Tax Evasion and Firm Survival in Competitive Markets

Tax Evasion and Firm Survival in Competitive Markets

Dedicated with love to my nephew Kristian Alexander

Tax Evasion and Firm Survival in Competitive Markets Filip Palda Professor of Economics, École nationale d’administration publique, Montreal and Senior Fellow, Fraser Institute, Canada

Edward Elgar Cheltenham, UK • Northampton, MA, USA

© Filip Palda 2001 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without the prior permission of the publisher. Published by Edward Elgar Publishing Limited Glensanda House Montpellier Parade Cheltenham Glos GL50 1UA UK Edward Elgar Publishing, Inc. 136 West Street Suite 202 Northampton Massachusetts 01060 USA

A catalogue record for this book is available from the British Library

Library of Congress Cataloging in Publication Data Palda, Filip Tax evasion and firm survival in competitive markets / Filip Palda. p. cm. Includes index. 1. Corporations–Taxation. 2. Business enterprises–Taxation. 3. Tax planning. 4. Tax evasion. I. Title. HD2753.A3 P35 2001 336.24'316—dc21 00–061741 ISBN 1 84064 413 3

Contents List of tables Acknowledgements

vi vii

1. 2. 3. 4.

1 6 55

Introduction Tax evasion Are subsidies evaded taxes? Tax evasion analysis extended to regulation evasion: the case of the minimum wage 5. Tax evasion, regulation evasion and rent-seeking 6. Conclusion

76 115 124

References Index

127 133

Tables 4.1 Deadweight loss and employment effects of minimum wage Wmin without evasion 4.2 Deadweight loss and employment effects of minimum wage Wmin when workers evade 4.3 Deadweight loss and employment effects of minimum wage Wmin when firms evade

vi

83 91 98

Acknowledgements This book grew in part out of a series of papers I wrote and presented over the course of a year at the Queen’s University public finance workshop. I thank Robin Boadway for inviting me to participate in this workshop and for his detailed comments on my papers. My former professors of public finance at Queen’s, Neil Bruce, Jack Mintz and Dan Usher helped me develop my thinking on tax evasion by providing detailed comments on an initial working paper I sent them in the summer of 1997. It is to Dan Usher that I attribute an early theoretical treatment of displacement deadweight loss in a 1983 paper which I hope one day receives the recognition it deserves. Jim Brander, editor of the Canadian Journal of Economics, carefully edited a paper on tax evasion I submitted to his journal and his tireless comments as well as the comments of anonymous referees he chose to evaluate my paper were of great help in shaping the thoughts behind this book. My colleague at the École nationale d’administration publique, Michel Boucher, helped me in my thinking on the question of displacement through many long conversations. Mark Harrison of the Australian National University has given me invaluable comments on the relation between tax evasion and minimum wage evasion. I thank Tom Borcherding, Stan Winer, Orley Ashenfelter, Klaus Stegeman and Martin Prachowny for their written and spoken comments on the working papers that were the seeds of the present book. My parents have been of tremendous support and I thank them most of all for their help and their boundless patience. Finally, I thank Ctibor Blattny for the conversation that got the whole thing rolling.

vii

1. Introduction Shell Brasil, the Brazilian subsidiary of the Anglo-Dutch oil group, is to sell 285 service stations and six fuel deposits to Agip do Brasil, the local subsidiary of Eni, the Italian group. Shell said the move was part of efforts to concentrate on the most profitable parts of its business in Brazil, but it is understood to have sold the stations, in remote central and western regions of the country, after failing to compete with smaller distributors undercutting bigger companies by evading taxes. (Financial Times of London, 25 February 2000, page 18)

In 1997 I visited the Czech Republic and got to know one of the main wholesalers of cut flowers. He made his living by importing flowers from Holland and selling them to hotels and flower stands across the Czech Republic. I learned from him how a Dutch auction works, how purchasers rate the quality of flowers, and the how wholesalers and retailers guess at demand and race against the clock to sell flowers before they wilt. My discussion with the wholesaler filled a chasm in my practical education about markets left by the theoretical excesses of graduate school. These discussions also showed me that there can be distance between what producers on the front line of markets find to be a market failure, and what professors of economics believe hinder markets. The wholesaler’s hair was greying because the government did not apply taxes evenly to him and his competitors. Rogue merchants would travel to Holland in small unrefrigerated vans in which it was easy to smuggle flowers across the Czech border. The cost of flowers that withered in the vans was more than balanced by the border tariffs the rogues managed to avoid. Major wholesalers who delivered their flowers intact and paid their full customs duties saw small, inefficient suppliers slowly pushing them out of the market. The competitive edge of the small suppliers was not a zest for efficiency that brought flowers to the market intact, nor a keen eye that spotted the flowers Czechs wanted. The small suppliers were thriving because they were good at evading taxes. Between 1994 and 1997, the value of smuggled flowers had risen from 16.4 per cent of sales to 29.4 per cent of sales, according to official Czech and Dutch customs statistics compiled by Tulipa Praha SRO (1998). This competition from the underground economy harmed my friend’s welfare, but it also seemed that a larger harm came from the damage to efficient flower sellers. The example of the Czech flower sellers and of the Brazilian gas stations suggests there exists a form of social loss that arises from government’s inability to make all firms pay their full tax. A tax system that rewards tax evasion will 1

2

Tax evasion and firm survival

advance the fortunes of producers who are good at evading taxes. When an inefficient producer who is good at tax evasion displaces an efficient producer who is a poor tax evader, there is a social loss. The loss is the difference between the costs of the two producers. This loss is not reflected in higher prices, but rather in lower profits. Consumers do not care whether a producer with low production costs and poor evasive abilities supplies them or whether a producer with high production costs and excellent evasive abilities supplies them. All consumers care about is price. Whether that price is the sum of low production costs and high taxes or high production costs and low taxes is a matter of indifference to consumers. Displacement losses are social losses because they strike at an economy’s revenue. Low profit firms are not able to pay generous wages or dispense fat dividends. What seems to be at work in the example of the flower producers is a failure of markets brought on by a failure of governments. The mix of free markets with unequal enforcement corrodes economic efficiency. This corrosion comes in a variety of forms. What is true of taxes is also true of price controls, regulation of pollution, fishing quotas and other attempts by government to impose laws for the common good. Firms that pay the full minimum wage to their workers may stumble behind firms that violate the minimum wage. Fishermen and fisherwomen with nets that damage their catch, but in possession of fast boats that evade the quota police, may steal the market from competitors who do not damage their catch but who respect the allowable catch. In these examples regulations make nonsense of the market’s purpose of matching eager buyers to efficient producers. Welfare economists are aware that taxes and regulations may discourage consumers and producers from making trades that in the absence of taxes and regulations would bring benefits to all. Textbooks say little about how taxes and regulations encourage exchanges between high cost producers and eager purchasers. In the pages that follow I refer to ‘displacement deadweight loss’ as the amount by which the cost of the inefficient producers exceeds the cost of the efficient producers they have ousted. Like vultures circling above injured prey, deadweight losses signal to the researcher a crippled market. Adding the ability to evade taxes to the ability to produce efficiently creates markets that may not encourage survival of the most efficient firms. Governments that cannot enforce rules evenly are not just unfair governments, they are brake-pads pressing against an economy’s progress. Governments seem aware of the deadweight loss from encouraging survival of firms that evade rules. A 1996 publication of the Quebec Ministry of Finance explains that: Businesses that pay their taxes in full are also seriously affected by unreported work and tax evasion. They face unfair competition on the part of businesses that offer goods and services at lower prices because these businesses did not pay or collect

Introduction

3

income tax or other taxes or they do not comply with the regulations in force (Quebec Ministry of Finance p. 24).

The International Monetary Fund has warned that corruption is a manifestation of poor enforcement of rules that may weaken the labour market. Vito Tanzi (1994), a senior economist at the IMF, explains that corruption can restrict the right jobs to the wrong people. Corruption leads to an arbitrary hiring and promotion of individuals who would not have been selected or promoted on the basis of fair and objective criteria and ‘the selection of these individuals will damage the economy not only by lowering the quality of decisions made by them and by increasing the frequency of mistakes but also by discouraging more able but less well-connected individuals from pursuing particular careers if they feel that the decks are stacked against them’ (Tanzi, 1994, p. 12). Governments try to minimize the loss from unfair competition in two ways. The first way of avoiding displacement loss is the obvious one of trying to enforce rules evenly among producers. ‘Evenly’ means that similar producers pay similar taxes or are subject to the same regulations. This prescription for efficiency is simple, but, as with those prescriptions for a good life laid down in the ten commandments, talking the talk is easier than walking the walk. A government may not be able to apply taxes evenly if tax evaders smuggle their wares in boats too fast for excise officers to catch, and if evaders befuddle tax officials with offshore accounts. Bribes and threats from tax evaders may also keep a government from enforcing taxes evenly. After the fall of communism, the Russian government gave special tax breaks to firms who were friends of high Russian officials. A large part of being a friend in the world of Russian tax collection consisted of unmarked envelopes bulging with cash. Part of Russia’s problem in developing its economy may come from the rise of producers who are good at bribing and threatening, but poor at producing and distributing a product efficiently. A government without political institutions that resist corruption will have trouble keeping down the displacement deadweight losses from evasion of taxes and regulations. The second way governments keep down displacement losses is to encourage a split between evasive and productive abilities. Evasion deadweight loss comes from the jointness of production and evasion. If governments could somehow encourage inefficient producers to give up their rights of production to efficient producers, deadweight losses could be contained. This is the principle that seems to be at work with tradable quotas. Fishermen get quotas limiting their catch. Inefficient fishermen sell their quotas to efficient fishermen. Provided government has set the quota at a level that solves the common property problem, there will be no deadweight losses of any sort. The most efficient producers will pay the most for the rights to production and will come to dominate the market, just as a land-developer with the ability to build

4

Tax evasion and firm survival

a profitable shopping mall will buy out dozens of smallholders whose best use of the land is to grow potatoes. A well-developed political system that allows lobbyists to thrive may also be a device for containing the deadweight losses from evasion. Political lobbying is a legal form of exchange between evaders and producers. Lobbyists market their talents at getting special government favours, such as investment grants, to firms who can make the most of these favours. Two supermarkets may seek an exception to a commercial zoning law that would allow one of them to build in a residential area. The efficient supermarket with weak political connections might lose out to the inefficient supermarket with strong political connections. By hiring a lobbyist, the efficient supermarket may prevail. A political system with open lobbying and a leadership open to persuasion may help to minimize the adverse selection of talents that leads to a displacement loss. Perhaps this is why the tax systems of developed economies are complicated. Complication allows producers and evaders to specialize and trade with each other through the political market. The costs of organizing these political markets, often referred to as rent-seeking costs, may be seen as an echo of the deadweight losses that would have resulted from adverse selection. I am not the first economist to have discovered the notion that there is a gain from trade when individuals specialize in their comparative advantage, and that markets develop in part to encourage non-jointness in production. But most discussions of specialization show the benefits of putting one’s energies in one of several productive activities. This approach to specialization has created the field of international trade economics and is at the basis of many other branches of economics. In the present book I want to draw attention to how equilibrium arises in markets where each participant has a productive talent and an unproductive talent. Using very simple and general assumptions I will build a case that many private and government institutions have evolved to avoid the deadweight losses that could arise when inefficient producers with some illicit talent for survival bump efficient producers out of the market. Government institutions have sought to allow individuals to peel away productive from unproductive talents, to specialize in one or the other and to trade production for evasion. The chapters that follow have several goals. The first goal, which is technical, is to model tax evasion in a general equilibrium context. Modelling is interesting to economists, and I devote some space to explaining the new analytical tools I have developed. But modelling should have some payoff. I show that surprising insights come from the models I build and the techniques I use; insights which might not follow directly from intuition, but which arose from the modelling. For example, I discovered that tax evasion can raise government revenues, that the evasion of minimum wages forces some changes on the standard view of labour market equilibrium, and that subsidies given to

Introduction

5

maximize a positive externality from production impose on society the same sorts of displacement deadweight losses as tax evasion imposes. My second goal is to show that tax evasion is part of a larger problem of the uneven enforcement of government rules. This uneven enforcement carries a trademark social loss which can be measured using a specialized calculus I present in the chapters that follow. I show that the displacement losses from tax evasion have a counterpart in the world of price controls, quota regulations, subsidies to business, and the granting of monopoly licences. The present book responds to the alarm sounded by Vito Tanzi (1994) in his work for the International Monetary Fund. Tanzi warned that economic efficiency would suffer from the arbitrary application of rules and regulations which gave preference to some individuals over others. He cited the allocation of import permits, subsidized credit, zoning permits, permits related to various economic activities, and government officials turning a blind eye to tax evasion by favoured companies as examples of government-granted advantages that furthered the fortunes of politically savvy producers over the fortunes of efficient producers. Finally, the chapters that follow emphasize that tax and regulation evasion are threats to economic development. I believe I am not alone in thinking this way and that a large part of the justification for ‘fairness’ as an ideal of government policy is to ensure that efficient producers are not discouraged and pushed to the margins of markets. Fairness is efficient. I show that even under the most benign of assumptions about how evasive talents are distributed in society, the deadweight losses from evasion of regulations and taxes can rival the traditional deadweight losses associated with these government interventions. Any deadweight loss so important will provoke a reaction among government leaders. I suggest that much of government policy is devoted to cleansing society of the deadweight losses from evasion I have discussed here. These losses are non-antagonistic. Getting rid of them would not lead to a fall in government revenue. No interest groups would suffer from seeing these deadweight losses go. We can then expect to see government bending to ensure that these losses do not get out of hand. Governments that succeed in taming these losses may be the ones that have shepherded their economies to sustained economic growth. It is customary at this stage in an introduction to give a blow-by-blow description of the chapters that follow. Instead of sitting the reader down to this ritual of tedium I will summarize the book in one sentence: when inseparable productive and unproductive talents determine the survival of a producer, the most efficient producers may not survive and government will do its best to organize markets so that productive talents predominate. How all of this happens and what this means for economic modelling is the topic of the present book.

2. Tax evasion In 1990 William Baumol published an instant classic in the Journal of Political Economy. ‘Entrepreneurship: productive, unproductive, and destructive’ was a rare piece for a leading journal. Not a single line of math scarred the pages, nor did Baumol blight the papyrus with charts and figures. Instead, Baumol made his case with a simple bit of economic reasoning. Entrepreneurs are the same the world over and across the ages. They look for new products, new means of producing them, new markets. Whether these entrepreneurs add only to their private fortunes or whether their activities help others depends on the rules of the markets in which they work. If the rules reward entrepreneurs who keep their costs down and devise products or services consumers want, an economy grows. If the rules of markets favour entrepreneurs who cheat, steal, and bribe the government for monopoly power over the market, an economy stagnates or at best grows slowly. In Baumol’s view, the changing character of entrepreneurs and the mix of criminal and honest entrepreneurs was important, but he emphasized the changing rules of the game under which they worked that determined economic progress. Baumol’s article came to be a primer in the 1990s on productive and unproductive entrepreneurship and sensitized the economics profession to the need for rules of the market ‘game’ that make participants play productively. He did not emphasize that the mix of good and bad entrepreneurs could be an important drag on an economy if government did not enforce taxes and regulations evenly. Vito Tanzi (1982, p. 88) noted this when he wrote that ‘untaxed underground activities will compete with taxed, legal ones and will succeed in attracting resources even though these activities may be less productive. ... There will of course be significant welfare losses associated with this transfer.’ Jonathan Kesselman (1997, p. 300) made a related point: ‘If pure tax evasion is concentrated in particular industries or sectors it will raise net returns from activities in those sectors, and this will in turn tend to expand those sectors and their products as against the efficient pattern arising with uniform compliance.’ The media are also aware of the problem of uneven enforcement. In the 23 October 1999 edition of The Economist, the Moscow correspondent wrote that ‘The prime cause of all this waste is that Russian business competes on the basis of political connections rather than costs, quality and price. The distortions embedded in the system – tax breaks, access to cheap land or energy and 6

Tax evasion

7

freedom from bureaucratic harassment – mean that, though competition is often intense, the least productive companies can come out winners.’ Economists studying the industrial organization of crime have noted the possibility of an improper selection of entrepreneurs due to the existence of non-productive factors determining who participates in the market. In the case of crime, the non-productive factor is intimidation. Criminal bid-rigging conspiracies in which all participants are allotted fixed market shares permit inefficient firms to stay in the market and prevent efficient firms from growing. Diego Gambetta and Peter Reuter (1995, p. 130) explain that when the Mafia makes life dangerous for entrepreneurs, ‘those very few who venture to take up entrepreneurial activities must be selected from risk-prone individuals. Even discounting for the lack of incentives for efficient production enjoyed by Mafia cartels, this group is most unlikely to contain characters versed in proper entrepreneurial tasks.’ The implication is that government rule-breakers, such as the Mafia, may diminish economic efficiency by creating an atmosphere in which a tolerance for risk is more important than entrepreneurial savvy for participating in the market. As the above comments show, prominent researchers are aware that uneven enforcement of taxes and regulations can impose a variant of Gresham’s law, under which bad entrepreneurs chase out good entrepreneurs. The intuition seems clear. But how do evasive and productive talents fit into an economic model and what comes out of the exercise? Neutral assumptions about who is good at evading and who is good at producing, wedded to a simple model of demand and supply, reveal that the deadweight losses from uneven enforcement of taxes rival the traditional triangle losses associated with the work of Arnold Harberger (1971). What is perhaps surprising about the deadweight loss from bad entrepreneurs chasing out good entrepreneurs is that it has empirical implications. In other words, this deadweight loss I highlight can be tested for. The model I develop predicts that average industry costs will rise with the tax level, which runs counter to public finance wisdom that industry costs should fall with as taxes rise and only the most efficient producers are able to survive. Modelling evasive and productive abilities also sprouts a crop of unexpected insights. Under some joint distributions of these abilities, tax evasion may raise government revenues above what they would be in the absence of tax evasion. To limit the displacement of efficient by inefficient firms governments may wish to set up tax systems that allow efficient evaders to specialize as tax lawyers or lobbyists and efficient producers to specialize at producing. The two may then exchange services to help avoid the deadweight losses from displacement. These insights are not at first apparent. To get to them let us ask first off how public finance economists have studied the uneven enforcement of rules.

8

Tax evasion and firm survival

PAST INQUIRIES Going back to the Pharaohs who estimated annual taxable crops by measuring the level of the Nile, and Caesar Augustus who surveyed the population and assets of the Roman Empire, governments have thirsted for estimates of the size of the economy, both above and underground. Economists have been most obliging in providing the estimates of the underground economy. There is a small industry of specialists who have made their names by putting a dollar sign to the activities of those denizens of the economic deep who prefer to work outside the ruled margins of the national accountant’s ledgers. Edgar Feige (1997), Rolf Mirus and Roger Smith (1981), and Bruno Frey (1989) are a few of the prominent diviners of the size of the underground economy. Estimates on the same economies vary from between 2 per cent to 20 per cent. Friedrich Schneider and Dominik Enste (1999) provide a review of efforts by these and other researchers. Less progress has been made in analysing and measuring the underground economy’s social costs than in measuring its size. The economics profession’s views are mixed on whether activities outside the zone of taxation are good or bad for society. Bruno Frey (1989, p. 111), one of the founders of the Public Choice school of politics and economics, wrote that ‘One of the major benefits [of the unobserved economy] is often considered to be the fact that it is one of the most productive sectors of the economy, without which the population would be materially much worse off.’ In his analysis of free markets The Other Path, Hernando De Soto (1989) sees the informal sector as a competitive market wriggling out of the oligopolistic strictures imposed by corrupt states. In his view, informal markets are a source of economic strength. Friedrich Schneider and Dominik Enste (1999) echo these views when they write that ‘the exit option “shadow economy” is an important restriction on the Leviathan state and can secure economic freedom and liberty’. Patrick Asea (1996) has argued that the underground economy can contribute to ‘the creation of markets, increase financial resources, enhance entrepreneurship, and transform the legal, social, and economic institutions necessary for accumulation’. The contrary view is that the underground economy is a burden to society. Anne Witt (1996, p. 133) writes that ‘when some members of society pay less than their full tax liability, the rest of us suffer’. A more subtle extension of the concern for fairness is that if a large tax burden is forced onto a shrinking part of the population, the deadweight losses per dollar of government income raised will increase exponentially with the flight of workers to the untaxed underground economy. Like rowers carrying their shell to the river, the first rower to lower his shoulder from the load does not do much harm. As others shirk, the weight on the few who remain becomes intolerable. Raymundo Winkler (1997, p. 219) gives the example from Mexico where because of tax

Tax evasion

9

evasion ‘the top marginal tax rate for individuals, 35 percent, is reached by people earning no more than US$8,000 a year. This situation tends to feed back into informal activities and/or tax evasion, creating a vicious circle.’ Governments that are forced by the underground economy to levy taxes on a narrow base of payers avoid building the infrastructures that would help the economy grow. Even if these governments could coerce a small number of taxpayers to fund infrastructure, such an exercise would be fruitless. The deadweight loss that accompanies the tax on the few would be so large that it would outweigh any social benefits from infrastructures. By narrowing the tax base, the underground economy raises what Browning (1976) has called the social cost of public funds to the point where infrastructures are too expensive from a social cost–benefit point of view. According to Becker (1983), who modelled how governments make their decisions, such a social cost–benefit view has to be a part of how any government, democratic or dictatorial, decides on how to spend money. A government facing a large underground economy would make the cost–benefit calculation of building infrastructure and would be forced to neglect the political benefit of building infrastructures if the political resistance, determined in part by the social cost of public funds, were too great. With these ideas in mind, Norman Loayza (1996) modelled the underground economy and found that it could reduce economic growth if this economy reduced the availability of public services to all. Two prominent efforts to measure the social costs of the underground economy are by James Alm and Dan Usher. Alm (1985) saw the main cost of this economy as being the fact that the absence of tax in the underground economy drives a wedge between the marginal product of labour in the underground economy and the marginal product of the same labour in the taxed economy. This wedge means that society’s overall product would be higher if labour moved back to the taxed economy. The fact that labour does not move back leads to a social loss. Alm found that the deadweight losses from the sort of distortion he measured exceed the deadweight losses of taxation without evasion which Harberger (1964) had measured for the US economy. Alm estimated losses as large as 9 per cent of GDP. The problem with Alm’s analysis, as with that of all existing general equilibrium estimates of the underground economy, is that such models do not build individual firm supply curves which meld productive and evasive abilities. As such, these analyses fail to account for the loss that arises when less efficient firms with good evasive abilities displace more efficient firms with poor evasive abilities. As I shall illustrate throughout this book, and in a variety of contexts, there are reasons to suspect that such an omission is significant. Finally, Dan Usher’s (1986) work on the social costs of tax evasion should be mentioned. Usher’s approach had a different focus from that of Alm. Usher examined a world in which all tax evaders are alike. The main social cost of tax evasion on which he focused

10

Tax evasion and firm survival

was the effort that evaders devote to concealing their incomes. Because everyone is alike in their ability to avoid taxes, there is no displacement of more efficient agents by less efficient agents. The present book does not assume there are any costs from devoting effort to the underground economy, as Usher did, but takes up from where Usher (1986) left off by allowing evasive abilities to differ. The rest of this chapter is an introduction to modelling such abilities and measuring the social costs they impose.

HOW TAX EVASION DISTORTS SUPPLY To model how one producer displaces another it helps first to remind ourselves what a supply curve is. A supply curve is one firm’s or a group of firms’ rule for deciding how much to produce given all the parameters such as costs and prices a firm faces. Usually such curves are drawn in two dimensions and follow the bizarre Marshallian canon of putting price, which in competition is an independent variable for firms, on the vertical axis, and quantity produced, the dependent variable, on the horizontal axis. Supply depends on whether a market is competitive or monopolized. Under competition, when firms minimize costs, a firm’s supply curve is simply the firm’s marginal cost curve. Competition forces the firm to take price as given. This means it will increase production as long as a unit increase in its output costs less than the price the unit can fetch. The firm stops producing when price, which is the marginal gain of producing, equals the marginal cost of producing. This is how price changes trace out a firm’s continuous supply curve in competition. Market supply is the horizontal sum of the marginal cost curves of all firms. Firms with the lowest marginal costs will have the largest market shares. With many firms, each of roughly equal size, but unequal costs, economists can simplify their theoretical lives by assuming each firm produces an infinitesimal amount of the good. This assumption allows us to do away with considering a firm’s cost minimizing problem. Whether the assumption is justified depends on its realism and the aspects of the market upon which we wish to focus. The assumption that the market is a continuum of firms means the market supply curve becomes not the horizontal sum of continuous individual supply curves, but a continuous line made up of dots ordered from left to right. The dots represent each firm’s costs and the dots line up with the least cost firms at the left and the highest cost firms on the right. This is the sort of supply curve I will consider throughout the rest of the book. Interested readers may consult Telser’s (1978) use of such curves in a wide variety of contexts.

Tax evasion

Price

Production cost

Price

Quantity Figure 2.1

11

Tax

Quantity Figure 2.2

To illustrate how high cost producers can displace low cost producers consider a simplified version of the supply curve I have been talking about. Figure 2.1 shows five producers lined up in order of increasing production costs. Each vertical bar represents one producer’s unit output. The least cost producer is leftmost in the figure and the highest cost producer is rightmost. Now consider Figure 2.2 in which government levies a tax on each unit of output. Now each firm’s costs are the sum of production costs and taxes. Taxes in Figure 2.2 do not upset the order of producers in the supply curve. How does the supply curve change if producers evade taxes? The answer depends on which producers evade and by how much they evade. The story I told in the previous chapter about the Czech flower wholesalers suggests one possible pattern of evasion. Perhaps the producers who are least efficient at producing are best at evading. There is empirical evidence for this assumption but many objections can be raised. I will address these points later. For the moment let us see how the supply curve changes. Figure 2.3 is the first step towards the new supply curve. In this figure I have added tax costs to production costs, as I did in Figure 2.2, only now, the least cost firm pays the most taxes because it is least able or willing to evade. What Figure 2.3 shows is no longer a supply curve. To get supply we need to reorder the producers in Figure 2.3 from front to back. Because of the way I have rigged the ability to evade, what were once the firms with highest production costs are now the firms with the lowest sum of tax and production costs. These firms shift from right to left on the graph and firms that were leftmost shift rightmost. The result is Figure 2.4, which looks more like a supply curve than Figure 2.3. Figure 2.4 orders firms from left to right in order of increasing total production and tax costs, but it also places them left to right in order of increasing production costs. What has happened in this example is that a tax has ‘inverted’ the order of suppliers, so that at any given level of market output it is the least efficient producers who will be supplying. The deadweight loss from the inverted order would be the

12

Price

Tax evasion and firm survival

Price

Tax

Quantity Figure 2.3

Tax

Quantity Figure 2.4

cost of producing a certain output with the least efficient firms, less the cost of producing the same output with the most efficient firms. Throughout the rest of the book I will call this deadweight loss from the displacement of low cost producers by high cost producers ‘displacement loss’. My assumptions about how evasive and productive talents are related are at the heart of analysing the deadweight losses from displacement. When the most efficient producers are the least efficient tax evaders, rising taxes will favour the survival of good evaders. Good evaders push efficient producers out of the market. If we change the assumption on how productive and evasive ability is distributed among firms, the above analysis would have to change. Consider what the supply curve would look like if productive and evasive talents were granted randomly to producers. A high cost producer might be good at tax evasion, bad at tax evasion, or might be an average tax evader. Low cost producers could also span the range of possible evasive talents. The gifts nature handed out in the production department would have nothing to do with the gifts she gave producers for evading taxes. With unrelated productive and evasive talents the supply curve would no longer be inverted. Some low cost producers might find themselves at the far end of the supply curve, others would be bumped to the middle, and others would keep their place. The pattern of bumpings would depend on the statistical distribution nature used to determine who gets what talents. One would think that in this case the deadweight losses from inefficient producers bumping out efficient producers would be smaller than in the case when there is a total inversion of producers. In this instance as in many others I will mention throughout this book, surface intuition is wrong. Deadweight losses from displacement in the seemingly neutral case where evasive and productive talents are unrelated rival those in the seemingly extreme case where productive and evasive talents are negatively related.

