UNIVERSITÀ DEGLI STUDI DI NAPOLI

“PARTHENOPE” DIPARTIMENTO DI STUDI ECONOMICI

Financial Development and the Underground Economy

Keith Blackburn, Niloy Bosey,

Salvatore Capasso

WORKING PAPER N. 5.2008

JULY 2008

Redazione: Dipartimento di Studi Economici Università degli studi di Napoli “Parthenope” Via Medina, 40 80132 Napoli Tel. +39-081-5474736 – fax +39-081-5474750

La Redazione ottempera agli obblighi previsti dall’Art. 1 del D.L.L. 31.8.1945, n. 660.

Copie della presente pubblicazione possono essere richieste alla segreteria del Dipartimento.

Financial Development and theUnderground Economy

Keith Blackburn�, Niloy Bosey and Salvatore Capassoz

Abstract

We study the relationship between the underground economy and�nancial development in a model of tax evasion and bank interme-diation. Agents with heterogenous skills seek loans in order to un-dertake risky investment projects. Asymmetric information betweenborrowers and lenders implies a menu of loan contracts that induuceself-selection in a separating equilibrium. Faced with these contracts,agents choose how much of their income to declare by trading o¤ theirincentives to o¤er collateral against their disincentives to comply withtax obligations. The key implication of the analysis is that the mar-ginal net bene�t of income disclosure increases with the level of �nan-cial development. Thus, in accordance with empirical observation, weestablish the result that the lower is the stage of such development,the higher is the incidence of tax evasion and the greater is the size ofthe underground economy.

1 Introduction

The underground economy is a pervasive feature of countries throughout theworld. In one form or another, and to a lesser or greater degree, it hasexisted, and continues to exist, in all societies. Its e¤ects on economic andsocial development can be signi�cant and far-reaching as scarce resources

�Centre for Growth and Business Cycles Research, Economic Studies, University ofManchester.

yDepartment of Economics, University of Wisconsin (Milwaukee).zDepartment of Economics, University of Wisconsin (Milwaukee).

Address for correspondence: Niloy Bose, Department of Economics, Universityof Wisconsin (Milwaukee), Bolton Hall #864, Milwaukee, WI 53201-0413, USA.Telephone: 414 229 6132. Electronic mail: nbose@uwm.edu.

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are wasted or used ine¢ ciently, as purposeful regulations are circumventedand undermined, and as public �nances deteriorate to the detriment of publicpolicy. Of course, the presence of an underground sector is simply a re�ectionof individuals�incentives to conceal their economic activities, either becausethese activities would be less rewarding if practised in the formal sector, orelse because the activities are illegal to begin with. Understanding whatfactors might in�uence such incentives is an important avenue of researchwhich we pursue in this paper.By its nature, the underground economy is di¢ cult to study empirically.

Nevertheless, there has been a good deal of progress on ascertaining dataand developing techniques for quantifying its size and importance. Whilstdi¤erent approaches yield di¤erent estimates, the general conclusion is thatthe extent of informal economic activity is substantial. For example, Schnei-der and Enste (2002) report that, over the period 1988-2000, the averagesize of the shadow economy as a proportion of GDP ranged between 14-16percent in OECD countries; the equivalent numbers for developing countrieswere much higher at 35-44 percent, and in some cases reached the staggering�gure of 70 percent or more.1

For the most part, the key factors put forward as in�uencing undergroundactivity have been related to aspects of public policy and public administra-tion.2 Included amongst these are the burdens of taxation and social securitycontributions, the complexity and arbitrariness of the tax system, the extentof bureaucracy and regulations, and the incidence of corruption and rent-seeking (e.g., Friedman et al. 1999; Johnson et al. 1998a,b; Loayza 1996;Schneider and Enste 2000a; Schneider and Neck 1993).). Without under-mining the importance of any of these, our focus in this paper is on another,quite di¤erent, factor that has received rather less consideration - namely, thelevel of �nancial development. By way of motivating this, we draw attentionto two recent empirical studies which suggest that the functioning of �nan-cial markets has an important role to play in determining informal behaviour.The �rst - by Dabla-Norris and Feltenstein (2005) - reports a signi�cant nega-tive correlation between measures of �nancial development and the size of theshadow economy using aggregate cross-country data. The second - by Straub(2003) - provides evidence of a signi�cant positive e¤ect of credit market e¢ -ciency on the degree of business formality using cross-country �rm-level data.We obtain similar results from our own investigations, where we regress var-

1Examples of the latter include Egypt, Thailand and Nigeria, for which the under-ground economy during 1998-99 was estimated to be 69, 70 and 77 percent of o¢ cialGDP, respectively.

2For a comprehensive discussion of these (and other) factors, see Schneider and Enste(2000b).

