84 (1.92) 0.32 2.04 – 1.21 1.10 **

U.S.A. U.K. Netherlands France 1969– 1980– 1969– 1969– 1980– 1969– 1969– 1980– 1969– 1969– 1980– 1969– 79 90 90 79 90 90 79 90 90 79 90 90 Constant 0.69 (1.23) λ −0.21 (1.50) θ 1.40 (1.99) Dummy –

2.20 (3.74) −0.45 (3.81) 1.65 (6.95) –

1.02 (3.62) −0.38 (4.57) 1.74 (8.15) –

1.14 (1.47) −0.19 (1.29) 0.77 (1.88) –

2.73 (3.36) −0.41 (3.39) 0.86 (3.92) –

Trend DT DX

– – 0.49 (0.27) 0.47 2.05

– – 1.75 (1.45) 0.32 2.06

– – 0.64 (0.66) 0.24 2.03

– – 0.29 (0.27) 0.29 1.88

R2 D.W.

– – 0.29 (0.18) 0.28 1.91

1.65 (3.74) −0.30 (4.09) 0.76 (4.26) 0.36 (1.52) – – 0.46 (0.70) 0.22 1.95

2.66 (3.06) −0.47 (2.95) 0.21 (0.75) –

0.85 (1.89) −0.15 (1.70) 0.92 (1.18) –

– – −0.10 (0.14) 0.26 2.01

– – 1.06 (0.74) 0.34 1.97

0.75 (2.72) −0.14 (2.26) 0.39 (0.55) 0.03 (0.19) – – −0.08 (0.11) 0.21 1.99

1.24 (2.70) −0.27 (2.46) 0.90 (7.11) –

2.32 (3.92) −0.40 (3.64) 1.06 (7.20) –

– – 1.55 (2.76) 0.57 1.81

– – 2.45 (2.21) 0.45 2.07

0.76 (3.13) −0.20 (2.95) 1.11 (6.58) 0.34 (2.18) – – 2.25 (3.46) 0.32 2.01

Interest rates, inflation and taxes t(LM) F-test t-test

0.82 0.32 0.56 OK

0.33 0.66 7.60 12.01 2.76 3.46 NO NO

– 0.32 0.57 OK

– 0.41 0.64 OK

– 1.77 1.33 OK

0.03 8.21 2.86 **

0.51 0.09 0.09 **

83 1.21 0.73 0.85 **

– 0.58 0.76 OK

– 0.16 0.40 OK

– 0.43 0.65 OK

CONCLUDING REMARKS This chapter presents extensive evidence on the Fisher hypothesis for the eleven countries in our sample. A distinctive feature of this evidence is that it is also based on the methodology used in Chapter 3 which enables us to distinguish between the short-term and long-term aspects of the hypothesis. The results clearly show that the Fisher hypothesis is not robust, both across time and across countries, regardless of the maturity of the asset involved.

5 ON THE EXOGENEITY OF THE REAL INTEREST RATE Wicksellian monetary theory of interest rates suggests that the real rate of interest is the rate that equilibrates the demand for and supply of capital or loanable funds. The loanable fund market is described by a negatively sloped demand curve which reflects the diminishing marginal productivity of capital in industrial use and a positively sloped supply curve which represents the rate of savings available in the market. The rate of interest at which supply equals demand is referred to as the natural rate and is assumed to be determined by real forces of productivity and thrift. Using the loanable fund framework, assume that there is an exogenous decline (increase) in the marginal efficiency of capital. This causes the demand curve to shift downward (upward) causing the natural rate to fall (rise). Any attempt to prevent the market rate of interest from falling will result in a deflationary gap which causes income and employment to fall, resulting in a shift of the supply curve for funds. The fall in the supply of funds results in a fall in the market rate of interest towards its natural rate. As long as the interest rate stays above its natural rate, the unemployment rate stays above its natural level. In general, in the short-term, interest rates can deviate from their long-run equilibrium rate which is determined by the real forces in the economy, but in the long run they converge to the natural rate. Keynesian liquidity preference theory views nominal rates as the price that equilibrates the supply and demand for money or liquidity. The supply of money is controlled by the monetary authorities. The demand for money depends on the level of income and the nominal rates. The two theories of interest rate determination are usually conciliated through a combination of the ‘neoclassical synthesis’ based on principles of income determination and the Fisher hypothesis.1 Within this context, it is argued that if the monetary authorities manage the level of aggregate demand so as to achieve full employment of resources and price stability, real interest rates which equilibriate supply and demand for funds will reflect the real forces of productivity and thrift. Furthermore, real interest rates are viewed as the vehicle through which monetary disturbances affect aggregate demand and thus are transmitted to the real economy. In general, the hypothesis that real interest rate is exogenous is incompatible with theories that emphasize the role of real rates in transmitting monetary disturbances to the real economy.2 Litterman and Weiss (1985) tried to identify whether or not changes in the money supply have been an important factor in generating postwar U.S. business cycles. More specifically, they examined whether the observed co-movements between money, real interest rates, prices and output are compatible with existing monetary theories of income determination, which include both Keynesian and the informationally based equilibrium

On the exogeneity of the real interest rate

85

theories (Lucas, 1972; Barro, 1976). They found that ex-ante real rates in the U.S.A. are exogenous, or Granger-causally prior, relative to a universe containing money, prices, nominal rates and output. Since both Keynesian models and the equilibrium theories suggest the money to real interest rate to output links, their finding of real rate exogeneity is inconsistent with the nexus of money, real interest rates and output suggested by these models. It has to be noted that it is often difficult to interpret the presence of causal ordering as an indication of behavioural or structural relationship (Sims, 1972, 1980a). However, the failure to reject the null hypothesis of real rate exogeneity raises serious questions about the validity of theories that predict the presence of a causal ordering. For example, the ISLM models, in general, would not be consistent with the hypothesis of real interest rate exogeneity. Let us consider a simplified version of the IS-LM model examined by Litterman and Weiss (1985): (1) (2) is expected inflation, rt is the ex-ante real interest rate, A is autonomous where spending, and et and ut are random influences on real output and real money demand, respectively. The reduced form of this model for the endogenous variables rt and Yt are as follows: (3) (4) where

The reduced forms (3) and (4) show that unless the interest elasticity of investment demand β is infinite, monetary policy will affect output through its effect on the ex-ante real rate. As Litterman and Weiss (1985) discussed, the finding of real rate exogeneity can still be compatible with the above model under the following scenarios. The first possibility is that, during the period under study, the monetary authorities try to set the expected real rates so as to minimize the variance of output

. This occurs if

Interest rates and budget deficits

86

. If A follows a univariate autoregressive process, then so would rt.

Another possibility is that, during the period under study, the interest sensitivity of demand for money δ has been infinite. In this case, the IS curve is horizontal and variations in money supply or demand affect only output without any significant effect on interest rates. Finally, if during the period under study the variations in money supply mt were simply passive reactions to money demand shocks ut, real interest rates would appear to be exogenous to changes in money supply. All of these alternatives, even though possible, seem entirely implausible. Therefore, the hypothesis of real rate exogeneity casts serious doubt on the Keynesian notion of monetary transmission mechanism through which monetary policy affects real output in the economy.3 CAUSALITY-EXOGENEITY TEST In order to test whether real interest rates are exogenous in our study, we use the technique of causality test introduced by Granger (1969). The concept of causality is intuitively rather simple. If variable X causes Y, then changes in X should precede changes in Y. For X to be causally prior to Y two conditions should be satisfied. First, X should help to predict Y. Second, Y should not help to predict X. The idea is that if X can be used to predict Y and Y can help to predict X, then it is highly likely that one or more other variables are causing both X and Y. The concept of causality introduced by Granger (1969) states that a variable Yt is said to be Granger-caused by a variable Xt if the information contained in past and present Xt helps to improve the forecasts of the Yt variable. To formalize, suppose Ut contains all the relevant information in the universe accumulated up to period t and let Ut–Xt denote all this information apart from the information contained in Xt. Define σ2(Yt/Ut) to be the conditional mean squared error (MSE) of the optimal forecast Yt given the information in Ut. We can then say that the variable Xt causes variable Yt if (5) In other words, we say that Xt is causing Yt if we are better able to predict Yt using all available information than if the information apart from Yt had been used. Granger causality from Y to X can also be defined analogously. The above definition can be illustrated using a two-variable model. Let Zt=(Yt, Xt)′ be a vector of stationary and normally distributed bivariate vector of autoregressive process of order p as: (6) where θ’s are the 2×2 matrix of coefficients. We further assume that Zt contains all the relevant information in the universe. It can be shown that Xt does not Granger-cause Yt if

On the exogeneity of the real interest rate

87

and only if the upper right-hand elements of θ’s are zero or, alternatively, all θ’s are lower triangular matrices. Similarly, it can be shown that Yt does not Granger-cause Xt if and only if all θ’s are upper triangular matrices. Therefore, in general, the lack of causality can be tested by testing zero restrictions on the coefficients of the vector autoregressive process (2). The null hypothesis of no Granger causality from X to Y can be tested using a standard F-test with test statistic

where ESSr and ESSu are the sums of squared errors obtained from OLS estimation of the restricted and unrestricted models, N is the number of observations, K is the number of estimated parameters in the unrestricted regression and p is the number of parameter restrictions. In the present case, the test statistic is only approximately distributed as F(p, N–K) since model (6) contains stochastic regressors. The test statistic is asymptotically distributed as χ2 with p degrees of freedom. However, in small samples, the F-distribution is preferred over the χ2 distribution because the F-distribution has a flatter upper tail which can account for replacing the unknown variance in the denominator by its estimated one. Granger (1969) noted that if all the relevant information is not contained in Zt, but in fact there is a third omitted series Dt which causes both Y and X, then spurious causality between X and Y may be found. However, the finding that Y is exogenous with respect to X is not, in general, sensitive to omission of relevant variables. For example, suppose the true reduced form relationship between Y, X and D is as follows: (7) Assume that (8) Then, in population, the regression coefficients of Yt on lagged X’s will be: (9) Equation (9) shows that it is highly unlikely that ηi will be equal to zero when αi are nonzero. Therefore, in general, we can argue that while the finding of the presence of causality relationship between different variables is sensitive to the omission of relevant variables, the finding of exogeneity of a variable is seldom altered as a result of the inclusion of omitted relevant variables. The Granger causality test can be generalized and applied to more than two time series. In this case, matrix Z will include more than two series. Sims (1972) proposed an alternative testing procedure for detecting the presence of causality between different time series. He showed that when Zt has an autoregressive representation, Y can be expressed as a distributed lag function of current and past X with a residual which is not correlated with any values of X, past or future, if, and only if, Y

Interest rates and budget deficits

88

does not cause X in Granger’s sense. We can always regress Y on current and past values of X. However, only in the special case where causality runs from X to Y can we expect that no future values of X would enter the regression if we allowed them. Hence, to test the exogeneity of X or, alternatively, whether there exists a unidirectional causality from X to Y, Sims (1972) proposed a testing procedure which regresses Y on past and future values of X and tests whether the future values of X have coefficients that are not significantly different from zero. The above testing procedures are theoretically equivalent but are different in practice since they have to be estimated based on a finite parametrization of the autoregression (for the Granger test) and distributed lag (for the Sims test). Geweke et al. (1982) examined different forms of causality tests and found that the Sims test was sensitive to failure to correct for serial correlation. They proposed an alternative test which regresses Y on lagged Y and past, present and future X, and tests whether the coefficients on the future values of X are jointly insignificant. The above testing procedures can be summarized as follows. To test whether X is exogenous in a bivariate relationship with Y, the three procedures estimate the following three regressions: • The ‘Granger test’ regresses X on lagged X and lagged Y and tests the lags of Y. • The ‘Sims test’ regresses Y on past, present and future X, and tests the leads of X. • The ‘Geweke et al. test’ regresses Y on lagged Y and past, present and future X, and tests the leads of X. INNOVATION ACCOUNTING AND FORECAST ERROR DECOMPOSITION Another closely related technique which we employ is that of innovation accounting popularized by Sims (1980a, 1981) and others. Granger causality concept measures the percentage of variation of a variable which can be explained by a distributed lag of other variables in a system. Innovation accounting, on the other hand, measures the percentage of variation of a variable which can be explained by a distributed lag of ‘surprises’ or ‘innovations’ in other variables. This procedure traces out the reaction of a system to a shock or innovation in one of the variables. According to the Wold decomposition theorem, each series in a multivariate linear time series model can be represented as a linear combination of current and past innovations in the variables in the system. These innovations, which are by construction serially uncorrelated, can also be transformed to become contemporaneously uncorrelated or orthogonalized. Then, the variance in each variable of the system can be unambiguously decomposed into components attributable to each innovation. Consider an m×1 vector of time series variables y(t). Assume that y(t) can be approximated by a finite linear combination of past y’s such as: (10)

On the exogeneity of the real interest rate

89

where a is an nth-order polynomial in positive powers of the lag operator, L, and u is a residual. We can apply least squares method to equation (10) and obtain estimates of the coefficients of the autoregressive representation (10), i.e., a(L). Denoting Y(t) as the best linear forecast of y(t) based on y(s) where s
Interest rates and budget deficits

90

(except for Sweden where we used M1 plus quasi-money) and output as measured by real GNP for Germany, Japan and the U.S.A., and real GDP for Australia, Canada, Italy, Sweden, the U.K., and industrial production index for France, Belgium and the Netherlands. The sample period, after allowing for lags, covers 1969:3 to 1990:4. As a sensitivity check, we test the real rate exogeneity on the full sample of 1969:3 to 1990:4, and on two partial data sets covering 1969:3 to 1979:4 and 1980:1 to 1990:4. In addition, the exogeneity test is performed on both estimates of the ex-ante real short-term interest rates.5 Table 5.1 presents the results of the Granger test of ex-ante real rate exogeneity relative to a universe that contains money, output and expected rate of inflation. This table also shows that, over the entire period of 1969:3 to 1990:4, the Granger causality test cannot reject exogeneity of ex-ante real interest rates with respect to money, inflationary expectations and real output at the 1 per cent level of significance for Australia, Belgium, Canada, France, Japan, the Netherlands and the U.S.A. The exogeneity of real rates is rejected for Germany for both measures of ex-ante real rates, and for Italy and the U.K. when the Mishkin estimate of real short-term rates are employed and for Sweden when the autoregressive estimate of real

Table 5.1 Granger causality test of the ex-ante real short-term interest rate 1969:3–1990:4

1969:3–1979:4

1980:1–1990:4

RHMISHK RAUT RHMISHK RAUT RHMISHK RAUT Australia

1.05

1.64

1.27

2.45

1.33

2.15

Belgium

0.56

0.91

1.72

1.28

0.77

1.89

Canada

1.39

1.35

0.74

4.30

1.94

3.80

France

1.70

1.29

1.01

4.04

2.28

2.05

Germany

2.44

2.72

1.36

2.02

1.32

3.42

Italy

2.52

1.54

1.11

1.15

1.00

1.25

Japan

1.51

1.78

2.95

2.99

1.72

6.63

Netherlands

1.28

1.26

1.70

2.58

1.81

5.08

Sweden

1.39

2.38

0.66

3.74

0.86

1.69

U.K.

3.13

2.15

2.85

2.34

4.64

1.51

U.S.A.

1.36

1.09

0.63

0.42

2.17

2.50

Critical value (5 per cent)

1.67

1.67

2.90

2.90

2.61

2.61

Critical value (1 per cent)

2.20

2.20

4.73

4.73

4.02

4.02

rate is employed. When we increase the level of significance to 5 per cent, France and Japan join the rank of the countries for whom the real rate exogeneity hypothesis can be rejected at least for one measure of the real interest rate.

On the exogeneity of the real interest rate

91

For the sub-period 1969:3 to 1979:4, the exogeneity of real rates cannot be rejected at 1 per cent marginal significance level for any of the countries. However, when we consider the tests at the 5 per cent level of significance, we can reject the null of exogeneity for Canada, France, Japan and Sweden at least for one of the real rate measures. For the sub-period 1980:1 to 1990:4, the exogeneity of real rates can be rejected at 1 per cent marginal significance level for the Netherlands when autoregressive estimate of ex-ante real rate is used, for the U.K. when Mishkin estimate is employed and for Japan when autoregressive estimate of real rate is used. Increasing the level of significance to 5 per cent only affects the result of the test for Canada when autoregressive estimate of real rate is employed. It is clear from Table 5.1 that the exogeneity test is sensitive to the measure of real rate used, period under consideration and the level of significance chosen. Only for a few countries the test is robust with respect to the estimate of the real rate and the period selected. More specifically, irrespective of the measure of real rate chosen and the period selected, the exogeneity hypothesis cannot be rejected at 1 per cent level of significance for Australia, Belgium, Canada, France and the U.S.A. When the level of significance is increased to 5 per cent, the hypothesis cannot be rejected for only Australia, Belgium and the U.S.A.

Table 5.1 Granger causality test of the ex-ante real short-term interest rate 1969:3–1990:4

1969:3–1979:4

1980:1–1990:4

RHMISHK RAUT RHMISHK RAUT RHMISHK RAUT Australia

1.05

1.64

1.27

2.45

1.33

2.15

Belgium

0.56

0.91

1.72

1.28

0.77

1.89

Canada

1.39

1.35

0.74

4.30

1.94

3.80

France

1.70

1.29

1.01

4.04

2.28

2.05

Germany

2.44

2.72

1.36

2.02

1.32

3.42

Italy

2.52

1.54

1.11

1.15

1.00

1.25

Japan

1.51

1.78

2.95

2.99

1.72

6.63

Netherlands

1.28

1.26

1.70

2.58

1.81

5.08

Sweden

1.39

2.38

0.66

3.74

0.86

1.69

U.K.

3.13

2.15

2.85

2.34

4.64

1.51

U.S.A.

1.36

1.09

0.63

0.42

2.17

2.50

Critical value (5 per cent)

1.67

1.67

2.90

2.90

2.61

2.61

Critical value (1 per cent)

2.20

2.20

4.73

4.73

4.02

4.02

Interest rates and budget deficits

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Table 5.2 Proportions of forecast error K quarters ahead, produced by each innovation (Australia: 1969:3–1990:4) Triangularized innovation in Forecast error in Ex-ante real rate

Money

Real output

Expected inflation

K

Ex-ante real interest rate Money (Mishkin)

Real output

Expected inflation (Mishkin)

1

100.00

0.00

0.00

0.00

4

82.90

16.35

0.32

0.42

8

70.67

23.91

0.87

4.55

16

67.29

25.12

2.59

5.00

24

63.59

27.97

3.65

4.79

1

2.22

97.78

0.00

0.00

4

19.42

75.98

1.82

2.78

8

46.24

42.74

7.46

3.56

16

41.59

30.89

20.14

7.38

24

39.85

26.52

28.83

4.80

1

0.08

1.20

98.72

0.00

4

3.38

4.96

76.16

15.49

8

7.64

18.87

59.56

13.93

16

14.01

18.21

56.23

11.56

24

18.96

17.25

53.51

10.29

1

43.47

0.26

14.88

41.40

4

31.56

2.76

24.11

41.57

8

35.68

8.31

18.96

37.05

16

23.30

28.13

13.94

34.63

24

23.25

27.14

18.10

31.51

As we discussed above, the Granger causality tests reported in Table 5.1 reveal whether the information in the lags of money, inflationary expectations and real output can be used to reduce the one-step-ahead forecast errors of ex-ante real rates. It has to be noted that the absence of Granger causality between the ex-ante real rates and other variables in the system does not necessarily mean that the ex-ante rates are exogenous to money, income and expected rate of inflation since there may be non-zero contributions of contemporaneous values of money, output and inflation to the forecast error variance decomposition of real rates. Therefore, as a further examination of the exogeneity of real rates, it is useful to decompose the variance in ex-ante real interest rates into components attributed to innovations in money, real output and expected rate of inflation at different

On the exogeneity of the real interest rate

93

time horizons.6 As we discussed before, in general, we expect the variance of an exogenous variable to be reveals that a substantial fraction of variance of money is explained by innovations in ex-ante real interest rates and real output. Innovations in the expectation of inflation do not seem to explain a significant portion of the variance of money supply. However, the tests of the hypothesis that all lagged values of real rate, output or expected rate of inflation in the money equation have zero coefficients were easily accepted. Only in the case of the real rate the hypothesis of zero coefficients could not be rejected at the 10 per cent level. Concentrating on the variance of real output in Australia, we observe that at 4-quarter time horizon, innovations in inflationary expectations explain about 15 per cent of the variance of output. Innovations in money and real interest rates do not explain a significant portion of the variance of output in the short run. As forecast horizon lengthens, the proportion of variance in real output accounted for by innovations in inflationary expectations drops from 15 to 10. At the same time, the proportion of variance of real output explained by real interest rate and money innovations increases to 19 and 17 per cent, respectively. At 24-quarter time horizon, about 54 per cent of the variance of real output in Australia is explained by its own innovations. The rest are accounted for by innovations in real interest rate, money and inflationary expectations. The null hypothesis that all lagged values of money, ex-ante real interest rate or inflationary expectations in the output equation have zero coefficients were easily rejected. Finally, Table 5.2 shows that, in the short run, innovations in real interest rates and output account for a significant portion of variance of inflationary expectations. The percentage of variance of inflationary expectations explained by innovations in money increases as forecast horizon lengthens. At 24-quarter forecast horizon, about 27 per cent of the variance of inflationary expectations are explained by innovations in money. Innovations in real rate and output account for about 23 and 18 per cent of the variance of inflationary expectations, respectively. The rest, or about 31 per cent of the variance in inflationary expectations, is explained by its own innovations. As a final examination of the exogeneity of real interest rate, Figure 5.1 shows the responses of ex-ante real interest rate to orthogonalized unit shocks in money, real output and expected rate of inflation for Australia. The vertical axis is measured in percentages and the horizontal axis shows time in terms of quarters. Figure 5.1 demonstrates that shocks to money, output and inflationary expectations have a significant short-term impact on the ex-ante real interest rate in Australia. However, the effect of these shocks dissipates after 24 quarters. In the long-run, the ex-ante real rate in Australia seems to converge to its equilibrium state. The above results are in line with our findings in Table 5.1 that real rate in Australia has behaved as if it is Granger-causally prior. Table 5.3 presents the results of a decomposition of variance for the four-variable system for Belgium along the same lines as that for Australia in Table 5.2. Table 5.3 shows that more than 85 per cent of the variance of the ex-ante real interest rate over a 24-quarter time horizon is explained by its own innovations. In other words, the real rate in Belgium has behaved as if it is Granger-causally prior. We can

Interest rates and budget deficits

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Figure 5.1 Responses of the ex-ante short-term real interest rates to innovations: Australia also see that innovations in money, real output and inflationary expectations do not account for a significant variation of the ex-ante real rate in Belgium. The tests of the hypothesis that all lagged values of money, output or inflation in the real rate equation have zero coefficients were easily accepted. Considering the money supply, Table 5.3 reveals that about 48 per cent of its variance at 4-quarter forecast horizon is explained by innovations in the real interest rate. At 24quarter forecast horizon, about 52 per cent of the variance in money is accounted for by innovations in the real rate and 23 per cent is explained by innovations in real output. Innovations in the expectation of inflation account for only about 7 per cent of the variance of money supply. However, the tests of the hypotheses that all lagged values of real rate, output and inflation in money equation have zero coefficients were easily accepted. Turning to the variance of real output in Belgium, we observe that innovations in expected real interest rate explain about 61 per cent of the variance of output. Innovations in money and expected rate of inflation do not explain a significant portion of the variance of output in the short run. The null hypothesis that lagged values of money do not affect output was easily accepted. However, the null hypothesis that all lags of exante real interest rates in the output equation have zero coefficients was rejected. At 24quarter forecast horizon, about 24 per cent of the variance of real output in Belgium is explained by its own innovations.

On the exogeneity of the real interest rate

95

Table 5.3 Proportions of forecast error K quarters ahead, produced by each innovation (Belgium: 1969:3–1990:4) Triangularized innovation in Forecast error in Ex-ante real rate

Money

Real output

Expected inflation

K

Ex-ante real interest rate (Mishkin)

Money

Real output

Expected rate of inflation (Mishkin)

1

100.00

0.00

0.00

0.00

4

94.96

0.70

0.85

3.48

8

90.00

0.69

4.90

4.41

16

85.85

2.99

5.37

5.78

24

85.70

3.09

5.40

5.81

1

8.85

91.15

0.00

0.00

4

47.61

46.99

4.35

1.05

8

31.97

36.74

23.31

7.98

16

41.86

23.41

26.81

7.91

24

51.73

17.49

23.34

7.44

1

1.21

10.37

88.42

0.00

4

6.84

12.81

71.44

8.91

8

49.86

9.21

36.34

4.59

16

58.48

8.50

26.88

6.14

24

61.16

9.03

24.34

5.47

1

41.68

0.00

0.10

58.23

4

60.69

4.44

2.46

32.41

8

68.82

5.78

2.16

23.23

16

55.46

11.11

12.73

20.70

24

59.11

10.13

13.05

17.70

With regard to the variation in the expected rate of inflation, Table 5.3 shows that innovations in the real interest rate account for a significant fraction of variance in the expected rate of inflation. At 24-quarter forecast horizon, innovations in real rate, money and real output explain about 59, 10 and 13 per cent of the variance in the expected rate of inflation, respectively. The rest, or about 18 per cent of the variance of the expected rate of inflation, is explained by its own innovations. The null hypothesis that all lagged values of the real rate in the inflation equation have zero coefficients was easily rejected. Lagged values of money and output in the inflation equation were not significantly different from zero.

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Finally, to further examine the exogeneity of the ex-ante real rate of interest, Figure 5.2 presents the responses of ex-ante real interest rate to orthogonalized unit shocks in money, real output and expected rate of inflation for Belgium. Figure 5.2 shows that shocks in money, real output and expected rate of inflation have short-term effects on the ex-ante real rate of interest in Belgium. However, the effect of these shocks dissipates after 16 quarters and the ex-ante real interest rate converges to its equilibrium state. The above results confirm our findings in Table 5.1 that real rate of interest in Belgium has behaved as if it is exogenous in a Granger sense relative to the universe that includes inflation, output and money. Table 5.4 presents the results of a decomposition of variance for the four-variable system for Canada. It shows that more than 75 per cent of the variance of the ex-ante real interest rates in Canada after 24 quarters is explained by its own innovations. The table shows that innovations in money, output or inflationary expectations do not account for a significant part of the variance of the real rate even after 24-quarter period. The tests of the individual hypothesis that all lagged values of money, output or inflation in the real rate equation have zero coefficients were easily accepted. In other words, real rate in Canada has behaved as if it is Granger-causally prior. This further supports the exogeneity results in Table 5.1. In terms of the variation in money supply in Canada, Table 5.4 demonstrates that over a 4-quarter time horizon, innovations in ex-ante real rates explain about 44 per cent of the variance in money supply. As time horizon lengthens, the proportion of the variance accounted for by innovations in the real rate drops while innovations in the expected rate of inflation become dominant. At 24-quarter forecast horizon, innovations in expected

Figure 5.2 Responses of the ex-ante short-term real interest rates to innovations: Belgium

On the exogeneity of the real interest rate

97

Table 5.4 Proportions of forecast error K quarters ahead, produced by each innovation (Canada: 1969:3–1990:4) Triangularized innovation in Forecast error in Ex-ante real rate

Money

Real output

Expected inflation

Ex-ante real interest rate (Mishkin)

Money

Real output

Expected rate of inflation (Mishkin)

1

100.00

0.00

0.00

0.00

4

82.43

0.02

12.91

4.64

8

77.63

5.34

13.32

3.71

16

74.66

7.21

13.56

4.57

24

75.57

7.10

12.92

4.40

1

18.03

81.96

0.00

0.00

4

44.03

48.34

1.76

5.87

8

39.28

37.37

1.39

21.96

16

26.00

27.17

1.11

45.71

24

23.98

27.26

2.62

46.13

1

13.10

0.01

86.89

0.00

4

13.73

13.58

67.69

5.01

8

44.92

7.89

24.05

23.13

16

52.11

17.24

8.77

21.88

24

46.76

19.89

7.32

26.02

1

23.96

0.00

1.65

74.39

4

29.19

2.80

12.42

55.59

8

25.97

7.01

12.16

54.85

16

39.07

7.85

9.49

43.60

24

51.28

6.49

9.22

33.01

rate of inflation explain about 46 per cent of the variance in money supply. The test of the hypothesis that all lagged values of expected rate of inflation in the money equation have zero coefficients was rejected. Similar tests for the significance of lags of output in the money equation could be rejected at the 6 per cent level. Therefore, it appears that variation in the supply of money in Canada has been responsive to innovations in the expected rate of inflation and to a lesser extent to innovations in output. Considering the variance of real output in Canada, Table 5.4 shows that innovations in the real rate of interest account for most of the variance of output in Canada. At 24quarter forecast horizon, innovations in real rate explain about 47 per cent of variance in real output. At 24-quarter forecast horizon, innovations in money and expected rate of

Interest rates and budget deficits

98

inflation account for about 20 and 26 per cent of the variance in real output in Canada, respectively. The tests of the hypothesis that all lagged values of real rate or expected rate of inflation in the output equation have zero coefficients were easily rejected. On the other hand, the null hypothesis that all lags of money in the output equation have zero coefficients was easily accepted. It appears that real output in Canada has been responsive to the innovations in the real rate and the expected rate of inflation. At the same time, money supply in Canada does not seem to influence the real output. Concentrating on the variance of the expected rate of inflation, Table 5.4 shows that innovations in real interest rates account for a significant portion of the variance in the expected rate of inflation. The percentage of variance of inflationary expectations explained by innovations in money and real output is rather small. At 24-quarter forecast horizon, more than 50 per cent of the variance of inflationary expectations are explained by innovations in the ex-ante real interest rates and about 33 per cent is explained by its own innovations. Test of the hypothesis that all lagged values of real rates in the inflation equation have zero coefficients was rejected. However, lags of money and output were not significantly different from zero. Finally, it is useful to examine the responses of ex-ante real interest rate to orthogonalized unit shocks in money, real output and expected rate of inflation for Canada. This is provided in Figure 5.3. It clearly shows that the effect of shocks in money, real output and expected rate of inflation on the ex-ante real interest rate in Canada has been only temporary and has lasted about 10 quarters after which the ex-ante rate returns to its initial equilibrium position.