Tax evasion

13

PUTTING SOME STRUCTURE ON THE IDEAS The above discussion suggests that to model displacement loss we need to have some idea of how productive and evasive abilities are distributed in the population. In this section I model the case where evasive and productive abilities are inversely related. The assumption is crude and perhaps unrealistic, but should be seen as a ride in training wheels for the theoretical development of complicated assumptions about the joint distribution of evasive and productive talents. To put some structure on Figures 2.1 to 2.4 consider an industry where producers share output equally. Producers are infinite in number, indexed by f, and distributed along the interval [0, N] with frequency 1. There is no randomness here, just an ordering and a weighting scheme. The parameter N is not the number of firms but rather the ‘measure’ of firms in the market. Costs of firm f are a linear function of its index f. Costs are also a function of the tax T which is levied on each unit of output (this tax could also be thought of as a social security levy imposed on each labourer the firm hires). The levy has nothing to do with the firm’s profits and is proportional to the firm’s inputs and in consequence, to its outputs. I assume each firm evades the tax in inverse proportion to its costs. Put more formally, each producer evades a part f/N of the lump-sum tax of T. This gives the cost function of firm f: f   C f =  f + T 1 −   df   N 

(2.1)

The above equation says that the least efficient producers are the best tax evaders. The ability to avoid taxes rises with the firm’s production costs f. The df represents the fact that each firm only gets an infinitesimal fraction of total output. This is not the only possible way to model an inverse relation between productive and evasive talents, but has the advantage that the relation is linear. A linear relation helps greatly in solving the equations that follow for equilibrium. Before developing the formal model of equilibrium, a refinement of the graphs in Figures 2.1–2.4 might help. Figure 2.5 shows the supply curve when the measure of firms is N = 10. Several aggregate supply curves appear. The lowest curve represents aggregate supply in the absence of tax. Each producer whose cost is less than equilibrium price participates in the market and shares output equally with the rest. Firms are ordered from left to right on a scale of increasing production costs. So far, so normal. As taxes rise the supply curve rotates counterclockwise around the point 1. The curve rotates because the highest production cost firms pay none of the tax increase and the lowest

14

Tax evasion and firm survival

production cost firms pay the full tax increase. When taxes are $10, the aggregate supply curve flattens, indicating that at this tax rate all firms have the same sum of production and tax costs. A $10 tax forces even the lowest production cost firms to have the same total cost (taxes plus production costs) as the highest production cost firms. In the next section I will refer to this critical tax which evens out all costs as Teven. The supply curve at a tax of $10 says nothing about how producers are ordered on the scale of productive efficiency because in this case order does not determine who produces.

Demand

Supply when T = 15

T = N = 10

1 2

C

A

4

3

Production cost and supply when T = 0

B

Production cost when T = 15

Q sT = 15

Q sT = 0

N – QsT = 15

i N

Figure 2.5 For any tax level above $10 the supply curve takes a twist. There is a complete ‘inversion’ of talents. The least efficient producer all of a sudden becomes the producer with lowest overall cost, the most efficient producer becomes the producer with the highest costs, and so on. As explained in the

Tax evasion

15

previous section, the reason for this jump lies in the inefficient producer’s superior ability to evade taxes. Past a tax of $10 this talent kicks in and becomes the dominant factor in determining the sum of production and tax costs. The supply curve when T = $15 is not a traditional supply curve in that it does not order producers from left to right by increasing production costs. Instead it orders producers by decreasing production costs. I have decomposed part of this supply curve into a cost curve labelled ‘production cost when T = $15’. This curve is a perfect reflection of the supply curve when taxes are zero. Not only do taxes reduce the number of active suppliers from QsT = 0 to QsT = 15, but those who remain are the least efficient producers. The difference between their production costs and the costs of production that would have prevailed had government rooted out all tax evaders is the displacement deadweight loss. This loss is due to a severe adverse selection that leads to a complete ‘inversion’ of talents. Displacement loss appears as the shaded trapezoid A between QsT = 0 and QsT = 15. The top border of this trapezoid between the points labelled 1 and 2 represents the production costs of firms who find it profitable to produce at the prevailing price. The top border is downward sloping because under inversion, the least efficient producers have the lowest overall sum of production and tax costs, and so place leftmost along the quantity axis. Being the least efficient producers they are drawn from the rightmost end of the zero-tax supply curve between index values [N – QsT = 15, N]. This is the segment that stretches between 3 and 4. The production costs of these firms sum to: N

∫N − Q

s T =15

f df =

(

)

2 1 2 N − N − QTs =15    2

(2.2)

To measure deadweight loss from displacement we must subtract what production costs would have been if only the most efficient firms had supplied the market with QsT = 15: QTs =15

∫0

f df =

QTs =15 2

2

(2.3)

The difference between actual and minimum production costs (i.e. the area A) is the difference between equations (2.2) and (2.3), and can easily be shown to be QsT = 15 × (N – QsT = 15). The formula for the trapezoid A is simple in this case because firm costs are a linear function of the index f. A non-linear cost function would yield a more complicated expression for displacement loss. How does this displacement loss compare with the traditional triangle loss associated with the work of Harberger (1971)? One must exercise caution in discussing triangle loss in the context of tax evasion. In Figure 2.5 I suggest that

16

Tax evasion and firm survival

the triangle loss should be measured by the triangle which is the sum of B and C. The reader’s initial objection to this measure of triangle loss is that it would overstate the true triangle loss and that the proper measure is simply the triangle C, which is the difference between the discouraged benefit of consumers (as given by the height of the demand curve) and what the cost of producing those goods would have been (as given by the production cost curve when T = 15 and not the supply curve when T = 0). To see why we have to add B we simply note that without the tax, there would have been no tax evasion and the least cost firms would have been producing between QsT = 15 and QsT = 0. This explains why we must calculate the Harberger triangle under tax evasion by considering the costs of the producers who would have produced had there been no taxation. As one can see from the area A, the deadweight loss from displacement of low cost firms by high cost firms may exceed the traditional triangle deadweight loss from discouraged consumption. The sceptical reader may question whether government would ever allow producers to be so radically inverted along the supply curve. The answer, to which I will suggest an answer in the next section, is ‘No’. A government that pushed taxes so high as to invert the order of suppliers would find itself on the wrong side of the Laffer curve, with a plunging discontinuity at the critical tax level where talents invert. On this wrong side only the best tax evaders would be producing. The proof I present in the next section is more than an excursion into an academic crossing of t’s and dotting of i’s. A spin-off from the proof is the discovery that government revenues may be larger under tax evasion than under complete compliance with tax authorities. The proof will also lay the ground for more realistic and complex analyses of the displacement costs of tax evasion. As in those Colin Dexter detective novels where six or seven people are murdered weekly in Oxford, the reader is asked, for a time, to suspend disbelief and explore the mysteries of inversely correlated productive and evasive talents.

GOVERNMENT REVENUE UNDER TAX EVASION The purpose of this section is to show that in very general circumstances, government would not set taxes so high as to invert the order of suppliers. To see this, we need to examine government revenues at taxes below, equal to, and above the critical tax that inverts the supply curve. To calculate government revenues we need to calculate market equilibrium. Equilibrium is a three-part function of the price–quantity pair (P*, Q*). The equilibrium relations fall into three zones defined by the level of tax. As described in the graphical example of Figure 2.5, at some tax Teven all producers have the same sum of taxes and production costs (Cf as defined by equation (2.1) is the same for all). This is a peculiarity due to the linear nature of the cost function I have chosen.

Tax evasion

17

Case 1: T < Teven Finding the equilibrium price, quantity, and government revenues comes from setting demand equal to supply. Demand above a > 0 and b < 0 is given as some function of price Qd = a + bP. Supply comes from asking how many firms have costs below the going market price. A firm f will choose to be a supplier if its costs are below the market price, that is, if f + T (1 – f/N) ≤ P. Supply is the proportion of such firms willing to supply Pr multiplied by their measure (or maximum market output) N: f   Q s = N × Pr  f + T 1 −  ≤ P   N  

(2.4)

N  = N × Pr  f ≤ ( P − T ) −T N 

(2.5)

= N∫

(P−T )

0

= (P − T )

N N −T

1 df N

N N −T

(2.6) (2.7)

In moving from the proportion to the integral above I have used the assumption that the cost indexes f of firms are distributed uniformly on the interval [0, N]. The next step is to solve for equilibrium price P* explicitly by equating the equilibrium quantity supplied to the equilibrium quantity demanded which gives P* = [a(N – T) + TN]/[N – b(N – T)]. The equilibrium quantity can be found by substituting P* into the demand equation. The revenue that government earns in the tax range T < Teven is the sum of revenue collected from those firms with indices ranging from 0 to Q*. R = N∫

Q*

0

f 1 T 1 −  df  N N

Q * = TQ * 1 −  2N 

(2.8)

(2.9)

Case 2: T = Teven What about equilibrium at Teven? This happens when T = N. At this level of tax the cost for all firms as given in equation (2.1) is the same. To see this simply set T = N in the cost equation:

18

Tax evasion and firm survival

f C = f + T 1 −   N f = f + N 1 −  = N  N

(2.10)

(2.11)

The equilibrium price given by this flat aggregate supply curve is simply P* = T = N and one substitutes this value back into the demand equation to find the equilibrium quantity produced and consumed Q*. The identity of those firms that end up producing is not certain. If each firm has a chance Q*/N of being among those whose production sums to Q* then expected government revenues are R=∫

N

0

=

Q*  f T 1 −  df  N N

TQ * 2

(2.12)

(2.13)

Case 3: T > Teven The final case to consider is when T > Teven. Once again, a firm supplies if its costs f + T(1 – f/N) ≤ P which can be rearranged to give f(1 – T/N) ≤ P – T. What differs from Case 1 is that T > N. This means there is a reversal of the inequality sign when isolating f. So a firm supplies if f ≥ (P − T )

N N −T

(2.14)

The output of such firms is, following the logic set out in Case 1, N  Q s = N × Pr  f ≥ ( P − T ) N − T  

(2.15)

N  (P−T ) 1  N −T = N 1 − ∫ df  0 N  

(2.16)

= N − (P − T )

N N −T

(2.17)

Tax evasion

19

The difference in functional form between Cases 1 and 3 is that in Case 3 for taxes greater than Teven the suppliers with the greatest production costs become the suppliers with the lowest overall costs. As explained earlier, there is a complete inversion of the supply curve. This happens because past a level of tax, the ability to avoid taxes dominates low production costs as a determinant of a firm’s overall costs. The costs of those firms producing now span the range [Q*, N], whereas in Case 1 where the lowest cost producers survived, costs spanned the range [0, Q*]. Solving for equilibrium price gives: N  N − ( P * − T ) = a + bP* ⇒  N −T P* =

(2.18)

( N − a)( N − T ) + TN b( N − T ) + N

(2.19)

For brevity I omit the equilibrium quantity, which is easily calculated by substituting the above price into the supply or demand equations. Government revenues are collected from producers indexed in the range [Q*, N]. These revenues sum to: R = N∫

N

Q*

f 1 T 1 −  df  N N

(2.20)

T ( N − Q *) (2.21) 2N As mentioned earlier, in this zone of taxes there is a deadweight loss due to the complete inversion of productive talents along the supply curve. This loss is calculated as the difference between how much it costs the actual high cost supplier to provide the quantity N – Q* less how much it would cost if the least cost suppliers in the range [0, N – Q*] were to provide this quantity. This deadweight loss due to displacement is 2

=

DWLdisplacement = ∫

N

Q*

f df − ∫

N − Q*

0

f df

= Q * N − Q *2 This displacement loss can be added to the traditional triangle loss:

(2.22) (2.23)

20

Tax evasion and firm survival

DWLtriangle = ∫

QT = 0 N − Q*

(P

d f

)

− f df

(2.24)

 a (1 − b)  a (1 − b)   = QT = 0 − + QT = 0  − ( N − Q *)− + ( N − Q *) b b b b 2 2     (2.25) where QT = 0 is the quantity produced in equilibrium when taxes are zero. The sum of both losses, equations (2.23) and (2.25), is the total deadweight loss. Explicit expressions for government revenue based on the above model contain squared terms and ratios that are tedious to analyse. Instead, to prove the point that government would not want to invert the supply curve because this inversion happens only on the wrong side of the Laffer curve, I have performed simulations. Figure 2.6 assembles the three components of the Laffer (1981) curve with the evasion derived above to show that government revenues vary as a function of the tax level. I take as demand curve Qd = 10 – 0.75P. I have chosen the parameters of demand simply to make sure demand and supply cross. Provided demand and supply cross, the main result I now discuss is unaffected by assumptions about the demand parameters. The government revenue curve as a function of the tax level in Figure 2.6 falls off at taxes higher than $10. This is precisely the tax at which the supply curve inverts and the least cost efficient, most tax evading producers are left in the market. That government revenues should fall when the supply curve inverts should be no

Government revenues

25

Evasion

20 15

No evasion

10 5 0 –5

0

5

10 Tax level

15

Figure 2.6 Laffer curves under evasion and honesty, a = 10, b = –0.75

20

Tax evasion

21

surprise. When the best tax evaders are the only producers left standing, government revenues will fall off. If finding out that government does not want to invert the supply curve because an inversion would send it to the wrong side of the Laffer curve is the only insight that comes out of the above development, the preceding exercise would seem tedious and overwrought. It is simple to understand that when only the best tax evaders survive because taxes are high, government will be collecting small sums. The exercise has two purposes that go beyond this insight. The first purpose of the exercise is to get us ready for the more realistic and complicated analyses of displacement loss. The second purpose of the exercise is that surprising insights can come from modelling tax evasion as I have done. The surprising insight is that government revenues can be higher under tax evasion than if no one evades taxes. If productive and evasive talents are inversely related government may, through a lump-sum tax, discriminate between those who can pay and those who cannot pay. This tax discrimination allows government to raise potentially more revenue than if there was no tax evasion. To see how tax evasion can boost government revenues we need to calculate a benchmark Laffer curve in a world where no one evades taxes. In a world without tax evasion the cost function of the total costs of firm f is: Cf = (f + T)df

(2.26)

Market supply is the measure of firms N (or maximum potential market output) multiplied by the proportion of firms who supply: Q s = N × Pr [ f + T ≤ P] = N∫

P−T

0

1 df N

= P−T

(2.27) (2.28) (2.29)

Government revenue is R=∫

f*

0

T df = T f * =

a b T+ T2 1− b 1− b

(2.30)

which is a quadratic equation with a negative coefficient attached to the squared term (since b < 0), and so can be seen to have the familiar concave shape of the Laffer curve.

Government revenue

22

Tax evasion and firm survival

50 45 40 35 30 25 20 15 10 5 0

No evasion

Evasion

0

5

10 Tax level

15

20

Figure 2.7 Laffer curves under evasion and honesty, a = 10, b = –0.40 Going back to Figure 2.6 the reader will notice that I have included the Laffer curve without evasion as well as with evasion for the demand curve Qd = 10 – 0.75P. The maximum revenue possible under tax evasion exceeds the maximum possible without tax evasion. Past a critical tax level the revenue in the case of tax evasion plummets. This is the critical tax at which talents become inverted and only the least efficient, least tax-paying producers are left in the market. Figure 2.7 is for the case where demand is Qd = 10 – 0.40P. Here the Laffer curve with evasion is completely beneath the no-evasion Laffer curve. Tax revenues are higher without evasion in this case because demand elasticity is low. A tax will not lead to much shrinkage of the market. In this case the taxbase-preserving properties of evasion are not as telling as when demand elasticity was high. In a low demand elasticity environment without evasion, government does not see its base shrink by as much and collects full revenues from all producers. Think of the extreme case where demand is completely inelastic. Clearly evasion in this case could only diminish government revenues. For readers who are interested in seeing how the evasion and no-evasion Laffer curves change with the elasticity parameter, I have presented Figure 2.8, which is a three-dimensional compilation of the sorts of cross-sections presented in Figures 2.6 and 2.7. My derivation of the result that government revenues may be higher under tax evasion should not be compared with the work of Laurence Weiss (1976) who argued that under certain conditions, if people are allowed to cheat on their income tax, government revenues could rise. He examined a second-best world where lump-sum taxes were excluded. The taxes that could be levied were those that would diminish work. Under a utility function whose absolute risk aversion

Tax evasion

23

35 30

Honesty

25 Evasion

20 Revenue

15 10 5 0 0 2 4 6 Tax

8

–0.8 10 –0.6

–1

–1.4 –1.2

–1.6

–1.8

–2.0

b

Figure 2.8 Laffer curves under honesty and tax evasion for a = 10 falls sharply with wealth Weiss found that the incentive to cheat raises labour supply and so can increase the tax base rapidly enough to allow government to recoup the losses from cheating. This is Laffer’s argument about the level of tax rates transposed to the probability of being caught cheating. In Weiss’ world, governments can be on the wrong side of a Laffer curve in (government revenue, probability of detection) space. My argument that tax evasion can raise government revenue has nothing to do with being on the wrong side of any variant of the Laffer curve. My argument rests on showing that the Laffer curve under tax evasion can lie above the Laffer curve without tax evasion and that the cause of such a manifestation is that tax evasion, as I have represented it, can allow government to act as would a price discriminating monopolist. Government revenue may be greater under tax evasion than without evasion, but at what social cost does this revenue come? Figure 2.9 focuses on the range where government is on the left side of the Laffer curve with evasion for the case where Qd = 10 – 0.75P. In this range I show the ratio of triangle deadweight loss (there is no inversion deadweight loss on the left side of the evasion Laffer curve) under evasion and without evasion for equivalent levels of government revenue. Figure 2.9 shows that triangle loss is several times larger without (yes, without) tax evasion than with tax evasion for the same levels of revenue. The reason is that government is able to raise the same tax revenue under tax evasion

24

Tax evasion and firm survival

4 Ratio of triangle losses

4 3 3 2 2 1 1 0

0

5

10 Equivalent value

15

20

Figure 2.9 Ratio of honesty triangle loss to evasion triangle loss for equivalent government revenue, a = 10, b = –0.75 without imposing as high a tax rate as if there were no evasion. With evasion, less demand is discouraged for the same level of revenue than without evasion because the pattern of evasive abilities allows government to convert a flat tax into a variable tax in which each pays according to his ability to evade. In this example ability to evade is positively tied to ability to afford the tax. So by the happy chance that evasive abilities are negatively correlated with firm costs, government is able to act like a price discriminating monopolist would in a market for some good. The result is that less triangle loss is generated with evasion than without evasion. Triangle loss under no evasion continues to exceed that under evasion even for cases where demand is less elastic. This may surprise the reader who gleaned from the previous paragraphs that when demand is less elastic, maximum government revenue under no evasion can exceed maximum revenue under evasion. There is no mystery here. The comparison I am making is for deadweight losses under equal revenues. There is no such equivalent comparison possible when looking at maximum revenues under evasion and no evasion.

CRITIQUES Several critiques of the above approach come to mind. 1. Whenever a new deadweight loss trumpets its arrival on the theoretical scene, witnesses to the event may rightly ask whether the deadweight loss

Tax evasion

25

is new or is an old form of a deadweight loss got up in fresh linens. The sceptical reader might suggest that the same sort of loss is to be found in the case of an industry with one producer with decreasing costs. A tax would decrease output and create a rise in costs similar to that found in the case of an inversion of the supply curve. Does it really matter for the social loss from the tax whether the loss is at the extensive margin as in my example of inversion, or at the intensive margin, as in the case of one producer with decreasing costs? It matters if one is interested in public policy. The prescription for reducing deadweight loss is different in the case of displacement loss from what the prescription would be when a producer has diminishing costs. With displacement of efficient by inefficient firms, the prescription for policy would be to strive for even enforcement of the tax law. With the diminishing cost industry, policy might prescribe a government takeover of the industry followed by price controls. The critical feature of displacement loss is that this loss is either the child of the inability of rulers to enforce their rules evenly, or it is the outcome of a government that follows discretion rather than rules. There is also a world of difference in how the loss from restricting the output of a diminishing cost industry is modelled and how displacement deadweight loss is modelled. 2. The weakness of displacement loss is that to know whether it is a problem one needs to know how evasive and productive abilities are distributed in the population. Knowing the slope of the demand and supply curves as in the case of ordinary deadweight losses is not enough to tell us anything about displacement loss. Displacement loss is not prone to the same problems of interpretation that plague a loss of consumer’s surplus. There are no line integrals to worry about, the order of price changes does not matter, and there is no confusion about which measure, compensating or equivalent variation, is appropriate. Displacement loss is distinct from the loss of producer surplus familiar to students of introductory public finance textbooks. This familiar producer surplus loss measures the profits producers lose when consumption of their goods dries up due to a tax increase and is in no way related to the loss that arises when inefficient firms displace efficient firms. 3. Perhaps the most obvious critique is that firms in my model do not vary their decisions on how much tax to evade. It is more common to take a partial equilibrium approach. Studies such as those by Allingham and Sandmo (1972), Watson (1985), Jung et al. (1994), Yaniv (1994), and too many others to cite here, treat tax evasion as a decision by agents who weigh the risk of detection against the gains of evasion. I do not model the decision to evade taxes (or equivalently, the decision process), but take each individual’s decision on how much to evade as given. I then model the consequences for equilibrium tax collection of a distribution of evasive decisions. By not

26

Tax evasion and firm survival

depending on how agents arrive at their decisions to evade, my analysis is general and does not hang on whether producers are risk averse, risk-seeking, nor on the detection strategies of tax authorities. The blizzard of assumptions that go into the partial equilibrium approach is not important for the modelling approach I adopt here. Partial equilibrium assumptions are only important for the present analysis if they have some bearing on the joint distribution of evasive and productive abilities. This point is simple but is perhaps the one that meets greatest resistance among researchers steeped in the partial equilibrium school of tax evasion analysis. The reader is right to criticize and be sceptical of my assumption that evasive and productive abilities are negatively related. The next section loosens this assumption.

PRODUCTIVE AND EVASIVE ABILITIES UNCORRELATED In an essay on the policy implications of the underground economy, Jonathan Kesselman (1997, p. 300) wrote that ‘if pure tax evasion is randomly distributed across industries and sectors of the economy, it is unlikely to affect resource allocation other than through the need to recoup revenues lost through higher tax rates.’ In this section I show the opposite of what Kesselman postulates. A random distribution of evasive talents can lead to a large misallocation of losses. What is a random allocation of tax evasion? Consider what the supply curve would look like if productive and evasive talents were granted randomly to producers. One would think that in this case the deadweight losses from inefficient producers bumping out bad ones would be smaller than in the case when there is a total inversion of producers. In this case as in many others I will mention throughout this book, surface intuition is wrong. Deadweight losses from displacement in the seemingly neutral case where evasive and productive talents are unrelated rival those in the seemingly extreme case were productive and evasive talents are negatively related. As in the case where talents were inversely related, in the uncorrelated case the procedure I follow is to model equilibrium output and prices and compare production costs to what the minimum cost of production would be in the case of no tax evasion. The equilibrium is found by equating supply with demand. This sounds simple. The only wrinkle is in coming up with an expression for supply. Suppliers evade the tax, and it is they who need to be given a look. Supply As in the case of a negative relation between evasive and productive abilities, I assume a continuum of firms, with each producing an infinitesimal amount,

Tax evasion

27

and none having any influence on price. A firm’s total costs are the sum of its production costs and the taxes it pays. The difference from the previous case is that now these two components of cost are unrelated. Firm f draws its productive abilities i from a set of is distributed on the interval [0,1]. The i represents a fraction of some number K, the production costs of the least efficient firm in the industry. Firm f draws its evasive abilities j also from a set distributed on [0,1]. The j represents the fraction of the official tax level T that firm f pays. The higher is j, the less able is the firm to evade the tax. Both evasive and productive abilities are independently distributed and firm f ends up with total costs of Cf = (iK + jT)df

(2.31)

The df term reflects that the firm’s output is infinitesimal. As before, the index f can be thought of as running from [0,N] where N represents the industry’s potential output. To get a grasp on the above expression for cost, suppose that N = 20, the official tax is set at T = $3 per unit of output (so that without any evasion a firm would pay $3df in taxes) and the costs of the least efficient firm imaginable are K df = $5df. Suppose the firm indexed by f = 8 draws an i of 0.4 and a j of 0.2. This means its total costs are (0.4 × 5 + 0.2 × 3)df = $2.6df. If this turns out to be less than the market price, then firm 8 will decide to produce. Think of performing this exercise with each of the remaining firms in the range of fs between zero and 20, never knowing whether for each firm a low or a high draw for evasive ability will be accompanied by a low or a high draw for productive efficiency. The language I have used above may seem strangely disembodied from reality. What does it mean for a producer to ‘draw’ his evasive ability from a statistical distribution? Does such a producer actually come up to the podium as would a guest on a game show and pull a certificate of evasive ability from an urn? The answer is that even though the language may seem artificial, my approach to modelling talents is close to the ground. From the works of psychometricians such as Thurstone (1941) we have an inkling that fundamental endowments of talent can be modelled as random processes. What people do with these talents can then be interpreted through a model. My method of proceeding is to assume a uniform distribution of productive and evasive talents, and wed this to my model of tax evasion to see what sort of supply emerges. My approach can be criticized on many grounds. Why assume that evasive and productive talents are independently drawn? Why assume they have a uniform distribution? For the moment my plea for these assumptions is that they are simple to work with and seem to be ‘neutral’. A uniform distribution is what Bayesian statisticians call a diffuse prior, which is a euphemism for ‘I don’t know’. Independence of evasive and productive talents is a benchmark

28

Tax evasion and firm survival

case which can be complicated to include different levels and directions of correlation between these two variables. To rescue this chapter from being an exercise in metaphysics, in a later section I try to explain why uniform distributions might not be too far removed from reality. Supply falls out of an infinite number of firms, each asking itself whether the sum of its tax and production cost is below the market price P. The sum of answers to these many questions is summarized by the supply function: Q s ( P) = N ∫∫ (i, j ):iK + jT ≤ P g(i, j )didj { }

(2.32)

The term N as before is the potential industry output (the ‘measure’ of firms). The term g(i,j) is the joint probability density function of the cumulative density function G(i,j). As stated earlier, I assume that i and j are independently and uniformly distributed. The above integral may look simple in principle, but in practice it poses a challenge. The challenge is not in carrying out the integration, but in figuring out what the distribution of a sum of independent distributions looks like. Students in advanced statistics courses are familiar with the care needed to solve such problems. The challenge is always to figure out what the limits of integration look like. The term in curly brackets at the bottom of the integral is a general statement of the area over which the sum is to be taken. The term in curly brackets is similar to the statement that the USA is bounded by two great oceans, Canada, and Mexico. To put such a statement into practice we need to know something about the Atlantic, the Pacific, Canada, and Mexico. To return to the world of tax evasion, this means drawing a picture of the range of evasive and productive abilities that exist and finding from this picture the subset of such talents that satisfy the requirement that costs be less than price. The proportion of firms Pr who fall within this subset can be multiplied by the total number of firms N to get the amount supplied. This is the solution to the above integral. Recall that I assume productive and evasive talents are uniformly and independently distributed. That is, i ~ U[0,1] and j ~ U[0,1]. In this case the proportion of firms producing can be gleaned from Figure 2.10. The line P = iK + jT shows the extreme combinations of costs and evasive abilities under which a firm will be willing to produce given a price P. Any firm below and to the left of this line has total cost less than price. It chooses to produce. The fraction of firms producing is the area to the left of the price line within the unit square. In this diagram price is always less than K. When price is also less than T the area A represents the fraction of firms producing (K may be greater or less than T). This area times the total number of potential producers F gives supply when P ≤ K ≤ T or P ≤ T ≤ K

Tax evasion

29

i 1

B A 1

    

  

When P < T but K > T, the proportion of producers is P/K less B

    

When P < T and P < K the proportion producing is A, which is the proportion  of firms for which  costs are < price  P —  K

P — T

T — K P = iK + jT P≥T P≤K

j

P = iK + jT P≤T P≤K

Figure 2.10 Qs =

NP 2 2 KT

(2.33)

The above has the reassuring features a supply curve should have. Supply rises with price and the number (in this case the measure) of firms. Supply falls with a rise in costs and a rise in taxes. Before rejoicing too much we should keep in mind that this is not the complete supply curve. It is a supply curve that obtains only in special circumstances. There are other circumstances to explore. When T ≤ P ≤ K, the proportion of firms producing will be the area of the (P/K) × 1 rectangle less the area given by B. In this case supply works out to P 1 T Q s = N 1 × − × 1 ×   K 2 K =

N ( P − 0.5T ) K

(2.34) (2.35)

When price exceeds K we shift to Figure 2.11. When K ≤ P ≤ T the proportion of firms producing is (as always) the area to the left of the price line, which comes to C + D. Output is then

30

Tax evasion and firm survival

P K K 1 Qs = N × 1 ×  −  + N × × 1 × T T T 2 =

N ( P − 0.5K ) T

(2.36) (2.37)

Finally, when K ≤ T ≤ P or T ≤ K ≤ P the proportion of firms producing is 1 less the area E, which gives a supply of: 1 Q s = N 1 − [ K + T − P]2   2 KT

(2.38)

The reader may wonder why I have considered the above sequence of six inequalities involving K, T, and P. These are the parameters of supply. There are 3! = 6 ordered combinations of the above three parameters. Order matters for determining the areas that represent proportions of firms producing. Equilibrium price and output are found by equating one of the above four equations with the demand equation (I will use the form Qd = a + bP). But which supply equation do we choose? Figure 2.12 shows how to resolve the

i P — K

    

1

When P > K but < T, the proportion producing is C + D

( —PT – —KT ) Ε

C

    

