Journal of Economic Behavior & Organization Tax Evasion, the Underground Economy and Financial Development

We study the relationship between the underground economy and financial development in a model of tax evasion and bank intermediation. Agents with heterogeneous skills seek loans in order to undertake risky investment projects. Asymmetric information between borrowers and lenders implies a menu of loan contracts that induce self-selection in a separating equilibrium. Faced with these contracts, agents choose how much of their income to declare by trading off their incentives to offer collateral against their disincentives to comply with tax obligations. The key implication of the analysis is that the marginal net benefit of income disclosure increases with the level of financial development. Thus, in accordance with empirical observation, we establish 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 of the underground economy.


Introduction
The underground economy is a pervasive feature of countries throughout the world. In one form or another, and to a lesser or greater degree, it has existed, and continues to exist, in all societies. Known by many other names (e.g., the hidden, shadow, uno¢ cial, informal and black market economy), its e¤ects on economic and social development can be signi…cant and far-reaching as scarce resources are wasted or used ine¢ ciently, as purposeful regulations are circumvented and undermined, as national accounts become inaccurate and incomplete, and as public …nances deteriorate to the detriment of public policy. Of course, the presence of an underground sector is simply a re ‡ection of individuals'incentives to conceal their economic activities, either because these activities would be less rewarding if practised in the formal sector, or else because the activities are illegal to begin with. Understanding what factors might in ‡uence such incentives is an important avenue of research which we pursue in this paper. 1 By its nature, the underground economy is di¢ cult to study empirically. Nevertheless, there has been a good deal of progress on ascertaining data and developing techniques for quantifying its size and importance. Whilst di¤erent approaches yield di¤erent estimates, the general conclusion is that the extent of informal economic activity is substantial. For example, Schneider and Enste (2002) report that, over the period 1988-2000, the average size of the shadow economy as a proportion of GDP ranged between 14-16 percent in OECD countries; the equivalent numbers for developing countries were much higher at 35-44 percent, and in some cases reached the staggering …gure of 70 percent or more. 2 For the most part, the key factors put forward as in ‡uencing underground activity have been related to aspects of public policy and public administration. 3 Included amongst these are the burdens of taxation and social security contributions, the complexity and arbitrariness of the tax system, the extent of bureaucracy and regulations, and the incidence of corruption and rent-seeking (e.g., Friedman et al. 2000;Johnson et al. 1998a,b;Loayza 1996;Schneider andEnste 2000, 2002;Schneider and Neck 1993).). Without undermining the importance of any of these, our focus in this paper is on another, quite di¤erent, factor that has received rather less considerationnamely, the level of …nancial development. By way of motivating this, we draw attention to two recent studies which suggest that the functioning of …nancial markets has an important role to play in determining informal behaviour. The …rst -by Dabla-Norris and Feltenstein (2005) -reports a significant negative correlation between measures of …nancial development and the size of the shadow economy using aggregate cross-country data. The second -by Straub (2005) -provides evidence of a signi…cant positive e¤ect of credit market e¢ ciency on the degree of business formality using cross-country …rmlevel data. We obtain similar results from our own investigations, where we plot various standard indicators of …nancial development against the partial residuals of a regression used to estimate other potential determinants of the shadow economy. 4 The plots, shown in Figure 1, reveal persuasively that the e¤ect of …nancial development on the size of the shadow economy is both strongly and robustly negative. Further con…rmation of this is given in a more thorough investigation by Bose et al. (2009).