Figure 5.3 Responses of the ex-ante short-term real interest rates to innovations: Canada

On the exogeneity of the real interest rate

99

Table 5.5 presents the results of a decomposition of variance for the four-variable system for France. It shows that more than 74 per cent of the variance of the ex-ante real interest rates in France is explained by its own innovations. At 24-quarter forecast horizon, innovations in the expected rate of inflation account for about 18 per cent of the variance in the real rate. Test of the hypothesis that all lagged values of the expected rate of inflation in the real rate equation have zero coefficients was rejected. Table 5.5 shows that innovations in money and real output do not account for a significant fraction of the variance in the real rate. The tests of the hypothesis that all lagged values of money or output in the real rate equation have zero coefficients were easily accepted. This result suggests that the rejection of the exogeneity hypothesis for France suggested in Table 5.1 is not due to the presence of a link between money and real interest rate, but is due to the relationship between expected inflation and the real rate of interest. Considering the variation in money supply in France, Table 5.5 shows that most of the variance in money supply in France is explained by its own innovations. At 24-quarter forecast horizon, innovations in the ex-ante real rate, real output and expected rate of inflation explain about 8, 10 and 14 per cent of the variance in money supply, respectively. The tests of the hypotheses that all lagged values of ex-ante real rate or expected rate of inflation in the money equation have zero coefficients were easily accepted. However, the same hypothesis for real output was strongly rejected. This suggests that the supply of money in France has been sensitive to innovations in real output. Concentrating on the variance of real output in France, Table 5.5 shows that more than 52 per cent of the variance in real output is explained by its own innovations. At 24quarter forecast horizon, innovations in real rate and expected rate of inflation explain about 35 and 11 per cent of variance in real output, respectively. Innovations in money do not account for a significant portion of the variance of output. The tests of the hypotheses that all lagged values of real interest rate, money or expected rate of inflation in the output equation have zero coefficients were accepted. This suggests that money has been neutral in France. Considering the variance of the expected rate of inflation, Table 5.5 shows that innovations in real interest rates account for a significant portion of the variance in the expected rate of inflation. The test of the hypothesis that lagged values of real rate in the inflation equation have zero coefficients was rejected at 90 per cent confidence level. The percentage of variance in inflationary expectations explained by innovations in money and real output is insignificant. At 24-quarter forecast horizon, about 55 per cent of the variance of inflationary expectations are explained by innovations in the ex-ante real interest rates and about 29 per cent is explained by its own innovations. Finally, the responses of ex-ante real interest rate in France to orthogonalized unit shocks in money, real output and expected rate of inflation is provided in Figure 5.4. It shows that the ex-ante real rate in France has not been sensitive to shocks in the supply of money. The effect of unit shocks in the real output seem to be short-term in nature and disappear after 16 quarters. However, unit shocks in inflationary expectations seem to have a significant short-term

Interest rates and budget deficits

100

Table 5.5 Proportions of forecast error K quarters ahead, produced by each innovation (France: 1969:3–1990:4) Triangularized innovation in Forecast error in Ex-ante real rate

Money

Real output

Expected inflation

K

Ex-ante real interest rate (Mishkin)

Money

Real output

Expected rate of inflation (Mishkin)

1

100.00

0.00

0.00

0.00

4

92.73

0.23

4.76

2.28

8

79.08

0.25

7.41

13.26

16

76.11

0.33

7.13

16.43

24

74.06

0.50

6.87

18.57

1

0.06

99.94

0.00

0.00

4

2.63

95.57

0.04

1.76

8

6.63

84.36

1.12

7.89

16

6.08

75.78

6.76

11.38

24

8.40

67.96

9.66

13.97

1

2.86

1.20

95.93

0.00

4

6.18

4.89

78.59

10.35

8

33.10

2.53

59.69

7.67

16

39.60

1.70

48.25

10.44

24

35.15

1.70

51.92

11.24

1

41.83

1.22

2.50

54.44

4

68.20

1.99

6.89

22.92

8

63.03

3.63

13.00

20.34

16

61.71

6.23

9.83

22.23

24

54.63

8.27

7.72

29.38

On the exogeneity of the real interest rate

101

Figure 5.4 Responses of the ex-ante short-term real interest rates to innovations: France impact on the real rate and it appears to take more than 30 quarters before the effect of the shocks dissipates. Our findings based on Figure 5.4 support the findings of Table 5.5 that the real rate in France has been sensitive to innovations in the expected rate of inflation. Table 5.6 presents the results of a decomposition of variance for the four-variable system for Germany. It shows that about 90 per cent of the variance of the ex-ante real interest rates in Germany at a 24-quarter forecast horizon is explained by its own innovations. However, despite the fact that a small fraction of the variance of the real rate is explained by other variables, Table 5.1 shows that we can reject the null hypothesis of exogeneity of the ex-ante real rate for Germany over the entire period of 1969:3 to 1990:4. To further investigate the behaviour of ex-ante real rate in Germany, we tested the individual hypothesis that all lagged values of money or real output or expected rate of inflation in the real rate equation have zero coefficients. The hypothesis that the lags of money or expected rate of inflation are statistically insignificant was easily accepted. However, the hypothesis that all lagged values of real output have zero coefficients was rejected at the 5 per cent level. Therefore, our results suggest the absence of a link between money and real interest rate in Germany. Nevertheless, real rate in Germany has not behaved as if it is Granger-causally prior with respect to real output.

Interest rates and budget deficits

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Table 5.6 Proportions of forecast error K quarters ahead, produced by each innovation (Germany: 1969:3–1990:4) Triangularized innovation in Forecast error in Ex-ante real rate

Money

Real output

Expected inflation

K

Ex-ante real interest rate (Mishkin)

Money

Real output

Expected rate of inflation (Mishkin)

1

100.00

0.00

0.00

0.00

4

98.83

0.12

0.88

0.17

8

92.03

1.04

5.14

1.80

16

89.93

2.73

5.29

2.05

24

89.54

3.04

5.31

2.12

1

7.27

92.73

0.00

0.00

4

29.22

60.29

0.23

10.26

8

20.88

57.91

1.83

19.38

16

10.23

67.05

1.83

20.89

24

10.70

67.49

2.19

19.61

1

0.39

1.22

98.38

0.00

4

0.85

33.81

62.78

2.56

8

8.72

57.99

20.33

12.96

16

12.69

59.98

10.04

17.28

24

12.80

62.48

8.09

16.63

1

7.81

0.07

0.10

92.02

4

49.62

6.63

0.72

43.03

8

33.49

31.14

2.24

33.13

16

18.48

45.26

1.27

34.99

24

15.48

49.51

1.33

33.68

Turning to the variation in money supply in Germany, Table 5.6 demonstrates that over a 4-quarter time horizon, innovations in ex-ante real rates and expected rate of inflation explain about 29 and 10 per cent of the variance in money supply, respectively. As time horizon lengthens, the proportion of the variance accounted for by innovations in the real rate drops while innovations in the expected rate of inflation become dominant. At 24-quarter forecast horizon, innovations in the real rate of interest and expected rate of inflation explain about 11 and 20 per cent of the variance in money supply, respectively. It appears that supply of money in Germany has been responsive to innovations in the ex-

On the exogeneity of the real interest rate

103

ante real interest rate and the expected rate of inflation. The hypotheses that all lagged values of real interest rate or expected rate of inflation have zero coefficients in the money equation were rejected. Innovations in the real output do not account for a significant part of the variance in money supply. At 24-quarter forecast horizon, about 67 per cent of the variance in money supply is explained by its own innovations. It appears that money supply in Germany has been sensitive to innovations in real rate of interest and expected rate of inflation. Concentrating on the variance of real output in Germany, Table 5.6 shows that innovations in money supply account for most of the variance of output in Germany. At 24-quarter forecast horizon, innovations in money supply explain about 63 per cent of variance in real output. However, the hypothesis that all lagged values of money have zero coefficients in the output equation could be rejected only at the 90 per cent confidence level. At 24-quarter forecast horizon, innovations in ex-ante real rate and expected rate of inflation account for about 13 and 17 per cent of the variance in real output in Germany, respectively. The tests of the hypotheses that all lagged values of real rate and expected rate of inflation in the output equation have zero coefficients were easily accepted. Considering the variance of the expected rate of inflation, we can observe that innovations in money supply have accounted for a significant portion or about 49 per cent of the variance in the expected rate of inflation in Germany. The hypothesis that all lagged values of money have zero coefficients in the inflation equation was easily rejected. Innovations in the real interest rate account for about 16 per cent of variance in the expected rate of inflation. Innovations in real output do not account for a significant fraction of variance of inflation. Finally, at 24-quarter forecast horizon, 34 per cent of the variance of inflationary expectations are explained by its own innovations. Therefore, it appears that the expected rate of inflation in Germany has been sensitive to innovations in the money supply. The responses of ex-ante real interest rate to orthogonalized unit shocks in money, real output and expected rate of inflation for Germany is provided in Figure 5.5. It shows that the effect of unit shocks in money, output, inflation and real rate of interest on the ex-ante real interest rate in Germany has lasted about 24 quarters after which the effect of the shocks is diminished substantially. Table 5.7 presents the results of a decomposition of variance for the four-variable system for Italy.8 This table also shows that after 24 quarters, only about 31 per cent of the variance of the ex-ante real interest rates in Italy is explained by its own innovations. We saw in Table 5.1 that in the case of Italy for the entire period of 1969:3 to 1990:4 the null hypothesis of exogeneity of ex-ante real rate based on Mishkin estimate was rejected. Table 5.7 shows that at 24-quarter forecast horizon innovations in money, output and expected rate of inflation explain about 22, 11 and 36 per cent of the variance in the exante real rate, respectively. The tests of the hypotheses that all lagged values of money or real outpu t in the real rate equation have zero coefficients were easily accepted. However, the hypothesis that all lagged values of the expected rate of inflation in the real rate equation have zero coefficients was easily rejected. Therefore, it appears that the rejection of the exogeneity hypothesis found in Table 5.1 is not due to the link between

Interest rates and budget deficits

104

money and the short-term real rate, but is caused by the presence of a relationship between expected inflation and the real rate of interest.

Figure 5.5 Responses of the ex-ante short-term real interest rates to innovations: Germany Considering the variation in money supply in Italy, Table 5.7 demonstrates that over a 24-quarter time horizon, innovations in the expected rate of inflation explain about 67 per cent of the variance in the money supply. At the same time horizon, innovations in the ex-ante real rate and real output do not account for a significant variation in the money supply. Finally, at 24-quarter forecast horizon, about 27 per cent of the variance in the money supply is explained by its own innovations. The hypothesis that all lagged values of real rate or expected rate of inflation in the money equation have zero coefficients could be rejected only at 90 per cent confidence level. Lags of real output in the money equation were insignificant. It appears that the supply of money in Italy has been relatively sensitive to innovations in real rate and expected rate of inflation. Concentrating on the variance of real output in Italy, Table 5.7 shows that in the short run of about 4 quarters, innovations in money supply dominate the variation in output and account for about 27 per cent of the variance in output in Italy. As forecast horizon lengthens, innovations in the expected rate of inflation become the primary source of variation in output. We can observe that at 24-quarter forecast horizon, innovations in money supply and expected rate of inflation explain about 32 and 37 per cent of variance in real output, respectively. The hypothesis that all lagged values of money have zero coefficients in the output equation was rejected at the 5 per cent level. However, the tests

On the exogeneity of the real interest rate

105

Table 5.7 Proportions of forecast error K quarters ahead, produced by each innovation (Italy: 1969:3– 1990:4) Triangularized innovation in Forecast error in Ex-ante real rate

Money

Real output

Expected inflation

K

Ex-ante real interest rate (Mishkin)

Money

Real output

Expected rate of inflation (Mishkin)

1

100.00

0.00

0.00

0.00

4

90.34

0.93

3.72

5.01

8

59.60

18.21

12.09

10.10

16

50.82

22.61

14.51

12.07

24

30.86

22.31

10.39

36.44

1

5.92

94.08

0.00

0.00

4

7.71

88.51

0.51

3.27

8

3.42

58.38

1.89

36.31

16

3.27

31.68

1.03

64.02

24

3.92

26.91

2.40

66.78

1

0.48

1.16

98.35

0.00

4

0.66

26.50

72.18

0.66

8

6.52

38.57

51.95

2.96

16

5.15

36.80

28.38

29.67

24

5.50

31.98

25.92

36.60

1

71.49

0.21

0.10

28.29

4

66.99

3.31

6.62

20.07

8

61.51

8.71

9.77

20.01

16

44.23

17.17

10.50

28.09

24

21.03

21.02

16.19

40.87

of the hypotheses that all lagged values of real rate or expected rate of inflation have zero coefficients were easily accepted. This suggests that money supply in Italy has not been neutral. However, its effect on real output does not seem to be through its influence on the short-term real rate of interest. As we shall see in the next section, the transmission mechanism through which money affects output seems to run through the link between money, medium-term real rate and output. Considering the variance of the expected rate of inflation, we can observe that innovations in the ex-ante real rate and money supply account for a significant portion of the variance in the expected rate of inflation in Italy. The hypothesis that all lagged values of real rate in the inflation equation have zero coefficients was rejected. At 24-

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quarter forecast horizon, innovations in the ex-ante real rate, money supply and real output account for about 21, 21 and 16 per cent, respectively, of the variance in the expected rate of inflation in Italy. Lagged values of money or output in the inflation equation were insignificant. Finally, Tables 5.1 and 5.7 show that most of the variance in the ex-ante real interest rate in Italy is explained by innovations in money, output and expected rate of inflation. In other words, we find that the ex-ante real rate in Italy does not seem to be exogenous relative to the universe that contains money, output and inflation. It is therefore useful to examine its response to orthogonalized unit shocks in money, real output and expected rate of inflation. This is provided in Figure 5.6. It shows that unit shocks to money, real output and expected rate of inflation seem to have a long-term impact on the ex-ante real interest rate in Italy. Results of Figure 5.6 provide further support for the findings of Tables 5.1 and 5.7, suggesting that real rate in Italy has not behaved as if it is Grangercausally prior. Table 5.8 gives the results of a decomposition of variance for the four-variable system for Japan. It shows that, at 24-quarter forecast horizon, innovations in money and real output explain about 18 and 19 per cent, respectively, of the variance in the ex-ante real rate of

Figure 5.6 Responses of the ex-ante short-term real interest rates to innovations: Italy

On the exogeneity of the real interest rate

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Table 5.8 Proportions of forecast error K quarters ahead, produced by each innovation (Japan: 1969:3–1990:4) Triangularized innovation in Forecast error in Ex-ante real rate

Money

Real output

Expected inflation

K

Ex-ante real interest rate (Mishkin)

Money

Real output

Expected rate of inflation (Mishkin)

1

100.00

0.00

0.00

0.00

4

94.22

2.87

1.80

1.11

8

69.72

14.88

14.49

0.91

16

62.75

18.47

17.59

1.19

24

60.39

17.81

19.07

2.73

1

0.94

99.05

0.00

0.00

4

29.04

63.49

5.69

1.77

8

43.12

50.08

3.85

2.96

16

38.13

43.89

4.44

13.53

24

26.04

32.99

4.76

36.21

1

0.01

2.71

97.28

0.00

4

4.37

3.47

87.52

4.64

8

19.21

12.77

57.84

10.17

16

30.43

13.44

45.09

11.05

24

29.62

13.06

42.74

14.58

1

96.71

0.02

0.00

3.27

4

92.72

2.24

1.71

3.33

8

66.44

8.97

13.77

10.83

16

38.30

18.91

10.39

32.39

24

20.26

17.00

5.70

57.03

interest in Japan. Innovations in the expected rate of inflation do not explain a significant part of the variance in the real rate. Table 5.1 shows that even though the hypothesis of real rate exogeneity based on the Mishkin estimate for Japan was not rejected for the entire period and the 1980s, it was rejected for the earlier period of 1969:3 to 1979:4. To re-examine the exogeneity hypothesis, we tested the hypothesis that all lagged values of money or output or expected rate of inflation in the real rate equation have zero coefficients. The latter two hypotheses were easily accepted. The hypothesis that all lagged values of money in the real rate equation have zero coefficients could not be rejected at the 5 per cent significance level. This implies that innovations in money have

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exerted a significant influence on the short-term ex-ante real rate of interest in Japan. In other words, real interest rate in Japan is not Granger-causally prior relative to money. This result is different from that obtained in Table 5.1, suggesting that while the joint hypothesis that all lagged values of money, output and expected inflation in the real rate equation have zero coefficients can be easily accepted owing to a wide confidence interval, the individual hypothesis of money to real rate causality cannot be rejected. Considering the variation in money supply in Japan, Table 5.8 demonstrates that in the short term or about 8-quarter time horizon, innovations in the ex-ante real rate account for about 43 per cent of the variance in the money supply. As forecast horizon lengthens, innovations in the expected rate of inflation become dominant. At 24-quarter forecast horizon, innovations in the real rate and expected rate of inflation account for about 26 and 36 per cent, respectively, of the variance in the money supply. After 24 quarters, about 33 per cent of the variance in the money supply is explained by its own innovations. Innovations in the real output do not account for a significant variation in the money supply. The tests of the hypotheses that all lagged values of real rate and output in the money equation have zero coefficients were rejected. The same test for the expected rate of inflation could be rejected at 90 per cent confidence level. Therefore, it appears that the supply of money in Japan has been sensitive to innovations in the real rate, output and expected rate of inflation. Turning to the variance of real output in Japan, Table 5.8 shows that innovations in exante real rate of interest dominate the variation in the real output in Japan. At 24-quarter forecast horizon, innovations in the ex-ante real rate account for about 30 per cent of variance in the real output. The hypothesis that all lagged values of ex-ante real rate in the output equation have zero coefficients was rejected at 5 per cent level of significance. Innovations in money and expected rate of inflation play a smaller role in explaining the variance in the real output in Japan. At 24-quarter forecast horizon, innovations in money supply and expected rate of inflation account for about 13 and 15 per cent of variance in the real output, respectively. The hypothesis that all lagged values of money have zero coefficients in the output equation was easily accepted. However, the hypothesis that all lagged values of the expected rate of inflation in the output equation have zero coefficients was rejected only at 10 per cent level of significance. These results suggest the presence of the link between money, real rate and output in Japan. Regarding the variance of the expected rate of inflation, we can observe that at 24quarter forecast horizon, innovations in the ex-ante real rate and money supply account for about 20 and 17 per cent, respectively, of the variance in the expected rate of inflation. More than 57 per cent of the variance in the expected rate of inflation is explained by its own innovations. Innovations in the real output do not explain a significant fraction of the variance in the expected rate of inflation. Tests of the hypotheses that all lagged values of the real rate, money or real output in the inflation equation have zero coefficients were easily accepted. Finally, Table 5.1 showed that the exogeneity test of the real interest rate in Japan was sensitive to the definition used and the period employed. We also found that the hypothesis that all lagged values of money in the real rate equation have zero coefficients was rejected at 99 per cent confidence level. Therefore, it is useful to examine the response of the real rate to orthogonalized unit shocks in money, real output and expected rate of inflation. This is provided in Figure 5.7. It shows that the effects of shocks to real

On the exogeneity of the real interest rate

109

rate of interest and real output seem to decline as the forecast horizon lengthens. However, shocks to money supply and expected rate of

Figure 5.7 Responses of the ex-ante short-term real interest rates to innovations: Japan inflation seem to have a long-term impact on the ex-ante real interest rate in Japan. Table 5.9 presents the results of a decomposition of variance for the four-variable system for the Netherlands. It shows that most of the variance in the ex-ante real interest rate in the Netherlands is explained by its own innovations. At 24-quarter forecast horizon, innovations in money, real output and expected rate of inflation explain about 12, 6 and 15 per cent of the variance in the ex-ante real rate of interest, respectively. Tests of the hypothesis that all the coefficients of money, output or expected rate of inflation in the real rate equation have zero coefficients easily accept the null hypothesis. Only in the case of money, the hypothesis was rejected at 10 per cent level. This provides a weak support for the presence of a link between money and real rate of interest. This result suggests that, as was the case with Japan, while the joint hypothesis of zero coefficients for money, output and inflation in the real rate equation is easily accepted (Table 5.1), the individual hypothesis of money to real rate link cannot be rejected at 10 per cent level. We can therefore reject the hypothesis that the real rate in the Netherlands is Grangercausally prior relative to money at 10 per cent level.

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Table 5.9 Proportions of forecast error K quarters ahead, produced by each innovation (Netherlands: 1969:3–1990:4) Triangularized innovation in Forecast error in Ex-ante real rate

Money

Real output

Expected inflation

K

Ex-ante real interest rate (Mishkin)

Money

Real output

Expected rate of inflation (Mishkin)

1

100.00

0.00

0.00

0.00

4

88.05

10.54

0.36

1.05

8

74.74

11.56

6.66

7.04

16

66.86

11.88

6.50

14.77

24

65.92

12.42

6.34

15.32

1

59.69

40.31

0.00

0.00

4

47.94

46.53

1.88

3.65

8

31.44

50.08

10.92

7.56

16

25.91

48.52

17.87

7.70

24

23.56

45.41

21.11

9.92

1

0.33

2.87

96.79

0.00

4

3.46

13.52

77.33

5.69

8

6.99

17.78

66.36

8.87

16

11.46

18.76

59.88

9.90

24

12.00

19.78

58.37

9.85

1

4.05

5.81

1.81

88.33

4

2.87

6.16

3.38

87.59

8

5.35

8.20

8.45

78.00

16

7.31

10.04

6.24

76.40

24

7.76

9.93

6.22

76.08

Considering the variation in money supply in the Netherlands, Table 5.9 demonstrates that in the short term most of the variation in the money supply is explained by innovations in the ex-ante real interest rate. However, as forecast horizon lengthens, the relative importance of innovations in the ex-ante real rate drops and the share of real output increases. At 24-quarter forecast horizon, innovations in ex-ante real rate and real output account for about 24 and 21 per cent of the variance in the money supply, respectively. Test of the hypothesis that all lagged values of ex-ante real rate in the money equation have zero coefficients was rejected at 5 per cent level. At 24-quarter

On the exogeneity of the real interest rate

111

forecast horizon, about 45 per cent of the variance in the money supply is explained by its own innovations. Innovations in the expected rate of inflation do not account for a significant variation in the money supply. Turning now to the variance of real output in the Netherlands, Table 5.9 shows that in the short term of about 4 quarters, most of the variation in real output is explained by its own innovations. As forecast horizon lengthens, the share of the innovations in the money supply in explaining the variance in real output increases. At 24-quarter forecast horizon, innovations in the money supply account for about 20 per cent of variance in the real output. The hypothesis that all lagged values of the money supply in the output equation have zero coefficients can be rejected at 10 per cent level of significance. At 24quarter forecast horizon, innovations in the ex-ante real rate and expected rate of inflation do not account for a significant part of the variance in the real output. With regard to the variance of the expected rate of inflation, we can observe that most of the variance in the expected rate of inflation is explained by its own innovations. At 24-quarter forecast horizon, innovations in the ex-ante real rate and money supply and real output account for about 8, 10 and 6 per cent, respectively, of the variance in the expected rate of inflation. Tests of the hypothesis that all lagged values of the real rate, money or real output in the inflation equation have zero coefficients were easily accepted. We saw above that the ex-ante real interest rate in the Netherlands behaves as if it is Granger-causally prior. However, we observed a weak link between innovations in money and the real rate in the Netherlands. Therefore, it is useful to examine its response to orthogonalized unit shocks in money, real output and expected rate of inflation. This is provided in Figure 5.8. Figure 5.8 shows that unit shocks in the money supply, real output and expected rate of inflation have only short-term impacts on the ex-ante real interest rate. Effects of these shocks seem to disappear in the long term. Figure 5.8 provides further support for our previous findings of real rate exogeneity in the Netherlands. Table 5.10 shows the results of a decomposition of variance for the four-variable system for Sweden. It shows that more than 64 per cent of the variance in the ex-ante real interest rate in Sweden is explained by its own innovations. At 24-quarter forecast horizon, innovations in money, real output and expected rate of inflation explain about 15, 9 and 12 per cent of the variance in the ex-ante real rate of interest, respectively. The tests of the hypothesis that all coefficients of money or output or expected rate of inflation in the real rate equation have zero coefficients were easily accepted.