1–

D

When P > K and P > T the proportion producing is 1 – E 1–

( —KP – —KT ) P = iK + jT P≥K P≥T

1

j

          P K — –— K T

Figure 2.11

K — T

P = iK + jT P≥K P≤T

Tax evasion

31

dilemma. The figure is drawn on the assumption that T ≤ K. A look at the four previous equations and the inequalities under which each applies reveals that assuming T ≤ K narrows the supply curve down to three possibilities: one for P ≤ T ≤ K (equation 2.33), one for T ≤ P ≤ K (equation 2.35) and one for T ≤ K ≤ P (equation 2.38). The final supply curve relevant for calculating equilibrium is a piecewise combination of these three curves. By flipping this hybrid supply curve on its side and viewing quantity as a function of price one notices a logistic curve, as would be the case when the market price sweeps across a unimodal distribution of reservation prices (the distribution of the sum of two independently and uniformly distributed random variables has a tentshape that roughly resembles the normal distribution). What I have derived may appear as ‘ordinary’ supply curves appear, but differs in substance from them. ‘Ordinary’ supply curves order producers from left to right by increasing levels of production cost. The present supply curve weaves and crosses evasive and productive abilities to produce an ordering that is not wholly based on one or the other. This mixed up ordering is what gives rise to a displacement deadweight loss of firms from taxation. This is also why the tax does not split the supply curve into a reaction curve and a cost curve. In standard public finance analyses, tax drives a wedge between the cost curve and the reaction curve (more familiarly referred to as the supply curve). The reaction curve lies above the cost curve because the minimum bid needed to P

N Qs = — (P – 0.5T ) K

K+T 1 Qs = N 1 – —— [K + T – P ] 2 2KT

(

)

NP 2 Qs = —— 2KT

K=5 T=3

N Figure 2.12

Q

32

Tax evasion and firm survival

convince producers to participate in the market is not just their production cost, but the sum of their production and tax costs. When producers evade, there is no distinction between reactions and cost curves. Reaction and cost curves are fused. Equilibrium The notion that supply is a mix of productive and evasive abilities, factors that pull market efficiency in opposite directions, contains the clue needed to calculate the deadweight loss from displacement. To do this we first need to calculate equilibrium. The calculation is vexing at first glance because when we commit to some T and K such as T ≤ K there are three possible supply curves. Which intersection of demand and supply is right? Suppose we find that demand crosses all three supply curves in such a way that price falls between T and K. According to the way we derived the supply curves, only the curve (2.35) satisfies this T ≤ P ≤ K. When demand intersects the supply curves so that, in all three cases, equilibrium price is less than T, we use the same logic to deduce that the relevant supply curve is equation (2.33). For price in any other range, take the supply curve given by (2.38) as the relevant supply curve. This is the algorithm to use when generating a range of simulated equilibrium prices and quantities for different levels of tax. When T > K, a slightly different supply curve must be used. It differs from the above analysis only in that its middle segment is given by (N/T)(P – 0.5K). Deadweight Loss from Displacement Knowing how to calculate equilibrium price and outputs is the first step in calculating displacement loss per dollar of tax revenue. It remains to derive an expression for this loss, as well as an expression for the taxes government collects. The deadweight loss from displacement can be calculated by first measuring the cost of producing equilibrium output Q* if only the most efficient firms were chosen for the task. What the reader must keep in mind is that Q* is the quantity produced under tax evasion. The way to calculate displacement loss is to measure a least cost benchmark in the absence of taxes that can be compared to actual costs of production under taxation. The least cost of producing output under evasion Q* is the area between [0,Q*] under what the industry supply curve would be if there were no evasive talents. In this case industry supply would be Qs(P) = N × Pr(iK ≤ P)

(2.39)

Tax evasion

33

1 di K

(2.40)

= N∫

P

0

=

N P K

(2.41)

We need to invert the above equation to isolate P, which in this case would represent the height and cost of the industry supply curve. The curve’s height represents costs. The integral under this supply curve in the range [0,Q*] is then the least cost way of producing Q*: Q*

∫0

K K Q *2 QdQ = N 2N

(2.42)

There is a second, less obvious way of deriving this minimum industry cost. Industry cost is the sum of each firm’s cost index i, over the range of firms whose index is below P/K, multiplied by the measure of firms and the maximum cost index K: P

N ∫ K iKdi = 0

NP 2 2K

(2.43)

Noting from equation (2.41) that P = QK/N we can substitute this into the above equation to find the same expression for costs in terms of Q as in equation (2.42). This method of deriving costs is superfluous in the case of no evasion. When producers evade, the method is essential. With productive and evasive talents we can no longer simply integrate under the supply curve to get costs. Under tax evasion the supply curve does not order producers according to productive ability, but according to a mix of productive and evasive abilities. We could attempt to draw a cost curve but it would look like a scatter of dots, with the scatter depending on how each producer drew his productive ability. A producer with low overall tax and production costs might have very high production costs. The producer next to him in the supply curve has similar overall costs but could have extremely low production costs. Such a cost curve would be discontinuous at every interval and integrating it would pose problems. When producers evade, we calculate total industry cost as the sum of each producer’s cost iK didj in the region where iK + jT ≤ P multiplied by the measure of firms N. This way of proceedings rids us of the worry of integrating a scatter of points swarming around the supply curve. Formally, industry costs are:

34

Tax evasion and firm survival

N ∫∫ (i, j ):iK + jT ≤ P iK didj { }

(2.44)

The final shape the cost equation takes depends, as in the case of the supply equation, on the bounds of integration. Here is where all those tedious efforts at establishing the bounds of integration pay off handsomely. Figure 2.10 is our recipe and shows that when P ≤ K ≤ T or P ≤ T ≤ K the bounds of integration give the following industry cost function P

N∫T∫

P − jT K

0 0

iK didj = =

NK 2

P T

2

 P − jT  dj K 

∫0 

NP 3 6 KT

(2.45) (2.46)

The idea behind this integral can be understood with the following mental experiment. Gather all active producers in a room, pick a value for the index of evasive talent j, say, 0.5 and then ask those producers with j = 0.5$ to step forth and have their costs counted. Some will have high, low, or in between costs. The range of costs possible for this group will be determined by the line P = iK + jT. The parameters T and K are fixed beforehand and market competition produced an equilibrium P. The values of these parameters limits the range of costs of active producers who have j = 0.5. If, for example K = 10, T = 5, and P = 8, then for j = 0.5, i can only vary between [0, 0.55] and we sum the costs of producers in this range, before scanning all the other js between zero and one. As the j index in the outer integral advances (i.e. we consider those sectors of the industry where evasive abilities are weak), the uppermost possible cost index i must fall. Another way of thinking of this derivation of costs is that it is the sum of is over the area A in Figure 2.10. The displacement loss is the difference between actual costs and minimum costs: displacement loss =

NP 3 K − Q *2 6 KT 2 N

(2.47)

Figure 2.10 shows that when T ≤ P ≤ K the bounds of integration change slightly because now we are considering the sum of is over the area 1 – B. The cost function becomes: N∫

1

∫

P − jT K

0 0

iK didj =

NK  3P 2 + T 2 − 3PT    K2 6  

(2.48)

Tax evasion

35

As before, the displacement loss is the difference between the above actual industry costs and the minimum costs of producing the same amount as given by equation (2.43). To conserve space I omit the explicit expression for displacement loss. When K ≤ P ≤ T, Figure 2.10 indicates we must sum i’s over the area C + D to get costs. This gives the industry cost function: N∫

P− K T

0

1

∫0

P

iK didj + N ∫PT− K ∫ T

P − jT K

0

iK didj

(2.49)

The explicit expression is not difficult to work out and once again I leave it out. When K ≤ T ≤ P or T ≤ K ≤ P we must sum the cost indexes i in the zone 1 – E. Figure 2.11 shows that the bounds of integration in this case give the industry cost function: N∫

P− K T

0

1

∫0

1

iK didj + N ∫P − K ∫ T

P − jT K

0

iK didj

(2.50)

As before, the displacement loss is the above cost less the minimum cost of producing the same amount. Tax Revenues The last step in the analysis is to figure out what are government revenues so that we can compare displacement losses relative to dollars of tax raised. Tax revenues are measured using the same approach as that taken with costs. Sum the evasive indexes of those firms producing and multiply this sum by the tax level and the measure of firms. In general, tax revenues from the industry are N∫ ∫

{(i, j :iK + jT ≤ P)}

jTdjdi

(2.51)

I have reversed the order of integration to make the exposition intuitive. The intuition is that we are adding all the evasive indexes for firms with productive abilities within a range defined by iK + jT ≤ P. The above sum first looks at producers with very high productive efficiency (low i) and sums government revenues for those producers who exist in this range. The range of evasive talents to be found in equilibrium among those producers with high productive efficiency is large. When we consider those producers who are very inefficient (large i) we find by the stricture iK + jT ≤ P that they will be all very good evaders (high j).

36

Tax evasion and firm survival

Figure 2.13 shows how to put meat on equation (2.51). When P ≤ K ≤ T or P ≤ T ≤ K the bounds of integration cover the area A + C and give the following industry tax revenue function: P P − iK NT N ∫ K ∫ T jTdjdi = 0 0 2 144244 3

area A + C

=

P K

∫0

2

 P − iK  di  T 

(2.52)

NP 3 6 KT

(2.53)

The logic for the bounds of integration is the same as that for equation (2.46) in the case of industry costs but because we are summing over j indexes first, our perspective becomes perpendicular to that taken in Figures 2.10–2.11. When T ≤ P ≤ K, Figure 2.13 shows that the bounds of integration must cover the i 1

P — K

B C

D P — T

  

A

1

P–T ——– K

P = iK + jT P≥T P≤K

j

P = iK + jT P≤T P≤K

Figure 2.13 rectangle C + D defined over the range where j lies between zero and one, and where i lies between zero and (P – T)/K. The bounds of integration must also cover the area of the remaining triangle under the price line A + B. This gives industry tax revenues of:

Tax evasion P−T

P

1

37 P − iK

N ∫ K ∫ jTdjdi + N ∫PK−T ∫ T jTdjdi 04 0 44 0 1 42 3 1K442443 area C + D

(2.54)

area A + B

The complete expression is easy to calculate but too lengthy to present here. When K ≤ P ≤ T, Figure 2.14 indicates we must sum js over the area A + C. This gives industry tax revenues of: P − iK 1 NT  3P 2 + K 2 − 3PK  N ∫ ∫ T jTdjdi =   04 04244 T2 6   1 3

(2.55)

area A + C

When K ≤ T ≤ P or T ≤ K ≤ P we must sum the evasive indexes i in the zone A + B + C + D to get industry tax revenues of: 1

P − iK

P−T

1

N ∫P −T ∫ T jTdjdi + N ∫0 K ∫ jTdjdi 0 0 44 14 42 3 1K442443 area C + D

(2.56)

area A + B

The complete expression is omitted for brevity. i P — K

1 Β

C

D

P — T

Figure 2.14

      

Α

P–T ——– K

1

P = iK + jT P≥K P≤T

P = iK + jT P≥K P≥T

j

38

Tax evasion and firm survival

Simulations What has come out of this storm of integrals and diagrams? The above derivations express supply as a hybrid of two characteristics that pull economic efficiency in opposite directions. The technique has called for an application of the theory of summation of statistical distributions to the theory of supply. Going through the derivations has sensitized us to the fact that in the real world there may be no split between reaction and cost curves and that supply curves lose their traditional interpretation of ordering suppliers by level of productive efficiency. Not all facets of a model though can be readily glimpsed through its equations. Where comparative statics are opaque, simulations can bring understanding. The simulation I consider has twenty firms (or more precisely, the measure of firms is twenty, N = 20), maximum possible cost K = 5, the official tax level T varying between zero and 50, and demand taking the form Qd = 10 – 0.75P. I have calibrated demand to make sure that supply and demand curves cross for a tax level of zero. Demand and supply continue to cross until the tax level reaches 50 at which point the simulations do not proceed. In the simulations that follow the reader should realize that even though the curves look smooth, behind the scenes much effort is going into the simulations. For each tax level I have followed the algorithm outlined above. I have asked what sort of relation the tax has to maximum possible cost, and based on this I have decided which of the four possible supply equations is the correct one to use for deriving equilibrium. Figure 2.15 shows how price and quantity vary with the tax level. Price rises as taxes rise. Price is not always greater than the tax level, as would be expected 14 Price

12 10 8 6

Quantity

4 2 –

0

10

20

30 Tax level

Figure 2.15

40

50

Tax evasion

39

when there is no tax evasion. Evasion allows price to be under the tax level. Quantity falls as taxes rise. Figure 2.16 shows the average costs of producing one unit of output for a range of tax levels in the instance where firms cannot evade taxes and in the instance where they can evade. When firms cannot evade taxes, unit costs fall with the tax level (the line labelled ‘unit costs without evasion’). This is a standard result from public finance. Rising taxes chase out firms and leave behind them only the most efficient firms. When firms can evade, rising taxes lead to rising average unit costs. This is not a standard result, and is not what surface intuition would suggest. Costs rise because rising taxes reward firms with strong evasive abilities, be they of low or high cost. The difference between actual unit costs and what costs would be in the absence of evasion is the unit displacement loss. This rises steadily with the tax level, as Figure 2.16 shows.

Unit costs and losses

2.5

Unit costs with evasion

2.0 Unit displacement loss 1.5 1.0 0.5 –

Unit costs without evasion 0

10

20

30

40

50

Tax level Figure 2.16 How do displacement losses compare to triangle losses? Figure 2.17 shows the ratio of displacement to total deadweight losses (the sum of displacement and triangle losses). The triangle loss is the area A of Figure 2.5 and is calculated by taking the integral of the difference between the height of the demand curve, and the height of what would be the supply curve if no one evaded (the logic for this method is described earlier in the chapter in the discussion of Figure 2.5). If demand is Qd = a + bP, then the height of the demand curve is P = (Q – a)/b. As shown earlier, the height of the supply curve without evasion is (K/2N)Q2. When, say, the tax level is $5 per unit, the integral of the difference between these two curves over the range [QT = 5,QT = 0] is the triangle loss and can easily be shown to be:

40

Tax evasion and firm survival

K  a 1 Triangle loss = QT2 = 0 − QT2 = 5  − − (Q − QT = 5 )  2b 2 N  b T = 0

(

)

(2.57)

Figure 2.17 shows that at low tax levels displacement loss is the major form of deadweight loss. As the tax level rises, firms increasingly sort themselves in order of evasive ability and once this sorting approaches completion the opportunity for displacement tails off. As tax rises, the increasing sensitivity of the demand curve to increases in price pushes triangle loss into prominence. 80 70 Percentage

60 50 Ratio of displacement loss to total deadweight losses

40 30 20 10 0

0

10

20

30

40

50

Tax level Figure 2.17 I speculate, and suggest as an avenue for further research, that we would find some degree of displacement loss even if evasive and productive talents were positively correlated. Provided the correlation is less than perfect, some firms with good evasive abilities but poor productive abilities will be able to displace more productive but less evasively gifted firms. The number of displacements would fall as the correlation reached one. At one there is no inversion of talents and taxation only causes a triangle loss. How do displacement and triangle losses compare to each other as a proportion of the value of industry output P × Q? Figure 2.18 shows triangle and displacement losses as a fraction of the value of industry output, and to get an idea of how a tax level T translates into tax as a percentage of value of industry output I also include a curve labelled tax revenue as a per cent of P × Q. When taxes are close to 30 per cent of output value, as is currently the case in the USA, triangle loss is in the neighbourhood of 2 per cent to 5 per

Tax evasion

41

Loss as a percentage of P × Q

70 60

Triangle loss

50 Tax revenue as a percentage of P × Q

40 30

Selection loss

20 10 0

0

5

10

15

20

25 30 Tax level

35

40

45

50

Figure 2.18 cent. This is roughly what Harberger (1964) estimated from his general equilibrium model for the USA. Displacement loss in this range of taxes lies between 8 per cent and 11 per cent. What is interesting about these numbers is that out of a simulation based on rudimentary assumptions about demand and supply, a triangle loss of the order of magnitude of Harberger appears, and a displacement loss appears which exceeds the triangle loss. What may appear troubling about Figure 2.18 is that the triangle loss seems to be linear in the tax level. Ordinarily one associates linear increases in the tax level to exponential increases in the triangle loss. This troubling aspect of Figure 2.18 disappears if we graph deadweight loss against revenues raised. Figure 2.19 shows that for each extra dollar of revenue raised, triangle loss increases at an increasing rate. Triangle loss even bends back, indicating that past a certain tax level, revenues decrease but triangle loss continue to increase. Figure 2.19 also shows that displacement loss increases at a decreasing rate. This means that the marginal social cost of public funds is a mix of accelerating and decelerating social losses. The sum of displacement and triangle losses is graphed in Figure 2.19 and shows this mixed tendency of the marginal cost of public funds to diminish at first and then to rise. Figure 2.20 gives us a more precise idea of the marginal social cost of public funds. In addition to the triangle loss component of the marginal cost of public funds as expounded by Browning (1976), the present analysis suggests that a second component to Browning’s marginal cost, one that takes account of displacement, needs to be added to the triangle component. Figure 2.20 maps the contribution to the marginal cost of

42

Tax evasion and firm survival

40

Deadweight loss

35 30 25

Displacement + Triangle loss

20

Triangle loss

15 10 5 –

Displacement loss 0

5

10 15 Tax revenue

20

25

Figure 2.19

4.0

40.0 Revenue

3.5

35.0

3.0

30.0

Total deadweight

2.5

25.0

2.0

20.0

Triangle

1.5

15.0

1.0 0.5

Displacement

0

–0.5

0

Figure 2.20

5

10 15 Government revenue

20

25

10.0 5.0 0.0

Revenue as a percentage of P × Q

Marginal social cost public funds ($)

a dollar of public funds of triangle and displacement losses. For government revenue which comes to roughly 33 per cent of the value of output, triangle loss adds $1 to the marginal cost of a dollar raised, and displacement loss adds $0.60, so that the marginal social cost of public funds at this tax level is $2.60. The $1 figure for triangle loss is well within ranges estimated by many researchers. What is new in the calculation is the $0.60 component to the marginal cost of

Tax evasion

43

public funds added by displacement. A government that takes note of this added cost will be further discouraged from undertaking public works. Figure 2.21 shows two types of Laffer curve. One Laffer curve comes from the above derivations of government revenue under evasion. The figure shows that past a tax of $38 per unit of output, government revenue begins to fall. This is the familiar turning point of the Laffer curve. Figure 2.21 also shows what the Laffer curve would look like without tax evasion. The no-evasion Laffer curve calculates what government revenues would be under that tax rate at which equilibrium quantity produced is the same as in the case where there is evasion and evasive and productive talents are uncorrelated. This allows us to compare the no-evasion Laffer curve to the evasion Laffer curve. The noevasion Laffer curve is derived by first getting an idea of equilibrium output without evasion. It is a simple matter to calculate output without evasion (j = 1 for all firms). In this case the proportion of firms producing is Pr(iK + T ≤ P). This proportion works out to (P – T)/K and supply is N(P – T)/K which by equating it to the demand function solves for an equilibrium quantity of Q* = N(a + bT)/(N – bK). We can then isolate the tax as a function of the equilibrium quantity and other parameters to give the tax rate T* = Q*(N – bK) – Na]/bF without evasion that would generate the same quantity of output as the tax T under evasion generates. We multiply T* by the actual quantity produced under evasion to give us how much tax revenue that quantity would generate without evasion. What the comparison of these curves shows is that when productive and evasive abilities are uncorrelated, the seemingly magical result that tax

($) 80 70

Amount evaded

60 Laffer curve without evasion

50 40

Potential revenue gain

30 20

Laffer curve with evasion

10 –

0

10

20

30 Tax level

Figure 2.21

40

50

44

Tax evasion and firm survival

evasion can raise government revenue disappears. When evasive and productive abilities are uncorrelated government loses its ability to tax-discriminate. This is why tax evasion in this case unambiguously lowers government’s revenues. Figure 2.21 also makes one ponder the meaning of ‘revenue lost to the underground economy’. Revenue lost to the underground economy is a term without precise meaning. One can only speak of how much larger government revenues would be if government enforced full compliance, and of how much tax existing firms evade. Potential revenue gain from full tax enforcement and taxes evaded are different quantities. This may sound counter-intuitive, but it is really the same sort of distinction that one must make when thinking of Bill Gates’s fortune. Gates’s fortune is said to hover around $100 billion. Yet if he sold his stocks this might precipitate a fall in the price of Microsoft. What then is the correct valuation of Gates’s wealth? In the same way, if non-compliant firms were made to pay their full tax burden, some would drop out of the market. So it is incorrect to think of taxes evaded and how much larger government’s revenues would be if it enforced complete compliance as the same amounts. Figure 2.21 includes the potential revenue gain. It is simply the difference between the full-compliance and non-compliance Laffer curves. In Figure 2.22 I show this potential revenue gain as a fraction of actual revenues under evasion. For low tax levels the potential revenue gain is roughly 7 per cent. As taxes rise, potential revenue gain converges to 60 per cent. How does this compare to evaded taxes? The firms producing under evasion are not the firms who would produce if there were no evasion. This means that the difference between the two Laffer 90 80

Evaded tax as proportion of total tax

Percentage

70 60 50 40 30 20

Proportion potential revenue gain as a fraction of actual revenues

10 0

0

10

20

30 Tax level

Figure 2.22

40

50

Tax evasion

45

curves in Figure 2.21 does not measure how much tax is being evaded. How much a non-compliant firm evades is the official amount it evades (1 – j)T df if its after-cost and after-tax revenues are large enough to cover this sum. The amount it evades is its profits (P – iK – jT)df if profits are less than the official amount evaded. Put differently, the firm’s net revenue could be smaller than the evaded tax or it could be equal to or greater than the evaded tax. Some firms will earn enough to be able to pay all their evaded taxes. Some firms might only be able to pay off a fraction of the taxes they evade, because their production costs are too high to produce profits equal to or greater than evaded taxes. The amount evaded then must be calculated in consideration of two types of firm. Those firms who can pay the full tax are the ones for whom −3 P −4iK jT ≥ 1 24 profits

1 − j )T (12 4 4 3

(2.58)

tax liability evaded

These firms are the ones for whom i ≤ (P – T)/K. The amount of revenue they could pay back to the state would be: N∫ ∫

{(i, j ):iK + jT ≤ P}

(1 − j )Tdjdi

(2.59)

To get an explicit expression for the above there are once again four cases to consider. • Case 1A: When P ≤ K ≤ T or P ≤ T ≤ K, then (P – T)/K ≤ 0 which means that the firms we need to consider are those with index i ≤ 0. There are no such firms and so in this case revenues dodged from this group are zero. • Case 2A: When T ≤ P ≤ K revenues evaded are N∫

P−T

0

K

1

∫0 (1 − j )Tdjdi

(2.60)

This is the sum of revenues evaded over the region C + D in Figure 2.13. This region satisfies for the constraint that i should be less than (P – T)/K and the inequality T ≤ P ≤ K. • Case 3A: When K ≤ P ≤ T revenues evaded are zero by the same logic as in Case 1A. • Case 4A: When K ≤ T ≤ P or T ≤ K ≤ P revenues evaded are calculated using the same expression as in Case 2A, by the same logic as in Case 2A.

46

Tax evasion and firm survival

Our work does not end here. To the above amount evaded by firms who can afford to repay everything they have evaded we must add the partial repayment that poorer firms could afford. These firms have profits less than evaded taxes: P −4iK −3 jT ≥ 1 24 profits

1 − j )T (12 4 4 3

(2.61)

tax liability evaded

Which says that firms that could partially repay what they have evaded are the ones for whom i ≥ (P – T)/K. The amount of revenue they could pay back to the state would be their profits: N∫ ∫

{(i, j ):iK + jT ≤ P}

( P − iK − jT )djdi

(2.62)

To get an explicit expression for the above there are once again four cases to consider. • Case 1B: When P ≤ K ≤ T or P ≤ T ≤ K, then (P – T)/K ≤ 0 which means that the firms we need to consider are those with index i ≥ 0. These are the firms in the area A + C of Figure 2.13. The revenue evaded they could repay is: P

P − iK

N ∫ K ∫ T ( P − iK − jT )djdi 0 444 0 1 4244443

(2.63)

area A + C

• Case 2B: When T ≤ P ≤ K revenues evaded are P

P − iK

N ∫PK−T ∫ T ( P − iK − jT )djdi 0 1K4444244443

(2.64)

area A + B

This is the sum of revenues evaded over the region A + B in Figure 2.13. This region satisfies the constraint that i should be greater or equal to (P – T)/K and the inequality T ≤ P ≤ K. • Case 3B: When K ≤ P ≤ T we can use Figure 2.14 to see that revenues evaded are 1

P − iK

N ∫ ∫ T ( P − iK − jT )djdi 0 444 0 1 424444 3 area A + C

(2.65)

Tax evasion

47

• Case 4B: When K ≤ T ≤ P or T ≤ K ≤ P Figure 2.14 indicates that revenues evaded are 1

P − iK

N ∫P −T ∫ T ( P − iK − jT )djdi 0 1K4444244443

(2.66)

area A + B

The total of evaded taxes is either the sum of revenues in Case 1A and Case 1B, or the sum in Case 2A and Case 2B, and so on. I have not derived the above expression in the interests of brevity, but they are simple to work out. I have put the sum of these evaded taxes in Figure 2.21 alongside the evasion and noevasion Laffer curves. What strikes one about taxes evaded is that they can be larger than the tax that would be collected if there were no tax evasion. This is because my concept of evaded taxes is the maximum amount of evaded tax each firm could pay if somehow government could identify these firms and know precisely how much to drain from their bodies while preserving their heartbeat. This drain would be the sort of tax discrimination we observed in the section on negatively correlated evasive and productive abilities. The odd result that evaded taxes can be larger than tax collection under no evasion shows how slippery is the notion of evaded taxes. I started out by using what seemed like an ordinary definition of amount evaded, and ended up with an eccentric result. The result is eccentric because it rests on the unrealistic assumption that government could discriminate finely between firms of different costs. The assumption was not evident when I set out to innocently measure the amount evaded but showed its nature when I came to put into numbers what I had put into words. Figure 2.22 shows evaded tax as a fraction of total tax. This fraction ranges from 55 per cent to 80 per cent.