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ious standard indicators of �nancial development on the shadow economy�spercentage share of GDP (after controlling for other determinants suggestedin the literature). ****NEED MORE - DESCRIPTION OF DATA, MEA-SUREMENT OF SHADOWECONOMY****. As is evident from the partialresidual plots in Figures 1 and 2, the e¤ect of �nancial development on thesize of the shadow economy is both strongly and robustly negative.The objective of the analysis that follows is to provide an explanation for

the above observations. We do so within the context of a simple model of taxevasion and �nancial intermediation. The basic idea is as follows. Supposethat individuals would like to undertake some investment project, but thatthe cost of doing so is greater than their current income or wealth so thatexternal �nance is needed. This �nance is acquired from banks according tothe terms and conditions of optimal loan contracts. Asymmetric informa-tion between borrowers and lenders leads to a menu of such contracts thatstipulate not only the rate of interest charged on loans, but also the probabil-ity that a loan will be granted (implying the possibility of credit rationing).Faced with these arrangements, an individual puts forward a loan applica-tion which requires her to decide how much of her current wealth to declare,or how much of it to conceal, by trading o¤ the costs and bene�ts of this.Typically, the costs of concealment - meaning the costs of participating inthe informal sector - are modelled in terms of exclusion from certain publicgoods and services (e.g., social infrastructure, property rights and the justicesystem), together with the possibility of �nes, incarceration and other suchpunishments. In our case the costs are related to the functioing of �nan-cial markets. Speci�cally, the more wealth that an individual hides, the lesscollateral she has to o¤er for securing a loan and the worse are the termsand conditions of the loan contract made available to her. Signi�cantly, thisdeterioration in credit arrangements is more pronounced at lower levels of�nancial development (as measured by higher costs of �nancial intermedia-tion). As regards the bene�ts of concealment, an individual who invests anypart of her wealth in the shadow economy enjoys the prospect of avoidingsome of her tax obligations. The key implication of our analysis is that themarginal net gain from greater wealth disclosure increases with the level of�nancial development. Accordingly, we establish the result that the lower isthe stage of such development, the higher is the incidence of tax evasion andthe greater is the size of the underground economy.Our analysis complements a small body of other theoretical research

which suggests other possible connections between the credit market andthe shadow economy. Dabla-Norris and Feltenstein (2005) construct a com-putable dynamic general equilibrium model for the purpose of estimatingthe impact of taxes on underground activity (and other macroeconomic phe-

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nomena) in Pakistan. Their numerical results indicate that, in the presenceof credit market imperfections, an increase in corporate taxation may notonly cause �rms to operate underground but, in doing so, may also lead toa reduction in the amount of collateral in the formal sector and, with this, areduction in the volume of loans and subsequent investments in that sector.In a slightly di¤erent vein, Straub (2005) develops a model in which agentsface a choice of participating in either a formal or informal credit market. Itis shown how this choice is in�uenced by the interaction between the cost ofentry into formality and the relative e¢ ciency of formal and informal creditmechanisms. Along related lines, Antunes and Cavalcanti (2007) present aframework in which agents can choose to become either workers or entrepre-neurs, with the possibility of practising entrepreneurship in either the formalor informal sector. The analysis demonstrates how the choice of occupation isa¤ected by entry barriers (regulation costs) and credit market imperfections.A common feature of these contributions is that the extent of undergroundactivity is a re�ection of individuals�all-or-nothing choice as to whether toparticipate in the shadow economy. By contrast, our own analysis centreson individuals�incentives to exploit uno¢ cial opportunities whilst still doingbusiness in the formal sector.The remainder of the paper is organised as follows. Section 2 sets out the

basic framework. Section 3 presents the solution to banks�optimal loan con-tracting problem. Section 4 presents the solution to individuals�optimal taxevasion problem. Section 5 reveals the equilibrium outcomes that transpirefrom these solutions. Section 6 contains a few concluding remarks.

2 The Basic Set-up

We consider a small open economy in which there is a countably in�nite num-ber of agents measuring a size of unit mass. Agents are identical in terms oftheir preferences, endowments of wealth and production opportunities, butmay di¤er according to their abilities and skills. These attributes, which arebestowed randomly, determine an agent�s performance in productive activ-ity that re�ects a choice of project, or occupation, which gives access to atechnology for generating output. For certain types of project to be under-taken, loans must be acquired from �nancial intermediaries under the termsand conditions of mutually agreeable loan contracts. Agents are obliged topay taxes on all sources of income at a rate determined exogenously by thegovernment. There are two main sources of imperfection in the economy -an imperfection in �nancial markets due to asymmetric information betweenborrowers and lenders, and an imperfection in governance due to asymmetric