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Figure 5.8 Responses of the ex-ante short-term real interest rates to innovations: the Netherlands Table 5.10 Proportions of forecast error K quarters ahead, produced by each innovation (Sweden: 1969:3–1990:4) Triangularized innovation in Forecast error in Ex-ante real rate

Money

Real output

K

Ex-ante real interest rate (Mishkin)

Money

Real output

Expected rate of inflation (Mishkin)

1

100.00

0.00

0.00

0.00

4

89.78

6.59

1.47

2.16

8

85.24

7.17

2.44

5.15

16

67.56

14.18

8.28

9.97

24

64.26

15.03

9.04

11.67

1

14.75

85.25

0.00

0.00

4

33.97

63.34

1.33

1.35

8

19.30

71.14

4.94

4.62

16

16.44

67.83

6.84

8.89

24

19.16

63.30

8.85

8.69

1

0.02

1.52

98.45

0.00

On the exogeneity of the real interest rate

Expected inflation

113

4

5.26

4.51

87.55

2.67

8

12.82

4.72

78.16

4.29

16

14.24

8.84

70.50

6.41

24

12.97

12.83

66.65

7.55

1

30.34

1.11

0.00

68.55

4

38.20

9.47

0.74

51.59

8

31.69

9.86

1.68

56.77

16

30.17

9.01

3.98

56.85

24

27.73

12.43

9.17

50.67

Therefore, the findings in Table 5.10 provide further support for the exogeneity of real rate in Sweden. Regarding the variation in money supply in Sweden, Table 5.10 shows that at 4quarter forecast horizon, about 34 per cent of the variance in the money supply is explained by innovations in the ex-ante real interest rate. However, as forecast horizon lengthens, the relative importance of innovations in the ex-ante real rate drops. At 24quarter forecast horizon, innovations in ex-ante real rate account for about 19 per cent of variance in the money supply. Innovations in the real output and expected rate of inflation account for about 9 per cent of the variance in the money supply. Tests of the hypothesis that all lagged values of ex-ante real rate, real output or expected rate of inflation in the money equation have zero coefficients were easily accepted. At 24quarter forecast horizon, more than 63 per cent of the variance in the money supply is explained by its own innovations. Turning to the variance of real output in Sweden, Table 5.10 shows that the real output in Sweden has not been very sensitive to innovations in the real rate or money or the expected rate of inflation. At 24-quarter forecast horizon, innovations in these variables account for about 13, 13 and 8 per cent of the variance in the real output, respectively. Tests of the hypothesis that all lagged values of the real rate, money supply or expected rate of inflation in the output equation have zero coefficients were easily accepted. Therefore, it appears that money supply in Sweden has been neutral. After 24 quarters, 67 per cent of the variance in real output is explained by its own innovations. With respect to the variance of the expected rate of inflation, we can observe that innovations in the ex-ante real rate account for more than 27 per cent of the variance in the expected rate of inflation. Innovations in money and real output do not account for a significant fraction of the variance in the expected rate of inflation. At 24-quarter forecast horizon, about 51 per cent of the variance in the expected rate of inflation is explained by its own innovations. Tests of the hypothesis that all lagged values of the real rate, money or real output in the inflation equation have zero coefficients were easily accepted. Finally, our findings in Tables 5.1 and 5.10 suggest that the ex-ante real interest rate in Sweden has behaved as if it is Granger-causally prior. As a final examination of the exogeneity of the real rate we examine its response to orthogonalized unit shocks in money, real output and expected rate of inflation. This is provided in Figure 5.9. It shows

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that the effect of shocks in money, output and expected rate of inflation on the ex-ante real rate of interest is short term in nature and diminishes as forecast horizon lengthens. Table 5.11 presents the results of a decomposition of variance for the four-variable system for the U.K. It shows that more than 60 per cent of the variance in the ex-ante real interest rate in the U.K. is explained by its own innovations. At 24-quarter forecast horizon, innovations in money, real output and expected rate of inflation explain about 8, 13 and 18 per cent of the variance in the ex-ante real rate of interest, respectively. However, we saw in Table 5.1 that the test of exogeneity of the ex-ante real rate in the U.K. was rejected for

Figure 5.9 Responses of the ex-ante short-term real interest rates to innovations: Sweden the periods of 1969:3 to 1990:4 and 1980:1 to 1990:4. Therefore, it is of interest to test the hypotheses that all the coefficients of money, output or expected rate of inflation in the real rate equation have zero coefficients. All three hypotheses were easily rejected confirming our previous finding in Table 5.1 concerning the link between money and short-term real interest rate in the U.K. Concentrating on variation in money supply in the U.K., Table 5.11 shows that the variance of money supply has been very sensitive to innovations in the ex-ante real rate and the expected rate of inflation. At 24-quarter forecast horizon, innovations in ex-ante real rate and expected rate of inflation account for about 36 and 23 per cent of variance in the money supply, respectively. Innovations in the real output account for about 10 per cent of the variance in the money supply. At 24-quarter forecast horizon, about 30 per cent of the variance in the money supply is explained by its own innovations. Considering the variance of real output in the U.K., Table 5.11 shows that the real output in the U.K. has been sensitive to innovations in the expected rate of inflation. At

On the exogeneity of the real interest rate

115

24-quarter forecast horizon, innovations in this variable account for about 35 per cent of the variance in the real output. Table 5.11 shows that innovations

Table 5.11 Proportions of forecast error K quarters ahead, produced by each innovation (U.K.: 1969:3– 1990:4) Triangularized innovation in Forecast error in Ex-ante real rate

Money

Real output

Expected inflation

K

Ex-ante real interest rate (Mishkin)

Money

Real output

Expected rate of inflation (Mishkin)

1

100.00

0.00

0.00

0.00

4

85.58

2.58

9.03

2.81

8

64.38

4.89

13.31

17.42

16

63.17

8.14

11.83

16.85

24

60.62

8.45

13.34

17.59

1

4.47

95.53

0.00

0.00

4

12.24

84.40

2.47

0.89

8

11.00

69.63

17.15

2.22

16

38.04

38.26

12.33

11.36

24

36.31

30.32

10.16

23.21

1

0.03

0.32

99.65

0.00

4

0.81

1.05

86.70

11.45

8

1.96

1.80

81.36

14.88

16

7.86

1.71

62.99

27.45

24

9.15

1.84

54.03

34.98

1

18.15

0.10

4.03

77.73

4

43.33

1.34

11.54

43.78

8

36.45

9.58

12.49

41.48

16

50.83

8.64

4.23

36.31

24

52.80

6.49

2.90

37.81

in the real rate and money supply do not account for a significant part of the variance in output in the U.K. It appears that money supply in the U.K. has not exerted a significant influence on real output. At 24-quarter forecast horizon, 54 per cent of the variance in real output is explained by its own innovations. Finally, the tests of the hypothesis that all lagged values of the real rate, money supply or expected rate of inflation in the output equation have zero coefficients were easily accepted.

Interest rates and budget deficits

116

With respect to the variance of the expected rate of inflation, Table 5.11 shows that innovations in the ex-ante real rate account for most of the variance in the expected rate of inflation. Innovations in money and real output do not account for a significant fraction of the variance in the expected rate of inflation. At 24-quarter forecast horizon, about 38 per cent of the variance in the expected rate of inflation is explained by innovations in the ex-ante real rate. At 24-quarter forecast horizon, about 53 per cent of the variance in the expected rate of inflation is explained by its own innovations. Finally, we tested the hypotheses that all lagged values of real rate, money or real output in the inflation equation have zero coefficients. Only the null hypothesis of zero coefficients for lagged values of money supply was easily accepted. The other two hypotheses were rejected. The results shown in Tables 5.1 and 5.11 show that the ex-ante real rate in the U.K. has been sensitive to innovations in money, output and the expected rate of inflation. As a final examination of the exogeneity of the real rate in the U.K., it is useful to look at the responses of the real rate in the U.K. to orthogonalized unit shocks in money, real output and expected rate of inflation. This is provided in Figure 5.10. It shows that shocks to money, real output and expected rate of inflation have a significant short-term impact on the ex-ante real rate. We can also observe that even though the effects of these shocks diminish as forecast horizon lengthens, they do not disappear completely. This finding provides further support for our previous findings that the real rate in the U.K. is not exogenous.

Figure 5.10 Responses of the ex-ante short-term real interest rates to innovations: U.K.

On the exogeneity of the real interest rate

117

Table 5.12 shows the results of a decomposition of variance for the four-variable system for the U.S.A. The table also shows that about 50 per cent of the variance in the ex-ante real interest rate in the U.S.A. is explained by its own innovations. We can also observe that, at 24-quarter forecast horizon, innovations in real output account for about 37 per cent of the variance in output. Innovations in money supply and expected rate of inflation do not account for a significant part of the variance in the ex-ante real rate of interest in the U.S.A. The tests of the hypothesis that all the lagged values of money, real output or expected rate of inflation in the real rate equation have zero coefficients were

Table 5.12 Proportions of forecast error K quarters ahead, produced by each innovation (U.S.A.: 1969:3–1990:4) Triangularized innovation in Forecast error in Ex-ante real rate

Money

Real output

Expected inflation

K

Ex-ante real interest rate (Mishkin)

Money

Real output

Expected rate of inflation (Mishkin)

1

100.00

0.00

0.00

0.00

4

81.23

2.96

12.58

3.24

8

63.62

6.70

26.01

3.67

16

50.98

6.63

39.16

3.23

24

51.73

6.12

37.03

5.12

1

8.75

91.25

0.00

0.00

4

21.46

50.25

2.51

25.78

8

21.74

34.20

6.61

37.44

16

11.61

30.35

15.74

42.30

24

7.66

32.69

26.63

33.02

1

10.72

5.34

83.94

0.00

4

13.46

4.35

77.78

4.41

8

35.25

4.43

50.18

10.14

16

52.92

2.93

30.42

13.73

24

49.17

6.72

29.81

14.30

1

5.74

0.35

3.44

90.48

4

28.23

1.61

12.54

57.61

8

21.74

1.97

28.57

47.72

16

37.36

3.71

25.53

33.40

24

39.21

5.40

33.11

22.27

Interest rates and budget deficits

118

easily accepted. This confirms our findings in Table 5.1 of the real rate exogeneity for the U.S.A. Weshould note that our finding of real rate exogeneity in the U.S.A. is in line with the findings of Litterman and Weiss (1985). Considering the variation in money supply in the U.S.A., Table 5.12 shows that about 50 per cent of the variation in the supply of money at 4-quarter forecast horizon is accounted for by innovations in the ex-ante real rate and expected rate of inflation. As forecast horizon lengthens, the importance of innovations in the real rate decline while that of real output increases. At 24-quarter forecast horizon, innovations in real rate account for about 8 per cent of the variance in money supply. The test of the hypothesis that all lagged values of the real rate in the money equation have zero coefficients was easily accepted. At 24-quarter forecast horizon, innovations in real output and expected rate of inflation account for about 27 and 33 per cent of the variance in money supply, respectively. At the same time, about 33 per cent of the variance in money supply is accounted for by its own innovations. The tests of the hypothesis that all lagged values of real output and expected rate of inflation have zero coefficients in the money equation were rejected. This implies that money supply in the U.S.A. has been sensitive to innovations in the expected rate of inflation and real output. Considering the variance of real output in the U.S.A., Table 5.12 shows that the real output in the U.S.A. has been sensitive to innovations in the ex-ante real rate and the expected rate of inflation. After 8 quarters, innovations in these variables account for about 35 and 10 per cent of the variance in the real output, respectively. As forecast horizon lengthens, variation in the real output explained by these variables increases. At 24-quarter forecast horizon, only 30 per cent of the variance in the real output is explained by its own innovations. At the same time, innovations in the real interest rate account for about 49 per cent of the variance in output. The test of the hypothesis that all lagged values of ex-ante real rate in the output equation have zero coefficients was rejected. Innovations in the expected rate of inflation explain about 14 per cent of the variance in output. Table 5.12 shows that innovations in the money supply do not account for a significant part of the variance in output. The tests of the hypothesis that all lagged values of money or expected rate of inflation have zero coefficients in the output equation were easily accepted. Therefore, it appears that real output in the U.S.A. has been responsive to changes in the ex-ante real interest rate and not to innovations in money. This suggests that the link between the money supply, real rate of interest and output suggested by existing monetary theories of the business cycle do not seem to hold for the U.S.A. Considering the variance of the expected rate of inflation, Table 5.12 shows that most of the variation in the expected rate of inflation is explained by innovations in the ex-ante real rate and real output. Innovations in money supply do not account for a significant fraction of the variance in the expected rate of inflation. At 24-quarter forecast horizon, about 40 per cent of the variance in the expected rate of inflation is explained by innovations in the ex-ante real rate. At the same time, innovations in real output account for about 33 per cent of the variance in the expected rate of inflation. The hypothesis that all lagged values of real rate in the inflation equation have zero coefficients was easily rejected. However, lagged values of money and output in the inflation equation were insignificant.

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Our findings in Tables 5.1 and 5.12 suggest that the ex-ante real rate in the U.S.A. has behaved as if it is exogenous relative to a universe that contains money, output and the expected rate of inflation. As a final examination of the exogeneity of the real rate in the U.S.A., we check its response to orthogonalized unit shocks in money, real output and expected rate of inflation. This is provided in Figure 5.11. It shows that the ex-ante real interest rate in the

Figure 5.11 Responses of the ex-ante short-term real interest rates to innovations: U.S.A. U.S.A. is sensitive to unit shocks in money, real output and expected rate of inflation in the short run. However, as forecast horizon lengthens, the effects of these shocks diminish significantly. SUMMARY: EXOGENEITY OF THE SHORT-TERM EX-ANTE REAL RATE OF INTEREST The last section examined the exogeneity of the short-term ex-ante real rate of interest in the countries of our sample. Employing the Granger causality test along with innovation accounting technique, we found that relative to a universe that includes money, real output and the expected rate of inflation, the ex-ante real rate of interest has behaved as if it is Granger-causally prior for Australia, Belgium, Canada, Sweden and the U.S.A. We also saw that even though the real interest rates in these countries have behaved as if they are Granger-causally prior, they have responded to the contemporaneous components of the innovations in money, output and inflation. The responses to innovations in these variables have sometimes lasted for more than 30 quarters.

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Real rate in France has been sensitive to innovations in the expected rate of inflation. The response to innovations in the expected rate of inflation has lasted for about 30 quarters. In Germany, the real rate of interest has been affected by the innovations in the real output. The effect of innovations in real output has lasted for about 25 quarters. Real rate in Italy has also been sensitive to innovations in the expected rate of inflation. The effects of these innovations have lasted for more than 40 quarters. In Japan, the real rate of interest has been sensitive to innovations in all variables and in particular to those in the money supply. The effects of shocks in money, output and expected rate of inflation show a long-lasting impact on the real rate in Japan. In the Netherlands, the link between the real rate and money cannot be rejected at 10 per cent level. In the U.K., the real rate of interest has been sensitive to innovations in money, output and the expected rate of inflation. Unit shocks in these variables show a long-term effect on the real rate of interest in the U.K. EXOGENEITY TEST OF THE MEDIUM-TERM EX-ANTE REAL INTEREST RATES To examine the exogeneity of ex-ante medium-term real interest rates, we follow the same procedure as on pages 106–39. More specifically, we first employ the test procedure suggested by Granger and test the joint restriction that past money, inflationary expectations and real output have no additional predictive content for current ex-ante medium-term real interest rates, given past real rates. The regressions include eight lags of each variable and a constant. Then, using the innovation accounting technique, we examine the extent to which the variation in each of the variables is explained by innovations in other variables. In addition, we also test the individual hypothesis that lagged values of money, output or inflation in the real rate equation have zero coefficients. As was the case for the short-term interest rates, we employ logs of the level of money as measured by M1 and output as measured by real GNP for Germany, Japan and the U.S.A., and real GDP for Australia, Canada, Italy, Sweden and the U.K., and industrial production index for France, Belgium and the Netherlands. The sample period, after allowing for lags, covers 1969:3 to 1990:4. As a sensitivity check, our Granger test of the real rate exogeneity will be carried out based on the full sample of 1969:3 to 1990:4, and on two partial data sets covering 1969:3 to 1979:4, and 1980:1 to 1990:4. Table 5.13 presents the results of the Granger test of ex-ante real medium-term interest rate exogeneity relative to a universe that includes money, output and the expected rate of inflation.9 The table also shows that, over the entire period of 1969:3 to 1990:4, the null hypothesis of exogeneity can be rejected at the 95 per cent confidence level for Canada, Italy, the Netherlands, Sweden and the U.K. However, if we consider a wider confidence interval of 99 per cent, the exogeneity hypothesis cannot be rejected for any of the countries in our sample. For the earlier period covering 1969:3 to 1979:4, the exogeneity of real interest rate cannot be rejected for any of the countries in our sample, except for the Netherlands, at 5 per cent level of significance. For the Netherlands, the exogeneity hypothesis can be rejected at the 99 per cent confidence level.

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For the later period of 1980:1 to 1990:4, the exogeneity hypothesis can be rejected at the 1 per cent significance level for Canada and the United States. For Australia and France the exogeneity

Table 5.13 Granger causality test of the ex-ante real medium-term interest rate 1969:3–1990:4

1969:3–1979:4

1980:1–1990:4

Australia

1.36*

1.30**

3.02

Belgium

1.07

1.51

1.50

Canada

1.70

1.90

5.85

France

1.42

1.16

2.94

Germany

1.41

2.53

1.23

Italy

1.76

2.57

2.16

Japan

1.57

1.63

1.35

Netherlands

1.99

4.72

2.41

Sweden

1.88

2.47

1.52

U.K.

1.74

1.17

1.21

U.S.A.

1.43

0.39

4.40

Critical value (5%)

1.67

2.90

2.61

Critical value (1%)

2.20

4.73

4.02

*Sample period covers 1973:1–1990:4. **Based on a sample period of 1973:1–1979:4 and four lags of each variable.

hypothesis cannot be rejected at the 5 per cent level of significance. For the rest of the countries the hypothesis cannot be rejected at 5 per cent marginal significance level. The above results show that the exogeneity test of the medium-term real interest rate is, to some extent, dependent on the level of significance chosen as well as the period under consideration. Therefore, it is useful to undertake further examination of the exogeneity hypothesis. For this purpose, we decompose the variance in ex-ante real interest rates into components attributed to innovations in money, real output and inflationary expectations at different time horizons. However, in this section instead of presenting and discussing individual tables and graphs for each country, we shall discuss and compare our findings concerning the medium-term ex-ante real rates with the previous findings related to the short-term real rates of interest for each country. Finally, in this section, we shall primarily concentrate on the link between money, real rate and output.

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Australia Using variance decomposition technique for Australia, we found that, both in the short and the long term, a significant portion of the variance in the real interest rate is explained by the innovations in the money supply. At 24-quarter forecast horizon, innovations in the supply of money account for about 39 per cent of the variance in the real rate. The null hypothesis that all lagged values of money in the real rate equation have zero coefficients was rejected at the 5 per cent level. Innovations in the output and expected rate of inflation account for about 4 and 5 per cent of the variance in the real rate, respectively. The tests of the hypothesis that all lagged values of real output or expected rate of inflation in the real rate equation have zero coefficients were accepted. Therefore, this result is different from the result of the joint hypothesis of zero values for all coefficients of money, income and inflation in the real rate equation and suggests that real rate in Australia has not been Granger-causally prior relative to money. Comparing these results with those obtained for the short-term ex-ante real interest rate, we find that the link between the money supply and the real interest rate suggested by the monetary theories of the business cycle seems to exist only for the medium-term real rate and not for the short-term rate in Australia. Turning now to the variance of output, we found that innovations in the real rate, money and expected rate of inflation explain a large fraction of the variation in the real output in Australia. At 24-quarter forecast horizon, about 39 per cent of the variance of real output is explained by its own innovations. The tests of the hypothesis that all lagged values of real rate or money in the output equation have zero coefficients were easily rejected. However, the null hypothesis of all lagged values of the expected rate of inflation in the output equation have zero coefficients was accepted. This finding is comparable to that obtained using short-term real rate of interest. Belgium Decomposition of variance of the medium-term real rate of interest in Belgium for the four-variable system showed that at 24-quarter forecast horizon, about 63 per cent of the variance in the real rate is explained by its own innovations. The tests of the null hypothesis that all lagged values of money, output or expected rate of inflation in the real rate equation have zero coefficients were easily accepted. Therefore, results concerning the medium-term real rate is similar to our previous findings that the short-term real rate in Belgium has behaved exogenously relative to a universe that contains money, output and expected rate of inflation. Turning now to the variance of output, we found that, after 24 quarters innovations in the real rate, money and expected rate of inflation explain about 10, 11 and 40 per cent, respectively, of the variance in the real output in Belgium. The tests of the hypothesis that all lagged values of real rate or money or expected rate of inflation in the output equation have zero coefficients were accepted. Comparing these results with those obtained for short-term real rate, we observe that while the real output in Belgium has been sensitive to short-term real rates, it has not been responsive to the medium-term real rates.

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Canada Decomposition of variance of the medium-term real rate of interest in Canada for the four-variable system showed that at 24-quarter forecast horizon, about 78 per cent of the variance in the real rate is explained by its own innovations. The tests of the null hypothesis that all lagged values of money or output in the real rate equation have zero coefficients were easily accepted. However, the null hypothesis that all lagged values of the expected rate of inflation have zero coefficients was rejected. This implies that the rejection of the real rate exogeneity hypothesis in the case of Canada is not due to the presence of a link between money and real rates, but is caused by the existence of a relationship between the expected inflation and the real rate of interest. Therefore, results concerning the medium-term real rate, to a large extent, support our previous findings that the real rate of interest in Canada has not been sensitive to innovations in money and output. Considering the variance of output in Canada, we found that after 24 quarters, about 35 per cent of the variance in real output was explained by its own innovations. The tests of the hypothesis that all lagged values of real rate, money or expected rate of inflation in the output equation have zero coefficients were accepted at the 5 per cent level. However, the latter two hypotheses could not be rejected at the 10 per cent level. Comparing the above results with those obtained for short-term real rate, we observe that while the real output in Canada has been sensitive to short-term real rates, it has not been responsive to the medium-term real rates. France The results of the decomposition of variance of the medium-term real rate in France showed that at 24-quarter forecast horizon, about 71 per cent of the variance in the real rate is explained by its own innovations. At 24-quarter forecast horizon, innovations in the supply of money account for about 14 per cent of the variance in the real rate. Innovations in the real rate and inflation do not account for a significant part of the variance in the real rate. The null hypothesis that all lagged values of money in the real rate equation have zero coefficients could be rejected at the 10 per cent level. Lagged values of output and expected rate of inflation in the real rate equation were insignificant. This result suggests that we can reject the hypothesis that real rate in France has been Granger-causally prior with respect to money at the 10 per cent level. Comparing these results with those obtained for the short-term real interest rates we observe that while the short-term real rate in France has been insensitive to movements in the money supply, the medium-term real rate seems to be responsive to innovations in the supply of money in France. Therefore, it appears that the link between money and real rate in France holds for the medium-term rate and not for the short term. Turning now to the variance of output, we found that innovations in the real rate, money and expected rate of inflation explain a large fraction of the variation in the real output in France. At 24-quarter forecast horizon, about 43 per cent of the variance of real output is explained by its own innovations. The tests of the hypothesis that all lagged values of real rate or expected rate of inflation in the output equation have zero coefficients were easily rejected. However, the null hypothesis of all lagged values of money in the output equation have zero coefficients could be rejected at the 10 per cent

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level. These results are in direct contrast with those obtained using the short-term real interest rate. We can conclude that real output in France, while not sensitive to innovations in short-term real interest rate, has been very responsive to innovations in the medium-term ex-ante real rate of interest. Germany The results of the decomposition of variance of the medium-term real rate in Germany showed that, at 24-quarter forecast horizon, about 46 per cent of the variance in the real rate is explained by its own innovations. Innovations in the supply of money, real output and expected rate of inflation account for about 25, 5 and 24 per cent of the variance in the real rate, respectively. The null hypotheses that all lagged values of money or real output in the real rate equation have zero coefficients were easily accepted. However, lagged values of the expected rate of inflation in the real rate equation were significantly different from zero. This suggests that while we can reject the joint hypothesis that all lagged values of money, output and inflation in the real rate equation have zero coefficients, we cannot reject the individual hypothesis of a link between inflation and the real rate. We can therefore conclude that the real interest rate in Germany has not been Granger-causally prior relative to the expected rate of inflation. Comparing these results with those obtained for the short-term real interest rates, we observe that the hypothesis of exogeneity of real rate is rejected for both short- and medium-term real rates in Germany. However, both rates in Germany have been insensitive to movements in the money supply. Turning now to the variance of output, we found that innovations in the real rate, money and expected rate of inflation explain a large fraction of the variation in the real output in Germany. However, the tests of the hypothesis that all lagged values of real rate, money or expected rate of inflation in the output equation have zero coefficients were easily accepted. These results are very similar to those obtained using short-term real interest rates. Therefore, it appears that real output in Germany has not been sensitive to innovations in either the real interest rate or money supply. Italy Decomposition of variance of the medium-term real rate in Italy showed that, at 24quarter forecast horizon, about 44 per cent of the variance in the real rate is explained by its own innovations. Innovations in money and the expected rate of inflation account for a significant portion of the variance in the real rate. The tests of the hypothesis that all lagged values of money or expected rate of inflation in the real rate equation have zero coefficients were easily rejected. However, lagged values of output in the real rate equation were not significantly different from zero. These results are in direct contrast to those obtained using the short-term real interest rates. Therefore, it appears that innovations in money supply, while not having any significant impact on the short-term real rate, exert a significant influence over the medium-term real rate of interest in Italy. Turning now to the variance of output, we found that at 24-quarter forecast horizon, innovations in the money and expected rate of inflation explain about 38 and 30 per cent of the variance in real output in Italy, respectively. Innovations in the real rate of interest

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do not account for a significant portion of the variance in real output in Italy. The tests of the hypothesis that all lagged values of real rate or expected rate of inflation in the output equation have zero coefficients were easily accepted. However, the null hypothesis that all lags of money have zero coefficients could be rejected at the 10 per cent level. These results are similar to those obtained using the short-term real interest rates. Japan Decomposition of the variance of the medium-term real rate in Japan showed that after 24 quarters about 59 per cent of the variance in the real rate is explained by its own innovations. The rest of the variance, or about 41 per cent, is explained by innovations in the supply of money, real output and expected rate of inflation. The null hypotheses that all lagged values of money or expected rate of inflation in the real rate equation have zero coefficients were rejected. However, lagged values of real output in the real rate equation were not significantly different from zero. This shows that the medium-term real rate of interest in Japan has not been Granger-causally prior relative to a universe that includes money, output and expected rate of inflation. Innovations in money have exerted a significant influence over the real rate. Comparing these results with those obtained for the short-term real interest rates, we observe that both short- and medium-term real interest rates in Japan have been sensitive to movements in the money supply. Considering the variance of output in Japan, we found that innovations in the real rate, money and expected rate of inflation explain a large part of the variance in real output in Japan. However, the tests of the hypothesis that all lagged values of real rate, money or expected rate of inflation in the output equation have zero coefficients were easily accepted. These results are different from those obtained using short-term real interest rates. Therefore, it appears that real output in Japan, while responsive to innovations in the short-term real rate, has been insensitive to innovations in the medium-term real rate of interest. The Netherlands Variance decomposition of the medium-term real rate in the Netherlands revealed that after 24 quarters about 64 per cent of the variance in the real rate is explained by its own innovations. At the same time, innovations in the expected rate of inflation explain about 28 per cent of the variance of the real rate. Lagged values of the expected rate of inflation in the real rate equation were significantly different from zero. Innovations in money and real output do not account for a significant fraction of the variance in the real rate. The null hypothesis that all lagged values of money or output in the real rate equation have zero coefficients were easily accepted. This suggests that the medium-term real rate of interest in the Netherlands has not been sensitive to movements in money. These results are slightly different from those obtained using short-term real rate of interest. We saw earlier that for the Netherlands we could not reject the null hypothesis that all lagged values of money in the short-term real rate equation have zero coefficients at 10 per cent significance level. In other words, there exists a weak link between money

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and the short-term real rate in the Netherlands. However, as we discussed above, that link does not seem to exist between money and the medium-term real rate in the Netherlands. Considering the variance of real output in the Netherlands, we found that at 24-quarter forecast horizon about 52 per cent of the variance in real output is explained by its own innovations. Innovations in the real rate, money and expected rate of inflation explain about 21, 16 and 11 per cent of the variance in output, respectively. However, the tests of the hypothesis that all lagged values of real rate, money or expected rate of inflation in the output equation have zero coefficients were easily accepted. These results are similar to those obtained using short-term real interest rates. In other words, real output in the Netherlands has not been responsive to innovations in real interest rates or money supply. Sweden Decomposition of the variance of medium-term real rate in Sweden revealed that after 24 quarters about 63 per cent of the variance in the real rate is explained by its own innovations. At the same time, innovations in money, real output and expected rate of inflation explain about 15, 15 and 17 per cent of the variance in the real rate, respectively. Lagged values of the expected rate of inflation in the real rate equation were significantly different from zero. However, the null hypotheses that all lagged values of money or output in the real rate equation have zero coefficients were easily accepted suggesting that the medium-term real rate of interest in Sweden has not been sensitive to movements in money. These results are similar to those obtained using the short-term real rate of interest, suggesting that while both short- and medium-term real rates of interest in Sweden have not been Granger-causally prior to the universe that contains money, output and inflation, they have however been insensitive to innovations in the money supply. Turning to the variance of real output in Sweden, we observed that at 24-quarter forecast horizon about 51 per cent of the variance in real output is explained by its own innovations. Innovations in real rate, money and expected rate of inflation explain about 22, 22 and 6 per cent of the variance in output, respectively. The null hypotheses that all lagged values of money or real rate or expected rate of inflation in the output equation have zero coefficients were easily accepted. These results are similar to those obtained using short-term real interest rates. In other words, real output in Sweden has not been responsive to innovations in real interest rates or money supply. United Kingdom The results of the decomposition of variance of the medium-term real rate for the U.K. showed that after 24 quarters about 64 per cent of the variance in the real rate is explained by its own innovations. At 24-quarter forecast horizon, innovations in money, output and expected rate of inflation account for about 8, 19 and 10 per cent of the variance in the real rate, respectively. The null hypothesis that all lagged values of real output in the real rate equation have zero coefficients was rejected. Lagged values of money and the expected rate of inflation in the real rate equation were insignificant.