FURTHER CRITIQUES Before accepting the results of the above simulations, several critiques need to be addressed. Uniform distribution Why assume that evasive and productive talents are uniformly distributed? Is this not a restrictive assumption? One of the outstanding discoveries of mathematical statistics is that the distribution of sums of independent distributions rapidly converges to the normal distribution, for many varieties of the underlying distributions of the random variables being summed. The frequency graph of a

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Tax evasion and firm survival

sum of two independently distributed uniform distributions has a tent shape which can be taken as a crude approximation to a normal distribution. This is not to argue that assumptions regarding the underlying distribution of random variables being summed are not critical for the derivation of the supply curve, but rather that no matter what distributions are being summed, there is a tendency towards the normal. Whatever the underlying distributions, and whatever deviations from normality may still reside in their sums, the qualitative results I have derived will be the same. Supply will remain a tightly interwoven mix of evasive and productive capacities. Correlation of talents Why have I only investigated the cases of perfectly negatively correlated productive and evasive talents, and of talents with zero correlation? Are not intermediate cases worth studying? These two cases are benchmarks that allow one to infer what would happen in a world where evasive and productive talents are positively, but less than perfectly correlated. Even in such a world some firms with poor productive ability but a verve for tax evasion will manage to survive and displace more productive but less wily rivals. The proportion of firms displaced in this manner drops as the degree of correlation between productive and evasive abilities rises. This proportion disappears when there is perfect positive correlation. This statement could be subject to analytical proof. The way of proceeding would be to postulate a joint distribution of productive and evasive talents. This jointness would considerably complicate deriving an expression for the sum of these distributions. The payoff would be that the degree of displacement loss could be parameterized in terms of the correlation of productive and evasive talents and thousands of potential economies, depending on the degree of correlation between talents, could be modelled. The techniques for deriving distributions of sums of correlated uniformly distributed random variables can be found in McFadden (1971, p. 135). Readers who want to think about this problem should consider that there is an infinite number of possible distributions one can construct for the sum of dependent uniform distributions. Each such distribution forces a rederivation of equilibrium with a necessary consideration of more complicated bounds of integration than those considered in Figures 2.10–2.11. I leave such a derivation to future researchers, but I will venture a guess as to what meager evidence there exists on the correlation of productive and evasive talents. No studies which I know have as their main object the measurement of the correlation between productive and evasive talents. Some empirical research contains the seeds of such information. In the theoretical tax evasion literature, under standard assumptions about an individual’s attitudes towards risk, a higher tax rate increases his or her declared income. The downside from tax evasion rises with income. Risk averse individuals will tend to fear punishment the

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more they have to lose. This would tend to favour the view that high productive skills are coupled with low evasion. Facts in support of this relation between evasive and productive skills come from de Juan et al. (1994). In a 1991 sample of 2406 taxpayers from Spain they found that, controlling for demographic and fiscal influences, tax evasion tends to fall as education level rises. If education can be taken as a signal of productive efficiency (and this may be a large ‘if’), their study might be interpreted as giving support to the notion that the least efficient producers are the most efficient tax evaders. Evidence farther afield comes from Witte and Tauchen (1994) who examined panel data on criminals in Philadelphia during the 1960s and 1970s. They found that, controlling for other factors, high IQ was positively associated with a lower tendency to commit crime. Studies based on US Internal Revenue Service data tend to show a different result. In the first empirical analysis of corporate tax evasion Rice (1992) found in a sample of 30,000 small corporations, that deviations from the sample-wide median profit rate corresponded negatively with tax compliance. Earlier, in an analysis of individual tax returns, Cox (1984) found that the least compliant taxpayers are on average those with the highest and the lowest incomes. Both the Rice and Cox studies are saying that there is no clear monotonic relation between evasive and productive skills. There is no reason to believe that there is one global correlation coefficient between productive and evasive abilities. Those wishing estimates of displacement losses may well have to calculate the correlation industry by industry. Non-endogeneity of evasion decision My model of tax evasion is a general equilibrium model in the sense that it takes people’s decisions on how much to evade as given, and derives the consequences for society of people’s different decisions. What insights would be gained by modelling each producer’s evasion decision explicitly and seeing how this feeds into and is affected by general equilibrium? This might be of importance if we thought that a change in tax changes the order of evaders, so that if tax rises a producer who evaded more before the tax rise than a fellow producer with the same production costs evades less than his rival after the tax rise. If the many changes in the order of evasion took on a systematic character a correlation would grow between evasive ability and production costs. There is no mechanism to date which I can guess or which has been suggested to me that would force such a systematic pattern into the relation between evasive and productive abilities. Demand curve Do not the wealth destroying effects of displacement loss shift the demand curve and so change equilibrium output and thus displacement loss? The answer here is a clear ‘No’. The demand curve exists in a world where inefficient

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Tax evasion and firm survival

producers are already displacing one another. The minimum cost supply curve is a benchmark which measures what costs would have been like had there been no evasion. We are not moving between this minimum cost world and the tax evasion world in the simulations, but rather we are comparing two worlds. There is consequently no need to consider the effects of a transition between two different forms of supply curve on the demand curve. Perhaps the most significant critique is why, if the deadweight loss I am proposing is comparable to Harberger triangle loss, has the alarm in politics and academia against displacement loss been so subdued? The answer may be that in practice the problem has already been taken care of. Where there are large deadweight losses from less efficient firms crowding out more efficient firms, there is a market waiting to be opened. The market might encourage firms with high evasive abilities to trade their talents to firms with high productive abilities. The market can only encourage such trades if productive and evasive talents can be separated. The displacement losses I have modelled arise because of an inseparability between productive and evasive talents. How might productive and evasive talents become separated and a market for exchange between the two be opened? Excise officials are familiar with a tax dodge in which a criminal organization with money to launder rents office space to legitimate businesspeople looking for a tax deduction. The organization rents the same office to each of ten businesspeople for $100 a month (each gets 3 days’ use) but issues each a receipt for $1,000. This receipt allows the businesspeople to get a tax break beyond what they pay for rent. The receipt also allows the criminal organization to deposit $10 × $1,000 of dirty money from gambling or prostitution into the bank. Criminals pay tax on this money of course, but that is the cost of laundering money. What falls out of this complicated exchange is that businesspeople produce, and the criminal organization evades. In this case there is no deadweight loss from displacement, just a deadweight loss from organizing the market in evasion. Political lobbying is a legal form of exchange between evaders and producers. Lobbyists market their talents at getting special government favours, such as investment grants, to firms who can make the most of these favours. A political system with open lobbying and a leadership open to persuasion may help to minimize the displacement of superior by inferior productive talents. Perhaps this is why the tax systems of developed economies are complicated. Complication allows producers and evaders to specialize and trade with one another in the political market. The costs of organizing these political markets, often referred to as rent-seeking costs echo the deadweight losses that would have resulted from displacement loss. The Leviathan model of the state as formulated by Brennan and Buchanan (1980) also predicts that income taxes will have complex structures, but as Winer and Hettich (1997) explain, the cause of such

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complexity is a desire to price discriminate between different taxed groups so as to maximize government revenues subject to a re-election constraint. To see how strong and weak evaders might benefit each other and society at the same time, consider the case of a market where the good produced sells for $12 and the unit tax on producers is $5. Focus on two producers, the first of which has production costs of $8 and no ability whatever to evade the tax. This firm’s total costs will be $13 and it will decide not to produce. Another firm has production costs of $10 but can evade $4 of the $5 tax. This evasive firm’s total costs are $11 and it stays in the market earning a profit of $1. Both firms could be made better off, no money lost to the taxman, and resource costs diminished if the two could arrange a trade in which the evasive firm could sell its evasive abilities to the low cost firm. If the evasive firm transferred $4 of tax evasion to the low cost firm, the low cost firm could start producing. Its production and tax costs would be $9 and it would earn a profit of $3. So there is a market in which the low cost firm is willing to pay the high cost firm up to $3 for its evasive abilities. If the two came to a price of $1.5 for the evasion of $4, then the high cost firm would increase its profits from $1 to $1.5 and the low cost firm would enter the market making a profit of $1.50. The high cost firm would stop producing, and so total production costs in the economy would have fallen from $10 to $8. Government revenues remain unaffected. This example is illustrated in Figure 2.23. Not all market participants would find it to their advantage to enter such a trade. It is for future research to determine how many producers displaced from

      

Firm 1’s $5 tax

  

Firm 1’s production cost of $8

Figure 2.23

      

Firm 1’s profits if it buys $4 of  evasion from  firm 2

Firm 2’s production cost of $10

Firm 2 evades $4 of tax Market price of $12 Firm 2’s profit of $1 if it produces

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Tax evasion and firm survival

the market could potentially find partners active in the goods market who are willing to trade their evasive abilities, but I will venture a guess here that nearly half the displacement loss has the potential to disappear. The assumption of uniformly distributed evasive and productive talents suggests that for every firm outside the market with a high productive but poor evasive talent, there is mirror image firm inside the market with strong evasive but poor productive talents. The good evader has to be only slightly better at evasion than the good producer is at production in order to open the market for a trade of the sort discussed in the preceding paragraph. Unfortunately, exchanges between parties with little to offer each other is not the function of markets. Markets rather unite parties who have a large surplus to divide. My guess is that the sub-market in evasive skills would attract the half most evasively gifted firms producing to switch places with the half most productively gifted firms not producing, in the same way that in a market without any evasion or tax, with uniformly distributed productive talents, and a demand curve calibrated to be symmetric with the supply curve, half the potential participants enter into trades. This claim should of course be subjected to rigorous mathematical modelling and explored under a variety of assumptions about the joint distribution of evasive and productive abilities. Such modelling is needed because it is possible to imagine deals in which low cost firms with a strong ability to evade sell evasion to high cost firms with a poor ability to evade. Without a notion of how equilibrium in trades for evasive ability comes about, all claims about displacement losses and institutions must be considered as tentative. The example of trading evasive talents shows that displacement deadweight loss is non-antagonistic. This is not true of Harberger triangle losses. To reduce triangle loss the government must reduce the tax level. But a lower tax level comes at the expense of beneficiaries of the tax. Becker (1983) argued that this antagonistic property of Harberger losses was behind much of the conflict between interest groups in their struggle for influence. A non-antagonistic loss such as displacement loss could be reduced in large part without harming anyone. This is why we must strongly suspect that government institutions have evolved to minimize this loss. Reducing the loss does no one harm and does some people good. The point is important because it could be used to criticize the premise of the present chapter. If governments take steps to eliminate nonantagonistic losses, will not the displacement losses which I have analysed be small or non-existent? It is possible that governments reduce displacement losses to low levels. Reducing this loss comes at a price. Government must think out and implement means of reducing non-antagonistic losses. The markets organized around tradable emission quotas and the bureaucracy of tax lobbying are social losses that may be the pill we must swallow to avoid a large loss from displacement. The concept of displacement is interesting because it hints that government intervention has deadweight losses above those suggested

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by Harberger. Displacement loss is also interesting because it can be referred to as a motive behind the creation of certain institutions designed to minimize that loss. It is not only the tax system that may be designed to avoid displacement losses, but regulations, and systems of subsidies. It is to these other manifestations of government control over the economy to which I turn my attention in the chapters that follow.

CONCLUSION I began the chapter with a discussion of how the economics profession is sensitive to the idea that the rules of the market may encourage entrepreneurs either to devote their energies to growing the national wealth or to dividing it. Instead of forcing an entrepreneur to become entirely a tax evader or entirely an honest producer I assumed the entrepreneur was endowed with both productive and evasive abilities which could not be separated. This inseparability of characteristics that pull economic efficiency in opposite directions gave rise to a special sort of supply curve which did not order producers by increasing levels of production cost, but rather ordered them based on a mix of productive and evasive abilities. Taxes interact with the underground economy to create an inefficiency. The inefficiency arises because for any given positive tax, some low production cost firms are displaced by higher production cost firms with better evasive skills. The evasive effect is a pure transfer from firms with less developed evasive abilities to firms with more developed evasive abilities. The higher production costs are a net cost to the economy. I looked at two possible cases under which good tax evaders displace good producers. Under the extreme assumption that more efficient producers are less efficient tax evaders, a tax may lead to a complete inversion of the supply curve in which the least productive suppliers become the suppliers able to offer the lowest price. When productive and evasive talents are uncorrelated we still find a deadweight loss from the displacement of firms that, at low tax levels, rivals the traditional triangle deadweight loss. The reasoning of this chapter may also apply to a world where evasive and productive talents are positively, but less than perfectly correlated. Even in such a world some firms with poor productive ability but a verve for tax evasion will manage to survive and displace more productive but less wily rivals. The proportion of firms displaced in this manner drops as the degree of correlation between productive and evasive abilities rises. This proportion disappears when there is perfect positive correlation. Future work could focus on several issues. The first would be to test the model’s implication that taxes may raise industry costs up to a point. This is a very general empirical implication of the model and sets off the above musings from being merely metaphysics, to being a testable theory of equilibrium under

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Tax evasion and firm survival

tax evasion. The second issue is how the implications of the model change when more than one market is taxed. In other words, a general equilibrium analysis of the deadweight losses from displacement is needed. We also need a close examination of institutions to see whether they have evolved to get around the problem of displacement deadweight loss. Finally, we should generalize the model by simulating government revenues under varying assumptions about the correlation between evasive and productive abilities, and then to seek empirical evidence on their correlation.

3. Are subsidies evaded taxes? In the preceding chapter I suggested that tax evasion does its harm by allowing producers who are good at evading taxes but poor at making a product to oust more efficient producers who lack the ability or inclination to evade taxes. The harm would not have arisen had everyone evaded taxes with equal aplomb. The insights of that chapter carry over to any government rule that some producers violate and other producers obey. In this chapter I propose that a business that asks for and receives a subsidy from the state may do the same harm to society as a business that evades taxes. On the surface a subsidy does not look like tax evasion. Bureaucrats and politicians grant subsidies as representatives of the people. Bureaucrats and politicians do not grant businesses leave to evade taxes. Such a distinction is of little importance to understanding the welfare costs of subsidies. If a business can get government money because it is good at talking to bureaucrats rather than being good at stamping out a product, that business may displace a more efficient business that does not have the wit to lobby government. The difference in costs between the two businesses is the same sort of displacement deadweight loss discussed in the previous chapter. To claim that subsidies are evaded taxes in disguise one must believe that subsidies are granted outside the rule of law. The rule of law prevails when elected representatives refrain from using the state’s power outside the limits prescribed by constitution or custom. The great legal theorist A.V. Dicey (1920) explained that the rule of law prevails in part when a citizen’s legal duties and his liability to punishment are determined by regular law and not by the arbitrary fiat of officials with wide discretionary powers. The arbitrary ruler sets himself up as the final authority on the public good and looks to himself as the fount of wisdom in matters of the state. He may shine before the looking glass, but little may distinguish him in the eyes of the people from the criminal who robs a bank, swindles a widow, or evades taxes. Arbitrariness flourishes, and the rule of law withers where the people find it costly to impose their will on their representatives in government. No organization can control to perfection how its functionaries behave. The costs of monitoring these functionaries gives functionaries room to indulge their views on how their organization should be run. If the cost of monitoring how politicians and bureaucrats hand out money to firms is high, citizens can expect the state will hand out some subsidies 55

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arbitrarily. Administrators who cannot be costlessly monitored may hand out grants to firms that bring benefits to society, but they may also give out grants at their whim, for bribes, or under duress from political masters who treat the rule of law with contempt. Arbitrary subsidies impose the same sort of displacement loss on society as tax evasion imposes and along this dimension, subsidies and tax evasion are impossible to distinguish. The public finance literature is aware that subsidies have costs. The main costs researchers have identified is that subsidies encourage excessive consumption. Subsidized firms drive down equilibrium price and entice consumers to buy at a price that is lower than the cost of producing the good. The excess of cost over value placed on the good can be measured as a variant of Harberger’s (1971) triangle loss for taxes. Public finance economists are willing to tolerate a triangle loss from subsidies provided that the subsidy buys a positive externality of a value greater than the triangle loss. They have recently started accepting lessons from the Public Choice field that warn of the lobbying costs from battles between interest groups for control of subsidies. What only one researcher, to my knowledge, has emphasized is that firm-specific investment grants may lead some inefficient firms to displace efficient firms. Dan Usher (1983, p. 41) wrote that ‘If the administrators of a program of investment grants believe they can spot externalities and they are wrong, then there is the presumption that the program will lower the average quality of investment by substituting bad investment for good.’ In 1975 (p. 34) Usher wrote ‘If the government failed to appreciate the impact of the subsidized investment project on the profitability of other contemplated investments or of existing facilities, a situation might arise in which the less efficient subsidized project drives out and replaces the more efficient unsubsidized project creating no extra capital on balance but leaving the designated area with a weaker economy’. More recent research on firm-specific investment subsidies by Barros and Nilssen (1999) recognizes firms are heterogeneous but does not explore the displacement losses from such subsidies. In the same line of inquiry the work of Neary and O’Sullivan (1999) looks at the welfare benefits of firmspecific subsidies but does not treat displacement. I take up where Usher left off to show that no matter how honest, or clever, or free of corruption are public officials, firm-specific investment grants carry with them an inescapable arbitrariness that always lowers the average quality of investment. I start with this most favourable case for those who champion subsidies and show how to calculate the displacement loss of subsidies that are given only to the most deserving firms and in accord with the social benefits these firms bring. I then argue that as grant administrators grow more arbitrary in their judgements firm-specific investment grants begin to resemble evaded taxes.

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THE DANGERS OF ARBITRARINESS In a submission to the Review of Business Programs, the Australian Industry Commission (1997) outlined its views of the benefits and the dangers of subsidies to business. The Commission proposed: 1. Good targeting. Programmes should focus support on new activity, rather than activity that would have occurred anyway. They should also target market failures generally, rather than particular firms or industries. In this regard, generally available support for activities such as R&D is preferable to firm-specific subsidies. Programmes should be open to all firms, rather than limited to (say) firms of any particular size. 2. Transparent support. Transparency eases monitoring and reporting the outcome of programmes. Transparency can be enhanced by clear eligibility criteria that limit administrative discretion in the allocation of funding to firms. The Commission went on to explain (p. 30) that ‘Favouritism, or “selectivity”, undermines competitive processes by disadvantaging an assisted firm’s competitors. Thus it typically results in less efficient outcomes. For example, the Commission found that the exclusion of some companies from the Factor f scheme for the pharmaceutical industry had reduced the value of the scheme.’ The Commission deepened these insights in a major study by Lattimore et al. (1998). The Industry Commission is not the only para-governmental body to hold such views. A visit to government websites in the USA, Canada, and the UK shows similar concerns that subsidies should not be arbitrary. The two means by which arbitrary subsidies can be avoided, the Commission underlines, are to avoided targeted, or firm-specific, subsidies. The second approach is to monitor the subsidy givers to ensure that their discretion is limited. In a working paper for the International Monetary Fund, Vito Tanzi (1994) sounded the alarm against arbitrariness and corruption in government policies. Tanzi wrote that corruption distorts economic efficiency ‘Through arbitrary (i.e. non-arm’s length) application of rules and regulations thus giving preference to some individuals over others. This may be particularly important in the allocation of import permits, subsidized credit, zoning permits, and permits related to various economic activities.’ In spite of the lip-service government agencies give to avoiding arbitrariness in aid to business, much of government aid to business has the potential to be allocated arbitrarily. In an international survey, Robert Ford and Wim Suyker (1990) catalogued that in 1988 aid to business made up between 0.6 per cent (for the USA) to 3 per cent (for Italy) of GDP in OECD countries. In

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their study of aid to the manufacturing sector of the European Community, they found that direct subsidies made up on average 49 per cent of the help companies received. Tax breaks were 30 per cent, government partnership with private business accounted for 9 per cent of aid, and loan guarantees were 5 per cent. It is more difficult to change the tax system on a case-by-case basis than it is to exercise discretion in the giving of direct subsidies, loan guarantees, and government partnerships in business. These potentially arbitrary forms of aid came to 70 per cent of the European average in manufacturing. An example of how arbitrary subsidies can get comes from a scandal in the Canadian government that erupted in January 2000. The Minister of Labour was forced by the opposition party to reveal that her department, with an annual budget of $80 billion (Canadian funds) had not accounted for how anywhere between $1 to $3 billion dollars of aid to business had been spent. Either the department did not know where the money had gone or applicants for funds were not required to make formal written requests that met universal standards of acceptability. Journalist Terrence Corcoran (2000) reported for the National Post that an $8 million dollar subsidy to a sock plant in Montreal had provoked the outrage of competitors who had received no subsidies and who were forced out of business. A deeper lack of accountability surrounded the Credit Lyonnais in France. Credit Lyonnais is a government bank that has lost over $20 billion to bad loans. In one case the bank lent the owner of the Marseilles football club Olympique the funds needed to buy the sporting goods giant Adidas. The club owner later joined the government as a minister and Adidas filed for bankruptcy. Officially the bank is supposed to be a for-profit organization. Unofficially it helps businesses the market has looked down upon and whose only recommendation is a nod from a friend in government. It is easy to see that arbitrary subsidies advance the fortunes of inefficient businesses. Efficient businesses that do not receive subsidies may lose their place in the market. I could model such a case and calculate its welfare benefits but such an exercise would be of limited interest. Few people believe that subsidies are given out with complete disregard for the externalities those subsidies can generate. Instead of taking this extreme route, it is more helpful to adopt the most favourable attitude to those granting subsidies. I will show that even if grant administrators give subsidies in accordance with the public finance precept that the subsidy should be in proportion to the externality it encourages, displacement loss will not only be found, but will be the same as if the subsidy were given with complete arbitrariness. Inescapable arbitrariness does not mean that such subsidies should not be given, but that the net benefits of such subsidies are smaller than researchers imagined. What may be difficult to grasp in the exercise is that there is no distinction between the displacement deadweight losses that well-administered subsidies and unaccountable subsidies

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generate. Both impose costs similar to the cost we found in the previous chapter flowing from tax evasion. To better grasp these points we must turn our attention to a concrete exposition of how grant administrators hand out money and the effects this has on market equilibrium.

EXTERNALITY AND EFFICIENCY UNCORRELATED How should bureaucrats grant money to firms they believe generate externalities? This depends on what they know about these firms. It is unlikely that bureaucrats will know much about a firm’s costs. Firms guard information about their costs and misrepresent these costs to their rivals and to government. Public utilities and telephone monopolies are notorious for inflating their cost figures in order to pass higher rates by government price control commissions. At best, bureaucrats will have an idea of cost distribution for the industry in question. It is more likely that bureaucrats know something about the externalities that firms generate. The business of government – if we are to believe public finance textbooks – is to spot externalities and correct them. Politicians are elected in part for their expertise in identifying the common good, of which externalities are a part. Bureaucrats follow the politicians’ broad directives and bring their own expertise to bear on identifying externalities. I model this imbalance of knowledge by assuming that bureaucrats know costlessly and perfectly the positive externality each firm faces, and know the industry distribution of costs but nothing about any particular firm’s costs. The assumption is not as stark as it seems. The assumption is a convenient, but not an essential way, of capturing that bureaucrats know more about externalities than they know about firm costs. Not being able to identify a firm’s costs means that bureaucrats lack the ability to finely discriminate between candidates for subsidies. The government’s ideal would be to give subsidies principally to high externality firms, not producing at going market prices, but who reside on the margin of indifference between producing and not producing. This would tend to minimize the displacement of low cost by high cost firms relative to the externalities encouraged. Without a knowledge of costs and externalities such a strategy is not feasible. The best bureaucrats can do is follow a strategy of subsidizing each firm in proportion to its externality. If the marginal cost of public funds as defined by Browning (1976) is zero, the welfare maximizing strategy of bureaucrats is to follow the Pigouvian strategy of fully subsidizing each firm’s externality, even though bureaucrats know that some firms would have produced without the subsidy and that the subsidy leads to a deadweight loss from the displacement of high cost firms. This rule can be understood with an example.

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Consider the case where there is only one demander with one unit of demand. There are only two firms each of which can produce only one unit of output. In other words, there is only room in this market for one firm. Market price is $10, firm 1 has costs of $11 and, if it produced (which it does not, because its costs are higher than market price) would generate an externality of $2. Firm 2 has costs of $10 and generates externalities of $0.50. A subsidy for the full amount of the externality would force firm 2 out of the market and bring firm 1 into the market. The overall costs of production are higher by $1, but externalities are higher by $1.50. If firm 2 had a lower externality than in the previous case, say of $1.49, its subsidy would be $1.49 and it could not displace firm 1. This is as it should be for a social planner, because if firm 2 displaced firm 1 in this case a net loss would result. The case where firms 1 and 2 receive a subsidy higher than the externality does not need to be explicitly treated. It is clear in such a case that the subsidy, if higher than the externality in the same proportion for each firm, would change nothing in the first example. If the subsidy were higher in an arbitrary fashion this would at best open the possibility of net deadweight loss from the subsidy as suggested by the second example. The conclusion is that the best the social planner can do when he can base his judgements only on a knowledge of externalities and not a direct knowledge of costs, is to subsidize up to the level of the externality. The following sections sketch the consequences of such a strategy. Supply As in the case of tax evasion, to trace the effects of a subsidy we need to know what demand and supply look like. Supply is the most difficult to model because it is supply which I am assuming is the target of the subsidy. The supply curve takes shape over several steps. The first step is to assume a continuum of firms, each producing an infinitesimal amount, and none having any influence on price. A firm decides to produce or to stay out of the market by subtracting its subsidy from production costs and seeing whether the result is less than what the product sells for. I make the neutral assumption that production costs and externalities are independently and uniformly distributed. The assumption is neutral in the sense that I could stack the deck in favour of finding large social losses from displacement of firms if I had assumed that high cost firms, on average also have high externalities, and low cost firms on average have low externalities. Firm f can be thought of as first drawing its productive abilities i from a set of is distributed on the interval [0,1]. The i represents a fraction of some number K, the production costs of the least efficient firm in the industry. Firm f draws its positive externality j (which is equivalent to the subsidy it receives) also from a set distributed on [0,1]. The j represents the fraction of the highest

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externality possible E. Bureaucrats decide to equate E to the maximum possible subsidy S a firm may receive. The bureaucratic selection mechanism for a firmspecific investment grant is to identify first that firm’s externality index j and then multiply it by S. It is very important to note that S by itself is not the subsidy. It is one component of the subsidy granting mechanism. From now on I use the symbol S to denote both the subsidy and the actual externality. The higher is j, the greater its subsidy. Both externality and productive abilities are independently distributed and firm f ends up with total costs of Cf = (iK – jS)df

(3.1)

The df term reflects the assumption that the firm’s output is infinitesimal. The index f can be thought of as running from [0,N] where N represents the industry’s potential output. To put some meat on this conceptual skeleton suppose N = 20, the maximum subsidy is set at S = $5 per unit of output (so that the best a firm can do is get S of subsidy), and the costs of the least efficient firm imaginable are Kdf = $8df. Suppose the firm indexed by f = 8 draws with its left hand a ball from an urn indicating that its i is 0.4. With its right hand it draws from another urn a ball with j = 0.2 painted on it. This means that from its perspective, the firm’s total costs are (0.4 × 8 – 0.2 × 5)df = $2.2df. If this turns out to be less than the market price, then firm 8 will decide to produce. Think of performing this exercise with each of the remaining firms in the range of fs between zero and 20, never knowing whether for each firm a low or a high draw for externality will be accompanied by a low or a high draw for productive efficiency. Supply falls out of an infinite number of firms, each comparing whether its production cost less its subsidy is below the market price P. The sum of positive answers to these many questions is summarized by the supply function: Q s ( P) = N ∫ ∫

{(i, j ):iK − jS ≤ P}

n(i, j )didj

(3.2)

The term N as before is the potential industry output (the ‘measure’ of firms). The term n(i,j) is the joint probability density function of the cumulative density function N(i,j). Throughout the rest of the chapter I assume that i and j are independently and uniformly distributed. That is, i ~ U[0,1] and j ~ U[0,1]. We could approach the problem of finding supply by looking at Figure 3.1 where (K – P)/S ≥ 1. The proportion of firms producing are all those for whom price exceeds costs, namely, those for whom P ≥ iK – jS. This comes down to the area below the line i = (P + jS)/K or A + B. This area times N is the number

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i

1

         

B

A

P = iK + jS (K – P)/S ≥ 1 S — K

P — K

j

1 Figure 3.1

of firms producing at any given level of price P, and subsidy and cost bounds S and K:   P S   Qs = N +  K  K 2 {  {  area A area B

(3.3)

A more tedious way of deriving supply when (K – P)/S ≥ 1 is by brute force integration over appropriately chosen bounds. These bounds define the area A + B: Qs = N ∫

1

P + jS K

0 ∫0

didj

(3.4)

P S  = N +  K 2K 

(3.5)

The brute force method is not pretty, nor needed to find supply. The method will prove essential later for calculating industry production costs with a subsidy, which is a weighted average of the variable index i over the areas A

Are subsidies evaded taxes?

63

and B and so has no easy graphical interpretation. This is why from now on I stick with the ugly-looking bounds of integration. The reader who has carefully followed the derivations in Chapter 2 will find no novelty in the derivations that follow. The above supply equation is the horizontal sum of the supply equation were no subsidy given, and a subsidy component. To see this, note that supply without a subsidy is given by the N times the proportion of firms for whom production costs are less than price, Pr(iK ≤ P): P Q s = N × Pr  i ≤   K

(3.6)

P

= N ∫ K di

(3.7)

0

=N

P K

(3.8)

This the first term in equation (3.3). The second term is a subsidy component that pushes the supply out to the right. The derivation of supply does not end here. As Figure 3.2 shows, the bounds of integration change when (K – P)/S ≤ 1. These bounds define the area C + D: i

P = iK + jT (K – P)/S ≤ 1

1

P — K

C

D

    

1 K –P ——– S

Figure 3.2

j

64

Tax evasion and firm survival

  K − P P + jS 1 1   Q s = N  ∫ S ∫ K didj + ∫K − P ∫ didj 0 0 0 4244 3 1S4243  14 Area C  Area D 

(3.9)

1   K − P P + jS = N ∫ S dj + ∫K − P dj  0   K S

(3.10)

 K P2 P = N 1 − − +  2 S 2 KS S  

(3.11)

Demand Even though demand is not the focus of this chapter some attention needs to be given to specifying the demand function, so we can pick demand parameters that assure us demand and supply cross. I assume an infinite number of consumers with measure C. Buyer reservation prices are uniformly distributed on the interval [0,R]. A buyer pulls a random variable pr from a uniform distribution on [0,1] and multiplies this by R to obtain a reservation price of prR. A buyer decides to buy di units of output if his reservation price is above the market price. The total number of buyers who demand the good is: Qd = C × Pr(prR ≥ P) P   = C1 − ∫ R dp r  0  

=C−

C P R

(3.12) (3.13) (3.14)

Equilibrium Equilibrium comes from equating demand and supply and solving for price and quantity. But which supply equation do we choose? Figure 3.3 shows how to resolve the dilemma. The figure shows both the above supply equations for K = S = 20 and N = 20 and a demand equation for C = R = 20. Where the two supply curves touch, (K – P)/S = 1. This is the point of transition between Figure 3.1 and Figure 3.2. To the left of the point where (K – P)/S = 1, we find (K – P)/S ≥ 1 and the relevant supply curve for determining equilibrium is the lower curve in Figure 3.3 (which comes from Figure 3.1). To the right of the

Are subsidies evaded taxes?