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 tax evasion and …nancial intermediation. The basic idea is as follows. Suppose that individuals would like to undertake some investment project, but that the cost of doing so is greater than their current income or wealth so that external …nance is needed. This …nance is acquired from banks according to the terms and conditions of optimal loan contracts. Asymmetric information between borrowers and lenders leads to a menu of such contracts that stipulate not only the rate of interest charged on loans, but also the probability that a loan will be granted (implying the possibility of credit rationing). Faced with these arrangements, an individual puts forward a loan application 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 in the informal sector -are modelled in terms of exclusion from certain public goods and services (e.g., social infrastructure, property rights and the justice system), together with the possibility of …nes, incarceration and other such punishments. In our case the costs are related to the functioing of …nan-cial markets. Speci…cally, the more wealth that an individual hides, the less collateral she has to o¤er for securing a loan and the worse are the terms and conditions of the loan contract made available to her. Signi…cantly, this deterioration in credit arrangements is more pronounced at lower levels of …nancial development (as measured by higher costs of …nancial intermediation). As regards the bene…ts of concealment, an individual who invests any part of her wealth in the shadow economy can avoid some of her tax obligations and earn a black market rate of return on her investment. For reasons alluded to later, we assume that this return is diminishing in the total volume of funds deposited in the black market. This means that there are interactions between tax evaders as each one's participation in this market imposes a negative externality on others. As such, an individual's incentive to engage in tax evasion may depend importantly on the aggregate incidence of this activity (i.e., how many other individuals are investing in the shadow economy). Against this background, we show that the marginal net gain from greater wealth disclosure increases with the level of …nancial development. Accordingly, we establish the result that the lower is the stage of such development, the higher is the extent of tax evasion and the greater is the size of the underground economy.
Our analysis complements a small body of other research which suggests various possible connections between the credit market and the shadow economy. Dabla-Norris and Feltenstein (2005) construct a computable dynamic general equilibrium model for the purpose of estimating the impact of taxes on underground activity (and other macroeconomic phenomena) in Pakistan. Their numerical results indicate that, in the presence of credit market imperfections, an increase in corporate taxation may not only cause …rms to operate underground but, in doing so, may also lead to a reduction in the amount of collateral in the formal sector and, with this, a reduction in the volume of loans and subsequent investments in that sector. In a slightly different vein, Straub (2005) develops a model in which agents face a choice of participating in either a formal or informal credit market. It is shown how this choice is in ‡uenced by the interaction between the cost of entry into formality and the relative e¢ ciency of formal and informal credit mechanisms. 5 Along related lines, Antunes and Cavalcanti (2007) present a framework in which agents can choose to become either workers or entrepreneurs, with the possibility of practising entrepreneurship in either the formal or informal sector. The analysis demonstrates how the choice of occupation is a¤ected by entry barriers (regulation costs) and credit market imperfections. A common feature of these contributions is that the extent of underground activity is a re ‡ection of individuals'all-or-nothing choice as to whether to participate in the shadow economy. By contrast, our own line of inquiry centres on individuals'incentives to exploit uno¢ cial opportunities whilst still doing business in the formal sector.
Whilst the primary objective of our analysis is to shed further light on the determinants of underground activity, our results may be viewed within the broader context of the potential linkages between the real and …nancial sectors of an economy. Over the past decade or so, a substantial body of research has been directed towards understanding such linkages, identifying channels through which …nancial market development can shape an economy's growth prospects. Out of this research has emerged a general consensus that …nancial development is conducive to growth because of the opportunities it creates for borrowers and lenders to increase both the volume and productivity of investment. These opportunities may arise for a number of reasons, such as a greater capacity to pool risks, an improvement in the quality of information and a reduction in the costs of transactions. Based on the evidence alluded to earlier, together with the analysis that follows, this paper suggests another, quite di¤erent, channel through which …nancial development may foster economic performance -namely, the shrinkage in the size of the shadow economy.
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 contracting problem. Section 4 presents the solution to individuals'optimal tax evasion problem. Section 5 reveals the equilibrium outcomes that transpire from these solutions. Section 6 contains a few concluding remarks.