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information between tax payers and tax collectors. In more detail the modelis described as follows.Agents are risk neutral, deriving linear utility from consumption of various

income streams that are realised at the end of the period. One source ofincome is an initial asset endowment, A > 0, that pays a gross rate of returnof � > 1 with certainty. The value of this asset is private information, as isthe income, �A, that it yields.3 Other sources of income are production (orinvestment) projects, of which there are two types. The �rst type involvesthe use of some basic (traditional) technology in some routine activity thatis costless and riskless: this is a safe occupation that requires zero capitaloutlay and that yields a �xed amount of income with certainty. The secondtype entails the operation of a more advanced (modern) technology in a morespeculative venture that is expected to be more productive but which is alsocostly and subject to uncertainty: this is a risky occupation that requiresK units of capital outlay and that yields a stochastic rate of return. Thepayo¤s from both projects depend on an agent�s abilities and skills that aredrawn randomly from a known probability distribution which accounts foragent heterogeneity. Speci�cally, an agent faces the prospect of being eitherhigh-skilled (type-H) with probaility p 2 (0; 1) or low-skilled (type-L) withprobability 1 � p.4 The realised distribution of skills is private informationto agents. Those who turn out to be high-skilled enjoy a greater expectedincome from each type of project than those who turn out to be low-skilled:for the safe project, the former produce sH > 0 units of output, whilst thelatter produce sL 2 (0; sH) units; for the risky project, the former earn arate of return of � > 1 with probability qH 2 (0; 1) and a rate of return ofzero with probability 1 � qH , whilst the latter earn the same returns withalternative probabilities qL 2 (0; qH) and 1�qL. The greater expected incomefrom the risky project is captured by the restriction qi� > si (i = H;L), andthe greater productivity of high-skilled agents is re�ected in the featuressH > sL and qH� > qL�. To save on notation in our subsequent analysis, wenormalise sL = 0 and qH = 1.Since all income is realised at the end of the period, an agent who wishes

to take on the risky project must acquire external �nance to the tune ofK. For reasons given below, equilibrium loan contracting involves di¤erenttypes of agent being o¤ered di¤erent terms and conditions on borrowing,including di¤erent rates of interest on loans. We denote by Ri the gross

3The assumption that A is the same for all agents is made for simplicity. Our resultswould not change were we to consider a distribution of A across agents.

4An alternative description of events is to assume that agents are endowed with identicalabilities, but are randomly allocated projects with di¤erent (high and low) risk character-istics.

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rate of interest charged to an agent of type-i. With probability qi, the riskyproject is successful and the agent pays back her loan to earn a �nal incomeof (�� Ri)K. With probability 1� qi, the risky project fails and the agentgoes bankrupt, earning a �nal income of zero.Agents are obliged to pay taxes on all of their incomes at the proportional

rate t 2 (0; 1). The government is able to observe the incomes from projects,but not the income from the asset endowment (since the value of the assetis known only to agents). As such, an agent may seek to evade part of hertax liabilities by misreporting her initial wealth. We denote by 2 [0; 1]the fraction of this wealth that an agent declares, the remaining fraction,1 � , being undeclared. By behaving in this way, the agent makes publicthat she has �A amount of asset income on which she is liable to pay tax.We assume that the agent can successfully conceal the undeclared fractionof her wealth by investing it in the hidden (or shadow) economy at a blackmarket gross rate of return of � � �. The �nal income from doing this is(1� )�A on which the agent does not pay any tax.5An agent�s declared value of wealth serves as collateral for securing exter-

nal �nance to run the risky project. Such �nance is acquired from competitive�nancial intermediaries (banks) that have access to a perfectly elastic sup-ply of loanable funds at the exogenous world (gross) interest rate, r. Thedesign of �nancial contracts is complicated by the prospect of adverse selec-tion as intermediaries are unable to observe the true skill characteristics ofagents. From the perspective of intermediaries, low-skilled agents are morerisky than high-skilled agents. We assume that the population of the formeris su¢ ciently large as to prevent intermediaries from pooling clients togetherand o¤ering a single contract. Instead, banks must design contracts in such away that induces self-selection by clients. The possibility of doing this arisesfrom the fact that the di¤erent borrower types receive di¤erent payo¤s fromtheir outside opportunity of running the safe project. This feature means thatthe indi¤erence curves of high-skilled and low-skilled agents satisfy the singlecrossing property which enables intermediaries to distinguish the two typesby o¤ering a menu of contracts that encourages self-selection in a separatingequilibrium (e.g., Bencivenga and Smith 1993; Bose and Cothren 1996). Asindicated above, one di¤erence between these contracts is the rate of intereston loans. Another di¤erence is the probability that a loan will actually be

5According to this description of events, an agent�s subterfuge in disposing of herundeclared income allows her to evade taxes with complete con�dence of impunity. Thisfeature is merely a simpli�cation, though it is probably near the mark for many developingcountries, where the will and wherewithal to �ght such practices are relatively weak. It isstraightforward to show that our results would not change if one was to assume that agentsface a risk of being caught as a consequence of some imprecise government monitoring.