65

point (K – P)/S = 1 we find that (K – P)/S ≤ 1. Here the higher supply curve becomes relevant for determining equilibrium. It is with regard to these inequalities that I choose the relevant supply curve for determining equilibrium, as I vary the level of the subsidy S. Figure 3.4 maps equilibrium output and price as the level of the subsidy rises. There are no surprises here. Quantity rises with the subsidy and price falls. 25 Point at which (K – P)/S = 1

20 (K – P)/S ≥ 1

Price

15

(K – P)/S ≤ 1

Supply when (K – P)/S < 1

10 5

Demand

0 –5

Supply when (K – P)/S > 1

0

5

10

15

20

25

Quantity Figure 3.3 ($) 16 14

Quantity

12 10 8 6

Price

4 2 –

0

Figure 3.4

5

10 15 Maximum subsidy S

20

25

66

Tax evasion and firm survival

The final supply curve relevant for calculating equilibrium is a piecewise combination of these two curves. By flipping this hybrid supply curve on its side and viewing quantity as a function of price one notices a resemblance to a logistic curve, as would be the case when the market price sweeps across a unimodal distribution of reservation prices (the distribution of the sum of two independently and uniformly distributed random variables has a tent shape that roughly resembles the normal distribution). This is not a supply curve as we normally understand it. ‘Ordinary’ supply curves order producers from left to right by increasing levels of production cost. The present supply curve weaves the granting mechanism and productive abilities together to produce an ordering that is not wholly based on one or the other. Precisely as in the case of tax evasion in the previous chapter, this mixed-up ordering is what gives rise to a displacement of low cost firms from subsidies. This is also why the subsidy does not split the supply curve into a reaction curve and a cost curve. When producers differ in their chances of getting grants, the reaction and cost curves are fused. The approach to the supply curve I take here is similar to that of Telser (1978, 1997) who was concerned about modelling equilibrium when firms and consumers are constrained to making decisions on their extensive margin rather than on their intensive margin. Telser dealt with questions of core theory and did not address that which concerns us here.

DISPLACEMENT LOSS AND NET BENEFIT OF SUBSIDY Some firms with high costs and high externalities will crowd out some firms with low costs but low externalities. These newly selected high cost firms insert themselves at every point along the supply curve. This means that between zero output and the equilibrium output with a subsidy there is a social loss for which to account: the difference between what it costs to produce the old equilibrium output Q* under a subsidy and the minimum possible cost of producing Q*. The least cost of producing Q* is the area between [0,Q*] under what the industry supply curve would be if there were no subsidy. As noted in equation (3.8), this supply is Qs = NK/P. We can invert supply to isolate P, which in this case would represent the height of the industry supply curve. The integral under this supply curve in the range [0,Q*] is then the least cost way of producing Q*: Q*

∫0

K K *2 QdQ = Q N 2N

(3.15)

Are subsidies evaded taxes?

67

The actual cost of producing the unsubsidized equilibrium Q* under a subsidy is trickier to find. When productive talents and eligibility for grants determine supply, we can no longer simply integrate under the supply curve to get costs. The supply curve does not order producers according to productive ability, but according to a mix of productive ability and subsidy-worthiness. Total industry cost is calculated as the sum of each producer’s cost iKdidj in the region where iK – jS ≤ P multiplied by the measure of firms N. More formally, industry costs are: N∫ ∫

{(i, j ):iK − jS ≤ P}

iKdidj

(3.16)

The final shape the cost equation takes depends, as in the case of the supply equation, on the bounds of integration. Here is where the tedium we experienced deriving the supply equation pays off. The bounds of integration come from the same reasoning provided earlier for the supply equation (3.3). When (K – P)/S ≥ 1 industry costs are N∫

1

P + jS K

0 ∫0

iKdidj =

NK 2

 P  2 1  S  2 PS  + 2   K   K 3  K 

(3.17)

The deadweight loss from displacement of low cost firms is the actual cost, given subsidy S, of producing the first Q* units (the unsubsidized equilibrium quantity) less the minimum cost of producing these units. The only problem with the above equation for finding the actual cost of producing the unsubsidized output is that the equation does not express costs as a function of output. The equation expresses costs in terms of price. So we need to go a step further and ask at what price P*, given the government’s subsidy policy (i.e. given S), firms would supply the unsubsidized equilibrium output level Q*. This allows us in the subsidy case to express price in terms of quantity and ultimately cost in terms of quantity. In other words, we must solve the subsidized supply equation for P. In the present case where (K – P)/S ≥1 this means isolating P* from Q* = N(P/K + S/2K), which gives P* = Q*(K/N) – S/2. Plugging this back in the cost function above, we get the cost of producing the first Q* units (the unsubsidized equilibrium quantity) under a subsidy. When (K – P)/S ≤1 the bounds of integration give the following industry cost function N∫

K −P S

0

P + jS K

∫0

1

1

iKdidj + N ∫K − P ∫ iKdidj S

0

(3.18)

68

Tax evasion and firm survival

Taking these integrals is straightforward and to save space I have left out the solution. Once again, to get the actual cost of producing Q* we have to solve the above equation for the P* under the subsidy that would induce firms to produce the equilibrium non-subsidy level of output Q*. Now we must isolate P* from supply equation (3.11). This involves solving a quadratic equation for P*. The procedure is simple and I omit the explicit solution. The deadweight losses derived above are not generated by bureaucrats who are arbitrary or corrupt, but are exactly the same sorts of displacements that would arise if officials were arbitrary or corrupt. The reason for the loss is that subsidies bear no relation to a firm’s costs. Grant administrators are wise only to the externalities a firm generates. This wisdom does not allow administrators to avoid inflicting the same costs on society as would corrupt administrators presiding over an economy in which a firm’s costs and its ability to bribe officials for subsidies were uncorrelated. Where the prescient administrators differ from corrupt administrators is in the benefits they generate by granting subsidies. Benefits from Subsidy Deadweight loss from displacement must be set beside the amount of externality that gives rise to it. Even though the bureaucrat pays each firm a subsidy equal to its externality, the sum of subsidies overstates the externalities those subsidies brought about, because even in the absence of the subsidy some firms generating externalities would have produced. There is no obvious way for government to avoid giving redundant subsidies. One could argue that all the government has to do is note which firms were producing before the subsidy and restrict the subsidy to new market entrants. In the short run this argument might have some weight. In the long run, firms who produce would have an interest to misrepresent their costs and argue that without the subsidy they would go out of business. Even in the short run every existing firm could argue that it is on the margin of survival and so should be equally considered for the subsidy. This may explain why in practice firm-specific investment subsidies seldom go only to new entrants. To calculate the amount of externality we need to calculate how much subsidy is given, how much externality would have been produced without the subsidy, and take the difference between these two sums. Subsidies are measured using the same approach as that taken with costs. To get the subsidy level, sum the subsidy-getting indexes j of those firms producing and multiply this sum by the maximum possible subsidy S and the measure of firms. In general, subsidies to the industry are

Are subsidies evaded taxes?

N∫ ∫

{(i, j ):iK − jS ≤ P}

69

(3.19)

jSdjdi

I have reversed the order of integration to make the exposition intuitive. The intuition is that we are adding all the subsidy-getting indexes for firms with productive abilities within a range defined by iK – jS ≤ P. i

1

         

B

A

P = iK + jS (K – P)/S ≥ 1 S — K

P — K

j

1 Figure 3.5

To make equation (3.19) operational we must refer to Figure 3.5. When (K – P)/S ≥ 1 we have to sum js over A and B. The sum of j over these two areas is included in the following two terms and multiplied by S and N to get at the total amount of subsidies given: P

1

P+S

1

N ∫ K ∫ jSdjdi + N ∫P K ∫iK − P jSdjdi 042 0 44 14 3 144 K S 2 443 subsidy over A

(3.20)

subsidy over B

When (K – P)/S ≤ 1 Figure 3.6 indicates that the sum of subsidies over areas C and D is: P

1

1

1

N ∫ K ∫ jSdjdi + N ∫P ∫iK − P jSdjdi 042 0 44 14 3 14 K S 42 443 subsidy over C

subsidy over D

(3.21)

70

Tax evasion and firm survival

Taking the integrals of the above two equations is simple and the results are omitted for brevity. i P = iK + jT (K – P)/S ≤ 1

1 C P — K

D 1

j

Figure 3.6 When there is no subsidy, some amount of externality would still have been produced. How much subsidy comes from looking at either Figure 3.5 or 3.6. Recall that with a subsidy the line defining whether a firm produces or not was i = P/K + j(S/K). When S = 0 this line becomes flat at the level P/K and we have only the rectangle A to worry about in deriving the externality. This means the externality produced without a subsidy is P

1

N ∫ K ∫ jSdjdi 0 0

=

S 2 {

average externality

P × N   K 123

(3.22) (3.23)

market output

The price used in the above calculation must be the equilibrium price in a market without subsidies (easily shown to be P = C/(N/K + C/R)). The first part of total externality is the average externality per firm. Here it is useful to recall that the maximum subsidy symbol S above also refers to the maximum possible externality E. The second part of total externality is the total output of firms.

Are subsidies evaded taxes?

71

The net amount of externality produced by the subsidy is the difference between equations (3.20) and (3.23) or (3.21) and (3.23), depending on whether (K – P)/S ≤ 1, ≥ 1. The above benefit counting exercise proceeds on the assumption that government funds the full externality of each firm (S = E). The interpretation of the net benefit is then the net benefit from fully subsidizing each firm for its externality. The above exercise is also flexible enough to admit a different interpretation. If government sets S ≤ E, then the above equation is the net benefit of subsidizing each firm in proportion to its externality, but not for the full sum of its externality. For example, when S = 0.5E, each firm is funded for half its externality should it choose to produce. This second interpretation will prove important when discussing whether bureaucrats should fully fund externalities. Triangle Loss The last ingredient needed to calculate the net benefit of the subsidy is the traditional triangle loss from a subsidy. This loss is the difference between the consumer value created by the increase in production, less the cost of producing the extra output. The consumer benefit of extra consumption is the area beneath the demand curve (which has height P = (C – Q) × (R/C)) between the unsubsidized equilibrium level of output QS = 0 and the subsidized level of output QS > 0. This area is calculated as R ∫Q (C − Q) C dQ QS > 0 S=0

(3.24)

The cost of producing this extra amount is the difference between the cost of producing QS > 0 as given by equations (3.17) and (3.18) and the cost of producing the unsubsidized quantity QS = 0 in the presence of the subsidy. As explained earlier the trick in calculating this latter cost is to calculate the price at which the unsubsidized quantity would be supplied in a subsidized world and plug this price into either of the relevant cost equations (3.17) or (3.18). The difference between the benefit of the extra consumption and its cost is the traditional triangle loss from a subsidy, though given the special nature of the supply curves derived here, the graphical analogy of a triangle is no longer strictly correct. Simulations We now have the apparatus needed to look at the costs and benefits of firmspecific investment grants. This allows us to get a feel for the displacement deadweight losses from firm-specific investment grants and allows us to ask

72

Tax evasion and firm survival

questions such as whether bureaucrats should fully subsidize the externalities firms generate. First it might help to get a feel for the size of the loss from displacement. Figure 3.7 maps the components of cost and benefit as well as the net benefit of the grant for different levels of the maximum externality E (remember, the government equates S with E in its granting mechanism). The net benefit is defined as net benefit = net externality – displacement loss – triangle loss

(3.25)

Figure 3.7 suggests that the costs of displacement are not to be neglected in the analysis of firm-specific investment grants. How does any of this help the bureaucrats asking themselves whether to fully subsidize the externalities of which they are aware? Recall that earlier I mentioned that the net benefit equation from subsidizing an externality fully could also be interpreted as the net benefit of a partial funding of the externality. If we set E = 20 but allow S to vary in the range [0,20] then Figure 3.7 shows the rising costs and benefits of approaching the point of fully subsidizing the externality and can instruct us in the rule bureaucrats should follow. Now the figure can help to answer whether the bureaucrat should stop short of fully funding each firm’s externality. The answer in this case is ‘No’. The net benefit of an increase in the subsidy is always greater than the net costs. This is in part due to the way I have chosen the model’s parameters, but it is also due to the fact I have left out of the calculations the social cost of raising the money to fund the subsidy. Browning (1976) found that the cost of raising government money, perhaps for subsidy ($) 80

Net externality Net benefit

60 40 20 –

Displacement loss

–20 Triangle loss –40

0

Figure 3.7

5

10 15 Maximum subsidy S

20

25

Are subsidies evaded taxes?

73

programmes, rises with the level of taxation. When one adds the rising cost of displacement proposed in the present model to Browning’s social cost, we must expect that some subsidy programmes which would have passed muster without the existence of this chapter, will now have to be delayed. Browning’s social cost of taxation could, when added to the social cost of displacement of firms, tip the balance against fully subsidizing the externality. How large are displacement losses due to subsidies relative to the size of the economy? Figure 3.8 graphs the displacement and triangle losses as a percentage of industry output value P × Q against the actual amount of subsidy given as a percentage of industry output value. If we were applying the analysis to the whole economy then industry output value would correspond to GDP. If the industry we are looking at is an ‘average’ industry then the analysis here can be projected to statements about the effects of subsidies in the entire economy. Figure 3.8 shows that for subsidies that come to roughly 20 per cent of the value of an industry’s output, the losses from displacement are slightly more than 1 per cent of industry output value. Even when an industry receives subsidies of up to 100 per cent of the value of its output (which happens more often than one would imagine), displacement losses are slightly more than 6 per cent of industry output value.

POLITICAL ECONOMY

Deadweight loss as a percentage of P × Q

If there are no externalities to firm-specific investment grants, my model becomes a means of identifying a new cost to rent-seeking activities. Tradi12 10 8

Triangle loss

6 4

Displacement loss

2 0

0

Figure 3.8

10 20 30 40 50 60 70 80 90 100 Actual subsidy as a percentage of industry output value P × Q

74

Tax evasion and firm survival

tionally the cost of rent-seeking has been taken as the effort people devote to getting a government favour. The rent-seeking literature has focused on Tullock (1967, 1980) rectangles and ignored the fact that if a skilful lobbyist with high costs manages to get a subsidy, he may displace from the market a rival who has lower production costs and weaker lobbying skills. The costs of displacement shown in Figure 3.7 show that this fallout from rent-seeking may come to as much as 10 per cent of the amount of the subsidy in a world of symmetric supply and demand, where the abilities to rent-seek and produce efficiently are uncorrelated and uniformly distributed. This is the worst case scenario for firm-specific investment grants. As I have emphasized earlier in the chapter, this worst case scenario plays out no matter how skilful are grant administrators at ‘picking winners’, that is, at identifying firms that produce an externality. At best we can hope there is some externality from the grant. At worst, the grant will produce no externality and will carry with it not only Browning’s social cost of public funds, but also a displacement deadweight loss which I have shown how to model. The deadweight losses from displacement due to a subsidy go away if firms that have low costs and firms that have a good ability to lobby politicians can specialize in lobbying for grants on behalf of firms that are good at producing. Such a division of labour would allow grant-getting and productive abilities to peel away from each other. When abilities separate there is no longer a risk of displacement losses. The costs that now have to be paid are the costs of specializing. Such specialization is most likely to be seen in large firms. The lobbying department of a large firm can be seen as a specialist who works in isolation from the firm’s production department. Isolation means that the firm chooses its lobbying department as it would a subcontractor on the market. It can hire the best lobbyists provided it believes it has the best chances of making money. Efficient firms with low costs will tend to have the most money for hiring efficient lobbyists. In such a world there will be little deadweight loss from displacement. Only a transfer of resources from producers to lobbyists. A social planner might not be pleased with specialization that allows an industry to avoid deadweight losses. Firms that get subsidies by buying the best lobbyists may chase away the danger of displacement losses, but they may also pervert a government’s intention to fund externalities.

CONCLUSION The present chapter has shown that firm-specific investment grants to encourage firms that generate positive externalities entail social costs not previously modelled in the public finance literature. The social cost arises because a grant may go to a high cost firm that displaces a low cost firm. The social cost from

Are subsidies evaded taxes?

75

displacement of firms is less than, but of the same order of magnitude as the net benefits of subsidizing the externality. When one counts the social cost of raising the money for a subsidy, the displacement costs modelled here suggest that bureaucrats must hold back from fully subsidizing externalities. I derived these result under the assumption that bureaucrats have full knowledge of the externality each firm generates but only a knowledge of the distribution of firm production costs. I assumed both externalities and production costs to be distributed independently of each other. The displacement of firms would have been stronger had I assumed production costs and externalities are positively correlated, and weaker (but nonetheless present) had I assumed them to be negatively correlated. When firms produce no externalities, subsidies encourage only a triangle loss, and a loss from the displacement of firms. This displacement loss has been ignored in discussions of political equilibrium. As political economy models have shown, we must take into account all social losses from political action in order to understand why those actions take place and whether institutions have evolved to minimize those losses. The final chapter of the book elaborates on the link between displacement loss and political equilibrium. For the moment we turn to displacement losses from regulation.

4. Tax evasion analysis extended to regulation evasion: the case of the minimum wage Government has the power to tax and to regulate. Economists often see taxes and regulations as brothers. Both instruments allow government to influence how people behave, both allow government to redistribute income, and both carry with them a deadweight loss. In the last two chapters I have shown that a deadweight loss previously unstudied by the public finance literature needs to be reckoned with. It is the loss that comes when inefficient firms who are good at evading taxes crowd out efficient firms that are poor tax evaders. In the present chapter I extend this insight to regulations that create shortages of output. A simple case to understand of displacement loss resulting from a regulation is that of fishermen who receive quotas from government. Each boat gets a maximum allowable catch. If government does not assign the most quota to the most efficient boats, inefficient boats will thrive simply because they have quotas. Efficient boats will not be able to push their inefficient rivals from the seas. If efficient fishermen were allowed to buy quotas from inefficient fishermen deadweight losses from displacement could be avoided. Suppose the market price were $200 per tonne of fish. An inefficient fisherman with costs of $100 per tonne of catch would be willing to sell his quota for a tonne to the efficient fisherman who can catch a tonne for $50. The sale price could be anything between $100 and $150. The total cost to society of catching fish would fall by $50 (the difference between the costs of the inefficient and the efficient fisherman). This $50 is the displacement deadweight loss from not allowing quotas to be exchanged. The displacement losses would be even worse if inefficient fishermen were better at evading quotas than efficient fishermen. These costs are so evident that, as Michael De Alessi (2000) has explained, New Zealand, Australia, Iceland, the USA, and Canada allow fishing quotas to be traded, or at least turn a blind eye to their exchange. The desire to avoid displacement losses is behind the logic of transferable pollution quotas as well. In the USA a market exists for sulphur dioxide pollution rights. These rights are actively traded on stock exchanges and as Casella (1999) explains, they can be bought from brokers such as Cantor Fitzgerald at their web page (www.cantor.com/bs). It is more difficult to analyse the displacement losses that come when governments regulate prices, than it is to analyse the dis76

Regulation evasion: the case of the minimum wage

77

placement losses from quantity controls. I pay special attention to the problem of price controls in the present chapter. Perhaps the most prevalent form of price regulation in western countries is the minimum wage. The minimum wage is the subject of ferocious political lobbying. Economists have focused their attention primarily on the employment effects of the minimum wage and have paid scant attention to its deadweight losses or the problems that might arise when some firms evade the minimum wage. In the present chapter I focus on the minimum wage, not just to illustrate the displacement losses of the wage, but to show how price controls in general may be analysed within the framework of the uneven enforcement of rules introduced in Chapter 2. To give the reader a roadmap to the chapter I will summarize here what he or she can expect. The basic insight of the present chapter is that even without evasion by firms or workers, the minimum wage produces a displacement deadweight loss from non-price rationing that may rival in size the traditional triangle loss associated with price controls. The chance of earning the minimum wage attracts workers whose reservation wages exceed the free market wage. These high reservation wage workers have the same chance of finding work as low reservation wage workers because the minimum wage short-circuits the ability of the low reservation wage workers to compete on price. When a highcost worker displaces a low-cost worker society suffers a social loss. I first show what these displacement losses look like in a world of complete compliance with the minimum wage. Next, I pay attention to Squire and Narueput’s (1997) warning that any discussion of the deadweight losses from the minimum wage must pay attention to non-compliance by firms. Their work centred on the transactions costs firms pay to evade the minimum wage and the enforcement costs governments incur. The present chapter looks to a different source of inefficiency: non-compliance produces a social loss by allowing some firms with good evasive skills but low outputs to put out of business firms with high outputs but poor evasive skills. Far from easing the social losses due to the minimum wage, non-compliance may make these losses worse. These insights rest on my assumption that non-compliance may be partial and that firms differ in their abilities to evade the minimum wage. This has been the approach I have taken to model firm displacements due to tax evasion and displacements due to subsidies. To date the literature on the general equilibrium consequences of minimum wage evasion has assumed that compliance is either complete or non-existent. I assume a continuum of evasive decisions by firms because I believe this accords better with reality. The payoffs to making this assumption are that it throws light on a previously unexplored social cost of the minimum wage. The price of getting to this insight is that the assumption of a continuum of non-compliance by firms complicates the modelling of equilibrium. One of the chapter’s novel implications is that the size

78

Tax evasion and firm survival

of the deadweight loss from firm displacement depends on whether firms are evading the minimum wage or whether workers are evading it. Such an analytical distinction is unheard of in the literature on labour markets, mainly because it is taken as given that firms are the ones who do not comply with the minimum wage, and also perhaps because of a working belief among public finance economists that the direct object of a tax or regulation has little or no bearing on the final results of that tax or regulation. When we consider evasive abilities jointly with productive abilities this irrelevance result disappears.

LABOUR MARKET WITHOUT EVASION Before discussing minimum wage evasion, it helps to form an idea of how the minimum wage works and what are its better known social costs. This section lays out a basic model of equilibrium in the labour market. The goal of the model is to establish a benchmark free market wage and employment level against which results from later modifications to the model can be compared. As in previous chapters we can begin by laying out the simple cost and demand structure of the industry. I start with an industry with an infinity of firms. The size or ‘measure’ of firms is F. The measure can be thought of as the size of the industry and is the continuous analogue of a finite, discrete number of firms. Each firm draws its particular productive ability mp from a uniform distribution over the range [0,MP]. Each firm produces a fixed, infinitesimal level of output mp × df. The df term emphasizes the atomistic nature of firms. The price of a unit of good is $1, so output and value of output are the same thing. I assume for analytical convenience that each firm hires only one worker. Such an assumption is of no substantive consequence provided one is not interested in capturing the effects of employer size on wages. Faced with a market wage of w the firm will demand a unit of labour if mp ≥ w. For example, firm 5 may draw mp = 8 and firm 6 may draw mp = 2. If the wage is $2.10, firm 5 will produce and firm 6 will not produce. The proportion of firms demanding labour is Pr(mp ≥ w). With F firms, this means that the industry demand for labour Ld(w) is: Ld(w) = F × Pr(mp ≥ w)

(4.1)

w 1  = F 1 − ∫ 0 MP  

(4.2)

w  = F 1 −  MP 

(4.3)

Regulation evasion: the case of the minimum wage

79

There is no randomness in the present model. The distribution function of firms serves simply to calculate the proportion of firms who will hire workers at any given wage. I have chosen a uniform distribution because this assumption seems the most neutral, and also because of the analytical convenience it brings to derivations of equilibrium. Convenience is not always a good reason for making an assumption, but as the reader will, I hope, see, whether a distribution is uniform, normal, or skewed, will have little bearing on the basic results that emerge from the analysis. These distributions serve simply to show how demand and supply curves emerge when reservation prices sweep across their path. There is an infinity of workers with measure N. Each worker supplies a fixed amount of labour. The worker draws his or her particular reservation wage wr from a uniform distribution on the interval [0,Wr]. The proportion of labourers that chooses to work is Pr(wr ≤ w). Since the measure of workers is N, aggregate labour supply Ls(w) is Ls(w) = N × Pr(wr ≤ w) = N∫

w

0

=

1 Wr

N w Wr

(4.4) (4.5)

(4.6)

The equilibrium free market wage wfree comes from setting labour demand and supply equal to each other. It is simple to show that in equilibrium this wage is w free =

MP × Wr F N × MP + F × Wr

(4.7)

Figure 4.1 illustrates these two curves. With these preliminary assumptions we can explore the consequences of imposing a minimum wage on this market and on all other markets where the minimum wage might bind (so that there is no covered and uncovered sector). The minimum wage is a price floor that creates deadweight loss in at least two ways. The first and best known loss is the traditional triangle deadweight loss. By restricting employment, the minimum wage drives a wedge between what the marginal employer is willing to pay and what the marginal worker is willing to be paid. The sum of such wedges between employment under a minimum wage Ld(Wmin) and employment in the free market Ld(Wfree) is the triangle loss. We need not worry that unemployed workers find work in other markets, because these too are under a minimum wage. The best these workers can do

80

Tax evasion and firm survival

W Ls MP

N/Wr

F/MP Wmin

A Wfree

Wmin/2 B

Ld Lfree

Ld(Wmin)

Ls(Wmin)

F

L

Figure 4.1 Deadweight loss and employment effects of the minimum wage: no evasion is enjoy the alternate uses of their time, perhaps in domestic production, whose value is given by the height of the supply curve. Triangle loss can be calculated by first calculating producer output between output before and after the imposition of the minimum wage. The maximum price any particular producer is willing to pay is his or her output from hiring labour mp. From equation (4.1) it is easy to see that the reservation price (the height of the demand curve) at some quantity of labour demanded L is mp = MP(1 – L/F). So lost producer output due to the minimum wage is

(

Ld W free

∫L ( W d

min

) MP1 −

)



(

)

(

L 1   dL = MP  Ld W free − Ld (Wmin ) − Ld W free F 2F  

)

2

2  − Ld (Wmin )   

(4.8)

Regulation evasion: the case of the minimum wage

81

The personal cost to workers (in the sense of the value of time they have forgone in the next best alternate use) of producing this output is, similarly, the area under the supply curve between the same range of labour supplies:

(

Ld W free

∫L ( W d

min

) Wr

) N

LdL =

(

Wr  Ld W free 2 N 

)

2

2 − Ld (Wmin )  

(4.9)

Subtracting saved worker costs (4.9) from lost output (4.8) gives the triangle loss. This loss is illustrated in Figure 4.1 as area A. Much of this is a standard, though generally neglected analysis of the deadweight losses of the minimum wage. The analysis appears in some textbooks, but is not the subject of intense study. Most attention has centred on the employment effects of the minimum wage. It comes as no surprise that analyses of the deadweight loss from the minimum wage do not abound. One rare creature in the menagerie of deadweight losses is the social cost of inducing workers with high reservation wages to work. Workers lucky enough to find employment are not necessarily those with the lowest reservation wages in the range [Ls(0), Ld(Wmin)] in Figure 4.1. Rather, willing job candidates flock from the broader range of reservation wages defined by [Ls(0), Ls(Wmin)] in Figure 4.1. Each one of the these workers has an equal chance of getting a minimum wage job because none can compete with the other on wages. An equal shot for workers uniformly distributed in the range of reservation wages [0,Wmin] means that the average reservation wage of a worker seeking a minimum wage job will be Wmin/2. The cost of total labour provided under the minimum wage will then be Wmin/2) × Ld(Wmin). This cost exceeds the minimum possible cost of supplying Ld(Wmin). The minimum cost is the area under the labour supply curve between the indicated ranges: Ld ( Wmin ) Wr

∫0

N

LdL =

Wr 2 Ld (Wmin ) 2N

(4.10)

Subtracting this minimum cost from the actual cost of providing Ld(Wmin) units of labour gives the deadweight loss of the minimum wage due to displacement of low by high reservation wage workers: displacement loss = Ld (Wmin )

Wmin Wr 2 − Ld (Wmin ) 2 2N

(4.11)

This loss is illustrated in Figure 4.1 as the area B. The concavity of the loss equation (4.11) indicates that as the minimum wage rises and labour employed

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Tax evasion and firm survival

falls, displacement loss will rise, and then fall. Two opposing forces are at work. At low minimum wages some jobs are lost and this would tend to mitigate displacement loss as the fewer workers there are the less such loss there can be. The opposing force that pulls overall displacement loss upwards is that, as the minimum wage rises, higher cost workers are enticed into the job search and the chance that any one low cost worker is displaced by a higher cost worker increases. This means that the displacement loss per worker increases. The balance of opposing tendencies between displacement loss per worker and overall number of workers determines whether displacement loss rises or falls with the minimum wage. It is easy to verify from equation (4.11) that below some critical level of labour demand elasticity, overall displacement loss rises with the minimum wage. An example can give a feel for displacement loss from non-price rationing (area B). Consider a minimum wage of $10. A farm boy has reservation wage of $8 an hour which represents in part the value of chores he can provide around the farm to help feed his family. If the farm boy gets the minimum wage job, the economic surplus created will be at least $2. A city boy with the same tastes for leisure as the farm boy has reservation wage of $2 an hour, which represents in part the limited value he can bring to his family from working around the house. If the city boy gets the minimum wage job he will create a surplus of at least $8. If both have an equal chance of getting the job, the expected cost of labour is 0.5 × $8 + 0.5 × $2 = $5. This is $3 more than the cost if the city boy were guaranteed the minimum wage job. This $3 excess is the rationing loss from the minimum wage. The minimum wage may improperly select a high cost worker where a lower cost worker could serve. I speak of expected costs in this example because there are only two workers. In the present chapter’s model there is an infinity of workers and so there is no expectation or uncertainty to deal with. To my knowledge the only researcher to have spoken of how jobs are arbitrarily allotted under a minimum wage is King (1974). He discusses how the lottery to get high paying jobs influences the payoffs to workers, but pays no attention to the deadweight loss from non-price rationing. Table 4.1, column (4) shows the rationing loss, simulated for increasing levels of the minimum wage. The parameters of demand and supply are N = 1,000, F = 1,000, Wr = 20, MP = 20. Equilibrium wage in an unregulated market would be $10 and the number of jobs would be 500. When a minimum wage is imposed, the number of jobs can be read from the labour demand function (column 2). Triangle deadweight loss (column 5) rises with the minimum wage, as we would expect from the well-known properties of this form of loss. The loss from non-price rationing (column 4) at first rises, but then falls with the minimum wage. Column (7) shows that at low levels of the minimum wage, displacement loss can exceed triangle loss. This is a result very similar to what I found for tax evasion in Chapter 2 and the getting of subsidies in Chapter 3.