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Comparing these results with those obtained for the short-term real interest rate, we observe that while short-term real rate in the U.K. has been sensitive to innovations in money supply, output and expected rate of inflation, the medium-term real rate seems to be responsive only to innovations in real output. Turning now to the variance of output, we found that more than 90 per cent of the variance in output is explained by its own innovations. The tests of the hypothesis that all lagged values of real rate, money or expected rate of inflation in the output equation have zero coefficients were easily accepted. These results are similar to those obtained using the short-term real interest rates. We can conclude that real output in the U.K. has not been responsive to innovations in real interest rates or money. United States of America The results of the decomposition of variance of the medium-term real rate for the U.S.A. showed that at 24-quarter forecast horizon, about 44 per cent of the variance in the real rate is explained by its own innovations. At 24-quarter forecast horizon, innovations in money, output and expected rate of inflation account for about 4, 41 and 12 per cent of the variance in the real rate, respectively. The null hypotheses that all lagged values of money, real output or expected rate of inflation in the real rate equation have zero coefficients were accepted. These results are similar to those obtained for the short-term real interest rates. In other words, both short- and medium-term real interest rates in the U.S.A. have not been sensitive to innovations in money supply. Turning now to the variance of output, we found that after 24 quarters about 32 per cent of the variance in output is explained by its own innovations. Innovations in real rate, money and the expected rate of inflation explain about 33, 28 and 7 per cent of the variance in output, respectively. The tests of the hypothesis that all lagged values of real rate, money or expected rate of inflation in the output equation have zero coefficients were easily accepted. These results are in contrast to those obtained using short-term real interest rates. In other words, while real output in the U.S.A. has been sensitive to innovations in the short-term real rate of interest, it has not been responsive to movements in the mediumterm real interest rate. CONCLUDING REMARKS This chapter examined the relationship between ex-ante real interest rates, money, real output and expected rate of inflation. We first tested the null hypothesis that the real rate of interest is exogenous relative to a universe that includes money, output and inflation, by testing the restriction that past money, output and prices have no additional predictive content for current ex-ante real rates, given past real rates. All the regressions include eight lags of each variable. Then, as an additional test of exogeneity of real rates, we decomposed their variance into components explained by orthogonalized innovations in money, output and expected rate of inflation and tested the individual hypothesis that all lagged values of money, output or expected rate of inflation in the real rate equation have zero coefficients. In addition, we analysed the relationship among these four variables by

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decomposing the variance in each variable to components explained by innovations in other variables. Finally, we plotted the response of real rates to unit shocks in money, output and inflation. Table 5.14 summarizes the results of the Granger causality tests of the hypothesis that ex-ante real interest rates are exogenous relative to the universe that includes money, output and expected rate of inflation. Table 5.14 shows that the Granger causality tests cannot reject the exogeneity of shortterm real interest rates at 5 per cent level for Australia, Belgium, Canada, Sweden and the U.S.A. For five of the countries in the sample, namely France, Germany, Italy, Japan and the U.K., the exogeneity hypothesis can be rejected at the 5 per cent level. For the case of the Netherlands, the hypothesis of exogeneity of the real rate with respect to money can be rejected at the 10 per cent level. When considering the medium-term real rates, the exogeneity hypothesis cannot be rejected only for Belgium and the U.S.A. For eight of the countries in the sample, namely Australia, Canada, Germany, Italy, Japan, the Netherlands, Sweden and the U.K., the exogeneity hypothesis can be rejected at the 5 per cent level. For France, the exogeneity hypothesis can be rejected at the 10 per cent level.

Table 5.14 Granger causality tests of exogeneity of ex-ante real rates (1969:3–1990:4) Country

Short-term real rate

Medium-term real rate

Australia

Yes

Rejected

Belgium

Yes

Yes

Canada

Yes

Rejected

France

Rejected

Rejected*

Germany

Rejected

Rejected

Italy

Rejected

Rejected

Japan

Rejected

Rejected

Netherlands

Rejected*

Rejected

Yes

Rejected

Rejected

Rejected

Yes

Yes

Sweden U.K. U.S.A. *Significant at 10% level.

In addition to testing the exogeneity hypothesis, we decomposed the variance of real rates into variations explained either by its own innovations or by innovations in other variables in the system. The basic assumption is that if a variable is exogenous or Granger-causally prior, its variations are primarily explained by its own innovations. Within the framework of a general vector autoregressive system, we also tried to shed some light on the links between money and real interest rates, between real rates and

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output, and between real rates and the expected rate of inflation, in different countries. Table 5.15 summarizes our findings concerning the presence of a link between money and real interest rates. Table 5.15 shows that the link between money and real interest rates suggested by existing monetary theories of business cycles exists for only five of the countries in our sample. More specifically, when we consider the ex-ante short-term real interest rates, the link between money and real interest rate exists only for Japan, the U.K. and the Netherlands. However, when we consider the medium-term real interest rate, the link exists for Australia, France, Italy and Japan. Our analysis shows the absence of a linkage between money and real interest rates for Belgium, Canada, Germany, the Netherlands, Sweden and the U.S.A. Table 5.16 summarizes the results of a test of the hypothesis that information in real interest rates explains a statistically significant fraction of the variance in real output. It shows that the link between

Table 5.15 Existence of a causal relationship between real rate and money supply (1969:3– 1990:4) Country

Short-term real rate

Medium-term real rate

Australia

No

Yes

Belgium

No

No

Canada

No

No

France

No

Yes*

Germany

No

No

Italy

No

Yes

Japan

Yes

Yes

Netherlands

Yes*

No

Sweden

No

No

U.K.

Yes

No

U.S.A.

No

No

*Significant at the 10% level.

Table 5.16 Existence of a causal relationship between real output and real interest rates (1969:3– 1990:4) Country

Short-term real rate

Medium-term real rate

Australia

Yes

Yes

Belgium

Yes

No

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Canada

Yes

No

France

No

Yes

Germany

No

No

Italy

No

No

Japan

Yes

No

Netherlands

No

No

Sweden

No

No

U.K.

No

No

U.S.A.

Yes

No

real interest rates and output exists for six of the countries in our sample. More specifically, when considering the short-term real rates, the link exists for Australia, Belgium, Canada, Japan and the U.S.A. However, if we consider the medium-term real rates the link exists for only two countries, namely, Australia and France. We were not able to find any significant link between the real output and real interest rates for Germany, Italy, the Netherlands, Sweden and the U.K. Finally, Table 5.17 shows the link between the real rate of interest and expected rate of inflation. We can observe that expected rates of inflation have exerted significant influence over the short-term rates in France, Italy and the U.K. When considering the medium-term real rates, we find that expected rates of inflation have significantly influenced the real rates in Canada, Italy, Japan, the Netherlands and Sweden.

Table 5.17 Existence of a causal relationship between real rate and expected rate of inflation Country

Short-term

Medium-term

Australia

No

No

Belgium

No

No

Canada

No

Yes

France

Yes

No

Germany

No

No

Italy

Yes

Yes

Japan

No

Yes

Netherlands

No

Yes

Sweden

No

Yes

U.K.

Yes

No

U.S.A.

No

No

6 BUDGET DEFICITS AND INTEREST RATES: THEORY In this chapter we address the contentious issue of the relationship between interest rates and budget deficits. Given that there are by now a number of studies summarizing this topic (see, for example, Bernheim (1987), Blanchard and Fischer (1989), among others), we do not provide a detailed treatment of the alternate paradigms proposed to examine this relationship. Instead, we briefly discuss the predictions of each of the paradigms and then propose a model which can be used to test the alternate predictions. THE ALTERNATE PARADIGMS The literature devoted to the study of the relationship between interest rates and budget deficits identifies three alternate paradigms: the Keynesian, the neoclassical and the Ricardian equivalence. Since our purpose is to isolate hypotheses, which can be eventually tested, we look at these paradigms in that light. From this perspective the most useful way in our view is to start in the spirit of Bernheim (1987). This we do by distinguishing between transitory and permanent budget deficits and then see what the predictions of each of the paradigms is in terms of the effects of the two types of changes on the interest rates. Starting with the Keynesian paradigm first, it is by now well known that in a fix-price world which is also characterized by unemployed resources and where a good proportion of the consumers are liquidity constrained and/or myopic, a tax-financed deficit is always expansionary and therefore conducive to higher interest rates. It is equally known, as demonstrated by Blinder and Solow (1973) that, assuming a stable equilibrium and plausible parameter values, debt-financed deficits are more expansionary than taxfinanced and therefore have the potential of inducing even greater changes in interest rates. As Bernheim so ably points out, the Keynesian paradigm essentially concerns itself with the effects of transitory deficits. This is so because, as shown by Blinder and Solow, the eventual outcome can be sensitive to parameter values. The Keynesian paradigm pays little attention to the intertemporal nature of the decision making by economic agents, which is the point of departure of the other two paradigms. In the neoclassical paradigm, which may be viewed as the finite horizon version of the Ricardian equivalence model (see Blanchard (1985)) agents are assumed to be far sighted and make decisions on the basis of lifetime considerations, both with respect to consumption expenditures and income. An important prediction of this paradigm is that permanent budget deficits have an unambiguously positive effect on interest rates. But this paradigm does not make specific predictions about the effects of

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the transitory changes in the deficits. Thus we see that the predictions of the Keynesian and the neoclassical paradigms are quite distinct. It should be noted though that a positive effect of transitory deficits, as predicted by the Keynesian paradigm, is not incompatible with the outcome of the neoclassical paradigm. The Ricardian paradigm is radically different in its predictions from the preceding two. It fundamentally denies any role for fiscal policy. It claims that, under certain conditions, the effect of government expenditures on aggregate demand and therefore on interest rates is insensitive to whether such expenditures are financed by taxes or by debt (see Ricardo (1951), Barro (1974), Buchanan (1988)). The basic idea is that debt- and tax-financing are equivalent, because financing by debt implies future tax liabilities, which are perfectly foreseen by economic agents and hence debt is not viewed as private wealth. In short, budget deficits, whether transitory or permanent, have no effect on interest rates. This equivalence proposition is based on a number of assumptions, in particular, that (a) economic agents have an infinite planning horizon; (b) that capital markets are perfect and that consumers are not liquidity constrained; (c) that taxes are non-distortionary; and (d) that economic agents are fully aware of the future course of fiscal policies. It has been demonstrated often that the violation of one or more of these assumptions could lead to departures from the Ricardian equivalence. Ultimately the question is empirical. It is clear from the above discussion that a rejection of the Keynesian paradigm does not necessarily indicate an acceptance of the Ricardian equivalence proposition. On the other hand, as Bernheim points out, finding a significantly positive effect of both transitory and permanent budget deficits is consistent with both the Keynesian and the neoclassical paradigms. A MODEL OF BUDGET DEFICITS AND INTEREST RATES As we can see from the brief discussion above, the crucial step in testing the validity of the alternate paradigms is the measurement of the two components of budget deficits, namely, the transitory and the permanent. However, any attempt to generate such measures, of necessity, must be arbitrary. To the extent that the results may be sensitive to how such regressors are generated, we may not be in a position to determine with certainty whether we have indeed tested the alternative paradigms appropriately. Consequently, a better alternative would be to develop an approach which would not require the use of such generated regressors. Our solution to this problem is to interpret the concepts of transitory and permanent changes to imply short-term and long-term effects, respectively, and then specify a model which would enable us to directly estimate the long-term effects, which we would view as the effects of permanent changes, without omitting the short-term effects, which we would identify as the effects of transitory changes in deficits. In effect, we argue that the existing literature is not able to test the Ricardian equivalence proposition and the competing paradigms properly, because it cannot adequately distinguish between the long-run and short-run effects of budget deficits. Our model, which is an extended version of Sargent’s (1969) loanable funds model, exploits a methodology proposed by Wickens and Breusch (1988) which enables us to

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derive the effects of permanent changes (the long-term effects) in budget deficits but at the same time also to identify the impacts of transitory (or short-term) effects. The starting point of the model is the following identity used by Sargent:1 (1) where rn(t) is the nominal rate of interest, rm(t) is the market rate of interest which is the nominal rate adjusted for the expected rate of inflation, and finally, re(t) is the real rate which equilibrates desired saving and desired investment. We now derive an equation for the equilibrium real rate of interest re(t). This is done within a model of ex-ante saving-investment behaviour in the spirit of Sargent. The function for desired private saving is specified as: (2) where Sp, Sg, Y, and Cg stand for private savings, government savings, total income and government consumption expenditures, respectively, and ε is an error term. The inclusion of Cg allows for direct crowding out, following Buiter (1977) and that of Sg allows for the effect of budget deficits. The standard procedure for estimating the long-run effect of Sg on Sp in this dynamic model is to obtain estimates of Σai and Σbi, and solve for (3)

and then calculate its variance; is the long-run effect of Sg on Sp. But, as Wickens and Breusch (1988) point out this is an unsatisfactory procedure since we have to estimate (2) and calculate as well as having to calculate an estimated variance for . A more satisfactory procedure would be to transform the dynamic equation (2) in such a way that it would yield a direct estimate of

and its variance. Following them, we can do this by

subtracting from both sides of (2), rearranging the other right-hand side variables and re-normalizing to give: (4)

where (5) and

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∆Xt−i =Xt−Xt−i It is immediately clear from (4) that λs(Σbi) provides a direct estimate of the long-run effect of Sg on Sp and λs(Σei) of Cg on Sp. And, of course, we would also get the estimate of their variances. Using the identity (6) we can write the equation for total desired saving as (7)

From equation (4), we know that λs(Σbi )=−1 by the Ricardian equivalence proposition. Therefore, its test in (7) implies the restriction that (1+λs(Σbi))=0. Similarly, complete crowding out of private consumption expenditures by government consumption expenditure in the long run implies the restriction that λs(Σei )=1 and no crowding out implies that λs(Σei )=0. The long-run marginal propensity to save is given by λs(Σci )>0. The desired investment function is specified as (8) where Ip and Ig stand for private investment and government investment, respectively, and where ∆Yt−i =Yt−i −Yt–i–1. The inclusion of Ig allows for direct crowding out of private investment expenditures by government investment expenditures, again, as suggested by Buiter (1977) and ∆Y represents the accelerator effect as incorporated by Echols and Elliot (1976). Again, following the Wickens and Breusch procedure, as applied to the saving function, (8) can be written as (9)

where (10) Using the identity (11)

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we can write the equation for total desired investment as (12)

Since in equation (9), complete crowding out in the long run implies that λI(Σβi )=−1, this in equation (12) implies that the coefficient of Ig be zero. The coefficient of ∆Yt in (9) gives the long-run marginal capital output ratio. Using (7) and (12), we can solve for re(t). Equating desired total saving and investment, i.e., setting (7)=(12), we get

where Dλ=(λsd-λIIθ)>0 Equation (13) can be rewritten to allow us to examine the effect of a given change in either Cg or Ig while keeping G constant. In other words, we can examine the effect of a change in the composition of G while keeping the total constant. This can be done by using the identity (14) and substituting for

or

in (13). Substituting, say, for

, we get (15)

From (15), we can estimate the effect of a change in Cg while keeping G constant. This is given by

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With G constant,

Since the terms in the parentheses are positive, we have that . In so far as the role of crowding out is concerned, the implications of (15) are rather interesting. It not only enables us to examine the role of a given change in G, which is the approach followed in other studies, but it also allows us to examine the effects of a change in the composition of a given G. To the extent that private expenditures are crowded out to different degrees by the two types of government expenditures, even if the total government expenditure does not change, the results can provide useful policy implications.2 Having derived the determinants of re(t), the determinants of the other two terms in equation (1) are assumed to follow Sargent’s specification. The spread between the market rate and the equilibrium rate (rm(t)–re(t)) is determined, following Wicksell, by the rate of growth of real money supply. Assuming linearity, we thus have:3 (16) where m is the rate of growth of real stock of money. The last term of equation (1) is assumed to depend, linearly and positively, on the expected rate of inflation, so that (17) where πe is the expected rate of inflation. We can now derive two alternate reduced-form equations for the nominal interest rate rn(t): one by substituting (13), (16) and (17) into (1) and the other one by substituting (15), (16) and (17) into (1). For reasons already given, our preference is for equation (15). Consequently, we only give the equation obtained by substituting (15), (16) and (17) into (1), namely, (18)

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Since our primary concern is with assessing the role of budget deficits on interest rates, we now incorporate budget deficit in question (18) explicitly. By definition, DEFt=Gt−Tt where DEF is budget deficit and T is tax revenue. Substituting for G (i.e. (Ig+ Cg)) and T(Sg=T−Cg or T=Sg+Cg) we obtain

. Equation (18) can be

expressed in terms of DEF. Through appropriate substitutions for Sg,

Ig and

we can get:

We can now see how the Ricardian equivalence proposition can be tested from (19). If ∂rn(t)/∂DEFt=0, we must have {1+λs(Σbi)}/Dλ =0. Because Dλ>0 since d>0, θ<0, and λs and λI are positive, this condition reduces to the requirement that (1+λs(Σbt)}=0. But we know from the saving equation that for the Ricardian equivalence proposition to hold {1+λs(Σbi)}=0, because λs(Σbi )=−1. Thus, testing the null hypothesis that the coefficient of DEFt in (19) is equal to zero provides us with a test for the long-term validity of the Ricardian equivalence proposition. The short-term effects can be read from the coefficients of ∆DEFt−i. If we were to adhere to the interpretations of the three paradigms as discussed above, then we could perform the following tests:

• The Keynesian hypothesis: –λsΣbi/Dλ is positive and significantly different from zero. • The neoclassical hypothesis: {1+λs(Σbi)}/Dλ is positive and significantly different from zero. • The Ricardian ‘equivalence’: both −λsΣbi/Dλ and {1+λs(Σbi)}/ Dλ are jointly not significantly different from zero. The interpretation of the Ricardian ‘equivalence’ proposition offered by Bernheim may be deemed to be overly restrictive, in so far as the proposition is really a long-run phenomenon. In that respect, we suggest that the single restriction, namely, the opposite of that required for the validity of the neoclassical hypothesis, is sufficient for the validity of the Ricardian ‘equivalence’ hypothesis. The above model has been specified for a closed economy, but it can be easily expanded to the case of an open economy. This can be done by redefining the equilibrium S=I as applied to an open economy as, for example, done by Echols and Elliot (1976). In the next chapter, we estimate the open economy version of the model.

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CONCLUDING REMARKS In this chapter, we have briefly discussed how deficits may affect interest rates and have proposed a testable model which can be used to verify the validity of alternate paradigms proposed in the literature. The next chapter uses this model to examine the extent to which budget deficits, in the countries included in our sample, may have been responsible for the recent movements in the real interest rates examined in the earlier chapters.

7 BUDGET DEFICITS AND INTEREST RATES: THE EVIDENCE The last chapter tried to model the effects of budget deficits on interest rates. This chapter addresses the empirical question: does there exist evidence to support the view that such effects do in fact exist in the countries included in our sample? We approach this question in a number of ways. First, we look at some descriptive data on real interest rates and deficits, both nominal and real, and examine whether the data reveal any regularities. While the regularities, if any, do not necessarily indicate causation, they may nevertheless be indicative of phenomena that need explaining. Second, we offer a brief summary of the evidence available in the literature on this issue. Finally, we estimate the model presented in Chapter 6. BUDGET DEFICITS AND REAL INTEREST RATES: SOME DESCRIPTIVE EVIDENCE Figures 7.1 and 7.2 present the relevant statistical data. The first figure plots the real interest rates against the nominal deficits (NDEFICIT) and the second against the real deficit (ADEFICIT). In each case interest rate is measured on the left axis while deficits are measured on the right axis. Figure 7.1 shows the movements of the short-term ex-ante real interest rates estimated according to the Mishkin procedure explained before, while Figure 7.2 does the same for the medium-term interest rates. Concentrating on the short-term interest rates, we can observe a number of interesting points. The first obvious point is that there are no uniform patterns across the eleven countries. This should serve as a cautionary note against any attempts at broad generalizations. Second, that even for the same country, we do not find an identical

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Figure 7.1 Ex-ante real (short) rate and budget deficit pattern between the real interest rates and the two measures of the deficit over time. This raises the, by now, well-known question as to whether we should be concerned with nominal or with real deficits while debating the issue before us. Yet another interesting observation relates to the temporal nature of the observed relationships. In a number of countries, the co-movements of the two variables seem

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to be closer for the 1970s than for the 1980s, a striking exception being the U.S.A., to some extent. If we concentrate on the behaviour of the two major countries which are deemed to be the pacesetters, namely, Germany and the U.S.A., and look at the adjusted real deficits only (and only the 1980s), we see some quite remarkable differences between the two countries. For Germany, there does not

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appear to be any relationship between real deficits and the real short-term rates. This contrasts sharply with what we observe for the 1970s. The U.S.A., on the other hand, displays a very different behaviour. The co-movement of the two variables is quite close except for the period after 1988. Moreover, this co-movement is closer than for the 1970s. A brief look at the U.K. is also interesting,

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because the two variables in this case show a pattern which is closer to that of the U.S.A. than that for Germany. This obviously raises interesting questions. Do we detect any differences if we turn our attention to the medium-term rates? To answer this question, we now look at Figure 7.2. Here again, the basic point is the same as above, namely, that the

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countries of the sample do not display a uniform pattern, regardless of the definition of the deficit used. But unlike the short rates, the co-movements seem to be closer for the 1980s than for the 1970s. On the whole, however, there are far more disparities in the pattern both across the countries and over time for any given country. As an illustration, we consider the G-7 countries. For Canada, the

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relationship seems to be the strongest for the period from mid-1970s to the mid-1980s, which, however, is not the case for France or for Germany. In fact, for Germany we see the same absence of close co-movement as we did for the short rate. Italy, on the other hand, shows very close movement for the real deficit and the real rates for almost the whole period, followed by lack of any such relationship

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for Japan. The relationship for Japan mirrors that one for the short rate. The U.K. shows the pattern very much like Italy, a rather close one. The U.S.A. follows the same kind of close pattern as was the case for the short rate. What can we conclude from the above descriptive evidence? As already pointed out, these data are not meant to be suggestive of a

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causal relationship. But ignoring that, it is evident that the above data do not reveal any consistent pattern either across the countries or for the same country over time. This should caution us about claims which are sweeping in their generality or attempts which try to offer a unique explanation for all of the countries. It may well turn out to be the case that explanations are country-specific, which can be both good news or bad, depending on how we view the world.

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A BRIEF REVIEW OF THE EMPIRICAL LITERATURE One of the major shortcomings of the empirical literature in this area is that, by far, most of the studies are confined to the U.S.A. As the evidence in the previous section suggests, the experience of the

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U.S.A. may not necessarily be indicative of the experiences of the other countries in our sample. With this caveat, we briefly summarize the findings for the U.S.A. as well as for the other countries which we have been able to find. The literature for the U.S.A. is quite large and varied. Extensive surveys of some of the literature are available in the U.S. Treasury

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Department (1984), the Congressional Budget Office (1987), and Bernheim (1987). The findings of the large numbers of studies are so diverse that one can find support for virtually any position one cares to favour. For example, Plosser (1982, 1987) reports no relationship between deficits and interest rates. His findings are supported by Evans (1987a, 1987b). On the other hand, Gupta and Moazzami

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Figure 7.2 Ex-ante medium rate and budget deficit (1991b) report a significant effect. As for the other countries, the evidence is very sparse, but the little that exists is again quite mixed. Evans (1987a, 1987b), for example, reports the finding that deficits have no effect on quarterly nominal interest rates for Canada, France, Germany, Japan, the U.K. and the U.S.A. Modigliani and Jappelli (1988) report that the permanent component of deficits raises nominal

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interest rates in Italy. Howe and Pigott (1991/92) examine the effects of debt ratio on the long-term real rates in Japan, Germany, the U.K. and the U.S.A. and reach somewhat opposite conclusions to those arrived at by Evans. Their general conclusion is that the increasing debt ratios have had an effect on the long-run equilibrium real interest rates, which may reflect higher financial risk.

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The results of the various studies are not comparable for the well-known reasons: differences in the sample period, methods of estimation, model specification, variables used, to name just a few. But a more crucial issue is the one addressed by Bernheim (1987) and which we highlighted in Chapter 6, namely, the short- versus the long-term nature of the relationship. Since we do not believe it

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would serve any useful purpose in dissecting the shortcomings of the existing studies in the field, our aim in the next two sections is to present new and extensive evidence for the eleven countries in our sample.

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ESTIMATION ISSUES AND SOURCES OF DATA In this section we estimate equation (19) of Chapter 6 for an open economy for the countries included in this study. Careful examination of equation (19) reveals that this model consists of two parts.

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The first part deals with the explanation of the equilibrium real rate of interest. As we discussed in Chapter 6, this part is based on the two transformed structural equations (4) and (9). The transformed equations (4) and (9) cannot be estimated by ordinary least squares since they both include current dependent variables among their explanatory variables. This obviously causes OLS estimation to be

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biased. In order to estimate these transformed equations we need to employ the instrumental variable estimation technique. Wickens and Breusch (1988) have shown that the estimation of equations (4) and (9) using the instrumental variable estimator with the original matrix of regressors from equations (2) and (8) as instruments will be identical to the OLS estimates of the original autoregressive equa-

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tions (2) and (8). However, the advantage of instrumental variables estimation of the transformed equations is that it provides direct estimates of the long-run parameters and their standard errors and thus does not require further computations as is the case with the OLS estimation of the autoregressive models. Since the first part of equation (19) is based on the two

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transformed structural equations, we need to employ all of the original predetermined variables appearing in the two structural equations (2) and (8) as instruments. The last part of equation (19) which consists of the rate of growth of real money supply, expected inflation rate and net exports in the open economy case simply means adding more instruments to the above-mentioned instruments needed to estimate (19).

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Following a general-to-specific modelling strategy suggested by Gilbert (1986), we introduced six lags on each of the regressors in the structural equations for eight countries for which quarterly data were available. Only annual data could be assembled for Belgium, Japan and Sweden. For these countries we introduced two lags on each of the regressors in the structural equations. The choice of lag

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structures resulted in fifty-four instruments for countries for which we used quarterly data and eighteen instruments for the remaining countries.1 In estimating equation (19), we encountered some difficulties due to the presence of collinearity among the set of instruments used. Such a large number of instruments also poses two additional problems. First, a large number of instruments used reduces degrees of freedom and therefore makes the standard errors of the estimated coefficients conservative. The second problem relates to the small sample bias of the instrumental variable estimator. Nagar (1959) showed that the small sample bias of the two-stage least squares estimator, assuming serially independent disturbances, is positively related to the number of instruments used. Interpreting all the existing estimators designed for estimation of a structural equation with autocorrelated error as a special case of a

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generalized instrumental variable estimator, Moazzami and Buse (1986, 1991) and Buse and Moazzami (1991) showed that the small sample bias of these estimators was positively related to the number of instruments used and negatively related to the amount of variability which existed in these instruments. In other words, a large number of instruments used in estimating model (19) can cause large biases in the estimated coefficients. Given that it is the variability and information content of the set of instruments that are of major importance, we decided to replace the above set of instruments by a smaller number of principal components. Before using this approach, we need to address two problems. The first relates to the number of principal components to be used. In our case, the number of principal components should be at least equal to the number of estimated coefficients minus one. A second problem relates to the criteria of selecting principal components. In the present study, we selected the components with the greatest eigenvalues. These are the components which account for the largest variance of the initial set of instruments.2 This method not only reduces the number of instruments used in the estimation, but also minimizes the loss of variability due to the choice of fewer instruments. Our initial estimates of equation (19) showed autocorrelation in the disturbance terms for France, Sweden and the U.S.A. which presented an additional estimation problem. If the error term is correlated with its past values, it would also be correlated with the lagged dependent variables appearing among the regressors of the original autoregressive models, and thus these variables cannot be used as instruments. To circumvent this problem, a two-step procedure was used. In the first step, a consistent estimate of autocorrelation coefficient was obtained by estimating (19) with the instrumental variable method employing the principal components of only the exogenous variables appearing in the structural equations. In the second step, using the estimated autocorrelation coefficient, we transformed equation (19) and then estimated it with the instrumental variable method based on the principal components of the entire set of instruments. As we discussed before, meaningful statistical inference based on the estimation results of equation (19) can only be made if the variables appearing in the model are all stationary. In testing for the presence of unit root, we found that some series showed seasonal variation while others had undergone major breaks. After allowing for the presence of seasonality and break in these series, we could reject the null hypothesis of unit root against the alternative of stationarity in all the cases.3 To ensure the validity of the final estimates for making statistical inference, we subjected the estimated models to a series of diagnostic tests. The presence of autocorrelation was tested by using the Lagrange multiplier test proposed by Breusch and Godfrey (1981). The results are shown in the row labelled t(LM) in the tables reported in the next section. The presence of autoregressive conditional heteroscedasticity was investigated by testing whether the error terms follow a first-order ARCH process. Results are shown in the row labelled χ2 (ARCH) in the tables reported in the next section. The data used in this chapter cover the period from 1965 to 1990 for all countries except for Italy and the Netherlands. For Italy, data were available from 1971:1 to 1990:4 and for the Netherlands from 1977:1 to 1990:4. We employed quarterly data for Australia, Canada, France, Germany, Italy, the Netherlands, the U.K. and the U.S.A. Quarterly data were not available for Belgium, Japan and Sweden. Therefore, we

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employed annual data for these countries. The data on budget deficit for all countries except for Canada and U.S.A. were obtained from various issues of International Financial Statistics (IFS). For Canada, seasonally adjusted national account deficits are obtained from various issues of the Bank of Canada’s reports. For the U.S.A. we used two alternative measures of deficit. First is the deficit based on the national accounts published by IFS and the other is the actual federal deficit published by the Department of Commerce in the Survey of Current Business (table 3.2) and Gordon (1987). The data on government expenditures, government consumption, money, exports and imports were obtained from the various issues of International Financial Statistics, Bank of Canada Report, and the Federal Reserve Bulletin. The data on private investment and private saving were obtained from various issues of OECD quarterly national accounts. For Italy and the Netherlands a complete data set for private savings and private investment was not available and had to be generated. Finally, we employed GNP deflator to deflate the series. ESTIMATION RESULTS In this section, we report the estimation result of equation (19) and attempt to test the three propositions outlined in Chapter 6, namely the neoclassical hypothesis suggesting that budget deficits have a significant and positive long-term effect on interest rates, Keynesian proposition implying that deficits have a positive short-run impact on interest rates and Ricardian equivalence hypothesis suggesting that deficits have no long-run effect on interest rates. These propositions are tested using both short-term and mediumterm interest rates. In reporting the estimation results, we have classified them into the long-run and short-run effects. The long-run effects are directly estimated and reported. For the shortrun effects, we have only reported the cumulative short-run coefficients from time ‘t−n’ to time ‘t’. Australia Table 7.1 presents the result of the instrumental variable estimation of equation (19) using short- and medium-term interest rates for Australia.4 The diagnostic tests reported in the last three rows of Table 7.1 show the absence of autocorrelation or heteroscedasticity in the estimated regressions. Concentrating on the impact of budget deficit, we can observe that the short-run and long-run coefficients of deficits are positive but insignificant for both the short-term and medium-term interest rates. Therefore, it appears that for the case of Australia, the data support the Ricardian equivalence hypothesis suggesting that deficits do not have any long-term or short-term effect on interest rates. Turning now to the discussion of other variables, we can observe that in the short run, government expenditure has exerted a positive and significant effect on interest rates. Government consumption shows a negative effect on interest rates in the short run. The long-run effect of government consumption on both interest rates has

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Table 7.1 Instrumental variable estimation: Australia Variables Constant

Short-run interest rate

Medium-term interest rate

−19.50

10.05

(2.29)

(1.77)

−1.21

−0.58

(1.31)

(1.27)

4.28

1.19

(4.88)

(1.84)

0.08

0.15

(0.58)

(1.10)

−0.08

−0.04

(2.19)

(1.69)

0.18

0.19

(1.15)

(0.98)

0.07

0.13

(0.28)

(1.56)

0.70

0.39

(1.96)

(1.97)

−2.16

−0.88

(3.13)

(1.47)

−0.12

0.12

(1.04)

(0.92)

0.63

−0.03

(2.45)

(0.17)

−0.19

0.07

(1.56)

(1.45)

−0.11

−0.08

(2.09)

(1.77)

Long-run effects Government expenditures Government consumption Deficit Output Change in output Short-run effects Deficit Government expenditures Government consumption Output Private investment Private saving Other variables Money growth

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Expected inflation

165

1.75

1.56

(2.66)

(2.16)

−1.83

−1.06

(5.75)

(5.13)

RBAR2

0.86

0.89

D.W.