The Basic Set-up
We consider a small open economy in which there is a countably in…nite number of agents measuring a size of unit mass. Agents are identical in terms of their preferences, endowments of wealth and production opportunities, but may di¤er according to their abilities and skills. These attributes, which are bestowed randomly, determine an agent's performance in productive activity that re ‡ects a choice of project, or occupation, which gives access to a technology for generating output. For certain types of project to be undertaken, loans must be acquired from …nancial intermediaries under the terms and conditions of mutually agreeable loan contracts. Agents are obliged to pay taxes on all sources of income at a rate determined exogenously by the government. There are two main sources of imperfection in the economyan imperfection in …nancial markets due to asymmetric information between borrowers and lenders, and an imperfection in governance due to asymmetric information between tax payers and tax collectors. In more detail the model is 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 of income is an initial asset endowment, A > 0, that pays a gross rate of return of > 1 with certainty. The value of this asset is private information, as is the income, A, that it yields. 6 Other sources of income are production (or investment) projects, of which there are two types. The …rst type involves the use of some basic (traditional) technology in some routine activity that is costless and riskless: this is a safe occupation that requires zero capital outlay and that yields a …xed amount of income with certainty. The second type entails the operation of a more advanced (modern) technology in a more speculative venture that is expected to be more productive but which is also costly and subject to uncertainty: this is a risky occupation that requires K units of capital outlay and that yields a stochastic rate of return. The payo¤s from both projects depend on an agent's abilities and skills that are drawn randomly from a known probability distribution which accounts for agent heterogeneity. Speci…cally, an agent faces the prospect of being either high-skilled (type-H) with probaility p 2 (0; 1) or low-skilled (type-L) with probability 1 p. 7 The realised distribution of skills is private information to agents. Those who turn out to be high-skilled enjoy a greater expected income from each type of project than those who turn out to be low-skilled: for the safe project, the former produce s H > 0 units of output, whilst the latter produce s L 2 (0; s H ) units; for the risky project, the former earn a rate of return of > 1 with probability q H 2 (0; 1) and a rate of return of zero with probability 1 q H , whilst the latter earn the same returns with alternative probabilities q L 2 (0; q H ) and 1 q L . The greater expected income from the risky project is captured by the restriction q i K > s i (i = H; L), and the greater productivity of high-skilled agents is re ‡ected in the features s H > s L and q H > q L . To save on notation in our subsequent analysis, we normalise s L = 0 and q H = 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 of K. Such …nance is acquired from competitive …nancial intermediaries (banks) that have access to a perfectly elastic supply of loanable funds at the exogenous world (gross) interest rate, r. For reasons given below, equilibrium loan contracting involves di¤erent types of agent being o¤ered di¤erent terms and conditions on borrowing, including di¤erent rates of interest on loans. We denote by R i the gross rate of interest charged to an agent of type-i. With probability q i , the risky enterprise is successful and the agent pays back her loan to earn a …nal project income of ( R i )K. With probability 1 q i , the enterprise fails and the agent goes bankrupt, earning a …nal project 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 asset is known only to agents). As such, an agent may seek to evade part of her tax 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 public that she has A amount of asset income on which she is liable to pay tax. The agent's motivation for declaring at least some of her wealth is that she can use this as collateral for securung a loan to run the risky project. We assume that the agent can successfully conceal the undeclared fraction of her wealth by investing it in the shadow economy at a black market gross rate of return of > 1. This return is exogenous to the agent, but endogenous to the shadow economy as whole: that is, its value is determined by the aggregate level of black marketeering activity. As mentioned previously, this feature plays an important role in our analysis, being one link in the chain that connects the size of the informal sector to the state of …nancial development. We shall return to it later. For now, we merely note that an agent's …nal income from her underground investment is (1 ) A on which he does not pay any tax. 8 This completes our description of the environment. Decision making takes place as follows. Prior to realising their skills and project returns, agents choose how much of their intial wealth to declare so as to maximise their expected utility, subject to the …nancial contracts o¤ered by intermediaries.
Subsequently, the distribution of skills is revealed privately to agents who then apply for loans. Given this private information, together with the part disclosure of wealth, intermediaries set the terms and conditions of contracts in agents'best interests, whilst ensuring that appropriate constraints on behaviour are observed. Out of their realised …nal incomes, agents pay o¤ any loans and tax liabilities before consuming the remainder. The equilibrium outcomes that transpire from these decisions are determined by solving backwards through the sequence of events -a matter to which we now turn.

Financial Contracts
The precise functioning of the credit market is as follows. At the beginning of the period, lenders are approached by prospective borrowers with a request for funding to undertake risky investment projects. A contract is o¤ered, acceptance of which implies a binding agreement that commits a lender to making a loan of size of K, and a borrower to making a subsequent repayment of this loan. A lender's information at this stage includes an agent's declared value of her initial wealth, A, together with the corresponding future income, A. Importantly, it does not include separate observations of and A, meaning that the lender is unaware of the agent's true wealth status and must therefore design a contract based only on what has actually been declared. Other information available to lenders includes the ex ante distribution of borrower types, p, the income from a borrower's outside opportunity, s i , the expected income from project investment, q i K and the cost of funds, r.