Regulation evasion: the case of the minimum wage

83

Table 4.1 Deadweight loss and employment effects of minimum wage Wmin without evasion (1) Wmin

10 11 12 13 14 15 16 17 18 19 20

(2) (3) (4) (5) (6) (7) Ld(Wmin) Ls(Wmin) Displacement Triangle Total Ratio displacement loss loss deadweight loss to triangle loss (4) + (5) loss (4) ÷ (5) 500 450 400 350 300 250 200 150 100 50 0

500 550 600 650 700 750 800 850 900 950 1,000

0 450 800 1,050 1,200 1,250 1,200 1,050 800 450 0

0 50 200 450 800 1,250 1,800 2,450 3,200 4,050 5,000

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000

9.00 4.00 2.33 1.50 1.00 0.67 0.43 0.25 0.11

Note: The parameters of supply and demand used in the above simulations are N = 1,000, F = 1,000, Wr = 20, MP = 20. The wage that would prevail in an unregulated market is $10 and the number of jobs created would be 500. Blanks indicate a calculation is not applicable.

Readers may wonder where go the efficient workers who lose the lottery for jobs. Can they not transfer their skills to another labour market, displace high cost workers there, and so make up for some of the social losses of the market they left? This secondary recapture of social gains need not concern us because I have assumed the minimum wage is imposed on all markets. The efficient workers who do not have jobs here have no higher chance of capturing jobs in other markets because those markets also choose workers by lottery. If these other markets were not covered by the minimum wage then the social loss from displacement would not be as large as the displacement loss implied by equation (4.11). The supply curve would then have to be interpreted as the value of workers in alternate labour market employment. What would happen to displacement loss if workers could spend resources equally effectively to raise their probability of employment? The payoffs to getting a minimum wage job, Wmin – wr, are greater for low reservation wage workers than for high reservation wage workers. Workers with low reservation wages would have an incentive to spend more money raising their probabilities than workers with high reservation wages. These efforts to raise the probability of getting a job would undo the displacement just described. In undoing the displacement loss, workers would expend resources. These resources are the costs of ‘rent-seeking’ and depend on the technology for transforming effort into probability of getting a job. John Lott (1990) has explored

84

Tax evasion and firm survival

the social cost of this sort of rent-seeking in a setting where workers with low reservation wages sink resources into keeping their minimum wage jobs. Later, these workers develop high reservation wages but cannot be bribed away by low reservation unemployed workers, because their investment in securing the job cannot be transferred and compensated. Lott does not devote attention to the deadweight losses from displacement described here. Lott’s work is in the same tradition as Yoram Barzel’s work on price controls, which has recently been updated by David Tarr (1994). Barzel (1974) argued that it is costly to stand in the queues to which price controls give rise. Only individuals who extract the most surplus from standing in a queue will wait. The value of their waiting time will exhaust the rents from success in getting the rationed good. Under a minimum wage, only workers with the lowest opportunity costs would wait in line to get their jobs. There would be no displacement loss of the sort I am modelling, but rather a rent-seeking loss from time spent waiting. Whether the Barzel–Lott rent-seeking costs or my displacement losses are the appropriate models depends on the institutions individuals have at their disposal for jumping the queue or raising their chances in the jobs lottery. This should not be taken to mean that Barzel–Lott losses and displacement losses are contradictory concepts. Barzel–Lott losses may be more prevalent than displacement losses, but the potential for displacement losses may be what gives rise to Barzel–Lott losses. The rent-seeking losses these researchers modelled are an echo of the displacement losses which this book highlights. The view that price controls can have as their main deadweight loss a displacement of efficient by inefficient firms is not widely applied in the literature on price controls. In a major opus on the subject, John Butterworth (1994) focuses instead on the allocative effects of price controls mainly under imperfectly competitive conditions. The analysis is usually of how one or several firms vary their output decisions at the intensive margin. Displacement losses do not figure in the discussion. Matthew Turner (1998) takes the same sort of approach in his treatment of quota programmes. The lack of attention to displacement is a topic which I now go on to address.

EVASION BY WORKERS The discussion of displacement loss in the previous section is a departure from the theme developed in the first two chapters of this book. In those chapters I suggested that when some producers evade taxes or are good at getting subsidies, they may displace from the market producers with lower costs but poorer evasive or subsidy getting skills. In this chapter I have shown that regulations produce displacement deadweight losses even when everyone obeys them fully. The loss arises because by short-circuiting a market’s normal means

Regulation evasion: the case of the minimum wage

85

of sorting participants from non-participants, the regulation opens the market to an arbitrary selection of producers or workers. The insight is novel, but can be carried further by asking what happens to displacement loss when some market participants evade the regulation, in whole or in part. Empirical research suggests that minimum wage evasion is important. Ashenfelter and Smith (1979) found that in the early 1970s only 65 per cent of US firms honoured the minimum wage law more in the observance than in the breach. In their view: While substantial, compliance with the minimum wage law is anything but complete. This implies that the most useful future analyses of the effects of this law will incorporate a thorough analysis of the compliance issue. Indeed the failure to do so can lead (and has led) economists to public policy predictions that are simply silly. (Ashenfelter and Smith, 1979, p. 349)

Card (1992) found that in California, 46 per cent of workers directly affected by the minimum wage were paid less than the minimum wage. The situation is comparable for developing countries. In a survey of research papers from various international labour organizations, Squire and Narueput (1997) report that in Mexico in 1988 as many as 66 per cent of women in certain sectors were paid less than the minimum wage. In Morocco more than 50 per cent of firms paid their unskilled workers less than the minimum wage. There also seems to be a variable pattern of evasion. Some firms evade a greater part of the minimum wage than others, and some firms are more likely to be evaders than others. Ashenfelter and Smith (1979) found that firms hiring a greater proportion of women than others were less likely than others to violate the law. Clearly, noncompliance is a phenomenon to be reckoned with by the researcher interested in the social costs of the minimum wage. How exactly does one ‘reckon’ with minimum wage evasion in a model of economic equilibrium? To date no one has attacked this problem in a way that recognizes that there is a variety of evasive tendencies. To answer this question I begin by assuming that workers evade the minimum wage, and then switch the assumption to one that firms evade the minimum wage. This may seem like an eccentric approach to the analysis of minimum wage evasion. It is unusual, and to my best knowledge, unheard of in the economic literature to treat workers as the ones who evade the minimum wage. Both popular lore and academic research take it as a matter of fact that firms are the ones who evade. The point does not seem controversial, and no effort has been made to see whether the identity of the evader matters. This indifference is perhaps due to the insight from public finance that the object of the tax has nothing to do with who ends up paying it. No such irrelevance result holds for the case of a price control such as the minimum wage. When evasive abilities are distributed among firms, the minimum wage affects employment and deadweight loss differently than

86

Tax evasion and firm survival

when evasive abilities are distributed among workers. The main result is that employment falls by less under a minimum wage when firms evade than when workers evade, that a range of wages will develop in a market with a minimum wage and firms evading, and that there is displacement of both firms and workers. How does one justify the assumption that workers evade the minimum wage? Minimum wage evasion is a broad term. The law does not acknowledge that workers can be the ones responsible for avoiding the minimum wage. Such evasion can be implicit and may arise through non-price competition. To justify being hired at a wage above his or her productivity a worker may be willing to forgo on-the-job amenities. He or she may take more risks on the job to justify his or her employment at the minimum wage. In this case, risk aversion and ability to avoid the minimum wage are the same creature. The minimum wage will introduce a market selection criterion that rewards high-risk behaviour on the job. An informal anecdote, for which I have no written proof, is that workers in the province of Quebec will sometimes show their hands with missing fingers and blame the minimum wage for their accident. The minimum wage in their minds forced them to take greater risks on the job so that they would maintain their employment. Gianni De Fraja (1999, p. 484) echoes this view in writing that ‘An increase in the minimum wage should bring about a worsening of the working conditions for the workers on the minimum wage.’ He also cites the work of Card and Krueger (1995) as providing indirect empirical support for this notion. What does it mean for a worker to evade the minimum wage? To answer this I assume, as in the previous section, that a worker can be thought of as drawing his or her reservation wage wr from a range [0,Wr]. My new assumption is that the worker can evade a part e of the minimum wage, so that the minimum price at which the worker is able to offer his or her services is Wmin – e. This evasive ability is drawn from a uniform distribution over the range [0,E] where, by necessity, E ≤ Wmin. For example, a worker may draw wr = 10 and e = 3. If the minimum wage is $14, then this worker can offer his or her services because he or she is able to offer a wage of $11, which is greater than his or her reservation wage. I assume that evasive ability and reservation wages are independently and uniformly distributed in order not to stack the results in favour of any particular outcome, and for analytical convenience. Equilibrium wage on the underground labour market Wu and employment Lu are found where supply and demand meet. The supply of workers is the number of workers times the proportion of workers for whom the reservation wage is less than the underground wage being offered Pr(wr ≤ Wu) and the extent of this proportion which is able to evade the minimum wage sufficiently Pr(Wmin – e ≤ Wu):

Regulation evasion: the case of the minimum wage

Ls(Wu) = N × Pr(Wmin – e ≥ Wu)Pr(wr ≤ Wu)

87

(4.12)

The area A in Figure 4.2 is the product of the two probabilities expressed above. The horizontal axis of Figure 4.2 shows the range of evasive talents Wmin – e. The vertical axis shows the range of reservation wages wr. The sum of areas A, B, C, and D comes to one. The area A + B is the proportion of workers with evasive skills below the underground wage Pr(Wmin – e ≤ Wu). The area A + C is the proportion with reservation wages below the underground wage Pr(wr ≤ Wu). These proportions overlap in the area A. The overlap is the proportion of workers who will offer their services at the underground wage. Wu

Wr B

D

A

C

Wu

Wu

Wmin – e

Wmin

Figure 4.2 Probabilistic basis of labour supply Noting that Pr(Wmin e ≤ Wu) = Pr(e ≥ Wmin – Wu), labour supply can be reduced to Ls (Wu ) = N 1 − ∫ 0 

Wmin − Wu

=

[

1  Wu 1 E  ∫0 Wr

(4.13)

]

N Wu2 + Wu ( E − Wmin ) E × Wr

(4.14)

88

Tax evasion and firm survival

The reader may verify that when the underground wage is equal to the minimum wage the above supply equation reduces to the supply equation in an unregulated market, namely Ls(w) = (N/Wr)w. Figure 4.3 shows both this supply equation for two levels of the minimum wage, and the supply equation that would hold over the entire range of wages if there were no minimum wage. The parameters have the same values as in the previous section (MP = 20, Wr = 20, N = 1000, F = 1000). At higher levels of minimum wage the supply curve is pulled and bent upward. Also, for higher levels of minimum wage the supply curve ends

Supply without minimum wage

Wmin = 18

Supply when Wmin = 18

Wu = 13.18 Wmin = 11 Wu = 10.34

Supply when Wmin = 11

Wmin – E = 8

Demand

Wmin – E = 1 L Lu = 341 Lu = 483 Note: Supply function generated from equation (4.13) in text and demand generated from equation (4.3). Labour supplies corresponding to each minimum wage are also shown in Table 4.2.

Figure 4.3 wages

Shadow wages and employment under two different minimum

Regulation evasion: the case of the minimum wage

89

not at zero, but at Wm – E, the lowest possible wage that any worker can offer. At this point it can be shown that the elasticity of the supply curve under evasion is twice that of the supply curve without evasion. As the minimum wage rises, the elasticities of both curves converge and both curves merge. This illustrates that when workers can avoid the minimum wage, the minimum wage becomes ‘woven’ into the supply curve as one of its parameters. This is not a supply curve as we usually understand it because the ordering from left to right is not only based on reservation wages, but on a combination of reservation wages and an ability to avoid the minimum wage. This is what leads to a deadweight loss from displacement of low reservation wage workers by high reservation wage workers. Demand as before is F × Pr(mp ≥ Wu) = F(1 – Wu/MP). Equilibrium is found by finding the Wu that equates supply and demand. Substituting this equilibrium underground wage into either supply or demand equations yields the equilibrium number of employed workers Lu. Figure 4.3 shows two such equilibria for two levels of the minimum wage. As in the previous section, the deadweight loss from the minimum wage has two components: the triangle loss described in the previous section, and the loss from the displacement of low by high reservation wage workers. The displacement loss in this case arises out of circumstances which differ from those of the previous section. Now, some workers with reservation wages close to zero may not be able to offer their services at the underground wage of Wu because they have very poor evasive skills. Such workers will be pushed out of the running by workers who derive less surplus from work but are endowed with greater evasive abilities. The cost incurred by these less efficient workers is the expected value of their reservation wages times the number of such workers. One can get this result simply by integrating the reservation wages in the range [0,Wu] and multiplying by Lu: Lu ∫

Wu

0

W wr dwr = Lu u Wu 2

(4.15)

The minimum cost of providing Lu can be found by integrating the inverse of the supply curve, w = L(Wr/N), between [0,Lu]: Lu

∫0

Wr W LdL = r L2u N 2N

This deadweight loss from displacement is then

(4.16)

90

Tax evasion and firm survival

Lu

Wu Wr 2 − Lu 2 2N

(4.17)

which could be further simplified by substituting the reduced forms of L and Wu into this above equation. Table 4.2 shows how deadweight losses and employment change as the minimum wage rises. The parameters are the same as in the no-evasion example with the addition of an upper bound on evasive skills of E = 10. The minimum wage can rise to as high as $30 without closing down the market, compared to a maximum minimum wage of $20 in the noevasion case. Apart from this, the table can be seen simply to be a spread-out version of Table 4.1. The new insights are that minimum wages can be pushed higher, and that minimum wages change the shape of the supply curve in a way that econometricians may wish to consider. By assuming that workers evade part of the minimum wage, we convert the analysis of the minimum wage from one of disequilibrium to one of equilibrium.

EVASION BY FIRMS Readers who do not find the above example of evasion by workers to be realistic will be more interested in an analysis of evasion by firms. The analysis when firms evade is more complex than when workers evade. The reason for this lack of symmetry in results, depending on who evades, will emerge from the following analysis. What does it mean for a firm to evade the minimum wage? As in the previous section a firm can be thought of as drawing its particular productivity mp from a range [0, MP]. The new assumption is that the firm can evade paying a part e of the minimum wage, so that the minimum price it will be able to offer willing workers for their services is Wmin – e. The firm draws its evasive ability from a uniform distribution over the range [0, E] where, by necessity, E ≤ Wmin. For example, a particular firm may draw mp = 10 and e = 5. If the minimum wage is $14, then the firm can make the worker an offer of as little as $9. Different firms may draw different values of e and mp. The variable evasion parameter e may strike the reader as having fallen from the sky. Where in the jungle of literature on labour economics has such a creature been spotted? General equilibrium treatments of the underground economy, such as those of Harris and Todaro (1970), treat evasion as all or nothing (implicitly e is either zero or one in their model). One innovation of my analysis is to treat non-compliance with the minimum wage as something that can vary across employers, so that e varies on a continuum between [0,E]. The evasion parameter e is shorthand for the detailed inquiries into what motivates individual

Table 4.2 Deadweight loss and employment effects of minimum wage Wmin when workers evade

91

(1) Wmin

(2) W*u

(3) Lu

(4) Ld(Wmin)

10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 19.00 20.00 21.00 22.00 23.00 24.00 25.00 26.00 27.00 28.00 29.00 30.00

10.00 10.34 10.70 11.07 11.46 11.86 12.28 12.72 13.18 13.65 14.14 14.65 15.18 15.72 16.28 16.86 17.46 18.07 18.70 19.34 20.00

500.00 482.96 465.15 446.56 427.16 406.93 385.86 363.93 341.13 317.45 292.89 267.45 241.13 213.93 185.86 156.93 127.16 96.56 65.15 32.96 0

500.00 450.00 400.00 350.00 300.00 250.00 200.00 150.00 100.00 50.00 0 0 0 0 0 0 0 0 0 0 0

(5) Displacement loss 0 164.60 324.18 477.28 622.30 757.46 880.86 990.41 1,083.92 1,159.01 1,213.20 1,243.91 1,248.43 1,223.97 1,167.71 1,076.76 948.20 779.12 566.63 307.86 0

(6) Triangle loss 0 24.29 57.12 106.12 173.24 260.57 370.32 504.81 666.48 857.86 1,081.58 1,340.30 1,636.76 1,973.71 2,353.95 2,780.22 3,255.28 3,781.84 4,362.55 5,000.00

(7) Total deadweight loss (5) + (6) 0 164.60 348.47 534.40 728.42 930.70 1,141.43 1,360.73 1,588.72 1,825.49 2,071.07 2,325.49 2,588.72 2,860.73 3,141.43 3,430.70 3,728.42 4,034.40 4,348.47 4,670.41 5,000.00

(8) Salary increase (Wmin – Wfree) * Lu 0 164.60 324.18 477.28 622.30 757.46 880.86 990.41 1,083.92 1,159.01 1,213.20 1,243.91 1,248.43 1,223.97 1,167.71 1,076.76 948.20 779.12 566.63 307.86 0

(9) Deadweight loss per dollar of salary increase (7) ÷ (8) 0 1.00 1.07 1.12 1.17 1.23 1.30 1.37 1.47 1.58 1.71 1.87 2.07 2.34 2.69 3.19 3.93 5.18 7.67 15.17 0

Note: The parameters of supply, demand, and evasion used in the above simulations are N = 1,000, F = 1,000, Wr = 20, MP = 20, E = 10. The wage that would prevail in an unregulated market Wfree is $10 and the number of jobs created would be 500.The equilibrium underground wage is W*u, Lu is equilibrium underground employment, and Ld(Wmin) is what employment would be under the minimum wage if no evasion were possible.

92

Tax evasion and firm survival

firms to evade the minimum wage. The most prominent among these are Ashenfelter and Smith (1979), Grenier (1982), Chang and Ehrlich (1985), Kim and Yoo (1989), Squire and Narueput (1997). They study the forces that drive a firm to evade the minimum wage. Their analyses are in the tradition of the Allingham and Sandmo (1972) optimal tax evasion literature which I discussed in Chapter 2. My analysis does not ask why some firms evade. As in Chapter 2 I assume that all firms evade to differing degrees and consider the consequences for equilibrium and social cost. Kim and Yoo (1989), Rauch (1991), Fortin et al. (1997), Squire and Narueput (1997) consider general equilibrium in a market where firms evade, but assume that firms evade the minimum wage either completely or not at all, and as a result are unable to focus on the deadweight loss consequences from the displacement of low cost firms by high cost firms. The present chapter differs from theirs in that it assumes that no two firms have the same evasive abilities. This heterogeneity in evasive skills drives the unconventional equilibrium and deadweight loss results that follow. How reasonable is the assumption that evasive abilities are uniformly distributed over firms? As mentioned earlier, studies of developed countries show large amounts of non-compliance but also show large amounts of compliance. This suggests that a distribution bunched at the low end of e is more realistic than a uniform distribution. For developing countries the issue is not so clear. I stick with the uniform distribution assumption in part because it may have some bearing on developing countries and in part because my objective is to make the point that non-compliance produces a deadweight loss due to displacement of low cost firms by high cost firms. Using a more complicated distribution would create important technical problems in modelling that would distract attention from this point. Even if it is not accurate for a developed country, the uniform distribution can still be of practical interest. The deadweight loss results will be more extreme using the uniform distribution assumption than using the assumption of a distribution grouped around the low end of e. This means my results will provide an upper bound on displacement loss. What may be a less reasonable assumption of my analysis is that evasive and productive abilities are uncorrelated. The consequence of this assumption is that the model will understate displacement losses if evasive and productive abilities are negatively correlated in reality, and will overstate these losses if there is a positive correlation between productive and evasive abilities. The reasoning in this matter was set out in Chapter 2. Demand Consider the aggregate demand curve for labour. Demand at any particular underground wage Wu in this market is the number of firms times the proportion

Regulation evasion: the case of the minimum wage

93

of firms for whom output exceeds what they pay for labour Pr(mp ≥ Wu) and the proportion of this proportion which is able to evade the minimum wage sufficiently Pr(Wmin – e ≤ Wu): Ld(Wu) = F × Pr(mp ≥ Wu)Pr(Wmin – e ≤ Wu)

(4.18)

The functional form is a simple multiple of probabilities because of the assumption that productive and evasive abilities are uncorrelated. Noting that Pr(Wmin – e ≤ Wu) = Pr(e ≥ Wmin – Wu), labour demand can be reduced to W 1 W −W 1 Ld (Wu ) = F 1 − ∫ u dmp 1 − ∫ min u de 0 MP 0   E 

=

F ( E − Wmin + Wu )( MP − Wu ) E × MP

(4.19)

(4.20)

For Wu > Wmin, i.e. a non-binding minimum wage, equation (4.20) reduces to equation (4.3), labour demand under no evasion. The Punctured Supply Curve Equation (4.20) will come in handy shortly, but first note the extremely unusual result that there cannot be just one underground wage W*u in equilibrium. Imagine gathering all firms and workers in the same room and telling them that only one underground wage will hold. An auctioneer then starts announcing wages and stops where demand is equal to supply. The problem with this auction is that after the hammer falls, firms who have high potential output but insufficient evasive ability to bid down to the unique equilibrium wage must, by the way I have constructed evasive and productive abilities, have unsatisfied demand. When an economist encounters a market that does not equilibrate using traditional concepts of equilibrium, he guesses at a different process by which the market comes to equilibrium. My guess, and it is important to underline that it is one of many possible guesses, is that frustrated firms are bound to advertise their presence to workers so as to get out of the one-wage auction. Workers will not even bother to participate in the auction. Instead Ls(Wmin) of them will flock to firms with the poorest evasive abilities and the highest salaries (e = 0 and mp ≥ Wmin). The highest wages being offered will be the minimum wage (at higher wages than this, evasive ability is irrelevant and firms are able to bargain with workers for lower wages). The proportion of firms offering

94

Tax evasion and firm survival

Wmin will be the proportion whose output is greater than the minimum wage Pr(mp ≥ Wmin) times the frequency f(e) of firms having precisely no evasive abilities (e = 0), which is f(e) = 1/E, in a narrow band de (note that f is the same for any level of avoidance because avoidance is uniformly distributed, a fact that I use later). Call this proportion α (e). The total number of workers to get jobs at these top-paying firms with zero evasive ability (e = 0) is Fα (0): Fα(e) = F × Pr(mp ≥ Wmin)f(e)de

(4.21)

W 1 = F 1 − min  de  MP  E

(4.22)

Firms with high productivity, but who are afflicted with poor evasive abilities, are not reticent about signalling their type to workers. If they do not advertise their desire to pay higher wages they will not be able to break out of one-wage underground auctions for workers. Without workers these high-productivity, low evasive ability firms go out of business. The remaining workers flock to firms with slightly better evasive abilities ε to earn an underground market wage of Wmin – ε. To figure out how many such workers offer their services we have to note that holes have been punched into the supply curve at even intervals between reservation wages of zero to Wmin. The weight of these holes in the supply curve is the fraction of workers who found jobs with firms paying Wmin, namely F α(0), to the number of workers who offered their services Ls(Wmin). So labour supply is now  Fα(0)  λ1 (Wmin − ε ) = 1 −  Ls (Wmin − ε )  Ls (Wmin ) 

(4.23)

Note that the new ‘punctured’ supply curve is the regular supply curve, multiplied by a factor less than one which accounts for the attrition of workers along the length of reservation wages between [0, Wmin] who managed to get a job with high paying, zero evasive ability firms. I call the new ‘punctured’ supply curve after this first iteration λ1. The subscript is very important to understand. Further iterations raise the subscript and change the functional form of supply. This means that λ1 and λ2 are different. Their relation lies in the recursiveness that follows from the exercise of calculating supply at ever greater increments of ε until the epsilons sum to e. The final iteration gives labour supply at Wmin – e. Next, an excess supply of workers flocks to firms offering 2ε less than the minimum wage. How many? Once again we have to note that some of the

Regulation evasion: the case of the minimum wage

95

workers who earlier flocked to firms offering Wmin – ε were successful at finding a job. The fraction of such successes was Fα(ε)/λ1(Wmin – ε) of the supply curve λ1(Wmin – ε). It is by this fraction that we must multiply what was left of the supply curve after workers flocked to firms offering Wmin, to give us the proportion of the supply curve that has been punctured away by the time workers offer their services at Wmin – 2ε. This second iteration of the punctured supply curve has the following form:  Fα(ε )  λ 2 (Wmin − 2 ε ) = 1 −  λ1 (Wmin − 2 ε )  λ1 (Wmin − ε ) 

(4.24)

After n iterations, punctured labour supply is   Fα((n − 1)ε ) λ n (Wmin − nε ) = 1 −  λ n −1 (Wmin − nε )  λ n −1 (Wmin − (n − 1)ε ) 

(4.25)

Supply at some underground wage Wu = Wmin – e (or alternately at some critical level of ε) is the limit of the above term as n tends to infinity and I designate this as λs(Wu). This produces a hybrid of what we would ordinarily consider to be the supply equation of labour, with a factor that accounts for the attrition of workers of different reservation wages being plucked randomly from the range of workers willing to offer their services. The fact that the minimum wage appears in both supply and demand equations illustrates that when firms can avoid all or part of the minimum wage, the minimum wage becomes ‘woven’ into the demand curve as one of its parameters. With evasion the demand curve is not as we usually understand it because the ordering from left to right is not only based on productivities, but on a combination of productivities and an ability to avoid the minimum wage. This is what leads to a deadweight loss from the displacement of high output firms by low output firms. The same holds for the punctured supply curve. As the underground wage falls, workers of both high and low reservation costs who did not manage to get a job with high-paying, evasively inept firms, are mixed together along the upper reaches of the supply curve. This mixing is what gives rise to the deadweight losses from displacement of low cost workers and high productivity firms. Equilibrium Range of Wages Equilibrium can be pinned down by the critical underground wage W*u (or identically at the critical sum of epsilons subtracted from the minimum wage)

96

Tax evasion and firm survival

where there is no further excess supply. This is the wage at which punctured supply (the workers left in the market after their lucky colleagues have found employment with high paying, low evasive ability firms) suffices to satisfy the demand of firms who are both able to pay the wage, due to their evasive ability, and willing to pay it, due to their productivity. Put differently, calculating the equilibrium is a matter of finding a W*u such that λs(W*u) = Ld(W*u). In other words, when we equate the demand curve Ld(Wu) expressed in equation (4.20) to the punctured supply curve λs( Wu), we obtain the equilibrium underground wage. Our work though is not yet done. The equilibrium will have the feature that there is a range of wages (W*u,Wmin] offered by different firms, and then one wage W*u offered by the remainder of firms. This remainder is the group who have among them the highest evasive talents and are left to bid against one another once the high productivity, evasively inept firms have all been satisfied by the excess labour that flocked to them. Total employment is calculated as Ld(W*u) (the sum of firms who each pay the same wage) plus H(W*), u the sum of high paying firms who faced an excess supply of workers and paid within the equilibrium range of wages (W*u,Wmin]. This sum of high paying firms is found by first identifying how many high paying firms with defective evasive skills there are at each wage level w between (W*,W u min]. At any wage level the number of such firms is the measure of firms F multiplied by the proportion who have a productivity higher than the wage Pr(mp ≥ w) and the extent of this proportion who are too evasively inept to avoid paying less than that particular underground wage f(w) = 1/E. We then sum these firms over the range of * underground wages (W*,W u min] to get H(W ): u