1.97

1.89

t(LM)

0.51

0.45

ARCH

0.66

0.23

Net exports

been positive and significant. Real output shows a negative effect on interest rates reflecting its role in the saving function in our model. The growth rate of money supply has a negative and significant effect on short-term rates. The influence of monetary growth on medium-term rates has been less significant. The expected rate of inflation has positive and significant effects on both the short-run and medium-term interest rates. The impact of net exports on interest rates has been negative and highly significant, suggesting perhaps the initial monetary effect of a change in net exports on interest rates. To further examine the effect of budget deficits on interest rates in Australia, we estimated the conditional forecasts of interest rates during the 1970s and 1980s under the assumption of budget deficits to be identical to zero. Figures 7.3 and 7.4 compare the time paths of the actual and fitted values of equation (19) with the conditional forecasts of short-term and medium-term interest rates for Australia. Figures 7.3 and 7.4 show that the time paths of actual, fitted and conditional forecasts of interest rates in Australia are remarkably close to each other, supporting our above findings that deficits do not seem to have had a significant effect on interest rates in Australia.

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Figure 7.3 Actual, fitted and conditional forecast of short-run interest rate: Australia

Figure 7.4 Actual, fitted and conditional forecast of medium-term interest rate: Australia

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Finally, as an additional test of the relationship between deficits and interest rates, we have compared the mean values of actual, fitted and conditional forecasts of interest rates during the two sub-periods of the 1970s and 1980s and tested the hypotheses that the mean of the actual and fitted values are identical to the mean value of forecasts of interest rates conditional upon deficits being identical to zero. Table 7.2 presents the results of this comparison using Australian data. Table 7.2 also shows that during the period under study the mean of the actual and fitted values of equation (19) are remarkably close to each other. We can also observe that the mean of the conditional forecasts are marginally below their fitted values in both periods and for both interest rates. The test results suggest that we cannot reject the hypothesis that the mean of the actual rates and conditional forecasts are identical for both interest rates during both periods. The hypothesis that the mean of the fitted values are identical to the mean of the conditional forecasts is rejected for both interest rates during the 1970s.

Table 7.2 Mean values of actual, fitted and conditional forecast of interest rates in Australia Nominal interest rates

1970:1–1979:4

1980:1–1990:4

Actual

8.66

14.60

Fitted

8.86

14.31

Conditional forecast

8.78

14.26

H0: fitted=forecast

0.08

0.05

(2.13)

(1.24)

−0.12

0.34

(0.49)

(1.41)

Actual

8.21

13.47

Fitted

8.48

13.18

Conditional forecast

8.30

13.08

H0: fitted=forecast

0.18

0.09

(2.21)

(1.24)

−0.10

0.39

(0.59)

(1.48)

Short-run interest rates

H0: actual=forecast Medium-term interest rates

H0: actual=forecast

Belgium Table 7.3 presents the results of the instrumental variable estimation for short-run and medium-term interest rates for Belgium.

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168

Concentrating on the effects of budget deficits on interest rates, we observe that, in the long run, budget deficits have exerted positive and significant influence on both the shortterm and medium-term interest rates in Belgium. We can also observe that the long-term effect of budget deficits on short-term interest rates has been larger than that for the medium-term rates. Table 7.3 also shows that the short-run effect of budget deficit on interest rates in Belgium has been negative but insignificant. The above results provide support for the neoclassical proposition that deficits exert long-term positive effects on interest rates. Considering the effect of government expenditures on interest rates, Table 7.3 shows that, in the long run, government spending has exerted a positive and significant effect on only the medium-term interest rate. In the short-run, government expenditure does not seem to influence either rates. Government consumption shows a positive and significant long-run effect on both rates. The coefficient of output is positive and significant for both interest rates. This

Table 7.3 Instrumental variable estimation: Belgium Variables Constant

Short-run interest rate

Medium-run interest rate

−0.27

6.05

(0.03)

(1.73)

0.01

0.01

(0.77)

(2.55)

0.07

0.06

(2.26)

(4.53)

0.02

0.01

(2.17)

(2.37)

0.01

0.01

(1.99)

(3.08)

0.01

0.01

(1.66)

(0.79)

−0.03

−0.02

(1.60)

(1.18)

−0.01

−0.01

(0.69)

(1.26)

0.04

0.02

Long-run effects Government expenditures Government consumption Deficit Output Change in output Short-run effects Deficit Government expenditures Government consumption

Budget deficits and interest rates: The evidence

169

(1.58)

(1.83)

−0.01

−0.01

(0.34)

(0.88)

−0.02

−0.02

(1.37)

(3.10)

0.01

0.02

(1.17)

(3.16)

0.02

−0.07

(0.13)

(1.16)

0.17

0.18

(1.18)

(2.93)

−0.04

−0.03

(3.20)

(5.51)

RBAR2

0.74

0.93

D.W.

2.00

2.06

t(LM)

0.12

0.24

ARCH

0.02

0.10

Output Private investment Private saving Other variables Money growth Expected inflation Net exports

suggests that the effect of change in output on investment demand has outweighed its effect on the level of saving. Money growth does not seem to have influenced either interest rates. Expected rate of inflation has positive and significant effects on the medium-term interest rates. Finally, net exports have shown a negative and highly significant effect on both interest rates. As we mentioned above, this can be due to the short-term monetary influence of changes in the net exports. To further examine the effect of deficits on interest rates in Belgium, once again we calculated the conditional forecast of interest rates based on the assumption that budget deficit in Belgium has been zero during the period under study. Figures 7.5 and 7.6 present the time paths of actual and fitted values of equation (19) along with conditional forecasts of both interest rates during the 1970–90 period. Figures 7.5 and 7.6 show that the actual interest rates and their fitted values are remarkably close to each other. The forecasts of the rates conditional upon deficits being identical to zero are significantly below the actual and fitted values, suggesting that the long-run positive effect of budget deficits have outweighed their short-run negative impact. In other words, budget deficits have been a major source of high interest rates in Belgium during the 1970–90 period.

Interest rates and budget deficits

170

Figure 7.5 Actual, fitted and conditional forecast of short-run interest rate: Belgium

Figure 7.6 Actual, fitted and conditional forecast of medium-term interest rate: Belgium

Budget deficits and interest rates: The evidence

171

Table 7.4 Mean values of actual, fitted and conditional forecast of interest rates in Belgium Nominal interest rates

1970:1–1979:4

1980:1–1990:4

Actual

7.77

10.36

Fitted

7.86

10.25

Conditional forecast

4.58

−0.20

H0: fitted=forecast

3.28

10.45

(5.69)

(11.79)

3.18

10.55

(5.79)

(11.97)

Actual

8.27

10.55

Fitted

8.31

10.50

Conditional forecast

7.00

5.71

H0: fitted=forecast

1.31

4.79

(4.42)

(8.57)

1.27

4.84

(5.02)

(8.70)

Short-run interest rates

H0: actual=forecast Medium-term interest rates

H0: actual=forecast

To obtain a quantitative estimate of the extent of the influence of budget deficits on interest rates, Table 7.4 presents the mean values of the actual, fitted and conditional forecasts of interest rates during the two sub-periods of 1970–80 and 1980–90. Table 7.4 demonstrates that as expected the mean of the actual and fitted values of both interest rates are very close to each other. However, the means of the conditional forecast of interest rates are much smaller than the actual interest rates in both periods. The test results show that the means of the actual and fitted values are significantly greater than the means of the conditional forecasts for both interest rates and during both periods. The effect of deficits on the medium-term rates seem to have been considerably smaller than that on the short-term rates, specially during the 1980–90 period. Canada Table 7.5 presents the results of applying the instrumental variable method to equation (19) using Canadian data. Concentrating first on the effect of budget deficits, we can observe that, in the long run, deficits have exerted a positive and significant impact on both short-run and medium-term interest rates in Canada. We can see that the numerical size of the impact is

Interest rates and budget deficits

172

much larger for the short-run interest rate. Similarly, in the short run, deficits have had a positive and significant impact on both interest rates. Again, the size of the impact on the short-term rate has been much larger than that on the medium-term rate. Comparing the short-run and long-run effects of budget deficits, we can say that, irrespective of the interest rate used, the short-run effects have been much smaller than the long-run effects. Therefore, it appears that in the case of Canada the data support both neoclassical and Keynesian propositions. Turning to the discussion of other variables, government expenditure has a positive and significant short- and long-run impact on both interest rates. Government consumption is found to have a positive short-run effect on interest rates. Real output shows a negative and significant long-term impact on interest rates reflecting its role in the saving function. Growth of money does not seem to have influenced interest rates in Canada. Expectation of inflation has shown both a positive and significant effect on both interest rates. Finally, net exports have shown a positive and highly significant effect on both interest rates in Canada, reflecting the increase in

Table 7.5 Instrumental variable estimation: Canada Variables Constant

Short-run interest rate

Medium-run interest rate

−4.70

−0.12

(2.86)

(0.10)

1.38

0.97

(5.61)

(5.66)

−0.07

0.39

(0.18)

(1.48)

0.66

0.38

(3.53)

(2.88)

−0.09

−0.05

(5.05)

(3.43)

0.07

0.06

(1.65)

(2.07)

0.37

0.16

(2.56)

(2.04)

0.66

0.42

(2.65)

(2.38)

1.09

0.64

Long-run effects Government expenditures Government consumption Deficit Output Change in output Short-run effects Deficit Government expenditures Government consumption

Budget deficits and interest rates: The evidence

173

(2.38)

(1.97)

0.05

0.02

(0.18)

(0.96)

0.01

−0.85

(0.47)

(1.64)

0.11

0.17

(0.95)

(1.11)

0.02

0.01

(0.96)

(0.25)

3.09

1.96

(10.04)

(8.92)

0.41

0.66

(2.86)

(6.59)

RBAR2

0.90

0.91

D.W.

1.97

1.85

t(LM)

0.56

1.10

ARCH

0.12

0.17

Output Private investment Private saving Other variables Money growth Expected inflation Net exports

investment-type expenditures and the resulting positive impact on the rates. Since budget deficits have influenced interest rates in Canada, it would be interesting to compare the conditional forecast of interest rates in the absence of deficits with the actual rates. This is done in Figures 7.7 and 7.8. Figures 7.7 and 7.8 show that the actual and fitted values of interest rates during the 1970–90 period are remarkably close to each other. We can also observe that the conditional forecasts of both interest rates are very close to the actual rates during the 1970s suggesting that budget deficits did not influence the rates during that period. However, the conditional forecasts of both interest rates are significantly below the actual rates during the 1980s reflecting the fact that budget deficits significantly influenced both short-term and medium-term rates in Canada during that period. To obtain a quantitative estimate of the size of the effect of deficits on interest rates in Canada, Table 7.6 presents the mean value of the actual, fitted and conditional forecasts of interest rates for the two sub-periods of the 1970s and 1980s. In addition, Table 7.6 reports the results of testing the hypotheses that the mean of the actual and fitted values of interest rates in Canada are significantly higher than what they would have been in the absence of the deficit.

Interest rates and budget deficits

174

Figure 7.7 Actual, fitted and conditional forecast of short-run interest rate: Canada

Figure 7.8 Actual, fitted and conditional forecast of medium-term interest rate: Canada

Budget deficits and interest rates: The evidence

175

Table 7.6 Mean values of actual, fitted and conditional forecast of interest rates in Canada Nominal interest rates

1970:1–1979:4

1980:1–1990:4

Actual

6.66

11.30

Fitted

6.76

11.32

Conditional forecast

6.18

7.85

H0: fitted=forecast

0.58

3.47

(3.09)

(17.28)

0.48

3.45

(2.26)

(13.20)

Actual

7.44

11.24

Fitted

7.52

11.23

Conditional forecast

7.12

9.20

H0: fitted=forecast

0.40

2.03

(3.74)

(18.93)

0.33

2.04

(2.28)

(13.57)

Short-run interest rates

H0: actual=forecast Medium-term interest rates

H0: actual=forecast

Concentrating on the short-term rates, we observe that the conditional forecasts were 58 basis points below the fitted values and 48 basis points below the actual rates during the 1970s. This gap increased sharply during the 1980s. The conditional forecast of shortterm interest rates was about 3.45 per cent below the actual rates during this period. The medium-term rates show a similar pattern. During the 1970s, the conditional forecast of medium-term interest rates was only 30 to 40 basis points below the actual and fitted values, respectively. However, during the 1980s, the conditional forecast was more than 2.04 per cent below the actual rates. The test results reported in Table 7.6 suggests that the mean of the actual and fitted values of interest rates have been significantly higher than their conditional forecast. In summary, we can argue that budget deficits have contributed significantly to higher interest rates in Canada, especially during the 1980s. France Table 7.7 presents the results of applying the instrumental variable method to equation (19) for France.

Interest rates and budget deficits

176

Considering the effect of budget deficits on interest rates, we can observe that the long-run coefficients of deficits have a negative and insignificant effect on both short-run and medium-term interest rates. In the short run, deficits have had a positive and significant impact on the short-term interest rates while leaving the medium interest rate unaffected. Therefore, it appears that, for the case of France, deficits have exerted only a short-run effect on short-term interest rates, thus offering some support for the Keynesian proposition. Turning to the discussion of the other variables, the long-run effect of government expenditure on both rates has been positive. The short-run effect of government spending has been negative and highly significant for the short-term interest rate. Government consumption has had a long-term positive and significant effect on the medium-term interest rate. In the long run, government consumption has not influenced the short-term interest rate. In the short run, government consumption expenditures have had a significantly negative effect on both interest rates. Real output shows a negative and significant long-term impact on both interest rates, reflecting its role in the saving function. As

Table 7.7 Instrumental variable estimation: France Variables Constant

Short-run interest rate

Medium-run interest rate

−6.15

10.85

(2.31)

(6.84)

0.08

0.02

(3.91)

(1.77)

0.01

0.06

(0.34)

(7.84)

−0.06

−0.01

(1.00)

(0.58)

−0.01

−0.01

(2.45)

(6.60)

0.01

0.01

(0.23)

(0.72)

0.02

0.01

(2.44)

(0.83)

−0.03

−0.01

(3.04)

(1.68)

−0.07

−0.03

Long-run effects Government expenditures Government consumption Deficit Output Change in output Short-run effects Deficit Government expenditures Government consumption

Budget deficits and interest rates: The evidence

177

(3.31)

(2.76)

0.01

0.01

(0.11)

(0.94)

0.02

−0.03

(0.91)

(2.38)

0.01

0.01

(0.81)

(0.76)

−0.02

−0.03

(2.53)

(1.52)

2.94

1.74

(10.03)

(9.95)

−0.04

−0.05

(2.43)

(5.07)

RBAR2

0.83

0.92

D.W.

1.91

1.95

t(LM)

0.11

0.09

ARCH

0.60

0.03

Output Private investment Private saving Other variables Money growth Expected inflation Net exports

expected, money growth had had a negative influence on both rates. Inflationary expectations have shown a positive and significant effect on both interest rates. Finally, net exports have shown a negative and highly significant effect on both interest rates in France. Given our above findings that deficits do not seem to have exerted a long-term influence on interest rates in France, it seems reasonable to assume that the conditional forecast of interest rates in the absence of the deficits would be very close to the actual interest rates. Figures 7.9 and 7.10 present the comparison between the actual and fitted rates with the forecasts of interest rates in the absence of the deficit. Figures 7.9 and 7.10 show that the actual, the fitted and the forecasted values of interest rates during the 1970–90 period are very close to each other. As a final test of the effect of deficits on interest rates in France, Table 7.8 presents the mean value of the actual, the fitted and the conditional forecasts of interest rates for the two sub-periods of the 1970s and 1980s. In addition, Table 7.8 reports the results of testing the hypotheses that the mean of the actual and fitted values of interest rates in France are different from the mean of the conditional forecasts of interest rates. Table 7.8 demonstrates that, as expected, the mean of the actual,

Interest rates and budget deficits

178

Figure 7.9 Actual, fitted and conditional forecast of short-run interest rate: France

Figure 7.10 Actual, fitted and conditional forecast of medium-term interest rate: France

Budget deficits and interest rates: The evidence

179

Table 7.8 Mean values of actual, fitted and conditional forecast of interest rates in France Nominal interest rates

1971:2–1979:4

1980:1–1990:4

Actual

8.42

10.76

Fitted

8.02

10.16

Conditional forecast

8.09

10.48

H0: fitted=forecast

−0.06

−0.32

(1.11)

(1.19)

0.33

0.28

(0.90)

(1.21)

Actual

8.42

10.76

Fitted

10.16

11.90

Conditional forecast

10.20

12.12

H0: fitted=forecast

−0.04

−0.22

(1.18)

(1.07)

−0.17

−0.12

(1.21)

(0.99)

Short-run interest rates

H0: actual=forecast Medium-term interest rates

H0: actual=forecast

the fitted and the conditional forecasts for both interest rates are very close to each other. The test results show that we cannot reject the hypotheses that the mean of the actual and fitted values are equal to the mean of the conditional forecasts for both interest rates and during both periods. Germany Table 7.9 presents the estimation results applying the instrumental variable method to equation (19) using the data for Germany. Concentrating first on the effect of budget deficits, we can observe that the long-run coefficients of deficits in both interest rates equations are negative and insignificant. In the short run, deficits have had a positive but insignificant impact on both interest rates. Therefore, it appears that for the case of Germany, the data support the Ricardian equivalence hypothesis. Turning to the discussion of the other variables, government expenditure, while exerting a positive and significant long-term impact on both interest rates, has had a negative and significant short-run impact on both rates. Government consumption is found to have a negative and significant long-term impact on both interest rates. In the

Interest rates and budget deficits

180

short run, however, government consumption has not exerted a significant influence on either rates. Real output shows positive and significant long-term and negative and significant short-term impacts on the short-term interest rate. Growth of money has had a negative and significant influence on both interest rates in Germany. Expectations of inflation have shown a positive and significant influence on both interest rates. Finally, net exports have had a negative and significant impact on the short-run interest rate. As a final test of the effect of budget deficits on interest rates in Germany, we compare the actual and fitted values of both rates with their forecasts during the 1970s and 1980s under the assumption of budget deficits to be identical to zero. Figures 7.11 and 7.12 compare the time paths of the actual and fitted values with the conditional forecasts of short-term and medium-term interest rates for Germany. Figures 7.11 and 7.12 show that both interest rates in Germany have been very volatile during the 1970–90 period. The estimated equations have not been able to track the actual rates very closely. However, the conditional forecasts seem to be above the fitted values of interest rates for most of the period. This is of course a reflection

Table 7.9 Instrumental variable estimation: Germany Variables Constant

Short-run interest rate

Medium-run interest rate

−12.28

0.48

(6.85)

(0.32)

0.52

0.25

(7.51)

(4.37)

−0.33

−0.17

(5.49)

(3.45)

−0.21

−0.15

(1.25)

(1.32)

0.01

0.01

(1.98)

(0.85)

0.01

0.01

(1.86)

(0.77)

0.31

0.11

(0.19)

(0.62)

−0.42

−0.17

(5.47)

(2.59)

Long-run effects Government expenditures Government consumption Deficit Output Change in output Short-run effects Deficit Government expenditures

Budget deficits and interest rates: The evidence

Government consumption

181

0.21

0.13

(0.76)

(1.19)

−0.01

0.001

(1.91)

(0.31)

−0.21

−0.13

(3.54)

(2.67)

−0.08

−0.07

(1.81)

(1.93)

−0.17

−0.13

(4.15)

(2.85)

1.53

1.51

(4.49)

(8.09)

−0.06

−0.02

(2.14)

(0.75)

RBAR2

0.81

0.61

D.W.

1.98

1.97

t(LM)

0.11

0.15

ARCH

0.09

0.86

Output Private investment Private saving Other variables Money growth Expected inflation Net exports

Figure 7.11 Actual, fitted and conditional forecast of short-run interest rate: Germany

Interest rates and budget deficits

182

Figure 7.12 Actual, fitted and conditional forecast of medium-term interest rate: Germany Table 7.10 Mean values of actual, fitted and conditional forecast of interest rates in Germany Nominal interest rates

1970:1–1979:4

1980:1–1990:4

Actual

5.93

6.43

Fitted

6.10

6.31

Conditional forecast

6.90

7.63

H0: fitted=forecast

−0.80

−1.32

(2.69)

(11.43)

−0.98

−1.20

(2.26)

(3.04)

Actual

7.94

7.44

Fitted

7.96

7.46

Conditional forecast

8.56

8.59

H0: fitted=forecast

−0.60

−1.19

(4.18)

(10.83)

−0.62

−1.15

(2.80)

(8.02)

Short-run interest rates

H0: actual=forecast Medium-term interest rates

H0: actual=forecast

Budget deficits and interest rates: The evidence

183

of the negative long-term coefficients of deficit in interest rate equations. To obtain a quantitative estimate of the difference between the actual and fitted values of interest rates and the conditional forecasts, we have calculated the mean values of these rates for the sub-periods of the 1970s and 1980s and tested the hypotheses that these means are identical. Table 7.10 presents the results. Table 7.10 shows that the mean values of the conditional forecasts of both interest rates have been significantly above the actual and fitted values of both rates during the 1970–90 period. Italy Table 7.11 presents the estimated results based on the instrumental variable method for Italy. Concentrating on the long-run effect of budget deficits we can observe that deficits have had a significant and positive long-run impact on short-term interest rates in Italy. However, deficits do not seem to have influenced medium-term rates in Italy in the long run. In the short run, budget deficits show a negative and significant

Table 7.11 Instrumental variable estimation: Italy Variables Constant

Short-run interest rate

Medium-run interest rate

−14.88

−29.18

(3.73)

(6.35)

0.01

−0.03

(0.64)

(1.01)

0.10

1.07

(0.59)

(6.01)

0.12

−0.02

(2.00)

(0.44)

2.21

0.01

(2.08)

(7.26)

1.63

0.01

(0.91)

(1.70)

−0.10

−0.32

(2.03)

(2.83)

−0.31

−0.07

(2.56)

(0.49)

Long-run effects Government expenditures Government consumption Deficit Output Change in output Short-run effects Deficit Government expenditures

Interest rates and budget deficits

Government consumption

184

0.78

1.31

(3.36)

(5.01)

−0.30

−0.01

(0.25)

(6.14)

−0.31

−0.36

(2.82)

(2.81)

0.01

0.28

(0.74)

(2.80)

−0.01

0.02

(0.29)

(0.63)

3.32

1.34

(9.53)

(3.62)

−0.45

−0.61

(3.76)

(4.20)

RBAR2

0.85

0.85

D.W.

1.92

1.97

t(LM)

0.04

0.18

ARCH

0.12

1.10

Output Private investment Private saving Other variables Money growth Expected inflation Net exports

effect on both short-run and medium-term interest rates. This can be due to the monetary effect of budget deficits in the short run. We shall examine this possibility later in this section. Turning now to the effect of the other variables, we can observe that output has exerted a significant and positive long-run effect on both interest rates. This can be due to the effect of changes in output on the level of investment-type expenditures in the long run. Government consumption seems to have a positive and significant short-term effect on both interest rates. Government consumption also shows a positive and significant long-term effect on the medium-term interest rate. Monetary growth does not seem to have exerted any influence on interest rates. Expected rate of inflation has had a positive and significant effect on both interest rates. Finally, net exports are found to have a negative and significant influence on interest rates, perhaps reflecting their short-term monetary effect. The above results suggest that budget deficits have only exerted a long-term influence on short-run interest rates in Italy. However, in the short run, deficits have had a negative and significant influence on both rates. It appears that while the long-term effect provides support for the neoclassical proposition concerning the effect of deficits on interest rates, the short-run impact is consistent with the Keynesian model in which deficits are, at least

Budget deficits and interest rates: The evidence

185

partially, monetized. To examine the possibility of this relationship between the deficit and money supply in Italy, we decomposed the variance of money supply to variation that is explained by innovations in money and the part that is explained by innovations in deficit. Table 7.12 presents the results. Table 7.12 shows that innovations in budget deficit have been responsible for about 25 per cent of the variance of money supply after 8 quarters. As time horizon lengthens, the percentage of variance of money explained by innovations in deficit increases. At 24quarter forecast horizon, about 50 per cent of the variance of money is explained by innovations in deficit. Therefore, the results presented in Table 7.12 provide support for the proposition that money supply in Italy has been sensitive to innovations in deficit. Since the long-term and short-run effects of budget deficits on interest rates in Italy are of opposite signs, it would be interesting to examine their net impact on interest rates in Italy. For this, we have estimated the forecasts of both interest rates conditional upon budget deficits to be identical to zero. Figures 7.13 and 7.14 compare the actual, fitted and conditional forecasts of interest rates during the

Table 7.12 Mean values of actual, fitted and conditional forecast of interest rates in Italy Nominal interest rates

1973:1–1979:4

1980:1–1990:4

Actual

12.38

14.72

Fitted

12.78

14.29

Conditional forecast

11.74

11.92

H0: fitted=forecast

1.04

2.37

(13.77)

(18.53)

0.64

2.80

(2.64)

(17.64)

Actual

11.78

14.39

Fitted

12.23

14.00

Conditional forecast

12.71

14.76

H0: fitted=forecast

−0.47

−0.76

(1.52)

(1.01)

−0.92

−0.37

(0.97)

(1.07)

Short-run interest rates

H0: actual=forecast Medium-term interest rates

H0: actual=forecast

Interest rates and budget deficits

186

Figure 7.13 Actual, fitted and conditional forecast of short-run interest rate: Italy

Figure 7.14 Actual, fitted and conditional forecast of medium-term interest rate: Italy 1973:1 to 1990:4 period for which deficit figures are available.