In practice, banks and other …nancial institutions incur various costs in conducting their operations, such as transactions costs associated with the management of asset portfolios and the provision of liquidity services, and agency costs associated with the processing of information, the enforcement of contracts and the screening and monitoring of borrowers (e.g., Diamond 1984;Fama 1980;Gurley and Shaw 1960). For the purposes of the present analysis, we consolidate these into a single composite cost of intermediation, denoted by > 0, which serves as our indicator of …nancial development. Two empirical measures of intermediation costs are banks'overhead expenditures as a proportion of total assets and banks' net interest rate margin (de…ned as the di¤erence between the interest income and interest cost per unit of interest-bearing loans). 9 It is well-documented that both measures tend to be higher in lower states of …nancial development, as typi…ed by the predominance of banks that operate on a relativley small scale, that hold relatively small amounts of capital and that are subject to relatively tight regulations (e.g., Demigurc-Kunt et al. 2003). Accordingly, we interpret lower values of as corresponding to improvements in the e¢ ciency of the …nancial system.
The design of …nancial contracts is made complicated by the fact that intermediaries are unable to observe the true skill characteristics of agents. From the perspective of lenders, low-skilled agents are more risky than highskilled agents. We assume that the population of the former is su¢ ciently large as to allow banks to design contracts in such a way that induces separation of their clients. The possibility of doing this arises from the fact that di¤erent borrower types receive di¤erent payo¤s from their outside opportunity of running the safe project. This feature means that the indi¤erence curves of high-skilled and low-skilled agents satisfy the single crossing property which enables intermediaries to distinguish the two types by o¤ering a menu of contracts that encourages self-selection in a separating equilibrium (e.g., Bencivenga and Smith 1993;Bose and Cothren 1996). 10 As indicated above, one di¤erence between these contracts is the rate of interest on loans. Another di¤erence is the probability that a loan will actually be granted as banks may be induced to ration credit by turning down some loan applications. We denote by i 2 (0; 1) the probability that an agent of type-i will be approved credit, 1 i being the probability that she will be denied such funds. In the event of the former, banks incur the cost of intermediation, , and earn an income that depends on whether or not the risky project succeeds: if so (i.e., with probability q i ), a bank is paid back in full, receiving R i K in loan repayment; if not (i.e., with probability 1 q i ), the bank recovers part of its loss by appropriating a borrower's collateral, A. It follows that an intermediary's expected income from lending to an agent of type-i is We assume that intermediaries operate in a competitive environment, and that the terms and conditions of available loan contracts are public knowledge. As such, an intermediary is approached by an agent only if the contract that it o¤ers is not dominated by the contracts o¤ered by its competitors. In equilibrium the pro…ts of intermediaries are driven to zero, a condition that we state as where q H = 1. From above, the left-hand-side of this expression is an intermediary's expected income from lending to an agent of type-i. The left-handside is the intermediary's total cost of lending, which comprises the cost of borrowing funds, rK, plus the cost of intermediation, .
A contract for an agent of type-i is de…ned by C i = fR i ; i g. The problem for intermediaries is to choose each R i and each i so as to maximise agents'expected utilities, subject to the zero pro…t condition in (1) and appropriate incentive compatibility constraints. The solution to this problem is summarised as follows.
Proposition 1 Assume that ( R H )K > s H and A < rK + . Then the equilibrium separating contracts are characterised by (2) Proof. The expression for each R i is given immediately by the zero pro…t condition in (1) (where q H = 1). To determine the associated i , proceed as follow. An agent of type-i derives an expected utility of (1 t) from the contract o¤er of C i = fR i ; i g (where q H = 1 and s L = 0). The …rst term in [ ] gives the net payo¤ from the risky project, ( R i )K, when a loan is granted (which occurs with probability i ) and when the project is successful (which occurs with probability q i ). The second term in [ ] gives the payo¤ from the safe project, s i , when a loan is not granted (which occurs with probability 1 i ). In each case the agent pays taxes, t, on her income. Let C F i denote the …rst-best contract that an agent of type-i would receive under full information. For each of these contracts, i = 1 and R i is determined as above. Given that . Suppose that lenders were to o¤er C F i in the presence of asymmetric information (as exists in the model). Clearly, there would be no incentive for high-skilled agents to reject C F H in favour of C F L by pretending to be low-skilled agents. Thus, in order to induce self-selection, lenders do not need to distort the contract for the low-skilled types, but are able to o¤er this group its …rst-best choices of R L and L (as summarised in (3)). The contract for the high-skilled group is then determined by solving the following problem: The constraint in (5) is the incentive compatibility condition for low-skilled agents, which requires that the expected utility from accepting C F L is no less than the expected utility that could be obtained from C H by pretending to be high-skilled (i.e., V L (C F L ) V L (C H )). Given that ( R H )K > s H , it is straightforward see that this constraint is binding: since V H (C H ) is strictly increasing in H , intermediaries will set this probability at the highest possible value, which is the value that makes (5) hold with equality, given the setting of each R i . High-skilled agents are therefore o¤ered a combination of R H and H that departs from their …rst-best choice (as revealed in (2)).