( )

Wmin

Pr( mp ≥ w ) f ( w )dw

(4.26)

1 − w  1 dw  MP  E

(4.27)

 W2 W *2  F =  Wmin − min − Wu* + u  2 MP 2 MP  E 

(4.28)

H Wu* = F ∫

Wu*

= F∫

Wmin

Wu*

The above can be recognized as the measure of firms F times the integral of α with the limits of integration recast into wages instead of evasive abilities. The result is identical in either case. Provided that demand and supply meet, total employment at the equilibrium underground wage is Ld(W*u) + H(W*u). If the minimum wage is very high relative to evasive abilities, there will be no equilibrium wage at which demand and supply cross, only an equilibrium lower

Regulation evasion: the case of the minimum wage

97

bound Wmin – E to the above integral, at which all firms who participate in the market will have been faced by an excess supply of labour. In that case, employment is simply H(Wmin – E). These points are illustrated in the examples that follow. Two Examples of Equilibrium There is no obvious solution to the recursion relation for punctured supply. The appendix to this chapter shows that a lower bound to punctured supply at some wage w is simply the ordinary ‘unpunctured’ supply at that wage less the number of workers who have been hired by the firms who paid within the range [w,Wmin]. I explain there why this lower bound produces slight underestimates of equilibrium employment. It is these underestimates, detailed in Table 4.3, I use in the remaining discussion. Figures 4.4 and 4.5 look at the equilibria that fall out of minimum wages of $11 and $18 (the supply curve used is the underestimate of supply described in the appendix). The demand curve in Figures 4.4 and 4.5 is taken from equations (4.3) and (4.20) with the same parameters used in the previous sections. Recall that without a minimum wage, market equilibrium would produce a wage of $10 and employment of 500. We can see that demand is backward bending. The downward sloping part of the curve at wages above Wmin is the piece of the W 20

Demand

Supply

Wmin = 11 9.9

5.8

1.0 450 Figure 4.4

Demand and supply when Wmin = 11

L

Table 4.3 Deadweight loss and employment effects of minimum wage Wmin when firms evade

98

(1) Wmin

(2) Wu (see note)

(3) Jobs offered by high paying firms (αF in equation 4.31)

(4) Jobs offered by low paying firms (see equation 4.25)

(5) Total employment (3) + (4)

(6) Firm displacement loss

10.00 10.40 10.80 11.20 11.60 12.00 12.40 12.80 13.20 13.60 14.00 14.20 14.21 15.00 16.00 17.00 18.00 19.00 20.00 21.00 22.00 23.00 24.00 25.00

10.00 9.99 9.95 9.88 9.79 9.65 9.47 9.24 8.92 8.48 7.75 6.78 6.60 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00

500.00 479.97 459.79 439.23 418.06 395.90 372.28 346.42 316.99 281.19 229.77 170.50 160.61 0 0 0 0 0 0 0 0 0 0 0

0 20.21 40.92 62.26 84.43 107.75 132.67 159.98 191.11 229.20 285.03 352.87 364.74 500.00 450.00 400.00 350.00 300.00 250.00 200.00 150.00 100.00 50.00 0

500.00 500.19 500.71 501.49 502.49 503.65 504.95 506.40 508.10 510.39 514.81 523.37 525.36 500.00 450.00 400.00 350.00 300.00 250.00 200.00 150.00 100.00 50.00 0

0 0.06 0.48 1.71 4.30 8.90 16.32 27.61 44.27 68.80 108.01 151.01 157.38 208.33 208.33 208.33 208.33 208.33 208.33 208.33 208.33 208.33 208.33 208.33

(7) Worker displacement loss 0 2.07 8.57 20.02 37.05 60.57 91.87 133.07 188.02 265.29 394.41 569.50 601.68 1,041.67 916.67 791.67 666.67 541.67 416.67 291.67 166.67 41.67 0 0

(8) Total displacement loss (6) + (7)

(9) Displacement loss per job (8) ÷ (5)

0 2.13 9.05 21.73 41.35 69.47 108.19 160.68 232.29 334.09 502.42 720.50 759.06 1,250.00 1,125.00 1,000.00 875.00 750.00 625.00 500.00 375.00 250.00 208.33 208.33

0 0.00 0.02 0.04 0.08 0.14 0.21 0.32 0.46 0.65 0.98 1.38 1.44 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50 na

Note: The parameters of supply and demand used in the above simulations are N = 1,000, F = 1,000, Wr = 20, MP = 20. Past a minimum wage of $14.21 there is no longer an equilibrium lower wage bound Wu which firms are willing to offer. For higher minimum wages than $14.21 all firms face an excess supply of workers. What then becomes relevant in determining how many firms will offer jobs is the lower bound of possible wages they are able to offer, namely Wmin – E. This is what appears in column (2) of the above table for values of Wmin > 14.21.

Regulation evasion: the case of the minimum wage

99

W 20 Supply

Wmin = 18 Demand

8.0 7.5

1.0 L Note: The curves in both Figures 4.4 and 4.5 are not schematic drawings, but precise renderings generated from closed form solutions derived in the main body of the text.

Figure 4.5

Demand and supply when Wmin = 18

‘ordinary’ demand curve above the minimum wage, as given by equation (4.3). The upward sloping part of the demand curve comes from equation (4.20) and incorporates the fact that below the minimum wage some firms can evade. W now becomes Wu. At lower levels of Wu there are two opposing forces. Firms with low productivity are enticed to demand labour. This would tend to raise demand. But firms with high productivity who cannot evade well are forced out of the market because they are willing but not able to offer the underground wage. This second effect dominates the first and gives the demand curve in this zone its downward slope. We normally understand a demand equation to be an ordering of firms according to their willingness to pay. The lower part of the demand equation in Figure 4.4 is a mix of willingness to pay and ability to pay. This is what gives the lower part of the curve its upward slope. At a minimum wage of $11 (recall that the free market wage is $10), demand and supply meet and as Figure 4.4 shows, the lower bound of wages W*u is $9.97. Equilibrium labour employed in this case is found by plugging $9.97 into the demand function for labour, Ld(9.97) = 449, and adding to this the number of firms H(9.97) = 49 who were constrained to pay higher wages spanning from this lower bound to Wmin. The result is an employment level of 498. This total cannot

100

Tax evasion and firm survival

be read off the diagram because, as explained, the crossing of supply and demand determine only the cutoff wage W*,u not the employment level. When Wmin = 18 the shape of both supply and demand curves changes. The change reflects that the minimum wage is a parameter woven not just into the supply curve, but also into the demand curve. In Figure 4.5, where Wmin = 18, supply and demand no longer meet. The rise in the minimum wage has created a situation where no lowering of the market wage will reduce the excess of labour supply over labour demand. In this case employment is just H(Wmin – E) = 350, which cannot be read from the graph. What takes some getting used to is that there is an equilibrium even though demand and supply do not cross. All firms in this case face an excess supply of workers at the wages they are able to offer. In columns (1) and (2) of Table 4.3 we see a sequence of minimum wages, and the lower bounds of wages these imply. The lowest of these lower bounds is $7.95 (see column 2) and occurs when the minimum wage is $17.50. For any minimum wage higher than this, demand and supply do not meet, which explains why at Wmin = 18 the curves separate. One of the striking things about equilibrium is that it takes place over a range of wages. There is an equilibrium price dispersion that has nothing to do with search, or uncertainty about the parameters of demand and supply. Prices are dispersed because the differing evasive abilities of firms interact with the minimum wage in such a way as to give workers some ability to act as price discriminating monopolists. An equilibrium of this sort has a surprising consequence for the incomes of employed workers. As Table 4.3 shows, provided evasive talents are large enough (so that Wmin – E is less than the free market wage), the equilibrium range of wages [W*u,Wmin] dips below the free market wage. In other words, some workers ‘lucky’ enough to find a job may discover they are working for wages below what they would be earning in a free market. The intuition is that workers lucky enough to crowd into high paying jobs are drawn from a broader range of reservation wages than would be the case without the minimum wage. Some workers in high paying jobs will be from the high end of this broadened band of reservation wages. This crowds low reservation wage workers into the contest for lower paying jobs where they cause a glut. The glut pushes wages for the remaining workers downward, and below what wages would be in a free market. Note that this is similar to the Harris and Todaro (1970) result that some workers will be made worse off by the minimum wage because employment falls in the covered sector, workers shift to the uncovered sector, bidding the wage down there. General Simulations Figure 4.6 graphs employment under different minimum wages in three cases: when no one evades, where workers evade, and when firms evade. It is based

Regulation evasion: the case of the minimum wage

101

on data in Tables 4.1–4.3. What strikes the eye about Figure 4.6 is that at low minimum wages employment falls little when firms evade compared with how much employment would fall without evasion. Employment is also larger initially than in the case where workers evade. Perhaps this is due to the ability of workers in the firm evasion case to price discriminate along the spectrum of high productivity, low evasive ability firms. We see though that as the minimum wage rises, the job creating effects of this ability to price discriminate are countered by the fact that at high minimum wages, the high paying, low evasive ability firms are knocked completely out of the market. The small employment effect of the minimum wage is in line with empirical findings by Card (1992), and Katz and Krueger (1992). The result holds because at low minimum wages, there is a sufficient number of firms with the correct combination of a relatively high output and relatively poor evasive ability. This combination allows many workers to find employment by the process of price discrimination described earlier. The large number of jobs open to price discrimination dampens the job-killing effect of the minimum wage. At higher minimum wages, there are too few firms that have the necessary high output to make price discrimination much of a brake against unemployment. When firms evade, a rise in the minimum wage shrinks the pool of firms with outputs high enough to exceed the wages they will have to pay. This simultaneously shrinks the pool of firms with potentially strong evasive abilities. Column (2) of Table 4.3 shows that the lower bound of discriminatory wages W*u decreases as the minimum wage rises. To see why the lower bound of wages decreases, note first that a higher minimum reduces the number of firms able 600

Employment

500

Firms evade

400 300 No evasion

Workers evade

200 100 –

–100

0

Figure 4.6

5

10

15 20 Minimum wage

25

30

102

Tax evasion and firm survival

to offer low wages. This would tend to put upward pressure on the lower equilibrium bound of wages. The rise in the minimum wage also has a contrary effect. It swells the number of workers seeking employment, by enticing workers with previously excessive reservation wages into the hunt for jobs. It so happens that this latter effect dominates in the model I have derived. As a result the lower equilibrium bound of wages declines with a rise in the minimum wage. Rauch (1991) has found a similar result in his modelling of formal and informal markets. In his model a rise in the formal sector wage squeezes workers into the informal sector where they bid wages down. He does not model a continuum of evasive abilities, but rather, assumes that firms either evade the minimum wage completely or evade it not at all. My results from modelling a continuum of evasive abilities show that the range of underground wages stretches downwards, to a point, as the minimum wage increases. Displacement Deadweight Losses The low drop in employment from the minimum wage comes at the cost of a deadweight loss from displacement of firms and workers. Recall that in the case when there was no evasion, the minimum wage led to the selection of workers with too high a reservation cost. This problem persists in the present case of evasion by firms. The workers who get the limited number of jobs once again may not be those with the lowest reservation wages. There is another source of displacement to account for. The firms who end up producing are not chosen entirely because of their efficiency. Evasive ability is a criterion of survival. This means that some high cost firms will displace low cost firms. To prepare the reader for the formal results about deadweight loss that follow it helps to take an extreme, and elementary example of displacement in the labour market. Consider again Figure 4.1, which portrays ordinary supply and demand curves for labour. The regular result is that equilibrium is at the intersection of both curves – at an employment level of 500 (recall that there are 1,000 firms and 1,000 workers). Output in such a market could be greater than this. Suppose the firm with the highest output were matched to the worker with the highest reservation wage. Match the firm with the next highest output to the worker with the next highest reservation wage. Keep doing this and what you get is that all 1,000 workers are employed and all 1,000 firms produce. Employment is high, but the surplus produced by this market is zero. Matching of this sort violates what markets are supposed to do, namely, to maximize economic surplus. Surplus is maximized by grouping people who value highly the good or service in question with people who can supply it efficiently. The matching scheme I have just outlined produces a lot of output but makes a mess of grouping people efficiently. This example is extreme because it rests on a matching mechanism that ensures workers with the highest reservation wages

Regulation evasion: the case of the minimum wage

103

get the choicest jobs and that low productivity firms are as likely to thrive as high productivity firms. This of course was not the case in the model I developed in the previous section. There, some efficient firms still managed to be matched to low reservation wage workers, so mismatching did not go haywire to the point where all surplus was dissipated and everyone earned a different wage. To calculate the deadweight loss from the minimum wage when firms evade, let us start with the displacement of low cost firms by high cost firms. We want to calculate the actual amount produced by firms and compare it to the amount that would be produced with the same labour if there were no displacement. The actual amount produced has two components. First there is the amount produced by firms to whom an excess supply of workers flock. At each wage level w between (W*,W u min] there are firms in the range [w,MP] who may produce, as highlighted in equation (4.28). The proportion of all such firms whose evasive abilities are precisely w is (1/E)dmp. The output of these firms is: F∫

MP

w

mp

MP 2 − w 2 1 1 dmp = F MP E 2 E × MP

(4.29)

The above is a small part of the total number of firms finding themselves being offered services by a surplus of workers. These firms pay wages falling in the range (W*,W u min], so that their total output is the integral of the above equation: Wmin

∫W

F

* u

[

MP 2 − w 2 F 3 − W *3 dw = MP 2 Wmin − Wu* − (1 / 3) Wmin u 2 E × MP 2 E × MP

(

)

(

)]

(4.30) The second component of total output comes from those firms who have an excess demand for workers. All of these firms have outputs greater than W*u and some range as high as MP. Their combined output is summed over this range and weighted by the proportion Pr(Wmin – e ≤ W*)u whose evasive abilities exceed W*:u F∫

MP

Wu*

mp

F 1 E − Wmin + Wu* dmp = E − Wmin + Wu* MP 2 − Wu*2 MP E 2 E × MP

(

)(

)

(4.31) The above two equations are added to get actual output. The output that would have been produced using the same number of workers L* is the integral of the height of the demand curve over the range [0,L*]. It is a simple matter to show that this comes to MP × L*[1 – L*/(2F)]. The difference between actual and

104

Tax evasion and firm survival

ideal output appears in column (6) of Table 4.3. This is the deadweight loss from the displacement of low cost firms by high cost firms. The cost of the displacement of low reservation wage workers by high reservation wage workers is calculated in a similar manner. First sum the reservation wages of those working. Then compare this to the sum of reservation wages for a similar level of employment in an unregulated market. The sum of reservation wages of those working has two components. Some of the workers who flocked in excess to high paying firms will have found work. At each level of wage w there are, as explained earlier in reference to equation (4.22), F × Pr(mp ≥ w)f(Wmin – w) such firms. The average reservation wage of workers flocking to these firms will be simply w/2. The sum of such reservation wages is then taken over all firms who find themselves beset by an excess of workers. Recall that these firms paid wages in the range (W*,W u min]: Wmin

∫W

* u

=∫

Wmin

Wu*

=

F × Pr( mp ≥ w ) f (Wmin − w ) w  1 w F 1 −  MP  E 2

2 − W *2 W 3 − Wu*3  F  Wmin u − min   2E  2 3MP 

w 2

(4.32) (4.33)

(4.34)

The second component of cost is the reservation wages of those employed by firms who together all bid W*u and together employ Lu units of labour: Lu ∫

Wu*

0

Wu* 1 w = L u Wu* 2

(4.35)

The two above components are summed to get total reservation cost. From this cost we then subtract the minimum cost of employing the same number of workers as represented in the above two equations. This cost was derived earlier and is given in equation (4.10). The resulting difference is the social loss from the displacement of low reservation cost workers. Columns (6) and (7) of Table 4.3 show the losses generated by the displacement of firms and workers. Column (8) shows that the ratio of displacement loss to triangle loss can be quite large at low levels of the minimum wage. The ratio is much larger than in the case of no evasion. With evasion, fewer jobs are lost at low levels of the minimum wage, meaning there is less triangle loss than for a similar wage in the case of no evasion. With evasion there is an extra source of displacement

Regulation evasion: the case of the minimum wage

105

loss: the improper selection of high cost firms. These factors combine to give the high ratios of displacement to triangle loss at low minimum wages. The pattern we see emerging from this and previous chapters, is that displacement loss, no matter what the subject or variety of the analysis, seems to have a steady relation with triangle loss. At first, displacement loss exceeds triangle loss, and then displacement loss falls below triangle loss.

EMPIRICAL IMPLICATIONS From an econometric point of view, minimum wage evasion poses daunting challenges. All of a sudden, the minimum wage becomes a parameter woven into the functional form of both supply and demand equations. It is beyond the scope of the present book to present a fully-developed econometric model of labour market equilibrium with such a weighty modification to established econometric norms. But something can be said about the distribution of underground wages under a minimum wage with evasion and some data can be invoked to provide indirect support of my model’s assumptions. What falls out of the equilibrium modelling of previous sections is that a minimum wage with evasion gives rise to an equilibrium distribution of jobs over a range of underground wages. This distribution has nothing to do with uncertainty or search. When the minimum wage rises, this underground wage distribution becomes more spread out over the higher end of underground wages and more concentrated at lower ends. To see this I present Figures 4.7 and 4.8 which are drawn from the simulations in Table 4.3. Figure 4.7 shows how many workers are employed at different underground wages for a minimum wage of $12.5. As described in detail earlier, there is a range of high paying firms who pay between W*u and Wmin. Then there are the low paying firms all bunched at W*u. When the minimum wage rises to $15 the job distribution becomes even more spread out over the high end of wages and more concentrated over the low end of wages. That is, non-compliance becomes more severe, if one judges noncompliance by the number and degree to which workers are paid below the minimum wage. Is there any indication of such a change in job distributions in the empirical literature? Card (1992) studied the rise in 1988 of California’s minimum wage from $3.35 an hour to $4.25 an hour. He found ‘a sharp decline in the percentage of California workers earning between $3.35 and $4.24 per hour’ (Card, 1992, p. 41) after the minimum wage was introduced. He goes on that: this change was accompanied by a sharp increase in the percentage of workers reporting exactly $4.25 per hour ... In contrast to the effect on the fraction earning $3.25–4.24 per hour, the increase in the minimum wage had virtually no effect on

Figure 4.7 Underground wage 10.00

9.95

9.90

9.85

9.80

9.75

9.70

9.65

9.60

9.55

9.50

9.45

9.40

9.35

9.30

9.25

9.20

9.15

9.10

9.05

9.00

106

Number of jobs 140

120

100

80

60

40

20

0

0

Figure 4.8 Underground wage 10.00

9.95

9.90

9.85

9.80

9.75

9.70

9.65

9.60

9.55

9.50

9.45

9.40

9.35

9.30

9.25

9.20

9.15

9.10

9.05

9.00

107

Number of jobs 250

200

150

100

50

108

Tax evasion and firm survival

the fraction earning less than $3.35 per hour. This stability implies that the subminimum wage work force ... increased after the effective date of the new law. Using Ashenfelter and Smith’s (1979) notion of a noncompliance rate, 31 per cent of all workers with wage rates less than or equal to the minimum wage in 1987 earned less than the minimum. With the rise in the minimum to $4.25, the non-compliance rose to 46 per cent.

Card was not looking for the effects on the distribution of underground jobs I have suggested could arise, but his results are consistent with the notions put forth in the present chapter. He found a worsening of non-compliance and a strong stability in the fraction of highly sub-minimum wage jobs even after the rise in the minimum wage. Another finding of Card’s is that when the minimum wage was $3.35 per hour, the average wage paid was $2.64 with very little spread. If one looks at Figures 4.7 and 4.8, one notices a very tight concentration of jobs around the lower end of underground wages, as Card’s data suggest existed in California. While these conjectures are tantalizing, a full testing of the notions in the present chapter would require that labour market equilibrium be derived under alternate assumptions about the distribution of reservation wages, firms productive abilities, and firms evasive abilities. My assumptions were that these variables were uniformly and independently distributed. Alternate assumptions such as those of a normal or skewed distribution, would give different functional forms for supply and demand for labour, and would give rise to varying likelihood ratio tests of the difference between observed job distributions over a range of underground wages and hypothesized distributions. Nonindependence of evasive abilities and production costs would further complicate matters. I have not pursued modelling labour market equilibrium under these alternate assumptions for reasons of tractability. These above alternate assumptions give rise to complicated closed form solutions which add little to the central theoretical points I wished to make in the present chapter. These points are that the minimum wage can give rise to a displacement of low reservation wage workers and low cost firms by high reservation workers and high cost firms when evasion by firms is considered. If a critique is to be made of the uniformity assumption, it is that the assumption might understate the degree to which a minimum wage can reduce employment. A normal distribution for productive talents and reservation wages could have given supply and demand curves with greater elasticity in their central portions. These, however, are not distinctions which detract from the theme of the present chapter. What is the empirical relevance of the present theoretical model? There are two ways to answer this. The first comes by looking at Figure 4.9 which shows the percentage of output lost per worker due to displacement (this includes output lost directly in the industry due to the displacement of low cost firms and output lost indirectly due to displacement of low reservation wage workers)

Regulation evasion: the case of the minimum wage

109

and the percentage of output lost due to triangle loss. These percentages were derived from Table 4.3. Against these percentages I graph the percentage loss in employment due to the minimum wage. The range of minimum wages I take is between $10 and $17 and this percentage loss in jobs is again derived from Table 4.3. At low levels of employment loss, displacement loss dominates the triangle loss effects of a minimum wage. Under what seems the extreme assumption (in light of a range of studies too broad to cite here but of which Neumark and Wascher (1992) might be taken as representative) that the minimum wage leads to a 20 per cent employment loss, the displacement losses come out to roughly 14 per cent of output. At the other extreme, as represented by Card (1992) of an employment loss close to zero, we still find displacement losses of close to 2 per cent of output. In calculations not shown here, I have varied the range of parameters of demand and supply but there has been no first order change in magnitudes of displacement reported above. If one accepts some of the general premises of the model in the present chapter as valid, then displacement losses may not seem huge but are nonetheless a cost to be reckoned with in discussions of minimum wages, even when those wages lead to almost no change in employment. To what sorts of economies are the present results applicable? Recall that ‘the present results’ encompass two sorts of economies. The first part of the chapter showed that there could be a deadweight loss from displacement of low cost workers and firms even in an economy where compliance is perfect. The second part of the chapter showed that when firms do not comply, there can also be 14 Percentage output lost

12

Selection loss

10 8 6 4 Triangle loss

2 0

0

Figure 4.9

5 10 15 20 Percentage reduction in employment from minimum wage

25

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Tax evasion and firm survival

an added social loss from displacement of low cost by high cost firms. The question then is, to which countries are these two parts of the chapter relevant? Squire and Narueput (1997) conclude that ‘Non-compliance occurs in a variety of countries and is significant even among industrialized countries.’ By significant they meant that in markets affected by the minimum wage, noncompliance can be significant. For example, according to Card’s (1992) analysis of California, the non-compliance rate was as high as 46 per cent. Squire and Narueput add that non-compliance is a relevant issue for only about 2 per cent of the entire US labour force. Among this labour force it is illegal immigrants who are likeliest to be the targets of non-compliance. North and Houstoun (1976) report a ratio of 0.59 for the relative wages of illegal aliens to similar legal workers in the USA. Bailey (1985) has similar findings. One could then think of the present chapter’s results on displacement loss with full compliance as being more directly applicable to legal workers in industrialized countries. Illegal workers in industrialized countries and workers in third world informal sectors might be better modelled with the second part of this chapter where non-compliance was the issue. Squire and Narueput, citing internal World Bank studies suggest that up to 16 per cent of men in Mexico’s large informal sector are the targets of minimum wage non-compliance. Regardless of which case one considers, non-compliance or compliance, the deadweight losses from the minimum wage predicted by the present model are similarly worth noting.

POLICY IMPLICATIONS Whenever a new deadweight loss is identified, we have to ask ourselves whether government or market institutions have not already moved to prevent the loss. Unions exercise monopoly power to raise their wages. They may also choose their members so that these members have low reservation wages. This preserves the surplus from high wages, and may be the union’s way of combatting needless deadweight losses from displacement. Even if unions do their part to keep down the deadweight losses from controlled wages, we must ask whether some government actions can help mitigate the problem. The USA seems to have hit upon a solution by exempting certain categories of workers from being paid the full minimum wage. These are usually young people living at home with their parents. These are likely to be individuals with low alternate values of their time and so are likely to have low reservation wages. Exempting them from part of the minimum wage makes them attractive to hire and helps them jump the queue ahead of higher reservation wage workers not exempted from the minimum wage. Unfortunately, micro-management of any part of the economy has proved a frustrating and ambiguous exercise for governments

Regulation evasion: the case of the minimum wage

111

and I am reluctant to see such an intervention as a major policy implication of the present chapter. A more fruitful application of the results presented here would be to use the present deadweight loss calculations to compare different methods of redistributing income. The minimum wage is, in all policy discussion, held as an income redistribution policy. But is it the best policy? Might the deadweight losses from taxation not be lower than those from the minimum wage, and as such the costs of redistributing through the income tax system cheaper than the deadweight losses of redistributing through wage control? Such questions have not been asked in the public finance or labour economics literature. The theoretical apparatus developed in the present chapter, and the earlier chapter on tax evasion, point to a means by which the optimal mix of redistribution through the tax system and wage controls might be calculated.

CONCLUSION In this chapter I have presented an analysis of what happens when firms and workers try to evade government’s attempt to reallocate resources through a price control. One might have thought the analysis would be similar to government’s reallocation of resources through taxation in the presence of tax evaders, but the analysis was significantly different. I took as my example the case of the minimum wage and found that even when there is perfect compliance with the minimum wage, there is a deadweight loss due to high reservation wage workers and firms displacing their lower cost counterparts from the market. The minimum wage attracts these workers to the labour market and allows them to vie for jobs with lower reservation wage workers. These lower reservation wage workers cannot compete on the margin of price and the labour market becomes a lottery in which some high reservation workers may displace low reservation wage workers. The difference in reservation wages of the actual and displaced workers is a measure of the costs that arise from the lottery for jobs induced by the minimum wage. When either firms or workers can evade part or all of the minimum wage a further displacement loss arises. The chapter discussed, first of all, worker evasion of the minimum wage. Not so much because this was deemed to be a realistic case, but to make the point that when studying the welfare effects of regulation evasion, it is important to specify who is evading. Raising the question of who evades also forces one to think of what evasion means. A worker’s evasion may be implicit. He or she may evade the minimum wage through non-price competition. Taking more risks on the job is an example of non-price competition. A firm’s ability to avoid the minimum wage could depend on the level of amenities it offered its workers before the price floor

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Tax evasion and firm survival

was imposed. Firms with low costs of providing amenities might provide more of these amenities. Once the minimum wage comes down these firms survive in greater numbers because they have a greater ability to lower amenities than their rivals. Selection of firms in a minimum wage market will not depend so much on who has the greatest output, as upon who has the greatest ability to save money by making life more miserable for its employees. Under the most general assumptions about evasive abilities, the minimum wage at low levels has minimal effect on employment. This result is obtained without appeal to monopsony behaviour by the firms who demand labour. Employment is resistant to the minimum wage because in the presence of firms with differing abilities to evade, the minimum wage allows workers to act as if they were part of a price discriminating monopolistic collective. When employers evade, market equilibrium is not represented by a single wage, but by a range of wages. Price dispersion has nothing to do with search costs or imperfect information about demand and supply parameters. Some wages in the range lie below what wages would be in a free market. Workers who find employment in the lower end of wages will find that their incomes have dropped from what they were before the arrival of the minimum wage. A striking feature of a market where producers or purchasers evade price controls is that equilibrium in such a market is an order of magnitude more complicated to model than the evasion of taxes. This is a surprising at first. Taxes and price controls are sometimes indistinguishable tools in a government’s kit. Both can be used to change output and to redistribute income. Yet to model price controls calls for a complicated notion of how workers sell their services to employers in a market where price is an imperfect rationing device. The punctured supply curve leading to a range of equilibrium wages in a world without uncertainty are two of the more striking implications for economic modelling that come from considering the general equilibrium effects of the evasion of price controls in a competitive market. These results, along with the novel results of earlier chapters on tax evasion, remind us that seemingly simple assumptions can have profound implications for modelling and that there is new juice to be squeezed from the grapes of Marshallian supply and demand.