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granted as banks may be induced to ration credit by turning down some loanapplications. We denote by �i 2 (0; 1) the probability that an agent of type-iwill be approved credit, 1� �i being the probability that she will be deniedsuch funds. In the event of the former, banks incur a cost of intermediation,� > 0, and earn an income that depends on whether or not the risky projectsucceeds: if so (i.e., with probability qi), a bank is paid back in full, receivingRiK in loan repayment; if not (i.e., with probability 1� qi), the bank recov-ers part of its loss by appropriating a borrower�s collateral, �A. ****NEEDMORE ON COST OF INTERMEDIATION - EXAMPLES OF WHAT ITCOULD BE****This completes our description of the environment. Decision making takes

place as follows. Prior to realising their skills and project returns, agentschoose how much of their intial wealth to declare so as to maximise theirexpected utility, subject to the �nancial contracts o¤ered by intermediaries.Subsequently, the distribution of skills is revealed privately to agents whothen apply for loans. Given this private information, together with the partdisclosure of wealth, intermediaries set the terms and conditions of contractsin agents�best interests, whilst ensuring that appropriate constraints on be-haviour are observed. Out of their realised �nal incomes, agents pay o¤any loans and tax liabilities before consuming the remainder. The equilib-rium outcomes that transpire from these decisions are determined by solvingbackwards through the sequence of events - a matter to which we now turn.

3 Financial Contracts

The precise functioning of the credit market is as follows. At the beginning ofthe period, lenders are approached by prospective borrowers with a requestfor funding to undertake risky investment projects. A contract is o¤ered,acceptance of which implies a binding agreement that commits a lender tomaking a loan of size of K, and a borrower to making a subsequent repay-ment of this loan. A lender�s information at this stage includes an agent�sdeclared value of her initial wealth, A, together with the corresponding fu-ture income, �A. Importantly, it does not include separate observationsof and A, meaning that the lender is unaware of the agent�s true wealthstatus and must therefore design a contract based only on what has actuallybeen declared. Other information available to lenders includes the ex antedistribution of borrower types, p, the income from a borrower�s outside op-portunity, si, the expected income from project investment, qi�K, the costof intermediation, �, and the cost of funds, r.We assume that �nancial intermediaries operate in a competitive envi-

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ronment, and that the terms and conditions of available loan contracts arepublic knowledge. Accordingly, an intermediary is approached by an agentonly if the contract that it o¤ers is not dominated by the contracts o¤eredby its competitors. In equilibrium the pro�ts of intermediaries are driven tozero.As indicated earlier, the di¤erence between borrower types in terms of

their outside opportunities means that intermediaries may be able to separatethe high-skilled from the low-skilled by o¤ering a menu of loan arrangements.In fact it is well-known that the only possible equilibrium in this case is aseparating equilibrium induced by borrowers�self-selection of di¤erentiatedcontracts (e.g., Rothschild and Stiglitz 1976). A contract in our model isde�ned by the interest rate charged on loans and the probability that a loanwill be granted: that is, for an agent of type-i, the contract is given byCi = fRi; �ig. Needless to say, contracts must be designed in such a way asto be both individually rational and incentive compatible for agents.The solution to the contracting problem is stated as follows.

Proposition 1 Assume that (� � RH)K > sH . Then the equilibrium sepa-rating contracts are characterised by

RH =rK + �

K; �H =

(qL�� r)K � � + (1� qL) �AqL[(�� r)K � �] ; (1)

RL =rK + � � (1� qL) �A

qLK; �L = 1: (2)

Proof. See Section A of the Appendix.

The above results have some straightforward intuition. As already men-tioned, any contract that yields positive pro�ts to lenders cannot survive ina competitive equilibrium. An intermediary�s expected income from lendingto an agent of type-i is qiRiK + (1 � qi) �A: that is, with probability qi,the risky project is successful and the agent pays back RiK in interest in-come, whilst with probability 1 � qi, the project fails and the agent handsover all of her collateral, �A. The intermediary�s total cost of lending is thecost of borrowing funds, rK, plus the cost of intermediation, �. Equatingexpected income and costs gives the zero pro�t condition, from which wededuce the expressions for Ri (recalling that qH = 1). Note that RH < RLif �A < rK + �, a condition that we assume to be satis�ed (otherwise theanalysis would be trivial as intermediaries would face no risk in lending).As regards the determination of �i, intermediaries induce separation of low-skilled and high-skilled agents by o¤ering the former their �rst-best contract

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(whereby each one of them is granted a loan with certainty) and presentingthe latter with a distorted contract (whereby a fraction of them are creditrationed).6 That separation is achieved at the expense of high-quality clientsfollows simply from the incentive compatibility condition and is a standardresult in the adverse selection literature.An important implication of the above results is the following.