Budget deficits and interest rates: The evidence

187

Figure 7.13 shows that the actual and fitted values of the short-run interest rate are very close. We can observe that the conditional forecasts of interest rates are very close to the actual values during the 1970s. However, during the 1980s, the conditional forecasts of short-term interest rates are uniformly below the actual and fitted values. This suggests that budget deficits have had a positive influence on short-run rates in Italy during the 1980s. Figure 7.14 demonstrates that the actual, fitted and conditional forecasts of mediumterm interest rates in Italy are very close to each other. In some circumstances the shortrun negative impact of budget deficits have caused the conditional forecast of mediumterm interest rates to be slightly higher than the actual rates. To obtain a quantitative estimate of the extent of the effect of budget deficits on interest rates in Italy, we can compare the mean values of the conditional forecasts of interest rates with the mean values of the actual and fitted interest rates. This is done in Table 7.13. Concentrating on the short-run interest rate, Table 7.13 shows that, during the 1970s, the conditional forecast of interest rates has been 1.04 per cent lower than the fitted values and 0.64 per cent

Table 7.13 Decomposition of the variance of money supply in Italy Forecast horizon (quarters)

Money supply

Nominal deficit

1

100.00

0.00

4

83.66

16.34

8

74.92

25.08

12

64.88

35.12

16

57.88

42.12

20

53.39

46.61

24

50.21

49.79

lower than the actual values. During the 1980s, the gap between the actual and fitted values and the conditional forecasts increases to 2.80 per cent and 2.37 per cent, respectively. The null hypotheses that the mean values of the actual and fitted short-term interest rates are significantly higher than the conditional forecast cannot be rejected. This implies that the short-term interest rates would have been lower in Italy, in the absence of the deficit. As far as the effect of budget deficits on the medium-term interest rates are concerned, Table 7.13 shows that the conditional forecasts are, in some cases, above the actual and fitted interest rates, emphasizing the short-term negative impact of deficits on medium-term rates in Italy. However, the hypotheses that the means of the actual and fitted interest rates are different from the conditional forecasts are strongly rejected. This implies that deficits have not influenced the medium-term interest rates in Italy.

Interest rates and budget deficits

188

Japan Table 7.14 presents the results of applying the instrumental variable method to equation (19) for Japan. Concentrating on the effect of budget deficit, we can observe that deficits have had no long-term impact on either interest rates in Japan. In the short run, budget deficits have had a negative and significant effect on short-run interest rate, but have not shown any significant influence on medium-term interest rate. The above results support the Ricardian equivalence hypothesis suggesting that deficits have had no long-term impact on interest rates in Japan. Turning to the effect of other variables, we can observe that government expenditure has exerted no short-term or long-term

Table 7.14 Instrumental variable estimation: Japan Variables Constant

Short-run interest rate

Medium-run interest rate

10.55

10.15

(5.66)

(3.21)

−0.25

0.11

(0.77)

(1.11)

0.11

0.98

(0.13)

(2.05)

0.24

−0.11

(1.11)

(1.00)

−0.01

−0.12

(0.40)

(2.15)

−0.05

0.01

(0.75)

(0.10)

−0.23

−0.10

(2.41)

(1.49)

0.06

0.18

(0.23)

(1.57)

2.54

1.34

(3.98)

(3.38)

0.02

0.12

(0.40)

(1.54)

Long-run effects Government expenditures Government consumption Deficit Output Change in output Short-run effects Deficit Government expenditures Government consumption Output

Budget deficits and interest rates: The evidence

Private investment

189

0.05

0.02

(0.43)

(1.21)

0.03

−0.02

(0.43)

(0.50)

−0.24

−0.08

(2.83)

(1.54)

−0.01

0.07

(0.04)

(0.90)

−0.03

−0.15

(0.28)

(2.73)

RBAR2

0.81

0.90

D.W.

1.98

2.06

t(LM)

0.12

0.21

ARCH

0.07

0.10

Private saving Other variables Money growth Expected inflation Net exports

influence on either interest rates. Government consumption spending has shown a positive long-run impact only on medium-term interest rates. In the short run, government spending has had a positive and significant impact on both rates. Monetary growth has been negatively related to both interest rates. Output has shown to have a negative long-run impact on medium-term interest rates reflecting its role in the saving function. Finally, net exports have shown a negative and significant effect on the medium-term interest rates reflecting their short-term monetary impacts. To further examine the effect of budget deficit on interest rates, we estimated the conditional forecasts of interest rates in the absence of the deficits. Figures 7.15 and 7.16 compare these forecasts with the actual and fitted values of both interest rates during the period under study. Figures 7.15 and 7.16 show that the actual and fitted values of both interest rates are very close to each other. We can also see that the conditional forecast of interest rate has been very close to the actual and fitted rates during the entire period of 1970–90. Finally, to measure the extent of the effect of deficits on interest rates in Japan, Table 7.15 compares the mean values of the conditional forecast of interest rates with the mean values of actual and fitted rates during the two sub-periods of the 1970s and 1980s.

Interest rates and budget deficits

190

Figure 7.15 Actual, fitted and conditional forecast of short-run interest rate: Japan

Figure 7.16 Actual, fitted and conditional forecast of medium-term interest rate: Japan

Budget deficits and interest rates: The evidence

191

Table 7.15 Mean values of actual, fitted and conditional forecast of interest rates in Japan Nominal interest rates

1970:1–1979:4

1980:1–1990:4

Actual

7.25

5.93

Fitted

7.31

5.90

Conditional forecast

7.42

5.71

H0: fitted=forecast

−0.11

0.19

(1.40)

(1.54)

−0.17

0.22

(1.44)

(2.50)

Actual

7.67

6.58

Fitted

7.66

6.60

Conditional forecast

8.02

6.41

H0: actual=forecast

−0.36

0.19

(1.74)

(1.20)

−0.34

0.17

(1.37)

(1.29)

Short-run interest rates

H0: actual=forecast Medium-term interest rates

H0: actual=forecast

Table 7.15 shows that the mean values of actual and fitted interest rates are very close to the means of the forecasted interest rates. Tests of the hypotheses that the mean of the actual and fitted values are identical to the mean of the conditional forecasts cannot be rejected in all except for one case. In the case of the short-run interest rate during the 1980s, the mean of the conditional forecast is significantly below the mean of the actual interest rate. The Netherlands Except for government expenditures, deficits and output, quarterly data on other series for the Netherlands were only available for the post-1977:1 period. Therefore, our estimation procedure for the Netherlands covers the period 1977:1 to 1990:4. Table 7.16 presents the results of applying the instrumental variable method using the instruments outlined on pages 182–4 to equation (19). The diagnostic tests reported in the last three rows of Table 7.16 show that the estimated equations do not suffer from autocorrelation or heteroscedasticity and thus can be used for making statistical inferences. Concentrating on the effect of budget deficits, we can observe that deficits do not seem to have exerted any long-term or short-run effect

Interest rates and budget deficits

192

on either interest rates in the Netherlands. Therefore, it appears that for the case of the Netherlands the data support the Ricardian equivalence hypothesis. Government expenditures have only had a negative and significant short-term impact on medium-term interest rates. Government consumption has had a positive and significant long-term effect on both interest rates. It should be noted that the effect of government consumption on the medium-term interest rate has been more significant but much smaller in size than the effect on the short-run interest rate. Monetary growth has not influenced either rates. Expected rate of inflation is found to have a positive and highly significant effect on both interest rates. Real output is found to have a long-term positive and significant impact on interest rates. This can be due to the effect of real output on investment in the Netherlands. Change in output has exerted a positive and significant influence on short-term interest rates due to its role in the investment function. Net exports are found to have a positive effect on both interest rates. However, the effect of net exports on the medium-term interest rate has been larger and more significant than the effect on the short-run interest rate. The positive effects of net

Table 7.16 Instrumental variable estimation: the Netherlands Variables Constant

Short-run interest rate

Medium-run interest rate

−28.64

−6.31

(3.30)

(1.19)

0.08

−0.08

(0.60)

(0.96)

0.36

0.18

(1.86)

(2.03)

−0.17

0.06

(1.72)

(1.44)

0.12

0.03

(4.34)

(2.01)

0.03

0.01

(2.18)

(0.44)

0.10

0.01

(1.62)

(0.35)

−0.10

−0.33

(1.18)

(2.97)

Long-run effects Government expenditures Government consumption Deficit Output Change in output Short-run effects Deficit Government expenditures

Budget deficits and interest rates: The evidence

Government consumption

193

−0.28

0.09

(1.14)

(0.58)

−0.03

0.01

(1.73)

(0.65)

−0.38

−0.43

(2.18)

(4.04)

−0.07

−0.06

(1.29)

(1.80)

−0.01

−0.07

(1.20)

(1.67)

1.84

1.38

(2.11)

(2.60)

0.12

0.16

(1.65)

(3.15)

RBAR2

0.72

0.80

D.W.

1.94

1.98

t(LM)

0.45

0.76

ARCH

0.04

0.17

Output Private investment Private saving Other variables Money growth Expected inflation Net exports

exports are due to their impact on the level of investment-type expenditures in the Netherlands. The above results suggest that deficits cannot explain the variability of interest rates in the Netherlands. As a final test of the relationship between deficits and interest rates in the Netherlands, we have estimated the forecasts of interest rates conditional upon budget deficits being identical to zero. Figures 7.17 and 7.18 present and compare the actual, fitted and conditional forecasts of short-run and medium-term interest rates in the Netherlands. As expected from the regression results, Figures 7.17 and 7.18 show that the forecasts of both interest rates conditional upon deficits being zero are not very different from their actual and fitted values. This confirms our above findings suggesting that deficits do not seem to have been responsible for the variation of interest rates in the Netherlands. To obtain a quantitative estimate of the difference between the conditional forecasts and actual and fitted values of interest rates, we have calculated their mean values during the two sub-periods of the 1970s and 1980s and presented them in Table 7.17. Table 7.17 shows that the mean values of the actual and fitted interest rates are relatively close to the mean values of the conditional forecasts. Tests of the hypotheses that the actual and fitted

Interest rates and budget deficits

194

Figure 7.17 Actual, fitted and conditional forecast of short-run interest rate: the Netherlands

Figure 7.18 Actual, fitted and conditional forecast of medium-term interest rate: the Netherlands

Budget deficits and interest rates: The evidence

195

Table 7.17 Mean values of actual, fitted and conditional forecast of interest rates in the Netherlands Nominal interest rates

1977:1–1979:4

1980:1–1990:4

Actual

7.64

7.03

Fitted

7.71

7.02

Conditional forecast

8.29

8.00

H0: fitted=forecast

−0.58

−0.98

(1.09)

(1.76)

−0.65

−0.97

(1.55)

(1.49)

Actual

7.98

8.19

Fitted

8.19

8.15

Conditional forecast

7.91

7.77

H0: fitted=forecast

0.27

0.39

(1.50)

(1.48)

0.06

0.42

(0.20)

(1.26)

Short-run interest rates

H0: actual=forecast Medium-term interest rates

H0: actual=forecast

values are different from the conditional forecasts cannot be rejected for both interest rates supporting our above findings that deficits have not influenced interest rates in the Netherlands. Sweden Table 7.18 presents the results of estimating equation (19) for Sweden using the instrumental variable method. Table 7.18 shows that the estimated equations do not suffer from autocorrelation or heteroscedasticity. Concentrating on the effect of budget deficit, we can observe that deficits have had a positive and significant long-term impact on both interest rates. However, the impact on the medium-term rate has been numerically smaller than that for the short-run rate. In the short term, deficits have not influenced either rates in Sweden. The above results provide strong support for the neoclassical proposition that deficits have a long-term positive influence on interest rates. Considering the effects of other variables, we can see that, in the long run, government expenditure has had a positive and significant impact on both interest rates. In the short

Interest rates and budget deficits

196

run, government spending has shown a negative and significant influence on the shortterm interest rates while leaving the medium-term rates unaffected. In the short run, government consumption has had a positive and significant influence on the short-run interest rates. Money growth has exerted a negative and significant effect on both rates. Inflationary expectations have not influenced interest rates in Sweden. Finally, net exports have shown a negative and significant influence on the short-run interest rates in Sweden. Since deficits have influenced interest rates in Sweden, it would be interesting to compare the actual and fitted values of both rates with their forecasts conditional upon the value of deficit being equal to zero. Figures 7.19 and 7.20 present this comparison. Figure 7.19 shows that the actual and estimated short-run interest rates are very close to each other. However, the conditional forecast is significantly below the actual and fitted values, especially during the 1977–87 period. Figure 7.20 shows that the actual and fitted values of the medium-term interest rates are very close to each other. The conditional forecast of the medium-term rate is also very close to the actual and fitted values except for the period of 1977–87 when the forecast values fall short of the other rates, suggesting that the interest rates would have been lower in the absence of the deficit.

Table 7.18 Instrumental variable estimation: Sweden Variables Constant

Short-run interest rate

Medium-run interest rate

2.01

4.32

(0.37)

(1.05)

0.12

0.60

(4.70)

(2.32)

−0.24

0.06

(1.50)

(1.13)

0.11

0.02

(4.19)

(1.90)

0.03

−0.02

(1.53)

(0.17)

0.09

0.01

(2.11)

(0.33)

−0.05

−0.02

(1.66)

(1.00)

Long-run effects Government expenditures Government consumption Deficit Output Change in output Short-run effects Deficit

Budget deficits and interest rates: The evidence

Government expenditures

197

−0.10

0.01

(3.57)

(0.57)

0.34

0.07

(3.40)

(0.94)

−0.12

−0.01

(3.24)

(0.48)

−0.01

−0.06

(3.13)

(1.89)

0.02

0.05

(4.15)

(1.75)

−0.17

−0.12

(3.06)

(2.96)

0.08

−0.10

(0.54)

(0.82)

−0.15

−0.03

(4.86)

(1.46)

RBAR2

0.94

0.95

D.W.

2.09

2.09

t(LM)

1.21

1.19

ARCH

0.37

0.45

Government consumption Output Private investment Private saving Other variables Money growth Expected inflation Net exports

Interest rates and budget deficits

198

Figure 7.19 Actual, fitted and conditional forecast of short-run interest rate: Sweden

Figure 7.20 Actual, fitted and conditional forecast of medium-term interest rate: Sweden

Budget deficits and interest rates: The evidence

199

Table 7.19 Mean values of actual, fitted and conditional forecast of interest rates in Sweden Nominal interest rates

1970:1–1979:4

1980:1–1990:4

Actual

6.43

11.84

Fitted

6.49

11.79

Conditional forecast

4.78

8.74

H0: fitted=forecast

1.71

3.05

(3.95)

(2.24)

1.65

3.10

(4.05)

(2.24)

Actual

8.55

12.13

Fitted

8.53

12.13

Conditional forecast

8.34

11.53

H0: fitted=forecast

0.19

0.60

(3.05)

(2.81)

0.21

0.60

(2.09)

(2.28)

Short-run interest rates

H0: actual=forecast Medium-term interest rates

H0: actual=forecast

Considering the effect of deficits on short-run interest rates, Table 7.19 shows that, on average, the actual and the fitted short-run interest rates were about 1.7 per cent above the conditional forecast during the 1970s. During the 1980s, this difference increased to about 3 per cent. Tests of the hypotheses that the mean values of actual and fitted interest rates are above the conditional forecasts could not be rejected. Concentrating on the medium-term interest rates during the 1970s, we observe that the actual and fitted interest rates were about 0.2 per cent higher than the conditional forecast. This difference increased to about 0.6 per cent during the 1980s. However, tests of the hypotheses that the means of the conditional forecast were significantly below the actual and fitted rates could not be rejected. These results provide further support for our above findings that deficits have positively influenced both rates in Sweden. United Kingdom Table 7.20 presents the results of applying the instrumental variable method discussed above to equation (19) using the U.K. data. Diagnostic tests reported in the last three rows of Table 7.20 show that the regression equations are well specified and do not suffer

Interest rates and budget deficits

200

Table 7.20 Instrumental variable estimation: U.K. Variables Constant

Short-run interest rate

Medium-run interest rate

−7.53

−0.20

(6.34)

(0.20)

0.05

0.04

(3.22)

(3.13)

−1.59

−0.60

(1.32)

(1.53)

0.16

0.17

(2.67)

(3.24)

0.07

0.01

(6.61)

(0.99)

−0.03

−0.01

(1.47)

(0.47)

−0.29

−0.24

(4.14)

(4.04)

−0.04

−0.02

(2.44)

(1.38)

1.77

0.08

(4.46)

(0.21)

−0.02

0.01

(1.11)

(0.75)

−0.32

−0.18

(2.01)

(1.13)

0.01

0.02

(0.11)

(0.23)

−0.01

−0.02

(0.91)

(2.31)

2.56

1.69

Long-run effects Government expenditures Government consumption Deficit Output Change in output Short-run effects Deficit Government expenditures Government consumption Output Private investment Private saving Other variables Money growth Expected inflation

Budget deficits and interest rates: The evidence

201

(10.32)

(7.43)

0.22

0.11

(2.05)

(0.98)

RBAR2

0.80

0.73

D.W.

1.94

1.96

t(LM)

0.23

0.37

ARCH

0.06

0.92

Net exports

from autocorrelation or heteroscedasticity. The results can therefore be used to make statistical inferences. Concentrating on the long-run effect of deficits on interest rates, we observe that budget deficits have had a positive and significant influence on both shortand medium-term interest rates. In the short run, however, the effect of budget deficits on both interest rates has been negative and significant. We can therefore argue that the long-term positive effect of deficit on interest rates in the U.K. provides support for the neoclassical proposition. The negative short-run impact of deficits on interest rates is consistent with the Keynesian model in which a part of the deficit is monetized. In terms of the magnitude of the effects, we tested the hypotheses that the short-run and long-run effects of budget deficits on both short-term and medium-term rates are of equal and opposite signs. Both hypotheses were accepted at 5 per cent level, suggesting that the negative short-run effects of budget deficits may cancel their positive long-term impacts on both interest rates. Turning now to the discussion of other variables, we can observe that government expenditures have had a positive and significant long-term impact on both interest rates. In the short run, government spending has had a negative impact on the short-run interest rate. Government consumption has shown a positive short-term impact on the short-run interest rate. Real output has had a positive and significant long-term impact on the shortrun interest rate. Growth of money has exerted a negative and significant impact on the medium-term interest rate. Inflationary expectations have had a positive and highly significant impact on both rates. Net exports have had a positive and significant impact on the short-run interest rate. As mentioned above, the negative short-run impact of deficits on interest rates can be due to the short-run impact of deficits on money supply. To examine the possibility of deficits affecting money supply in the short run, we decomposed the variance of money into the variation that is explained by innovations in money and those explained by innovations in deficit. As was the case in our earlier decompositions, we introduced eight lags of each variable and tested the hypothesis that all lagged values of deficit in money equations are identical to zero. This hypothesis was strongly rejected by the data. Table 7.21 presents the decomposition results. Table 7.21 shows that response of money supply to deficit reaches its maximum after 4 quarters and declines thereafter. At the

Interest rates and budget deficits

202

Table 7.21 Decomposition of the variance of money supply in the U.K. Forecast horizon (quarters)

Money supply

Nominal deficit

1

100.00

0.00

4

84.45

15.54

8

85.11

14.89

12

88.00

12.00

16

88.75

11.25

20

89.14

10.86

24

89.12

10.88

4-quarter forecast horizon, innovations in deficit explain about 16 per cent of the variance of money supply. This short-run response of money supply to deficit can be responsible for the negative short-run impact of deficits on interest rates in the U.K. Finally, as an additional test of the impact of budget deficits on interest rates in the U.K., we estimated the forecasts of interest rates conditional upon budget deficits being identical to zero. Figures 7.21 and 7.22 compare these conditional forecasts with their actual and fitted values. Figures 7.21 and 7.22 show that the conditional forecasts are very close to the actual and fitted values during the entire period of

Figure 7.21 Actual, fitted and conditional forecast of short-run interest rate: U.K.

Budget deficits and interest rates: The evidence

203

Figure 7.22 Actual, fitted and conditional forecast of medium-term interest rate: U.K. 1970–90. It appears that the positive long-term impacts of deficits on interest rates are, to a large extent, offset by their negative short-run effects resulting in a conditional forecast that is very close to the fitted and actual interest rates. Finally, it is useful to compare the numerical values of the mean of the interest rates in the absence of budget deficits with the actual rates during the two sub-periods of the 1970s and 1980s. This is done in Table 7.22. Table 7.22 shows that the mean of the conditional forecasts are slightly below the fitted values for both interest rates during the 1970s and 1980s. Tests of the hypotheses that the mean of the interest rates in the absence of deficits would have been lower than their fitted values cannot be rejected. Similarly, the conditional forecasts of interest rates are significantly smaller than the actual rates during the 1980s. We can therefore conclude that even though the positive long-term and negative short-term impacts of deficits on interest rates have, to a large extent, cancelled each other out, the conditional forecasts of interest rates are statistically significantly below the actual and fitted interest rates, especially during the 1980s. In other words, both interest rates would have been marginally lower in the absence of the deficits. United States of America As we mentioned above, in estimating equation (19) for the United States, we encountered some residual autocorrelation. Therefore, we adopted a two-step procedure of first estimating the autocorrelation coefficient and then estimating the reduced-form equation (19). Using the two-step procedure with the principal components described above still revealed some residual autocorrelation. Careful inspection of the residuals and the graphs of the actual and fitted values of interest rates revealed that the residual

Interest rates and budget deficits

204

Table 7.22 Mean values of actual, fitted and conditional forecast of interest rates in the U.K. Nominal interest rates

1970:1–1979:4

1980:1–1990:4

Actual

8.93

11.56

Fitted

9.47

11.30

Conditional forecast

9.19

10.87

H0: fitted=forecast

0.28

0.43

(2.30)

(4.00)

−0.26

0.69

(1.29)

(3.65)

Actual

10.29

11.52

Fitted

10.63

11.28

Conditional forecast

10.30

10.87

H0: fitted=forecast

0.33

0.42

(2.84)

(4.35)

−0.02

0.65

(0.10)

(3.37)

Short-run interest rates

H0: actual=forecast Medium-term interest rates

H0: actual=forecast

autocorrelation might be the result of a possible structural break in the interest rates some time after 1979, not captured by the estimated equation. Such a break has been reported earlier: see for example, Antoncic (1986) and Gupta and Moazzami (1991a). In order to investigate this possibility, we first estimated equation (19) for the period 1968–79 and then estimated it by adding 4 quarters at a time. We observed some parameter instability after 1979. This instability was further supported by the predictive Chow test which examined the possibility of a structural break anywhere between 1979:1 and 1981:4. We found that the data supported the presence of a structural break at 1981:2. Consequently, in our final regression, we employed a dummy variable which took the values of zero from 1968:1 to 1981:2 and unity thereafter. In estimating the equation for the U.S.A., we employed two measures of deficit. First is the deficit based on the national accounts published by the International Financial Statistics and the other is the actual federal deficit published by the Department of Commerce in the Survey of Current Business. Table 7.23 presents the estimation results for the U.S.A. The diagnostic testing showed that the estimated equations are well specified and can be used for statistical inference. Table 7.23 shows that the overall estimation results based on two measures of deficits are very close. This suggests that our conclusions are robust with respect to the measure of budget deficit used.

Budget deficits and interest rates: The evidence

205

Concentrating on the effect of budget deficit, we can observe that deficits have had a positive and significant long-term impact on medium-term interest rates. However, they have not influenced the short-run interest rates in the long run. In the short run, deficits have exerted a negative and significant influence on medium-term interest rates. The short-term effect of deficits on short-run interest rates depends on the definition of the deficit used. Only in the case of equations with real actual federal deficits is the shortterm impact negative and significant. Therefore, the above results provide support for the neoclassical proposition only when we consider the effect of deficits on medium-term interest rates. The short-term negative impact of deficits on interest rates is consistent with a Keynesian equation in which a part of deficit is monetized in the short run. We will examine this possibility later in this section. Turning to the effects of other variables, we can observe that government expenditure has exerted a positive and significant long-term impact on both interest rates. In the short term, however, government spending has not influenced either rate. Government consumption spending has shown no long-run or short-run impact on either interest rates. Real output has exerted a positive and significant long-term influence on both interest rates. Monetary growth has been negatively related to both interest rates. Inflationary expectations have had a positive and highly significant impact on both interest rates. Finally, net exports have shown a negative and significant effect on both interest rates, reflecting their short-term monetary impacts. We mentioned above that the short-run negative influence of deficits on interest rates is consistent with a Keynesian equation in which deficits are partly monetized. To investigate this possibility,

Table 7.23 Instrumental variable estimation: U.S.A Variables Constant

Short-run interest rate*

Short-run interest rate**

Medium-term interest rate*

Medium-term interest rate**

10.59

12.06

11.71

13.78

(3.04)

(3.35)

(3.80)

(4.24)

0.16

0.16

0.19

0.22

(3.01)

(3.20)

(4.02)

(4.79)

−0.27

−0.05

0.04

0.05

(0.41)

(0.71)

(0.67)

(0.86)

0.01

0.01

0.04

0.03

(0.05)

(0.51)

(2.33)

(2.18)

0.01

0.01

0.01

0.01

(2.69)

(3.07)

(2.08)

(2.33)

0.03

0.01

0.01

0.01

(0.85)

(0.89)

(1.21)

(1.40)

Long-run effects Government expenditures Government consumption Deficit Output Change in output

Interest rates and budget deficits

206

Short-run effects Deficit

−0.06

−0.01

−0.05

−0.01

(2.11)

(1.02)

(1.95)

(2.21)

0.02

−0.03

0.02

0.05

(0.19)

(0.33)

(0.22)

(0.66)

0.01

0.02

−0.02

−0.03

(0.12)

(0.33)

(0.35)

(0.43)

−0.02

−0.01

−0.03

−0.01

(0.52)

(0.17)

(0.95)

(1.47)

−0.04

−0.05

0.01

−0.02

(1.60)

(2.04)

(0.29)

(1.00)

0.01

0.01

0.01

0.02

(0.93)

(0.64)

(1.26)

(1.80)

−0.01

−0.01

−0.02

−0.05

(1.19)

(1.39)

(1.94)

(1.74)

3.82

3.79

3.03

2.64

(7.76)

(8.33)

(6.98)

(6.43)

−0.10

−0.10

−0.09

−0.09

(3.64)

(3.92)

(3.61)

(3.66)

5.16

5.17

5.37

5.66

(9.00)

(9.25)

(10.58)

(11.22)

RBAR2

0.86

0.86

0.87

0.86

D.W.

1.99

1.98

1.94

2.03

t(LM)

0.21

0.27

0.33

0.36

ARCH

0.08

0.65

0.21

0.18

Government expenditures Government consumption Output Private investment Private saving Other variables Money growth Expected inflation Net exports Dummy (1981:2)

*Equation with real actual federal deficit. **Equation with national account measure of real deficit.

we examined the effect of deficits on money supply using the innovation accounting technique discussed earlier, using eight lags of each variable in the regression equations. More specifically, we examine the percentage of variance of money supply that is explained by innovations in either definition of deficits. In terms of the significance of deficit variables in money equations, we found that the null hypothesis that all lagged values of deficits in money equations have zero coefficient were strongly rejected. Table

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207

7.24 presents the results of decomposing the variance of money supply using different measures of deficit. Let us first concentrate on the results of decomposition using the national account definition of deficit reported in the second column of Table 7.24. We can observe that after 4 quarters, about 23 per cent of the variance of money supply is explained by innovations in the budget deficit. As forecast horizon lengthens the percentage of variance of money explained by innovations in deficit increases. At 24-quarter forecast horizon, about 67 per cent of the variance in money supply is explained by innovations in deficit. The third column of Table 7.24 shows the decomposition result using the actual federal deficit. We can observe a similar pattern of increasing variance of money supply explained by innovations in budget deficit. In general, the percentage of variance of money explained by innovations in federal deficits is slightly higher than that explained by the national account deficit at all forecast horizons. We can therefore conclude that deficits have been responsible for a significant part of the variance of money supply in the U.S.A. This result is consistent with our above findings that deficits have exerted a negative and significant short-term impact on interest rates in the U.S.A.

Table 7.24 Decomposition of the variance of money supply in the U.S.A. Forecast horizon (quarters)

National account deficit

Nominal actual federal deficit

1

0.00

0.00

4

9.37

7.78

8

23.23

30.36

12

40.03

50.33

16

53.48

62.81

20

62.01

70.00

24

67.18

74.31

Given our above findings that deficits have influenced both interest rates in the U.S.A., it would be interesting to compare the level of interest rates in the absence of the deficits with the actual rates during the period under study. Figures 7.23 and 7.24 provide such comparison based on the equation using the real actual federal deficit. Figures 7.25 and 7.26 provide the comparison for both rates based on the equation using the real national account definition of deficit. Figures 7.23 and 7.24 show that the actual, fitted and conditional forecasts of short-run interest rates are remarkably close to each other. On the other hand, the conditional forecasts of the medium-term interest rate have been below the actual and the fitted rates, especially during the 1980s. This picture does not change when we consider Figures 7.25 and 7.26. Again the conditional forecast of the medium-term interest rate is clearly below the actual and fitted values, especially during the 1980s. Finally, it would be interesting to quantitatively assess the effect of budget deficits on interest rates during the two sub-periods of the 1970s and 1980s. Table 7.25 presents and

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208

compares the mean of the actual and fitted interest rates with their conditional forecasts during these sub-periods. Considering the short-run interest rate, we can observe that the

Figure 7.23 Actual, fitted and conditional forecast of short-run interest rate (real actual federal deficits): U.S.A.