APPENDIX The purpose of this appendix is to derive a lower bound to the exact expression for labour supply and to develop a technique for more closely approximating labour supply than this lower bound allows. The need to work with such bounds comes out of equation (4.25) in the main body of the text:

Regulation evasion: the case of the minimum wage

  Fα((n − 1)ε ) λ n (Wmin − nε ) = 1 −  λ n −1 (Wmin − nε )  λ n −1 (Wmin − (n − 1)ε ) 

113

(4.36)

Let us take the first four terms of this expression: λ 0 (Wmin ) = Ls (0)

(4.37)

 α(1) F  λ1 (Wmin − ε ) = 1 −  λ 0 (Wmin − ε )  λ 0 (Wmin )  = λ 0 (Wmin − ε ) − α(1) F

λ 0 (Wmin − ε ) λ 0 (Wmin )

 α(2 ) F  λ 2 (Wmin − ε ) = 1 −  λ1 (Wmin − 2 ε )  λ1 (Wmin − ε )  = λ1 (Wmin − 2 ε ) − α(2) F

λ1 (Wmin − 2 ε ) λ1 (Wmin − ε )

  α(3) F λ 3 (Wmin − ε ) = 1 −  λ 2 (Wmin − 3ε )  λ 2 (Wmin − 2 ε )  = λ 2 (Wmin − 3ε ) − α(3) F

λ 2 (Wmin − 3ε )

λ 2 (Wmin − 2 ε )

(4.38)

(4.39)

(4.40)

(4.41)

(4.42)

(4.43)

The ratio of λs on the right-hand side of the above expressions is less than one. If we were to replace this ratio by one, then each of the above expressions would be an underestimate of supply. With this modification the above could be written out as λ0(Wmin) = Ls(Wmin) λ1(Wmin – ε) = λ0(Wmin – ε) – α(0)F λ2(Wmin – 2ε) = λ1(Wmin – 2ε) – α(1)F λ3(Wmin – 3ε) = λ2(Wmin – 3ε) – α(2)F

(4.44) (4.45) (4.46) (4.47)

Repeated substitutions show that λ3(Wmin – 3ε) = Ls(Wmin – 3ε) – α(0)F – α(1)F – α(2)F – α(3)F

(4.48)

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Tax evasion and firm survival

If we iterated this process infinitely until the epsilons summed to some noninfinitesimal number e', we would find the underestimate of the punctured supply curve to be λ(Wmin − e' ) ≥ Ls (Wmin − e' ) − F ∫

0

Wmin − e'

α(e)de

(4.49)

The final term in the above expression is simply the amount of labour employed by firms who are the subjects of price discrimination. In the text an operator H(Wmin} – e') was derived for the amount of labour hired by these firms. What this says is that our underestimate of the punctured supply curve is the unpunctured supply curve, less the number of workers who represent the sum of punctures at some underground wage w = Wmin – e. λ(w) ≥ Ls(w) – H(w)

(4.50)

The critical w at which supply and demand cross is defined in the main text as W*u and is calculated by equating the above expression with demand as defined by equation (4.20) and solving for the wage which is the lower bound of wages offered by firms to whom an excess of workers flock. By using this underestimate of supply we underestimate the degree to which workers will be able to price discriminate against firms. By limiting this effect we can expect the above approximation of the supply curve to show the minimum wage having a more adverse effect on jobs than it really does. Another way of estimating labour supply is to treat the epsilon terms as discrete units. If I want to estimate labour supply at Wmin – e I can divide e into 40 parts δe and take 40 iterations of the equation (4.36). This is easily done with a spreadsheet. The results produced (not shown here but available, with spreadsheet, on request) by this technique produce an equilibrium labour supply of two or three workers above the lower bound estimate of labour supply. For some minimum wages, employment is above the free market level. This result cannot be taken to mean that the model shows that minimum wages can raise employment. Raising the iterations reduces the equilibrium labour supply, and it is possible that with an infinite number of iterations, equilibrium labour supply would be less than the free market level.

5. Tax evasion, regulation evasion and rent-seeking So far we have seen how when a productive talent is wedded to an unproductive talent, markets select some high cost producers over low cost producers. Firms with high production costs but excellent tax evasion skills could oust from the market competitors with lower production costs but less prominent evasive abilities. Displacement deadweight losses are not the fief of markets with tax evaders. Displacement losses weigh on markets where bureaucrats hand out subsidies, and where governments regulate prices. In all these cases, displacement loss is the consequence of a government that fails to enforce rules evenly. Popular lore equates even enforcement with fairness. Our strongly ingrained sense of the need for fairness is not just a fancy. Previous chapters have shown that fairness ensures efficiency. One of the potential critiques of previous chapters is that I took individual decisions to evade taxes and regulations or to demand subsidies as being fixed, and then explored the general equilibrium consequences of their decisions. I argued in those chapters that allowing some flexibility into individual decisionmaking would not change the tenor of the results. The present chapter backs up this claim by looking at the case of two firms either competing for a subsidy, a tax break, or a monopoly right, or vying with each other to evade taxes. I build a game-theoretic model of competition between two such firms to show that the same sorts of displacement losses arise as in previous chapters, even when individual firm behaviour is allowed to vary. As such, the results in the present chapter will not add new insights beyond those derived earlier, but will show that those earlier results can withstand a softening of the assumptions upon which they were derived.

A RENT-SEEKING MODEL In an article entitled ‘Purchasing monopoly’ Harold Demsetz (1984) explored the variety of deadweight losses that arise from granting a monopoly right to a firm. Demsetz alluded to displacement deadweight losses in writing that ‘The monopoly may turn out to be a more costly producer than the competitive industry being monopolized.’ Demsetz’s work into the social costs of regulations 115

116

Tax evasion and firm survival

came around the same time as the work of Gordon Tullock. Tullock (1967, 1980) focused on a political contest between two rivals seeking some prize from government. The efforts these firms invested in the contest to cut up the government pie produced nothing of use except to raise the probability that one rival or the other would win the contest. These socially wasteful efforts came to be known, unfortunately, as rent-seeking costs. Rent-seeking is a cryptic term that produces blank stares in policy makers. A term such as pie-cutting might have brought to the fore of the public debate on political reform the profound results Tullock and others derived. In spite of its awkward name, Tullock’s rentseeking model has gained wide popularity among researchers and is a good tool for illustrating displacement deadweight losses to which Demsetz alluded. The purpose of this chapter is to build a model of two rivals in the quest of some advantage they can snatch from government. The essence of the model is that each rival invests resources to influence its chance of gaining the advantage. The model is probabilistic, as are most contests in the real world. I will consider a world in which two firms compete for a monopoly licence to brew and sell beer in their region. Until recently, as documented by Irvine and Sims (1994), such restrictions existed in Canada. I could just as well apply the reasoning to two firms competing for a government subsidy. I could also apply the reasoning to a firm wishing to evade taxes by convincing a government official to look the other way. The official has a revenue quota to raise and knows he can get the sum either from one firm or from its rival. Which firm gets the blind eye depends on how powerfully each competes for the official’s favour. In this connection Vito Tanzi (1994) has warned that corruption degrades economic efficiency ‘by favouring taxpayers who, because of the special treatment they receive from tax inspectors, are able to reduce their tax liability. If the statutory tax system had been designed to be neutral, corruption will not only reduce the revenue collected by the government but it will also destroy the tax system’s neutrality by giving a competitive advantage to some producers over their competitors. The loser will be the well functioning of the market.’ The essence of whichever particular setting I choose would be that displacement losses arise when producer behaviour is allowed to vary in response to market equilibrium conditions. In previous chapters the firm either produced or did not produce. There was no continuity in its choices. To formalize the above ideas, consider a government offering a monopoly licence to brew and sell beer. Two firms vie for beer monopoly. Firm 1 spends E1 lobbying the official to exercise his favour on the firm’s behalf and to allow that firm to be the sole supplier of suds. The other producer spends E2 in the same quest. The winner gets a monopoly licence which brings revenues of Rmonopoly. The return to each firm’s lobbying expenses is uncertain because a firm does not know whether the political climate will allow the government to advance that firm’s

Tax evasion, regulation evasion and rent-seeking

117

cause. This uncertainty over whether firm 1 gets the monopoly licence is captured in a probability function that takes the logistic form familiar in rentseeking models: P=

a1 E1 a1 E1 + a2 E2

(5.1)

The above is the probability that the first producer snatches the monopoly licence. Here a1 is a parameter that measures the first producer’s ability to translate lobbying expenses into political pressure. The parameter a2 is the second producer’s lobbying ability and this producer’s probability of winning is (1 – P). I assume a1 + a2 = 1 for convenience. This logistic equation is widely used in rent-seeking models. Its basic meaning is that the more a firm spends the greater its chances of gaining the monopoly licence; the more its rival spends the less the firm’s chances of winning. Figure 5.1 shows this basic relation between firm 1’s chances of victory and spending by itself and its rival firm 2. Equation (5.1) indicates that firm 1’s probability of winning is a function both of its and its opponent’s abilities to win (a1, a2), which are parameters,

1 0.8 0.6 Prob1 0.4 0.2 0 5

5

4

4

3 E2

3

2

2

1

1

E1

0 0 Figure 5.1 Firm 1’s probability of winning as a function of firm 1 and firm 2 lobbying expense E1 and E2

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Tax evasion and firm survival

and of its and its opponents willingness to invest resources (E1, E2), which are variables, to win. Ability and willingness are linked through the optimization the candidate follows. Each producer seeks the prize of a monopoly licence worth Rmonopoly. If the first producer has constant production costs of C1, then it is competing for net revenue, or a ‘jackpot’, of J1 = Rmonopoly – C1. If the first producer takes its opponent’s lobbying expenditures as given, then it chooses E1 to maximize its expected gain from lobbying: P(E1, E2)J1 – E1

(5.2)

Because firm 1 takes its opponent’s expenses as given we can model this case as a Cournot game. The Cournot equilibrium to this game is E*1 = J1P*(1 – P*) and E*2 = J2P*(1 – P*). We obtain this result by noting that maximizing P(E1, E2)(J1 – E1) with respect to E1, the resultant first order condition implies that a1 ( a1 E1 + a2 E2 ) − a12 E1

(a1E1 + a2 E2 )

2

=

1 J1

(5.3)

If we multiply both sides of the above equation by E1 the resulting expression can be manipulated to give that P(1 – P)/E1 = 1/J1 which implies that E1 = J1P(1 – P). The same holds for firm 2. The equilibrium probability that producer 1 wins P* is found by substituting the optimized values of firm lobbying expenditures back into the probability function: a1 E1 a1 E1 + a2 E2

(5.4)

=

a1 J1 P * (1 − P *) a1 J1 P * (1 − P *) + a2 J2 P * (1 − P *)

(5.5)

=

a1 J1 a1 J1 + a2 J2

(5.6)

P* =

=

(

(

a1 R monopoly − C1

)

(

)

a1 R monopoly − C1 + (1 − a1 ) R monopoly − C2

)

(5.7)

Tax evasion, regulation evasion and rent-seeking

119

Figure 5.2 graphs the above equilibrium probability that firm 1 wins as a function of its cost and political ability parameters. This curve differs from the probability of winning function in Figure 5.1. Figure 5.1 was a simple technical relationship between political spending and probability of winning. Figure 5.2 is a behavioural relationship between parameters that affect candidates’ decisions on how they will influence their probabilities of winning. Figure 5.2 shows firm 1’s probability of winning on the assumption that the monopoly revenue is Rmonopoly = 10 and that firm 2’s costs are 5. The figure shows what happens when firm 1’s political ability varies from [0,1] and when its costs vary from [0,10]. When firm 1 has a low political ability (a1 close to zero), its probability of winning is low. Part of this is firm 1’s choice. A low political ability means any money spent to influence government will have a low return. Firm 1 will, as a result, not invest much and this will further lower its probability of winning. When firm 1’s costs are close to its monopoly revenue of 10, firm 1’s probability of winning is also close to zero, no matter how good is its political ability. Again, the firm sees no reason to invest much in a contest with a small return. This time the source of the small return is the small jackpot (its costs are close to the revenues promised by the monopoly licence).

1 0.8 0.6 Prob1 0.4 0.2 0 10 8 6 C1

4 2 0 0

0.2

0.4

0.6

0.8

1

a1

Figure 5.2 Firm 1’s probability of winning as a function of its costs, C1 and political ability, a1

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Tax evasion and firm survival

This derivation of equilibrium sets the stage for examining the traditional deadweight loss from rent-seeking as formulated by Tullock, and the displacement loss from the contest. Traditional rent-seeking expenditures are the equilibrium amounts spent on lobbying by firms 1 and 2. To get these amounts we substitute the equilibrium probability P* back into the formulae for E1 and E2 to give E1* =

a1a2 J12 J2

(a1 J1 + a2 J2 )2

and E2* =

a1a2 J1 J22

(5.8)

(a1 J1 + a2 J2 )2

The total costs of rent-seeking by both firms as traditionally conceived by Tullock (1980) are   aa JJ 1 2 1 2  E1* + E2* = ( J1 + J2 ) 2  ( a1 J1 + a2 J2 ) 

(5.9)

If political talents are identical (a1 = a2) and costs are identical (C1 = C2) then both firms vie for the same jackpot (J1 = J2 = J) and in equilibrium rent-seeking 5 4 3 Loss

2 1 0 10 8 6 C1

0.8 0.6

4

0.4

2 0 0

Figure 5.3 Traditional rent-seeking costs

0.2

a1

1

Tax evasion, regulation evasion and rent-seeking

121

costs are 0.5J; a familiar result (see Palda, 1992). Figure 5.3 maps the sum of firms 1 and 2’s Tullock rent-seeking costs. The main thing to note from this figure is that when both firms are evenly matched, in the sense that their costs and political abilities are identical, Tullock costs are at a maximum. This is a standard result from tournament theory. In close contests opponents maximize their efforts to win. There is also a displacement deadweight loss lurking in the details of Tullock’s rent-seeking model. Suppose C1 > C2 (i.e. firm 1 is a less efficient producer than firm 2, so that its jackpot is smaller). Should the high cost producer win the lobbying race then the excess of its cost above that of the low cost producer must be counted as a loss from the rent-seeking process. The probability in equilibrium that the high cost producer wins is P*, so that the expected cost from displacement of the low cost producer by the political process is P*(C1 – C2). The sum of traditional rent-seeking and displacement costs is:   aa JJ a1 J1 1 2 1 2 + + P * (C1 − C2 ) = ( J1 + J2 ) (C1 − C2 ) 2 14 4244 3 a J  ( a1 J1 + a2 J2 )  1 1 + a2 J 2  traditional cos ts displacement cos ts E2* ) (1E41* 2+ 4 3

(5.10) Figure 5.4 traces out the sum of displacement losses generated by firms 1 and 2. Under my simplifying assumption that firm 2’s costs are zero, displacement deadweight losses are simply P*(J2 – J1) = P*C1. Figure 5.4 suggests that a positive correlation between political ability and production costs leads to high displacement losses from the rent-seeking contest. This is in the spirit of the result derived in Chapter 1 for tax evasion when evasive and productive abilities are negatively correlated. An example from prohibition-era Chicago can show how this insight plays out on the street. In his work on Chicago gangsters Kobler (1971) explains that Chicago was a city in which hoodlums drove honest businessmen out of commerce. At the same time in New York, gangster Frankie Yale chased cigar producers out of the city and forced his own low quality smokes with his emblem onto shopkeepers. A ‘Frankie Yale’ became the synonym of a high priced, low quality cigar. The same issues arise today in transitional countries. Are the heads of banks and oil companies there because they are the best managers of business or because they are good at managing violence and graft? Are prominent Russian businessmen prominent because of their business savvy or because of their expertise in getting special tax dispensations from their friends in government? In all these cases the rent-seeking model I have outlined

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Tax evasion and firm survival

8 6 Loss 4 2 0 10 1

8 0.8

6

0.6

4

C1

0.4

2

0.2

a1

0 0

Figure 5.4 Displacement costs

8 Displacement 6 Loss 4 Traditional

2 0 10

1

8

0.8

6 C1

0.6 4

0.4 2

0.2 0 0

Figure 5.5 Traditional and displacement costs

a1

Tax evasion, regulation evasion and rent-seeking

123

above serves to illustrate the potential cost from displacement of efficient producers by inefficient producers. Figure 5.5 shows how the size of displacement loss compares to traditional rent-seeking costs. Figure 5.5 superimposes the displacement loss function of Figure 5.4 onto the traditional rent-seeking cost function in Figure 5.3 to show that displacement costs may rival or exceed traditional costs when the high cost firm has also a high political ability. The high cost firm’s strong political ability increases its chances of winning the political contest. Better chances for the high cost firm mean bigger expected deadweight loss from displacement. When a firm’s production costs are inversely related to its political talents, the radical effects of displacement loss are toned down.

CONCLUSION This chapter has shown that displacement losses arise in contests for political power between small numbers of rivals. A producer with good political savvy but poor productive skills can grab a monopoly licence, or convince its friends in government to overlook its tax evasion. Its political savvy gives it an edge that may allow it to oust from the market its more efficient competitor. What was new in the chapter was that I showed that displacement losses can arise in circumstances where individuals react to each other. This addressed a potential critique of previous chapters in which I took evasion and production as parameters in an individual’s step function to participate or not participate in the market. This chapter has examined what sorts of deadweight loss result when individuals can vary their decisions at the margin. The main result to appear is that no new results emerge beyond those derived in previous chapters. In other words, the insights of this book hold for a wide variety of assumptions about individual behaviour. The model of rent-seeking I developed here serves another function beyond that of verifying the global application of the notion of displacement loss. The existence of displacement loss in political contests may be a piece in the puzzle of why some countries develop and others stagnate. Displacement loss is lowered if inefficient producers with strong political abilities are able to specialize in lobbying. Such firms would close their factories and open consulting offices. These offices would sell rent-seeking services to efficient firms that bumble in the corridors of power. There would still be a waste from the activities of these firms, but this waste would be a faint echo of the waste from having a high cost firm do the work of a low cost firm. It is perhaps the countries that manage to separate politics from production that take a great leap forward on the road to economic growth.

6.

Conclusion

The size of the underground economy is a matter of academic dispute. Estimates for any one OECD country can range from 2 per cent to 20 per cent. Whether the underground economy is a matter for concern depends in part on whether this economy destroys resources. Researchers have catalogued how the underground economy may enhance a nation’s productivity by allowing citizens to produce and consume beyond the grasp of the tax collector. Other researchers have found that the underground economy may force an excessive burden of taxation on the legitimate economy and so cramp government’s efforts to raise revenues and provide the public goods needed for economic growth. The present book has added to the findings of this second group of researchers by highlighting a previously under-emphasized cost of the underground economy. This cost arises when efficient producers who are not good at evading taxes or regulations are ousted from the market by producers who are good evaders but poor producers. The difference in the costs of the ousted efficient and surviving inefficient firms is the displacement deadweight loss from the underground economy. Displacement loss arises in a variety of circumstances. The analysis of tax evasion, which has been the major focus of this book, showed that even under the innocuous assumption that there is no correlation between evasive and productive abilities, displacement losses could rival traditional Harberger triangle losses. The logic of modelling displacement losses of tax evasion carries over almost perfectly to firm-specific investment grants. In Chapter 3 I showed how these grants, even when given to reward positive externalities, give rise to the same sorts of displacement loss as found in the case of tax evasion. Tax evasion, and firm-specific subsidies may be hard to distinguish in their effects on firm survival and economic efficiency. Displacement losses also arise when firms evade regulations such as output quotas and price controls. Chapter 4 examined the case of the minimum wage, and found that minimum wage evasion is much more complicated to model than tax evasion, gives rise to a new concept of labour market equilibrium, but produces essentially the same sorts of displacement deadweight losses as with tax evasion. Chapter 5 abandoned the assumption that firms are atomistic and examined whether displacement losses arise in contests between two rival firms. The answer was ‘Yes’. Displacement losses influence the form that institutions take. In general, displacement losses arise when individuals are endowed with a productive and an unproductive characteristic. The productive characteristic allows the worker or 124

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firm to produce output or services. The unproductive characteristic allows the worker or firm to evade rules which when obeyed by all, advance the common good, but which when obeyed by most, advance by even more the fortunes of cheats, to the detriment of those who obey. If evaders could somehow be convinced with a side payment to stop evading, then the deadweight losses from displacement could be avoided. As I showed in the chapter on tax evasion, in the model of uniformly distributed evasive and productive talents there is ample room for side payments that avert displacement loss. The numerical example I gave there, showed that deadweight losses from displacement are nonantagonistic. No one would lose from the disappearance of non-antagonistic deadweight losses. This is not true of traditional Harberger triangle losses. Nonantagonistic deadweight losses are such a nuisance to all that we can expect government institutions will arise to root out these losses. The complexity of tax systems may be government’s attempt to minimize damages from the interaction of the underground economy and the tax system. A complex tax system allows good evaders to specialize as lobbyists and accountants and sell their services to good producers. The desire to avoid non-antagonistic deadweight loss has inspired the tradable pollution quotas and tradable fishing quotas. Empirical evidence has not been prominent in this book. Is the theory of equilibrium evasion I have outlined metaphysics or does it have empirical content? Two predictions emerge from the theory. The first is that if productive and evasive talents are uncorrelated, a rise in the tax rate will increase unit production costs of the industry being taxed. This may explain the puzzle of low productivity in countries such as Canada, which are slightly above the OECD average of taxation. In the last years of the millennium Canadian politicians debated why their country’s labour was losing its productivity. High taxes were cited as a possible reason. This is an unusual conjecture because usually, in a high tax environment, only the lowest cost, most productive firms survive. Rising taxes provoke a ‘selection effect’ which gives rise to a positive observed correlation between taxes and productivity. Instead, Canada seems to show the opposite correlation. There are two ways to explain this. Either Canada is running on a production function with diminishing costs, or inefficient producers who are good at dodging taxes are displacing efficient producers who are bad at dodging taxes, in the quest to survive a hostile tax environment. The second major empirical implication of the theory is that in labour markets with perfect information about wages there should be a spread of wages around the minimum wage. No matter how much empirical support is found for my models, the displacement losses on which I have pulled back the curtain may forever lurk in the shadows. No one has ever spotted a Harberger triangle. We must trace the outlines of these three-sided sprites of the mystical welfare economics forest from parameters of supply and demand. Neither will one observe a displacement loss. We must infer them from the parameters of supply and demand and

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the parameters of the statistical distributions that determine the joint allocation of productive and evasive talents. We can see their influence in the shape that government institutions have taken. What policy prescriptions emerge from earlier chapters? 1. Fairness is efficient. Being fair is like being democratic. Both terms mean pretty much whatever you want them to mean. In the present book, fairness would mean forcing everyone to pay their mandated tax and obey regulations to the full. A government that wished to eliminate displacement losses from tax evasion would seek to enforce payment of taxes equally while reducing the tax level so that after the exercise in enforcement, government was left with the same budgetary balance as before the exercise. If government decided to only increase enforcement it might well eliminate the displacement loss but the added revenues would come at the cost of a higher deadweight Harberger triangle loss. 2. Rent-seeking. Chapter 5 suggested that rent-seeking contests are wasteful not only because of Tullock deadweight loss but also because of the displacement losses such contests engender. Added losses from rent-seeking spur efforts by reformers to write constitutions which secure property rights and discourage the sale of power. 3. Avoid price controls. Even without evasion, price controls impose a displacement loss. The lottery to be a market participant under price controls means that some low cost or high enthusiasm market participants will be discouraged from entering into exchanges. Taxes must be considered superior instruments of policy. Every redistributive and allocative effect of price controls can be produced by taxes but without a displacement loss, provided there is no tax evasion. 4. Cost–benefit analysis. Displacement loss must be added to the social cost of public funds in calculating the social opportunity cost of a government project. Traditionally, only Harberger triangle loss has been included in this calculation. In spite of the detailed treatment I have given displacement losses, this book is not the last word on the subject. I have provided the framework for analysing markets in which productive and unproductive characteristics are fused to differing degrees in each individual. This is not a boast, but rather a lament. The economics profession has advanced without paying due attention to displacement losses. By bringing attention to a neglected area of public finance I hope to encourage others to fill the gaps which my preliminary research has opened. I believe the simple application of the principle that individuals are randomly endowed with positive and negative attributes can form the basis for further insights into the social costs of government intervention in the economy.

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Name index Allingham, M.G. 25, 92 Alm, James 9 Asea, Patrick 8 Ashenfelter, Orley 85, 92 Barros, Pedro 56 Barzel, Yoram 84 Baumol, James 6 Becker, Gary 9, 52 Brennan, Geoffrey 50 Browning, Edgar 9, 59, 74 Buchanan, James 50 Butterworth, John 84 Card, David 85, 101, 105, 108 Casella, Allesandra 76 Chang, Yang-Ming 92 Corcoran, Terrence 58 De Allesi, Michael 76 Demsetz, Harold 115–16 De Soto, Hernan 8 Dicey, A.V. 55 Ehrlich, Isaac 92 Enste, Dominik 8 Feige, Edward 8 Ford, Robert 57 Fortin, Bernard 92 Frey, Bruno 8

Kesselman, Jonathan 6, 26 Kim, Jae 92 Kruger, Alan 101 Lattimore, Ralph 57 Loayza 9 Lott, John 83–84 Mirrus, Rolf 8 Narueput, Sethaput 77, 85, 92, 110 Neary, Peter 56 Nilsson, Tore 56 O’Sullivan, Paul 56 Rauch, James 92, 102 Reuter, Peter 7 Sandmo, Agnar 25, 92 Schneider, Friedrich 8 Sims, William 121 Smith, Robert 85, 92 Squire, Lynn 77, 85, 92, 110 Suyker, Wim 57 Tanzi, Vito 3, 5, 6, 57, 116 Tarr, David 84 Telser, Lester 10, 66 Thurstone, Louis 27 Todaro, Michael 100 Tullock, Gordon 116, 120–21

Gambetta, Diego 7 Grenier, Gilles 92

Usher, Dan vii, 9–10, 56

Harberger, Arnold 7, 9, 15, 50, 52, 56 Harris, John 100 Hettich, Walter 50

Watson, Harry 25 Weiss, Lawrence 22–25 Winer, Stan 50 Winkler, Raymundo 8 Witte, Anne 8

Irvine, Ian 116 Jung, Y. 25

Yaniv, Gideon 25 Yoo, Byung 92 133

Subject index inverted order of suppliers 16 tax revenue higher under evasion than honesty 20–23

Arbitrary application of rules 5 Corruption 3, 57, 116 Cost benefit analysis of politics 9

Minimum wage California 105, 108 empirical implications of displacement 105 employment effect of 101 evasion 85 by workers 86 degree of 85, 92 general equilibrium context of 92 no evasion deadweight loss 80–81 no evasion deadweight loss exceeds triangle loss 82 no evasion equilibrium 79 partial equilibrium application of minimum wage evasion 92 range of equilibrium wages with evasion 102 measurement of compliance 85, 92 mismatching of talents 102 non-compliance 77, 85, 110 policy implication of displacement 110 rent-seeking and 83–4 risk avoidance and 92

Deadweight loss antagonistic 52 from price controls 84 from subsidies 56 of US taxation 9 Displacement calculation of with taxes 32–3 corruption 3, 56 critiques of 24–6 early definition of vii, 6 exceeds triangle loss 16, 91, 98, 109 general definition 2 inversion of supply 11 Mafia created displacement 7 minimum wage, basic argument 77 minimum wage, estimates 83, 91, 98 non-antagonistic quality 5, 51, 52 rent-seeking 121 simulation of with taxes 38–43 subsidy taxes 71–73 theory 66–68 Entrepreneurs 6 Evasive talents distribution of 27, 47–8, 92, 108 logistic form in rent-seeking game 117 parallel with lobbying ability 59, 116 punctured supply curve 93 random distribution of 26 splitting the supply curve 31 subsidies 59 Fishing quotas 76

Partial equilibrium approach to taxation 25 Price controls allocative effects of 84 deadweight loss from 84 Public funds, social cost of 9, 59, 74 Punctured supply curve basic theory 93–5 similarity to punctured supply 100 simulations of in equilibrium 98

Laffer curve difference between full and non-tax compliance 44

Rent-seeking costs 115–16 displacement cost of 121 135

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minimum wage and 83–4 origins of literature of 116 traditional costs 120–21 traditional model 117–18 Tullock costs 120 Restrictions on beer competition 116, 121 Risk avoidance and minimum wage evasion 92 Rule of law and arbitrariness 55

Tax evasion, partial equilibrium approach to 25, 92 Tax revenues larger under evasion than honesty 22–5 simulation of 20–23, 41–4 theory of 16–20, 35–7 Tax structure, complexity of 50 Tradeable insurance permits 76 Triangle loss 7, 15, 50, 52, 56

Subsidies arbitrariness 58 Canadian subsidy scale 58 deadweight loss from 56 displacement loss from 56 displacement loss theory 66–8 externalities 59 rules for efficient administration of 57 scope of subsidies in OECD 57 Supply curves, construction of 10, 66

Undercutting by tax evaders Czech wholesalers 2 prohibition-era Chicago 121 Quebec Ministry of Finance 2 Russia 6 Shell Brasil 1 Underground economy estimates of size 8 estimates of social cost of 9–10 negative function of 8–9 positive function 8 price discrimination 23, 100 tax dodge 50

Talents, distribution of 27