Corollary 1 The probability that a high-skilled agent will be given a loan isgreater the lower is the cost of �nancial intermediation and the higher is theagent�s declared value of wealth

Formally, @�H@�< 0 and @�H

@ > 0. The reason is that, as the cost of intermedi-

ation declines, or as the declared value of wealth increases, the interest ratecharged to low-skilled agents falls by more than the interest rate charged tohigh-skilled agents; this makes the contract o¤ered to the latter less attrac-tive to the former and thereby provides an opportunity for intermediaries toreduce the incidence of credit rationing whilst maintaining incentive compat-ibility.

4 Tax Evasion

The foregoing analysis reveals how the equilibrium arrangements for borrow-ing and lending are in�uenced by the declared asset position of agents. Thegreater is the initial wealth that agents reveal, the greater is the collateralthat can be used as security against a loan and the better are the termsand conditions of loan contracts. At the same time, revealing more wealthmeans that agents expose themselves to a higher burden of taxation. Anagent�s disclosure (or concealment) of her wealth status is therefore a deci-sion that involves optimising a trade-o¤. The agent solves this problem withthe knowledge of the contracts on o¤er, but without the knowledge of whichcontract she will actually be presented with as her skill type is not realiseduntil subsequently.The circumstances facing agents are summarised as follows. Each agent

pays the same tax rate, t, on all sources of income, except the income fromundeclared wealth. With probability �i, an agent of type-i acquires a loanto run the risky project. The project succeeds with probability qi and failswith probability 1 � qi. In the event of the former, the agent earns a netdisposable income of (1� t)(��Ri)K from the project, plus a net disposable

6The same parameter restriction as before, �A < rK + �, ensures that �H 2 (0; 1).

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income of (1� t) �A from her declared asset endowment, plus an income of(1 � )�A from her undeclared endowment. In the event of the latter, theagent earns only the last of these incomes, (1 � )��A. With probability1� �i, an agent of type-i is denied a loan. In this case the agent receives anafter-tax income of (1� t)si from running the safe project, plus an after-taxincome of (1� t) �A from her reported wealth, plus an income of (1� )�Afrom her unreported wealth. Collecting terms together and setting �L = 1(along with aL = 0 and qH = 1), we may write the expected utility of ahigh-skilled and a low-skilled agent as

E(UH) = (1� t)[�H(��RH)K + (1� �H)sH + �A] + (1� )�A; (3)

E(UL) = (1� t)[qL(��RL)K + �A] + (1� )�A: (4)

An agent�s choice of how much of her initial wealth to declare is a choiceof the value of . As indicated above, this decision is made prior to the agentrealising her skills, but in the knowldge of the contracts that will be available.Since the probability that an agent will turn out to be high-skilled (low-skilled) is p (1�p), is chosen so as to maximise U = pE(UH)+(1�p)E(UL),given that Ri and �i are determined according to (1) and (2). Appropriatesubstitution allows us to re-state this problem as

max U = (1� t)fp[�H((�� r)K � � � sH) + sH ]

+ (1� p)[(qL�� r)K � �] + �Ag+ (1� )�A: (5)

The behaviour of an agent is straightforward to deduce and we summariseit as follows.

Proposition 2 Let F (�) � (1 � t)p[(� � r)K � � � sH ]@�H@ and G(�) �[�� (1� t)�]A. Then assuming that �A < rK + �, an agent will optimallychoose = 1 if F (�) > G(�) and = 0 if F (�) < G(�):

Proof. See Section B of the Appenidx.

As before, the above results have a straightforward intuition. By declaringmore wealth (i.e., by increasing ), an agent incurs both a gain and a loss.The former is captured by the term F (�) and represents the marginal bene�tof putting up more collateral, which is the bene�t from the reduction in riskfaced by lenders and the consequent improvement in the terms and conditionsof the loan contract. The latter is given by the term G(�) and corresponds tothe marginal cost of investing more wealth in the formal sector, which is thecost of both a higher burden of taxation and the foregone interest income

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from the informal sector. Depending on which is greater, the agent willset at either its maximum or minimum value, implying either full or zerodisclosure of her asset endowment and therefore either full or zero compliancewith her tax obligations on asset income.7

In presenting the above results we have singled out two key parametersthat may in�uence an agent�s behaviour - namely, the cost of �nancial inter-mediation, �, and the return on underground investment, �. These are seento impact on the expected gains and losses from the disclosure of wealth. Inparticular, we make the following observation.