Figure 7.24 Actual, fitted and conditional forecast of medium-term interest rate (real actual federal deficits): U.S.A.

Budget deficits and interest rates: The evidence

209

Figure 7.25 Actual, fitted and conditional forecast of short-run interest rate (real national income deficits): U.S.A.

Figure 7.26 Actual, fitted and conditional forecast of medium-term interest rate (real national income deficit): U.S.A.

Interest rates and budget deficits

210

mean of the actual and fitted interest rates are very close to the means of their conditional forecasts. Using the real actual federal deficits, we cannot reject the hypotheses that the mean of the actual and fitted values are equal to their conditional forecasts during both sub-periods. However, using the national account measure of deficit, we can reject the above hypotheses in favour of the alternatives that the mean of the conditional forecast is significantly smaller than the mean of the actual and fitted rates. We have to note that the magnitude of the difference between the mean of the conditional short-run rate and the actual and fitted ones, even though statistically significant, is very small. Turning now to the impact of deficits on the medium-term interest rates, we observe that, irrespective of the measure of deficit used, the conditional forecasts are significantly below the actual and fitted values during both periods. It has to be noted that the difference between the rates is much greater during the 1980s as compared to the 1970s. We can therefore conclude that deficits have had a positive influence on interest rates in the U.S.A.

Table 7.25 Mean values of actual, fitted and conditional forecast of interest rates in the U.S.A. Nominal interest rates

1970:1– 1979:4*

1970:1– 1979:4**

1980:1– 1990:4*

1980:1– 1990:4**

Actual

6.29

6.29

8.74

8.74

Fitted

6.50

6.50

8.57

8.57

Conditional forecast

6.49

6.39

8.54

8.28

H0: fitted=forecast

0.01

0.11

0.02

0.29

(0.28)

(3.61)

(0.56)

(8.28)

−0.20

−0.10

0.10

0.46

(1.66)

(0.79)

(1.26)

(3.04)

Actual

7.27

7.27

10.22

10.22

Fitted

7.47

7.49

10.06

10.04

Conditional forecast

6.94

7.04

8.63

8.97

H0: fitted=forecast

0.53

0.45

1.43

1.08

(7.15)

(8.96)

(18.50)

(17.71)

0.32

0.23

1.60

1.26

(2.25)

(1.63)

(13.83)

(11.12)

Short-run interest rates

H0: actual=forecast Medium-term interest rates

H0: actual=forecast

*Equation with real actual federal deficit. **Equation with national account measure of real deficit.

Budget deficits and interest rates: The evidence

211

SUMMARY AND CONCLUSION The main objective of this chapter has been to examine the effect of budget deficits on short- and medium-term interest rates in eleven developed countries. For this purpose we developed a model in Chapter 6 that identifies the major determinants of nominal interest rates and estimated it for all the countries included in our study. An important feature of our model is that it distinguishes between the long-run or permanent effect of budget deficits and other interest rate determinants as distinct from their short-run or transitory impacts. Distinguishing between the long-run and short-run impacts of budget deficits enabled us to directly test the predictions of the three alternative paradigms, namely the Keynesian, neoclassical and Ricardian equivalence, concerning the long-term and shortterm impacts of deficits on interest rates. In addition to examining the impacts of deficits, we also investigated the effect of a number of other important variables such as money supply, inflationary expectations, real output and trade balance on interest rates. In this summary, we briefly summarize our findings in this chapter. Turning first to the discussion of budget deficit, which is the main focus of this chapter, Table 7.26 summarizes the impacts of deficits on short-run interest rates and also shows the acceptance or rejection of the predictions of the alternative paradigms. Table 7.26 shows that deficits have had a positive and significant long-term impact on short-run interest rates in Belgium, Canada, Italy, Sweden and the U.K. Therefore, for these countries data support the prediction of the neoclassical paradigm. For Australia, France, Germany, Japan, the Netherlands and the U.S.A. deficits do not seem to have exerted any long-term impact on short-run interest rates. Thus, for these countries the data support the Ricardian equivalence hypothesis. Considering the short-term impact of budget deficits, we can observe that deficits have exerted a positive and significant impact on short-run interest rates in Canada and France. For these two countries, therefore, data provide support for the prediction of the Keynesian paradigm. For Italy, Japan, the U.K. and the U.S.A. deficits have had a negative and significant short-term influence on short-run interest rates. The short-run negative impact of deficits on short-run interest rates is consistent with a Keynesian equation in which a part of deficits is monetized. We investigated this possibility for Italy, the U.K. and the U.S.A. and found that deficits

Table 7.26 Impact of deficits on short-run interest rates Country

Long-term effect

Short-run effect

Ricardian equivalence

Australia

No

No

OK

–

–

Belgium

Positive

No

–

OK

–

Canada

Positive

Positive

–

OK

OK

France

No

Positive

OK

–

OK

Germany

No

No

OK

–

–

Positive

Negative

–

OK

–

Italy

Neoclassical Keynesian

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212

Japan

No

Negative

OK

–

–

Netherlands

No

No

OK

–

–

Sweden

Positive

No

–

OK

–

U.K.

Positive

Negative

–

OK

–

U.S.A.*

No

Negative

OK

–

–

U.S.A.**

No

No

OK

–

–

*Real actual federal deficit. **National account measure of real deficit.

have exerted a significant short-term influence on money supply in these countries. Finally, deficits have not had any short-term influence on short-run interest rates in Australia, Belgium, Germany and the Netherlands. Overall, we can observe that deficits have not had any short-term or long-term impacts on short-run interest rates in Australia, Germany and the Netherlands. On the other hand, Canada is the only country for which deficits have had a positive short-term and longterm effect on short-run interest rates. Table 7.27 presents the impact of deficits on medium-term interest rates in the eleven countries. This table shows that deficits have exerted a positive and significant long-term impact on medium-term interest rates in Belgium, Canada, Sweden, the U.K. and the U.S.A. Therefore, for these countries our findings are consistent with the neoclassical predictions. At the same time, deficits have not had any long-term influence on mediumterm interest rates for Australia, France, Germany, Italy, Japan and the Netherlands. For these countries data support the Ricardian equivalence hypothesis. Considering the short-term effect, deficits have not had any short-term influence on medium-term interest rates in Australia, Belgium, France, Germany, Japan, the Netherlands and Sweden. In Canada, deficits have positively influenced medium-term interest rates even in the short run. For Italy, the U.K. and the U.S.A., deficits have had a negative short-term impact on medium-term interest rates. As we mentioned above, the negative effect of budget deficits on interest rates can be caused by their short-term monetary effects. Overall, deficits have not exerted any long-term or short-term impacts on mediumterm interest rates in Australia, France, Germany, Japan and the Netherlands. On the other hand, deficits have positively influenced medium-term interest rates in Canada both in the short and long term. In addition to the effects of deficits on interest rates, we also examined the impacts of changes in a number of other variables on interest rates. Here, we summarize the effects of three of those variables, namely money growth, inflationary expectations and trade balance on both interest rates. Table 7.28 summarizes the effect of money growth, inflationary expectations and trade balance on short-term interest rates. Table 7.28 shows that money growth has had a negative and significant effect on short-term interest rates in Australia, France,

Budget deficits and interest rates: The evidence

213

Table 7.27 Impact of deficits on medium-term interest rates Country

Long-term effect

Short-run effect

Ricardian equivalence

Neoclassical Keynesian

Australia

No

No

OK

–

–

Belgium

Positive

No

–

OK

–

Canada

Positive

Positive

–

OK

OK

France

No

No

OK

–

–

Germany

No

No

OK

–

–

Italy

No

Negative

OK

–

–

Japan

No

No

OK

–

–

Netherlands

No

No

OK

–

–

Sweden

Positive

No

–

OK

–

U.K.

Positive

Negative

–

OK

–

U.S.A.*

Positive

Negative

–

OK

–

U.S.A.**

Positive

Negative

–

OK

–

*Real actual federal deficit. **National account measure of real deficit.

Germany, Japan and Sweden. Money growth had not influenced short-term interest rates in Belgium, Canada, Italy, the Netherlands, the U.K. and the U.S.A. The Fisher effect is highly significant for all of the countries except Belgium, Japan and Sweden. Trade balance has not influenced short-run interest rates in Japan and the Netherlands. For Canada and the U.K., trade balance has exerted a positive and significant influence on short-term interest rates. This positive influence of net exports on interest rates is due to the long-term impact of increase in investment-type expenditures in these countries. For the majority of these countries, however, trade balance has had a negative and significant influence on short-run interest rates. This negative impact of net exports on short-run interest rates reflects the initial monetary effect of a change in net exports. Table 7.29 presents the effects of money, inflation and net exports on medium-term interest rates. The table also shows that money growth has exerted a negative and significant influence on medium-term interest rates in Australia, Germany, Sweden, the U.K. and the U.S.A. The Fisher effect is positive and highly significant for all countries except for Japan and Sweden. Finally, net exports have shown a positive and significant influence on medium-term interest rates in Canada and the Netherlands. This, as we mentioned above, can be due to the long-term effects of net exports on investment-

Interest rates and budget deficits

214

Table 7.28 Impacts of money, inflation and trade balance on short-run interest rates Country

Money growth

Inflationary expectations

Trade balance

Australia

Negative

Positive

Negative

Belgium

–

–

Negative

Canada

–

Positive

Positive

France

Negative

Positive

Negative

Germany

Negative

Positive

Negative

Italy

–

Positive

Negative

Japan

Negative

–

–

–

Positive

–

Negative

–

Negative

U.K.

–

Positive

Positive

U.S.A.*

–

Positive

Negative

U.S.A.**

–

Positive

Negative

Netherlands Sweden

*Real actual federal deficit. **National account measure of real deficit.

type expenditures in these countries. For Germany, Sweden and the U.K., net exports have not influenced medium-term interest rates. For the rest of the countries, namely Australia, Belgium, France, Italy, Japan and the U.S.A., net exports have had a negative and significant influence on medium-term interest rates perhaps due to the short-run monetary effects of changes in trade balances.

Table 7.29 Impacts of money, inflation and trade balance on medium-term interest rates Country

Money growth

Inflationary expectations

Trade balance

Australia

Negative

Positive

Negative

Belgium

–

Positive

Negative

Canada

–

Positive

Positive

France

–

Positive

Negative

Negative

Positive

–

–

Positive

Negative

Germany Italy

Budget deficits and interest rates: The evidence

215

Japan

–

–

Negative

Netherlands

–

Positive

Positive

Sweden

Negative

–

–

U.K.

Negative

Positive

–

U.S.A.*

Negative

Positive

Negative

U.S.A.**

Negative

Positive

Negative

*Real actual federal deficit. **National account measure of real deficit.

8 SOME LESSONS A number of useful general lessons can be drawn from this work. The first relates to the methodology used throughout. This has to do with modelling of the short-run versus the long-run aspects of the various relationships, be that the Fisher hypothesis, the equality of the interest rates across the countries or the effects of budget deficits and other variables. Careful modelling to capture this distinction has been shown to be of considerable importance in shedding light on the relevance of the alternate paradigms relating to the effects of budget deficits and the Fisher hypothesis, to take just two examples. Further, although the importance of analysing the time series properties of the underlying series is well recognized, it is nevertheless the case that in many studies relating to this topic, sufficient attention is not always paid. We have seen that an adequate treatment in this respect can help in designing appropriate specifications. Turning to the lessons from our empirical results, quite a few stand out. One of the most important ones is that despite the increases in the degree of integration of the financial and other markets of the developed countries, there are such marked differences in the behaviour of the nominal and real interest rates as to suggest that not only any grand generalizations would be hazardous but further that domestic factors require special attention for their determination. The significance of this observation stands out most glaringly when we consider the effects of three factors commonly cited as affecting them. These, of course, are liquidity, expected inflation, and budget deficits and debt. At the risk of repeating ourselves, it is best to summarize the main findings in the same order as those in the preceding chapters. Our study confirms the widespread belief that the ex-ante real interest rates were higher during the 1980s compared to the 1970s. In addition, the rates were lower in the second half of the 1980s than in the first half. This seemed to be the case both for the short as well as for the long rates. But the experience of the eleven countries differed widely, both in terms of the magnitudes of the rates as well as their variability. While significant linkages existed between the rates of the countries covered, complete equality did not exist except for two countries as far as the short rate was concerned. For the long rate this did not exist for any of the countries. This raises the obvious point that variations triggered by domestic factors played a crucial role in the observed behaviour of the rates. In terms of the validity of the Fisher hypothesis, it is found that the hypothesis is not robust, both across time and across the countries, regardless of the maturity of the asset involved. For example, using the short rate, we found that the hypothesis was rejected for all countries, except the U.K., Sweden and Belgium. In terms of the exogeneity of the two rates it was found that relative to a universe which included money, real output and the expected rate of inflation, the hypothesis of exogeneity of the short-term rate was rejected for France, Germany, Italy, Japan, the

Some lessons

217

Netherlands and the U.K. But even for the countries where the rate was Granger-causally prior, they responded to the contemporaneous components of the innovations in money, real output and expected inflation. The response to innovations in these variables sometimes lasted for more than 30 quarters. The exogeneity of the medium-term real rate, on the other hand, seemed to depend on the level of significance chosen and the time period under consideration. In addition to the evidence on exogeneity, we also found that innovations in real output, money and expected inflation explained some of the variance in the real rates. Of particular interest is the role of expected inflation. For the countries where the hypothesis of exogeneity was rejected, we found that innovations in expected inflation had a significant effect on the real rate. This was the case in France, Italy, Japan, the Netherlands and the U.K. Finally, we come to the most important findings from the policy point of view, namely, those relating to the role of budget deficits. We find that deficits had a positive and significant long-term effect on the short rates in five countries, namely, Belgium, Canada, Italy, Sweden and the U.K., thus supporting the neoclassical paradigm. For the other six countries, we find no such effect, thus supporting the Ricardian equivalence proposition. Considering the short-term impact of the deficits on the short rates, a positive and significant effect exists for Canada and France, and a negative and significant effect for Italy, Japan, the U.K. and the U.S.A. (the negative effect being due to the partial monetization of the deficit), thus supporting the Keynesian paradigm. On the whole, we find that deficits had no effect on the short rates, either in the long run or in the short run, in Australia, Germany and the Netherlands, thus supporting the Ricardian equivalence proposition. On the other hand, Canada is the only country in our sample where deficits have had a significant and positive effect both in the short and long term. As for the medium-term rates, deficits have not exerted any long-term or short-term impact in Australia, France, Germany, Japan and the Netherlands. On the other hand, once again, Canada is the only country in the sample where we find a positive and significant effect for the long and short term. As for the role of money growth, it had a negative and significant effect on the shortterm rates in Australia, France, Germany, Japan and Sweden, but no effect in Belgium, Canada, Italy, the Netherlands, the U.K. and the U.S.A. It also had the same effect on the medium-term rates in Australia, Germany, Sweden, the U.K. and the U.S.A. Finally, the Fisher effect, that is the effect of expected inflation, turned out to be significant for all countries except Belgium, Japan and Sweden for the short rate and for all but Japan and Sweden for the medium-term rate. Can we draw any general lessons from the above summary? Apart from the significance of our methodology pointed out above, the most important lesson is that it would be hazardous to treat all of the eleven countries as if they came from the same population. Even in terms of the most important policy question addressed here, namely, the effects of the budget deficits, we notice such extreme differences that we can hardly prescribe a common remedy. Certainly it would seem that the deficits are not necessarily the devil they are sometimes made out to be in so far as the interest rates are concerned, except in the case of some of the countries, particularly Canada. On the other hand, the role of inflation expectations is very important. To that extent we need to understand

Interest rates and budget deficits

218

much better how inflationary expectations are formed. Changes in the composition of government expenditure also play a role quite apart from whether there is any change in total outlays. This compositional role of government expenditures is very rarely emphasized in studies on this topic but deserves attention.

NOTES 3 ESTIMATES AND BEHAVIOUR OF EX-ANTE REAL INTEREST RATES 1 For example, in linear regression model Y=Xb+u, the usual statistical results depend on the assumption that the matrix T−1 X′X tends to a finite, positive definite matrix as the sample size T tends to infinity. In the presence of random walks this basic assumption is not satisfied. 2 For example see Dickey and Fuller (1979). 3 For example, see Campbell and Mankiw (1987a,b) and Phillips and Perron (1988). 4 Dickey and Fuller (1979, 1981) and Fuller (1976). 5 Blangiewicz and Charemza (1990) consider the problem of small sample applications of existing unit root tests. They argue that such small sample applications are beset by a lack of knowledge of the percentiles of distributions, and thus the power, of the unit root tests. See also Harris (1992). 6 One way to prevent the problems is to use the first difference of Y. This approach, however, results in a loss of ‘long-run’ information in the data. Other ways are to employ the concept of cointegration and error-correction discussed, among others, by Hendry (1986). 7 Davidson and McKinnon (1993) also tabulate asymptotic critical values for eight different tests for unit root. 8 See, for example, Olson and Bailey (1981).

4 INTEREST RATES, INFLATION AND TAXES 1 Barsky (1987), Clarida and Friedman (1984), Fama (1975), Fama and Bliss (1987), Fama and Gibbons (1982), Huizinga and Mishkin (1984, 1986), Mishkin (1981, 1984, 1988, 1990, 1991), Rose (1988), Summers (1983), Barth and Bradley (1988), Darby (1975), Hoffman and Schlagenhaug (1985), Lahiri et al. (1988), Makin and Tanzi (1984), Peek (1982), Gupta (1992), Moazzami (1990,1991) among others. 2 See, for example, Tanzi (1980) and Carmichael and Stebbing (1983). 3 See, for example, Garbade and Wachtel (1978), Antoncic (1986) and Yun (1984). 4 See Howe and Pigott (1991/92) and Atkinson and Chouraqui (1985), among others. 5 Note that in regression (10) we lose the first observation on the estimated error term and therefore this vector is not quite orthogonal to the constant term and the trend variable, at least in small samples. 6 A number of other cointegration tests have been proposed in the literature. References include Phillips and Ouliaris (1990), Johansen (1988, 1991) and Johansen and Juselius (1990, 1992). 7 Correcting for the sample size of 100 observations, the critical value would be equal to (−3.40).

Notes

220

5 ON THE EXOGENEITY OF THE REAL INTEREST RATE 1 For a clear exposition of the relationship between the loanable funds and the liquidity preference theories of interest see Kohn (1981). 2 Moore (1988) argues that real interest rates can only be explained as the difference between two largely independent components: the nominal rate which is determined exogenously within broad limits by national central banks and the inflation rate in the economy (p. 257). He argues that central banks determine nominal rates exogenously within relatively wide limits. These limits, however, are endogenously determined by the monetary authorities’ long-term unemployment targets. He argues that the central bank’s ability to establish shortterm interest rates exogenously is derived ultimately from its ability to set the supply price of liquidity, that is, the price at which it is willing to buy and sell assets for its portfolio. When in an open economy, however, the range of central bank discretion to vary nominal rates is constrained by the long-term unemployment, inflation and income considerations as well as interest rates in foreign markets (p. 271). 3 Litterman and Weiss (1985) also provide examples of the incompatibility of real rate exogeneity with the equilibrium theories discussed by Lucas (1972) and Barro (1976, 1980). 4 To determine the optimum number of lags included in each regression, we ran a series of regressions and found that in the majority of cases Akaike Final Prediction Error reached its minimum level at approximately eight lags. 5 In testing for the exogeneity of real rate in Italy, we used the first difference of the expected rate of inflation. 6 A complete description of this decomposition is given in Sims (1972). 7 Estimation is carried out using econometric time series analysis (RATS) employing the Choleski factorization. 8 Note that in Chapter 4 we found that the expected rate of inflation for Italy exhibited nonstationary behaviour. Therefore, we used the first difference of the expected rate of inflation in the four-variable decomposition system. 9 As was the case for the short-term rates for Italy, we used first differences of the expected rates of inflation for Italy and Sweden in this section.

6 BUDGET DEFICITS AND INTEREST RATES: THEORY 1 This model is taken from Gupta and Moazzami (1991b). 2 Kormendi (1983) has reported differential impact of the two types of government expenditures on private consumption expenditures in the U.S.A. 3 For further details, see Sargent (1969).

7 BUDGET RATES AND INTEREST RATES: THE EVIDENCE

1 It should be noted that the terms in ∆2Yt−t are simply a linear combination of the terms in ∆Y and ∆Yt−t. Therefore, they were not included either in the instrument set or in the estimates of equation (19). Also note that we dropped the current values of government saving, government consumption, and investment and output from our initial set of instruments to prevent a possible simultaneity between them and the nominal interest rate.

Notes

221

2 In estimating the Klein-Goldberger model of the U.S. economy, Klein used the principal component approach. He selected two sets of components, one that corresponds to the four largest and one based on the eight largest eigenvalues of the matrix of predetermined variables. Among the four estimators used, he found that the instrumental variable (IV) method based on only four components had a smaller absolute percentage error in forecasting GNP followed by the other IV method using eight components, OLS and full information maximum likelihood. See Klein (1969). 3 To save space, we have not reported the results of these tests in this chapter. We note that in Chapter 4 we found that short-run nominal interest rate and expected inflation for Italy and medium-term interest rate and inflationary expectation for Italy and Sweden exhibited nonstationary behaviour. For Sweden, using annual data and allowing for a break in 1981, we could reject the null hypothesis of non-stationarity in both series. For Italy, we used first differences of nominal interest rates and inflationary expectations. 4 In our estimates we employed data on actual instead of desired savings and investment. The desired level of saving or investment can be assumed to depend on the current and lagged values of actual savings and investment. Substituting the distributed lag of actual saving and investment for the desired levels in equation (9) would result in the same lag structure for savings and investment except for actual variables being substituted for desired savings and investment.

SELECT BIBLIOGRAPHY Antoncic, M. (1986) ‘High and Volatile Real Interest Rates’, Journal of Money, Credit and Banking 18, 18–27. Atkinson, P. and J.C.Chouraqui (1985) ‘The Origins of High Real Interest Rates’, OECD Economic Studies 5, 7–55. Baghestani, H. (1992) ‘Survey Evidence on the Muthian Rationality of the Inflation Forecasts of U.S. Consumers’, Oxford Bulletin of Economics and Statistics 54:2, 173–86. Banerjee, A., J.J.Dolado, D.F.Hendry and G.W.Smith (1986) ‘Exploring Equilibrium Relationships in Econometrics through Static Models: Some Monte Carlo Evidence’, Oxford Bulletin of Economics and Statistics 48, 253–77. Barro, R.J. (1974) ‘Are Government Bonds Net Wealth?’, Journal of Political Economy 82, 1095– 117. Barro, R.J. (1976) ‘Rational Expectations and the Role of Monetary Policy’, Journal of Monetary Policy 2, 1–32. Barro, R.J. (1980) ‘A Capital Market in an Equilibrium Business Cycle Model’, Econometrica 46, 1393–417. Barro, R.J. (1987) ‘Government Spending, Interest Rates, Prices, and Budget Deficits in the United Kingdom, 1701–1918’, Journal of Monetary Economics 20, September, 221–47. Barsky, R.B. (1987) ‘The Fisher Hypothesis and the Forecastability and Persistence of Inflation’, Journal of Monetary Economics 19, 3–24. Barth, J.R. and M.D.Bradley (1988) ‘On Interest Rates, Inflationary Expectation and Tax Rates’, Journal of Banking and Finance 12, 215–26. Bernheim, B.D. (1987) ‘Ricardian Equivalence: An Evaluation of Theory and Evidence’, Working Paper No. 2330, NBER, Cambridge, MA: 221–47. Bernheim, B.D. (1989) ‘A Neoclassical Perspective on Budget Deficits’, Journal of Economic Perspectives 3, 55–71. Blanchard, O.J. (1985) ‘Debt, Deficits, and Finite Horizons’, Journal of Political Economy 93, 223–47. Blanchard, O.J. and S.Fischer (1989) Lectures on Macroeconomics, Cambridge, MA: MIT Press. Blanchard, O.J. and L.H.Summers (1984) ‘Perspectives on High World Real Interest Rates’, Brookings Papers on Economic Activity, 2, 273–324. Blangiewicz, M. and W.W.Charemza (1990) ‘Cointegration in Small Samples: Empirical Percentiles, Drifting Moments and Customized Testing’, Oxford Bulletin of Economics and Statistics 52, 303–15. Blinder, A.S. and R.M.Solow (1973) ‘Does Fiscal Policy Matter?’, Journal of Public Economics 2, 318–37. Bonser-Neal, C. (1990) ‘Monetary Regime Changes and the Behavior of Ex-ante Real Interest Rates’, Journal of Monetary Economics 22, 329–59. Breusch, T.S. and L.Godfrey (1981) ‘A Review of Recent Work on Testing for Autocorrelation in Dynamic Simultaneous Equations’, in D.Currie, R.Norway and D.Peel (eds), Macroeconomic Analysis, London: Croom Helm. Buchanan, J.M. (1988) ‘Barro on the Ricardian Equivalence Theorem’, Journal of Political Economy 84, 337–42. Buiter, W.H. ‘“Crowding Out” and the Effectiveness of Fiscal Policy’, Journal of Public Economics 7, 309–28.

Select bibliography

223

Buse, A. and B.Moazzami (1991) ‘Some Evidence on the Dominance of Generalized Two Stage Least S0quares as an Autoregressive Estimator’, Empirical Economics 16, 335–49. Campbell, J.Y. and N.G.Mankiw (1987a) ‘Are Output Fluctuations Transitory?’, Quarterly Journal of Economics 102, 857–80. Campbell, J.Y. and N.G.Mankiw (1987b) ‘Permanent and Transitory Components in Macroeconomic Fluctuations’, American Economic Review Papers and Proceedings 77, 111– 17. Carmichael, J. and P.W.Stebbing (1983) ‘Fisher’s Paradox and the Theory of Interest’, American Economic Review 13, 619–30. Cebula, R.J. (1988) ‘Federal Government Budget Deficits and Interest Rates: An Empirical Analysis for the United States, 1955–1984’, Public Finance 43, 337–48. Clarida, R.H. and B.M.Friedman (1984) ‘The Behavior of U.S. Short-term Interest Rates Since October 1979’, Journal of Finance 39, 671–82. Congressional Budget Office (1987) The Economic and Budget Outlook: Fiscal Years 1988–1992, Part I, Washington, DC: U.S. Government Printing Office. Cukierman, A. (1977) ‘A Test of Expectational Process Using Information from the Capital Markets—The Israel Case’, International Economic Review 18, 3, October, 737–52. Cumby, R.E. and F.S.Mishkin (1985) ‘International Linkage of Real Interest Rates: The U.S.European Connection’, Journal of International Money and Finance 5, March, 5–23. Darby, N.R. (1975) ‘The Financial and Tax Effects of Monetary Policy on Interest Rates’, Economic Inquiry 13, 266–76. Davidson, R.E. and J.C.McKinnon (1993) Estimation and Influence in Econometrics, Oxford: Oxford University Press. Dickey, D.A. and W.A.Fuller (1979) ‘Distribution for the Estimators for Autoregressive Time Series with a Unit Root’, Journal of the American Statistical Association 74, 427–31. Dickey, D.A. and W.A.Fuller (1981) ‘Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root’, Econometrica 49, 1057–72. Dolade, J.J., T.T.Jenkinson and S.Sosvilla-Rivero (1990) ‘Cointegration and Unit Roots’, Journal of Economic Surveys 4(3), 249–73. Echols, M.E. and J.W.Elliot (1976) ‘Rational Expectations in a Dis-equilibrium Model of the Term Structure’, American Economic Review 66, 28–44. Engle, R.F. (1982) ‘Autoregressive Conditional Heteroskedasticity with Estimate of the Variance of United Kingdom Inflation’, Econometrica 50, 987–1007. Engle, R.F. and C.W.Granger (1987) ‘Cointegration and Error Correction: Representation, Estimation, and Testing’, Econometrica 55, 251–76. Engle, R.F. and B.S.Yoo (1987) ‘Forecasting and Testing in Cointegrated Systems’, Journal of Econometrics 35, 143–59. Engle, R.F. and B.S.Yoo (1991) ‘Cointegrated Economic Time Series: A Survey with New Results’, in R.F.Engle and C.W.J.Granger (eds), Long-run Economic Relationships: Readings in Cointegration, Oxford: Oxford University Press. Evans, P. (1987a) ‘Do Budget Deficits Raise Nominal Interest Rates? Evidence from Six Industrial Countries’, Journal of Monetary Economics 20, 281–300. Evans, P. (1987b) ‘Interest Rates and Expected Future Budget Deficits in the United States’, Journal of Political Economy 95, 34–58. Fama, E.F. (1975) ‘Short-term Interest Rates as Predictors of Inflation’, American Economic Review 65, 269–82. Fama, E.F. and R.R.Bliss (1987) ‘The Information in Long-maturity Forward Rates’, American Economic Review 77, 680–92. Fama, E.F. and M.R.Gibbons (1982) ‘Inflation, Real Returns and Capital Investment’, Journal of Monetary Economics 9, 297–324. Farley, J.U. and M.J.Hinich (1970) ‘A Test for a Shifting Slope Coefficient in a Linear Model’, Journal of American Statistical Association 65, 1320–9.