Corollary 2 The marginal bene�t (cost) to an agent of disclosing more wealthis higher the lower (higher) is the cost of �nancial intermediation (return onunderground investment).

Formally, F 0(�) < 0 and G0(�) > 0. The e¤ect of � is explained by the factthat a lower cost of intermediation makes the terms and conditions of loancontracts more attractive to agents. For those who turn out be high-skilled,there is a greater incentive to put up more collateral (i.e., to declare morewealth) and thereby improve the chances of acquiring a loan. The e¤ect of� is simply that a higher return from investing in the informal sector meansa higher opportunity cost of investing in the formal sector. The incenive todo the former (i.e., to conceal more wealth) is therefore greater.

5 Aggregate Outcomes

The results obtained above establish conditions under which an individualagent will seek to evade some of her tax obligations. These conditions dependon economy-wide factors that are relevant to all agents. One of these - thecost of intermediation - provides a measure of �nancial development. Forthe purposes of the present paper, we treat this is as exogenous since ourprincipal focus is on the causal role played by �nancial markets in governingevents elsewhere in the economy. By contrast, the other economy-wide factor- the return on underground investment - is an outcome that we treat asbeing determined endogenously on the basis of the aggregate behaviour ofindividuals. The e¤ect of this is to introduce important interactions which

7As shown in the Appendix, for the case in which D(�) > [�� (1� t)�]A, U is linearlyincreasing (decreasing) in up to (beyond) max =

rK+��A . The restriction �A < rK + �

means that max > 1 which is not a feasible choice since agents would be claiming to havemore wealth than A - a claim that they would need to substantiate (but never could) whenputting up collateral.

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the following analysis intends to reveal.A plausible assumption is that the rate of return earned in the informal

sector is a decreasing function of the total volume of funds channelled intothat sector. One justi�cation for this is simply the existence of diminishingreturns to informal productive activity: as more resources are devoted to suchactivity, the marginal gains from it decline. An alternative, more elaborate,motivation is as follows. Suppose that agents�subterfuge in concealing theirincome requires assistance from some other individuals who specialise in thistype of practice. These individuals are experts at directing funds into areaswhere they are di¢ cult to trace by the government, such as the undergroundeconomy and overseas bank accounts. In return for this service an agentmust pay a commission which increases with the total amount of funds beinglaundered because of the greater di¢ culty and greater costs of doing this. Asbefore, the agent�s net return on her own hidden income is lower the largeris the total amount of such income.We capture the above ideas by specifying the black market rate of return

to be a decreasing function of the total volume of undeclared wealth. Denot-ing by � 2 [0; 1] the fraction of agents who set = 0, the value of this wealthis �A and the black market return is posited as � = b�(�), where b�0(�) < 0.Given this, together with our previous results, we now proceed to determinethe equilibrium outcomes in the economy.We begin by de�ning �0 = b�(0) and �1 = b�(1), which are the respective

rates of return in the informal sector when every agent and no agent disclosesher initial wealth. Evidently, �0 > �1. The corresponding marginal costs ofdisclosure are G(�0) and G(�1), where G(�0) > G(�1). Since the marginalbene�t of disclosure, F (�), is a monotonically decreasing function, we maydeduce that, for each �i (i = 0; 1), there is a unique �i such that F (�i) =G(�i), F (�) > G(�i) for all � < �i and F (�) < G(�i) for all � > �i. Evidently,�0 < �1. These critical, or threshold, levels of �nancial development representboundaries between regions where the incentive to conceal wealth and evadetaxes is either present or absent. We are now in a position to establish ourmain result which we illustrate in Figure 1.

Proposition 3 The equilibrium fraction of tax-evading agents is given bythe following: (i) � = 1 for � > �1; (ii) � = 0 for � < �0; and (iii) � =b�(�) 2 (0; 1) for � 2 (�0; �1), where b�0(�) > 0.Proof. See Section C of the Appendix.

Based on the above, we are led to distinguish between three types ofregime for an economy: the �rst - a low �nancial development regime - is one

12

in which the incidence of tax evasion is always at its maximum (� = 1) forany given value of � above the higher threshold value, �1; the second - a high�nancial development regime - is one in which the incidence of tax evasionis always at its minimum (� = 0) for any given value of � below the lowerthreshold value, �0. And the third - an intermediate �nancial developmentregime - is one in which the incidence of tax evasion is somewhere in betweenits maximum and minimum (� 2 (0; 1)), and decreases monotonically as �decreases within the interval of the thresholds from �1 to �0. The intuitionis as follows.Each agent chooses to disclose or conceal her initial wealth according to

whether F (�) > G(�) or F (�) < G(�). Whichever of these conditions holdsdepends on the level of �nancial development and the return on undergoundinvestment: the higher is the former (i.e., the smaller is �) the better arethe terms and conditions of loan contracts (an inducement to disclosure),whilst the higher is the latter (i.e., the greater is �) the more attractive isparticipation in the informal sector (an inducement to concealment). Forany � > �1, we have F (�) < G(�1) < G(�0). In this case the level of�nancial development is so low that it never pays an agent to declare herwealth, even if she is faced with the lowest possible return on undergroundinvestment as a result of all other agents concealing their wealth. As such,each and every agent chooses to evade taxes in a unique equilibrium fromwhich there is no incentive to deviate. Conversely, for any � < �0, we haveF (�) > G(�0) > G(�1). In this instance the level of �nancial development isso high that an agent is always better o¤ by declaring her wealth, even if shecould earn the the highest possible return in the informal sector due to allother agents declaring their wealth. Consequently, the only equilibrium fromwhich defection will not occur is one in which each and every agent choosesnot to evade taxes. Contrasting these scenarios is the case of � 2 (�0; �1), forwhich we have G(�1) < F (�) < G(�0). In this intermediate range of �nancialdevelopment the bene�ts from declaring and concealing wealth exactly o¤seteach other in an equilibrium where some agents evade taxes and others donot. The fraction of tax evaders is the value of � that satis�es F (�) = G(�),where � = b�(�). Were this condition not to be satis�ed, then some agentswould be either declaring wealth when they would do better to conceal it(F (�) < G(�)) or concealing wealth when they would do better to declareit (F (�) > G(�)), in which case the number of tax evaders would eitherrise or fall until � reaches a value such that the condition is established. Inthis way, lower values of � lead to lower values of � so as to preserve themarginal agent�s indi¤erence between compliance and non-compliance in taxregulations.In summary, our analysis is able to explain the observed negative rela-

13

tionship between the level of �nancial development and the incidence of taxevasion. When the former is su¢ ciently low or su¢ ciently high, the latteris at its maximum or at its minimum; when the former is somewhere in be-tween, the latter is somewhere in between and decreases monotonically asthe e¢ ciency of �nancial markets improves. To the extent that �nancialdevelopment occurs endogenously as the economy, in general, develops, taxevasion may be a temporary phenomenon that a government might be willingto live with, especially if the costs of mitigating it are high. On the otherhand, an economy that staggers in its process of development may �nd itselfpermanently deprived of tax revenues that could otherwise be put to goodcauses. According to our analysis, �nancial development serves to combatthe incentives to engage in tax evasion only above some threshold level: ifthis threshold is not reached, then the underground economy will continueto thrive against a backdrop of �nancial repression.

6 Conclusions

The existence of a shadow economy has potentially serious implications foreconomic performance and public policy. Activities conducted in this sectorare neither protected nor regulated in the same way that applies to activitiesin the formal sector. Growth prospects can be compromised by encumbrancesto doing business due to the lack of social infrastructure. Public �nances cansu¤er as the tax base shrinks, thus weakening the government�s capacity togenerate revenue. And policy makers�assessments and recommendations canbe prone to greater error because of the poorer quality of o¢ cial statistics.For these and other reasons, the size of the informal sector is a matter of non-trivial concern and an important task is to understand what factors mightin�uence it.Informality in an economy is a re�ection of individuals�incentives to con-

ceal their activities or circumstances. This may take various forms, rangingfrom full participation in the underground sector (e.g., working exclusively inthe shadow labour market) to more subtle clandestine practices (e.g., misre-porting income and hiding invesments). In this paper we have focused on thelatter by considering a situation in which individuals may choose to concealtheir true wealth status for the purpose of tax evasion. Our central concernhas been to study how the temptation to engage in such behaviour might bein�uenced by conditions in �nancial markets from which individuals acquireloans to undertake business ventures. The crux of our analysis is that, in thepresence of �nancial market imperfections (i.e., asymmetric information), theamount of wealth disclosed by an individual a¤ects the terms and conditions

14

of the loan contract that is o¤ered. At the same time, the marginal bene-�t of disclosure increases with improvements in the functioning of �nancialmarkets, as represented by a lower cost of �nancial intermediation. In spiteof its simplicity, the model produces a rich variety of outcomes as a result ofthe mutual interaction between individual decision making and the aggregateeconomic environment. In particular, we are led to distinguish between threetypes of �nancial development regime with the implication that the fractionof tax-evading agents declines as the economy moves from a low, throughan intermediate, to a high development regime. This negative relationshipbetween the incidence of tax evasion (or size of the underground sector) andthe level of �nancial development accords well with empirical evidence.