Select bibliography

224

Feldstein, M.S. (1976) ‘Inflation, Income Taxes and the Interest Rates: A Theoretical Analysis’, American Economic Review 66, 809–20. Fisher, I. (1930) The Theory of Interest, New York: Macmillan. Fuller, W.A. (1976) Introduction to Statistical Time Series, New York: John Wiley & Sons. Garbade, K. and P.Wachtel (1978) ‘Time Variation in the Relationship between Inflation and Interest Rates’, Journal of Monetary Economics 4, 755–65. Geweke, J., R.Meese and W.Dent (1982) ‘Comparing Alternative Tests of Causality in Temporal Systems’, Journal of Econometrics 21, 161–94. Gilbert, C.L. (1986) ‘Professor Hendry’s Econometric Methodology’, Oxford Bulletin of Economics and Statistics 48, 283–307. Gordon, R.J. (1987) Macroeconomics, 4th edn. Boston: Little, Brown & Co. Gordon, R.J. and J.M.Veitch (1986) Fixed Investment in the American Business Cycle, Chicago: University of Chicago Press, 267–357. Granger, C.W.J. (1969) ‘Investigating Causal Relations by Econometric Models and Cross-spectral Methods’, Econometrica, 37, 424–38. Granger, C.W.J. (1980a) ‘Long Memory Relationships and the Aggregation of Dynamic Models’, Econometrica 14, 227–38. Granger, C.W.J. (1980b) ‘Testing for Causality: A Personal Overview’, Journal of Economic Dynamics and Control 2, 329–52. Granger, C.W.J. (1986) Developments in the Study of Cointegrated Economic Variables’, Oxford Bulletin of Economics and Statistics 48(3), 213–28. Granger, C.W.J. and P.Newbold (1974) ‘Spurious Regressions in Econometrics’, Journal of Econometrics 2, 111–20. Gupta, K.L. (1984) ‘Budget Deficits and Interest Rates in the United States’, Public Choice 60, 87– 92. Gupta, K.L. (1992) ‘Interest Rates, Income Taxes and Anticipated Inflation’, Journal of Banking and Finance 16, 973–81. Gupta, K.L. and B.Moazzami (1991a) ‘Recent Interest Rate Behaviour: The Error-Correction Modeling Approach’, Journal of Macroeconomics 13, 479–93. Gupta, K.L. and B.Moazzami (1991b) ‘Dynamic Specification and the Long-Run Effect of Budget Deficits on Interest Rates’, Public Finance 46, 208–221. Harris, R.I.D. (1992) ‘Small Sample Testing for Unit Roots’, Oxford Bulletin of Economics and Statistics 54, 615–25. Hendry, D. (1986) ‘Econometric Modelling with Cointegrated Variables: An Overview’, Oxford Bulletin of Economics and Statistics 48, 201–12. Hoffman, D.L. and D.E.Schlagenhaug (1985) ‘Real Interest Rates, Anticipated Inflation and Unanticipated Inflation’, Review of Economics and Statistics 67, 284–96. Howe, H. and C.Pigott (1991/92) ‘Determinants of Long-term Interest Rates: An Empirical Study of Several Industrial Countries’, Federal Reserve Bank of New York, Quarterly Review, Winter, 12–28. Huizinga, J. and F.S.Mishkin (1984) ‘Inflation and Real Interest Rates on Assets with Different Risk Characteristics’, Journal of Finance 39, 699–712. Huizinga, J. and F.S.Mishkin (1986) ‘Monetary Policy Regime Shifts and the Unusual Behavior of Real Interest Rates’, in The National Bureau Method, International Capital Mobility and Other Essays, edited by K. Brunner and A.H.Meltzer. Carnegie-Rochester Conference on Series on Public Policy 24, 231–74. Hylleberg, S. and G.E.Mizon (1989) ‘Cointegration and Error Correction Mechanisms’, Economic Journal 99, 113–25. Johansen, S. (1988) ‘Statistical Analysis of Cointegration Vectors’, Journal of Economic Dynamics and Control 12, 231–54. Johansen, S. (1991) ‘Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models’, Econometrica 59, 1551–80.

Select bibliography

225

Johansen, S. and K.Juselius (1990) ‘Maximum Likelihood Estimation and Inference on Cointegration—With Applications to the Demand for Money’, Oxford Bulletin of Economics and Statistics 52, 169–210. Johansen, S. and K.Juselius (1992) ‘Testing Structural Hypotheses in a Multivariate Cointegration Analysis of the PPP and UIP for the U.K.’, Journal of Econometrics 53, 211–44. Klein, L.R. (1969) ‘Estimation of Interdependent Systems in Macroeconomies’, Econometrica 37, 171–92. Kohn, M. (1981) ‘A Loanable Funds Theory of Unemployment and Monetary Disequilibrium’, American Economic Review 71, 859–79. Kormendi, R.C. (1983) ‘Government Debt, Government Spending, and Private Sector Behavior’, American Econoic Review 73, 994–1010. Lahiri, K. and M.Zaporowski (1988) ‘A Comparison of Alternative Real Rate Estimates’, Oxford Bulletin of Economics and Statistics 50, 303–12. Lahiri, K., C.Teigland and M.Zaporowski (1988) ‘Interest Rates and the Subjective Probability of Distribution of Inflation Forecasts’, Journal of Money, Credit and Banking 20, 233–48. Litterman, R.B. and L.Weiss (1985) ‘Money, Real Interest Rates, and Output: A Reinterpretation of Post-war U.S. Data’, Econometrica 53, 129–56. Lothian, J.R. (1985) ‘Equilibrium Relationships between Money and Other Economic Variables’, American Economic Review 75, 828–35. Lovell, M.C. (1986) ‘Tests of the Rational Expectations Hypothesis’, American Economic Review 76, 110–24. Lucas, R.E. (1972) ‘Expectations and the Neutrality of Money’, Journal of Economic Theory 4, 103–24. Lucas, R.E. (1980) ‘Two Illustrations of the Quantity Theory of Money’, American Economic Review 70, 1005–14. Lucas, R.E., Jr. (1991) ‘Comment on Real Interest Rates’, NBER Macroeconomics Annual 5, 69– 74. McKinnon, J.G. (1991) ‘Critical Values for Cointegration Tests’, in R.F. Engle and C.W.J.Granger (eds), Long-run Economic Relationships: Readings in Cointegration, Oxford: Oxford University Press. Makin, J.H. and V.Tanzi (1984) ‘Level and Volatility of U.S. Interest Rates: Role of Expected Inflation, Real Rates and Taxes’, in V.Tanzi (ed.), Taxation, Inflation and Interest Rates, Washington, DC: IMF, 110–42. Mishkin, F.S. (1981) ‘The Real Interest Rate: An Empirical Study’, in Consequences of Inflation, edited by K.Brunner and A.H.Meltzer. Carnegie-Rochester Conference Series on Public Policy 15, 151–200. Mishkin, F.S. (1984) ‘Are Real Interest Rates, Equal Across Countries? An Empirical Investigation of International Parity Conditions’, Journal of Finance 39, 1345–57. Mishkin, F.S. (1988) ‘Understanding Real Interest Rates’, Journal of Agricultural Economics 70, 1064–72. Mishkin, F.S. (1990) ‘What Does the Term Structure of Interest Rates Tell Us About Future Inflation?’, Journal of Monetary Economics 25, 77–95. Mishkin, F.S. (1991) ‘Is the Fisher Effect for Real? A Reexamination of the Relationship between Information and Interest Rates’, Working Paper No. 3632, NBER, Cambridge, MA. Moazzami, B. (1990) ‘Interest Rates and Inflationary Expectations, Long-run Equilibrium and a Short-term Adjustment’, Journal of Banking and Financed, 1163–70. Moazzami, B. (1991) ‘The Fisher Equation Controversy Re-examined’, Applied Financial Economics 1, 129–33. Moazzami, B. and A.Buse (1986) ‘The Small Sample Performance of Some Limited Information Estimators of a Dynamic Structural Equation with Autocorrelated Errors’, Journal of Statistical Computation and Simulation 26, 55–78.

Select bibliography

226

Moazzami, B. and A.Buse (1991) ‘Limited Information Estimation of a Dynamic Structural Equation with Autocorrelated Errors: A Correction and New Evidence’, Journal of Statistical Computation and Simulation 34, 195–208. Modigliani, F. and T.Jappelli (1988) ‘The Determinants of Interest Rates in the Italian Economy’, Review of Economic Conditions in Italy 9–34. Moore, B.J. (1988) Horizontalists and Verticalists: the Macroeconomics of Credit, Money, Cambridge: Cambridge University Press. Nagar, A.L. (1959) ‘The Bias and Moment Matrix of the General K-Class Estimators of the Parameters in Simultaneous Equations’, Econometrica 27, 575–95. Nelson, C.R. and N.Kang (1981) ‘Spurious Periodicity in Inappropriately Detrended Time Series’, Econometrica 49, 741–51. Nelson, C.R. and C.Plosser (1982) ‘Trends and Random Walks in Macroeconomic Time Series’, Journal of Monetary Economics 19, 139–62. Olson, M. and M.J.Bailey (1981) ‘Positive Time Reference’, Journal of Political Economy 89, 1– 25. Peek, J. (1982) ‘Interest Rates, Income Taxes and Anticipated Inflation’, American Economic Review 72, 980–91. Perron, P. (1989) ‘The Great Crash, the Oil Price Shock and the Unit Root Hypothesis’, Econometrica 57, 1361–401. Phillips, P.C.B. (1986) ‘Understanding Spurious Regressions in Econometrics’, Journal of Econometrics 33, 311–40. Phillips, P.C.B. and S.Ouliaris (1990) ‘Asymptotic Properties of Residualbased Tests for Cointegration’, Econometrica 58, 165–93. Phillips, P.C.B. and P.Perron (1988) ‘Testing for a Unit Root in Time Series Regression’, Biometrica 75, 335–46. Plosser, C.I. (1982) ‘Government Financing Decisions and Asset Returns’, Journal of Monetary Economics 9, 325–52. Plosser, C.I. (1987) ‘Further Evidence on the Relation between Fiscal Policy and the Term Structure’, Journal of Monetary Economics 20, 343–67. Ricardo, D. (1951) ‘Funding System’, in P.Sraffa (ed.), The Works and Correspondence of David Ricardo, Vol. IV, Pamphlets and Papers 1815–1823, Cambridge: Cambridge University Press. Rose, A.K. (1988) ‘Is the Real Interest Rate Stable ?’, Journal of Finance 43, 1095–112. Sargent, T.J. (1969) ‘Commodity Price Expectations and the Interest Rate’, Quarterly Journal of Economics 83, 127–40. Sims, C.A. (1972) ‘Money, Income, and Causality’, American Economic Review 62, 540–52. Sims, C.A. (1980a) ‘Macroeconomics and Reality’, Econometrica 48,1–48. Sims, C.A. (1980b) ‘Comparison of Interwar and Postwar Cycles: Monetarism Reconsidered’, American Economic Review 70, 250–7. Sims, C.A. (1980c) ‘International Evidence on Monetary Factors in Macroeconomic Fluctuations’, University of Minnesota Discussion Paper. Sims, C.A. (1981) ‘An Autoregressive Index Model for the United States, 1948–75’, in J.Kmenta and J.B.Ramsey (eds), Large-scale Macroeconomic Models, Amsterdam: North-Holland. Stock, J.H. (1987) ‘Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors’, Econometrica 55, 1035–56. Summers, L.H. (1983) ‘The Non-adjustment of Nominal Interest Rates: A Study of the Fisher Effect’, in James Tobin (ed.), A Symposium in Honor of Arthur Okun, Washington, DC: Brookings Institution. Summers, L.H. (1986) ‘Estimating the Long-run Relationship Between Interest Rates and Inflation’, Journal of Monetary Economics 18, 77–86. Tanzi, V. (1980) ‘Inflationary Expectations, Economic Activity, Taxes and Interest Rates’, American Economic Review 70, 12–21. Tanzi, V. (ed.) (1984) Taxation, Inflation and Interest Rates, Washington, DC: IMF.

Select bibliography

227

Tran, D.T. and B.L.Sawhney (1988) ‘Government Deficits, Capital Flows, and Interest Rates’, Applied Economics 20, 753–65. U.S. Treasury Department (1984) The Effect of Deficits on Prices of Financial Assets: Theory and Evidence, Washington, DC: US Government Printing Office. West, K.D. (1988) ‘Asymptotic Normality, When Regressors Have a Unit Root’, Econometrica 56, 1397–417. Wickens, M.R. and T.S.Breusch (1988) ‘Dynamic Specification, the Long-run and the Estimation of Transformed Regression Models’, Economic Journal 98, 189–205. Wormell, J. (1985) The Gilt-edged Market, London: George Allen & Unwin. Yun, Y.-S. (1984) ‘The Effects of Inflation and Income Taxes on Interest Rates: Some New Evidence’, Journal of Financial and Quantitative Analysis 19, 425–47.

INDEX Akaike Final Prediction Error 10, 54, 60 Antoncic, M. 229 ARCH model 58, 62, 76–80, 188 Australia: budget deficits 165, 176, 238, 240; ex-ante real interest rates 57–9, 63–4, 165, 176; exogeneity 109–12, 143; Fisher hypothesis 79–84, 91–5; Granger causality test 107–8, 142, 152; inflation 154, 241, 242; instrumental variable estimation 189–90; interest rate forecasts 191–3; money supply 153, 241, 242; nominal interest rates 26, 47; output 153; pre-tax ex-ante real interest rates, medium-term 27, 28, 29, 34/short-term 11, 13–15, 17, 34; stationarity 75, 88; trade balance 241, 242; unit root testing 54–5, 60, 61–2, 72, 74 autocorrelation 80, 187–8 autoregressive approach 6–7, 10, 25, 58 Banerjee, A. 70 Bank of Canada Report 188 Barro, R.J. 100, 156 Belgium: budget deficits 166, 177, 238, 240; ex-ante real interest rates 58–9, 63–4, 166, 177; exogeneity 111–14, 143–4; Fisher hypothesis 77–84, 91–5; Granger causality test 107–8, 142, 152; inflation 154, 241, 242; instrumental variable estimation 193–4; interest rate forecasts 195–7; money supply 153, 241, 242; nominal interest rates 26, 47, 72–3, 74; output 153; pre-tax ex-ante real interest rates, medium-term 27, 29, 34/short-term 11, 16, 17, 18, 34; stationarity 75, 88; trade balance 241, 242;

Index

229

unit root testing 54–5, 60, 61, 62, 72–3, 74 Bernheim, B.D. 157, 175, 178 Blanchard, O.J. 6, 28, 31–2, 156 Blinder, A.S 155–6 Bonser-Neal, C. 23 breakpoints 16, 18, 19, 21; monetary policy changes 23–4; structural 23, 68; unit root testing 61, 73, 88 Breusch, T.S. 55, 57–8, 62, 157, 159, 182, 188 Buchanan, J.M. 156 budget deficits: empirical literature 173–89; estimation results: see individual countries; medium-term interest rates 239, 240; model for 157–63; neoclassical paradigm 244; real interest rates 157–9, 164–73, 243; Ricardian paradigm 245; short-term interest rates 237, 238 Buiter, W.H. 159 Buse, A. 187 Canada: budget deficits 167, 169–70, 178, 238, 240, 245; ex-ante real interest rates 58–9, 63–4, 167, 169–70, 178; exogeneity 114–17, 144–5; Fisher hypothesis 77–84, 90–5, 96–8; Granger causality test 107–8, 142, 152; inflation 154, 241, 242; instrumental variable estimation 197–8; interest rate forecasts 199–201; money supply 153, 241, 242; nominal interest rates 26, 39, 43, 47, 72–3, 74; output 153; post-tax ex-ante real interest rates, medium-term 38, 43/short-term 37, 39; pre-tax ex-ante real interest rates, medium-term 27, 30, 32–3, 34/short-term 12, 16, 17, 18, 34; stationarity 75, 88; structural break 68; trade balance 241, 242; unit root testing 54–5, 60, 61, 62, 72–3, 74 causality: and exogeneity 101–4; inflation expectations 154; money supply 152, 153; output 152, 153 Cochrane-Orcutt procedure 67 cointegration, variables 69–70, 75–6, 89

Index

230

Cumby, R.E. 23 data sources 188–9 Davidson, R.E. 75–6 Dickey, D.A. 50, 51, 52, 54, 60, 72 Dolado, J.J. 52 Echols, M.E. 159, 163 Elliot, J.W. 159, 163 Engle, R.F. 58, 62, 69–70, 76 equality testing 55–9, 62–4 error correction 56–7, 69–70 Evans, P. 175, 176 ex-ante real interest rates: budget deficits 164–73, 176–86; equality testing 55–9, 62–4; estimation 4–8, 180–8; exogeneity 106–40, 141–51, 244, 248 (n2); Mishkin procedure 57–9; post-tax 36–43; pre-tax medium-term 4, 8, 25–35; pre-tax short-term 4, 8, 9–25, 34; statistical behaviour 49–50; trend-dependent variation 68–9; unit root testing 53–5; see also individual countries exogeneity 99–101; and causality 101–4; ex-ante real interest rates 106–40, 141–51, 244, 248 (n2); see also individual countries Farley, J.U. 68 Federal Reserve Bulletin 188 final prediction error 54, 60 Financial Times 35 financing, debt/tax 156 Fisher, I. 66 Fisher hypothesis 6; autocorrelation 80; estimation and results 76–84; non-stationary variables 69–71; post-tax interest rates 82–4, 96–8; pre-tax interest rates 90–5; testing methodology 66–9; validity 244, 245 forecast error 104–6, 109, 110, 113, 115, 118, 120, 123, 126, 129, 132, 135, 137 France: budget deficits 168, 179, 238, 240; ex-ante real interest rates 58–9, 63–4, 168, 179; exogeneity 117–20, 145; Fisher hypothesis 78–84, 91–5, 96–8;

Index

231

Granger causality test 107–8, 142, 152; inflation 154, 241, 242; instrumental variable estimation 201–2; interest rate forecasts 203–5; money supply 153, 241, 242; nominal interest rates 26, 39, 43, 46–8, 72–3, 74; output 153; post-tax ex-ante real interest rates, medium-term 38, 43/short-term 37, 39; pre-tax ex-ante real interest rates, medium-term 27, 30, 34/short-term 12, 17, 18, 19, 34; stationarity 75, 88; trade balance 241, 242; unit root testing 54–5, 60, 61, 62, 72–3, 74 Fuller, W.A. 50, 51, 52, 54, 60, 72 Gauss-Markov theorem 50 Germany: budget deficits 166–7, 169, 170, 180, 238, 240; ex-ante real interest rates 58–9, 63–4, 166–7, 169, 170, 180; exogeneity 120–2, 146; Fisher hypothesis 77–84, 90–5, 96–8; Granger causality test 107–8, 142, 152; inflation 154, 241, 242; instrumental variable estimation 205–6; interest rate forecasts 207–8; money supply 153, 241, 242; nominal interest rates 26, 40, 44, 48, 72, 74; output 153; post-tax ex-ante real interest rates, medium-term 38, 44/short-term 37, 40; pre-tax ex-ante real interest rates, medium-term 27, 28, 31, 34/short-term 13, 17, 18, 19–20, 34; stationarity 75, 88; trade balance 241, 242; unit root testing 54–5, 60, 61, 72, 74 Geweke, J. 104 Gilbert, C.L. 185 Godfrey, L. 58, 62, 188 Gordon, R.J. 109, 188 Granger, C.W.J. 50, 69–70, 101–1, 106, 107 Granger causality test 106–8, 142, 151, 152 Gupta, K.L. 175, 229 Hendry, D. 56 heteroscedasticity 58, 62, 188; see also ARCH model Hinich, M.J. 68 Howe, H. 177 Hylleberg, S. 52

Index

232

index-linked bonds 4–5, 8, 34–5 inflationary expectations: causality 154; Fisher hypothesis 66–9; innovations 244, 245; interest rate estimation 4–7, 10, 243; medium-term interest rates 241–2; short-term interest rates 239, 241; survey data 24–5; unit root 71–6, 86–8 innovation accounting 104–6 instrumental variables 190, 194, 198 202, 205–6, 209, 214, 218, 222, 225, 231 integration, real rate time series 51–3 interest rates: and budget deficits 155–7; equality testing 55–9, 62–4; equilibrium 49, 67, 158; exogeneity 99–101; forecasts 191–3, 195–7, 199–201, 203–5, 207–8, 211–13, 215–17, 219–21, 223–4, 227–9, 233– 6; and inflation 4–7, 66–9, 241–3; marginal tax rates 36; natural 99; real 164–73, 243, 248 (n2); see also ex-ante real interest rates; nominal interest rates International Financial Statistics 188, 230 investment function 159 IS-LM model 100–1 Italy: budget deficits 170–1, 181, 238, 240; cointegration 89; ex-ante real interest rates 58–9, 63–4, 170–1, 181; exogeneity 122–5, 146–7; Fisher hypothesis 78–84, 92–5, 96–8; Granger causality test 107–8, 142, 152; inflation 154, 241, 242; instrumental variable estimation 208–10; interest rate forecasts 211–13; money supply 153, 241, 242; nominal interest rates 26, 40, 44, 46, 48; output 153; post-tax ex-ante real interest rates, medium-term 38, 44/short-term 37, 40; pre-tax ex-ante real interest rates, medium-term 27, 31, 34/short-term 13, 17, 20–1, 34; stationarity 75, 88; structural break 68; trade balance 241, 242; unit root testing 54–5, 60, 61, 72–3, 74

Index

233

Japan: budget deficits 171, 182, 238, 240; ex-ante real interest rates 57–9, 63–4, 171, 182; exogeneity 125–9, 147–8; Fisher hypothesis 79–84, 92–5, 96–8; Granger causality test 107–8, 142, 152; inflation 154, 241, 242; instrumental variable estimation 213–15; interest rate forecasts 215–17; money supply 153, 241, 242; nominal interest rates 26, 41, 45, 48, 72, 74; output 153; post-tax ex-ante real interest rates, medium-term 38, 45/short-term 37, 41; pre-tax ex-ante real interest rates, medium-term 27, 28, 29–30, 32, 34/short-term 14, 16, 17, 19, 20, 21–2, 34; stationarity 75, 88; trade balance 241, 242; unit root testing 54–5, 60, 72, 74 Jappelli, T. 176 Kang, N. 50 Keynesian paradigm 99, 155–6, 163 Lagrange multiplier test 57–8, 62 Lahiri, K. 5, 24 linkage hypothesis 58, 65, 243–4 Litterman, R.B. 100–1, 109, 138 loanable fund market 99 Lothian, J.R. 67 Lucas, R.E. 67, 100 marginal tax rates 36 McKinnon, J.C. 51, 72, 75–6 Mishkin, F.S. 7–8, 23, 55–6, 66 Mishkin procedure 25, 57–9 Mizon, G.E. 52 Moazzami, B. 175, 187, 229 Modigliani, F. 176 monetary policy regime changes 23–4 money, supply/demand 99–100, 153, 241, 242 money growth 239, 241–2, 245 Moore, B.J. 248 (n2) Nagar, A.L. 187 Nelson, C.R. 50 neoclassical paradigm 156, 163, 244 Netherlands: budget deficits 172, 183, 238, 240; ex-ante real interest rates 58–9, 63–4, 172, 183;

Index

234

exogeneity 129–31, 148–9; Fisher hypothesis 78–84, 92–5; Granger causality test 107–8, 142, 152; inflation 154, 241, 242; instrumental variable estimation 217–19; interest rate forecasts 219–221; money supply 153, 241 242; nominal interest rates 26, 41, 45, 48, 72, 74; output 153; post-tax ex-ante real interest rates, medium-term 38, 45/short-term 37, 41; pre-tax ex-ante real interest rates, medium-term 27, 32, 34/short-term 14, 17, 18, 22, 34; stationarity 75, 88; trade balance 241, 242; unit root testing 54–5, 60, 61, 72, 74 Newbold, P. 50 nominal interest rates 9–10; and ex-ante real interest rates 43–9; medium-term 25–6; and pre-tax rates 45–6; unit root in short-term 71–6; see also individual countries non-linearity 57, 71 non-stationarity 50, 54–5, 60, 61, 69–71 oil price shock 72 ordinary least squares 50, 67–8, 70, 181–2 output 153 Perron, P. 50, 53, 55, 60, 61–2 Phillips, P.C.B. 50 Pigott, C. 177 Plosser, C. 50, 175 prediction error 10, 54, 60 price index 5, 10 random walk 49–50 rational expectations approach 4, 5, 7, 10 regressions, stationary/spurious 50 retail price index 5 Ricardian equivalence proposition 157, 159, 162–3 Ricardian paradigm 156, 163, 245 Ricardo, D. 156 Sargent, T.J. 157, 161 saving function 159–60 Sims, C.A. 100, 103–4 Solow, R.M. 155–6 standard method, inflation expectations 4, 6, 10

Index

235

stationarity 54, 60, 75, 88 Stock, J.H. 69, 70, 71 Summers, L.H. 6, 28, 31–2, 67 Survey of Current Business 188, 230 survey data 4, 5–6, 24–5 Sweden: budget deficits 173, 184, 238, 240; cointegration 89; ex-ante real interest rates 57–9, 63–4, 173, 184; exogeneity 132–4, 149; Fisher hypothesis 79–84, 91–5; Granger causality test 107–8, 142, 152; inflation 154, 241, 242; instrumental variable estimation 221–2; interest rate forecasts 223–4; money supply 153, 241, 242; nominal interest rates 26, 48, 72, 74; output 153; pre-tax ex-ante real interest rates, medium-term 27, 33, 34/short-term 15, 17, 22, 34; stationarity 75, 88; trade balance 241, 242; unit root testing 54–5, 60, 72, 74 Tanzi, V. 36 time series 50, 51–3 trade balance 239, 241–2 U.K.: budget deficits 167–8, 171, 174, 185, 238, 240; ex-ante real interest rates 57–9, 63–4, 167–8, 171, 174, 185; exogeneity 133–6, 149–50; Fisher hypothesis 78–84, 90–5, 96–8; Granger causality test 107–8, 142, 152; index-linked bonds 35; inflation 154, 241, 242; instrumental variable estimation 224–7; interest rate forecasts 227–9; money supply 153, 227, 241, 242; nominal interest rates 26, 42, 46, 48, 74; output 153; post-tax ex-ante real interest rates, medium-term 38, 46/short-term 37, 42; pre-tax ex-ante real interest rates, medium-term 27, 30, 33, 34/short-term 15, 17, 22–3, 34; stationarity 75, 88; trade balance 241, 242; unit root testing 54–5, 60, 74 U.S.A.: budget deficits 166–7, 171, 173–9, 186, 238, 240; ex-ante real interest rates 166–7, 171, 173–9, 186;

Index

236

exogeneity 137–40, 150–1; Fisher hypothesis 77–84, 90–5, 96–8; Granger causality test 107–8, 142, 152; inflation 24–5, 154, 241, 242; instrumental variable estimation 229–32; interest rate forecasts 233–6; Klein-Goldberger model 249 (n2); money supply 153, 232–3, 241, 242; nominal interest rates 26, 42, 46, 48, 72–3, 74; output 153; post-tax ex-ante real interest rates, medium-term 38, 46/short-term 36–9, 42, 47; pre-tax ex-ante real interest rates, medium-term 27, 28, 30–2, 34/short-term 16, 17, 20, 21, 23, 24, 34; stationarity 75, 88; structural break 68; survey data on inflation expectations 24–5; trade balance 241, 242; unit root testing 54–5, 60, 61–2, 72–3, 74 unit root testing 50, 51–3; breakpoints 61, 73, 88; ex-ante real interest rates 53–5, 60–2; inflationary expectations 74; nominal interest rates 71–6, 85–8; see also individual countries variables 50, 69–70, 75–6, 89, 109; see also instrumental variables Veitch, J.M. 109 Weiss, L. 100–1, 109, 138 West, K.D. 52 Wickens, M.R. 55, 157, 159, 182 Wicksell, K. 99, 161 Wold decomposition 104–5 Wormell, J. 4, 5 Yoo, B.S. 76 Zaporowski, M. 5