15

Appendix

A. Proof of Proposition 1

As indicated in the text, �nancial intermediaries earn zero pro�t from eachtype of loan contract. This condition, which amounts to qiRiK + (1 �qi) �A = rK + � (where qH = 1), delivers the expression for each of thecontractual interest rates, Ri. An agent of type-i derives an expected util-ity of Vi(Ci) = [qi�i(� � Ri)K + (1 � �i)si](1 � t) from the contract o¤erof Ci = fRi; �ig (where qH = 1 and sL = 0). The �rst term in [�] givesthe net payo¤ from the risky project, (� � Ri)K, when a loan is granted(which occurs with probability �i) and when the project is successful (whichoccurs with probability qi). The second term in [�] gives the payo¤ from thesafe project, si, when a loan is not granted (which occurs with probability1 � �i). In each case the agent pays taxes, t, on her income. Let CFi de-note the �rst-best contract that an agent of type-i would receive under fullinformation. For each of these contracts, �i = 1 and Ri is determined asabove. Since RH < RL (under our assumption that w < rK + �), thenVL(C

FH) > VL(C

FL ) and VH(C

FH) > VH(C

FL ). Suppose that lenders were to

o¤er CFi in the presence of asymmetric information (as exists in our model).Clearly, there would be no incentive for high-skilled agents to reject CFH infavour of CFL by pretending to be low-skilled agents. Thus, in order to induceself-selection, lenders do not need to distort the contract for the low-skilledtypes, but are able to o¤er this group its �rst-best choices of RL and �L (assummarised in (2)). Given this, then the contract for the high-skilled groupis determined by solving the following problem:

max�H

VH(CH) = [�H(��RH)K + (1� �H)sH ](1� t); (A1)

s.t. qL(��RL)K(1� t) � �HqL(��RH)K(1� t); (A2)

0 � �H � 1: (A3)

The constraint in (A2) is the incentive compatibility condition for high-skilledagents. Assuming that (� � RH)K > sH , it is straightforward see that thisconstraint is binding: since VH(CH) is strictly increasing in �H , interme-diaries will set this probability at the highest possible value, which is thevalue that makes (A2) hold with equality, given the setting of each Ri. High-skilled agents are therefore o¤ered a distorted combination of RH and �H (assummarised in (1)).

B. Proof of Proposition 2

16

It follows from (5) that

@U

@ = (1� t)p[(�� r)K � � � sH ]

@�H@

� [�+ (1� t)�]A

= F (�)�G(�): (B1)

The result in (1) implies that �H 2 (0; 1), @�H@ > 0 and F (�) > 0 for all up

to max =rK+��A

, at which point and beyond �H = 1 and @�H@

= F (�) = 0.Assume that �A < rK + �, implying max > 1. For the case in whichF (�) > G(�), @U

@ > 0 for < max and

@U@ < 0 for > max, so that the

agent will set = 1, its maximum value. For the case in which F (�) < G(�),@U@ < 0 for all , implying that the agent will set = 0, its minimum value.

C. Proof of Proposition 3

Suppose, �rst, that � > �1. Then F (�) < G(�1) < G(�0), implying that itpays each agent to set = 0, irrespective of what other agents are doing.That � = 1 (i.e., all agents set = 0) is the unique equilibrium outcomefollows from the fact that no agent has an incentive to deviate from this,whilst each agent has an incentive to deviate from � = 0 (i.e., the case inwhich all agents set = 1). Next, suppose that � < �0. In this instanceF (�) > G(�0) > G(�1) so that it now pays each agent to set = 1, irre-spective of what others are doing. As before, that � = 0 (i.e., all agents set = 1) is the unique equilibrium outcome follows from the fact that no agenthas an incentive to deviate from this, whilst each agent has an incentive todeviate from � = 1 (i.e., the case in which all agents set = 0). Finally,suppose that � 2 (�0; �1). Then G(�1) < F (�) < G(�0), implying that eachagent will set either = 0 or = 1, depending on what others are doing.That neither � = 1 nor � = 0 is an equilibrium outcome follows from the factthat agents have an incentive to deviate in each case - that is, to set = 1in the �rst case and = 0 in the second. Consider, however, a � 2 (0; 1)such that �0 > b�(�) > �1 and G(�0) > G[b�(�)] > G(�1). Then there exists aunique value of this � which supports an equilibrium with F (�) = G[b�(�)].Since F 0(�) < 0 and G0[b�(�)]b�0(�) < 0, then this � is an increasing functionof �, or � = b�(�) where b�0(�) > 0.

17

Figure 1 Equilibrium Tax Evasion

0( )G ρ

1( )G ρ

( )F δ

δ 1δ 0δ