In summary, the contractual interest rate is determined directly by lenders' zero pro…t condition, which re ‡ects the fact that any contract yielding positive pro…ts cannot survive in a competitive equilibrium. The restriction A < rK + , which implies that R H < R L , is necessary to make our analysis non-trivial (since in the absence of this restriction intermediaries would face no risk in lending). As it is, the restriction is necessarily satis…ed by virtue of a similar condition that we impose later (i.e., A < rK + ). With respect to the determination of i , intermediaries induce separation of lowskilled and high-skilled agents by o¤ering the former their …rst-best contract (whereby each one of them is granted a loan with certainty) and presenting the latter with a distorted contract (whereby a fraction of them are credit rationed). 11 That separation is achieved at the expense of high-quality clients follows simply from the incentive compatibility condition and is a standard result 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 is greater the lower is the cost of …nancial intermediation and the higher is the agent's declared value of wealth Formally, @ H @ < 0 and @ H @ > 0. The reason is that, as the cost of intermediation declines, or as the declared value of wealth increases, the interest rate charged to low-skilled agents falls by more than the interest rate charged to high-skilled agents; this makes the contract o¤ered to the latter less attractive to the former and thereby provides an opportunity for intermediaries to reduce the incidence of credit rationing whilst maintaining incentive compatibility. 12

Tax Evasion
The foregoing analysis reveals how the equilibrium arrangements for borrowing and lending are in ‡uenced by the declared asset position of agents. The greater is the initial wealth that agents reveal, the greater is the collateral that can be used as security against a loan and the better are the terms and conditions of loan contracts. At the same time, revealing more wealth means that agents expose themselves to a higher burden of taxation. An agent's disclosure (or concealment) of her wealth status is therefore a decision that involves optimising a trade-o¤. The agent solves this problem with the knowledge of the contracts on o¤er, but without the knowledge of which contract she will actually be presented with as her skill type is not realised until 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 from undeclared wealth. With probability i , an agent of type-i acquires a loan to run the risky project. The project succeeds with probability q i and fails with probability 1 q i . In the event of the former, the agent earns a net disposable income of (1 t)( R i )K from the project, plus a net disposable 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, the agent earns only the last of these incomes, (1 ) A. With probability 1 i , an agent of type-i is denied a loan. In this case the agent receives an after-tax income of (1 t)s i from running the safe project, plus an after-tax income of (1 t) A from her reported wealth, plus an income of (1 ) A from her unreported wealth. Collecting terms together and setting L = 1 (along with s L = 0 and q H = 1), we may write the expected utility of a high-skilled and a low-skilled agent as An agent's choice of how much of her initial wealth to declare is a choice of the value of . As indicated above, this decision is made prior to the agent realising 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 (lowskilled) is p (1 p), is chosen so as to maximise U = pE(U H )+(1 p)E(U L ), given that R i and i are determined according to (2) and (3).
The behaviour of an agent is straightforward to deduce and we summarise it as follows.
As before, the above results have a straightforward intuition. By declaring more 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…t of putting up more collateral, which is the bene…t from the reduction in risk faced by lenders and the consequent improvement in the terms and conditions of the loan contract. The latter is given by the term G( ) and corresponds to the marginal cost of investing more wealth in the formal sector, which is the cost of both a higher burden of taxation and the foregone interest income from the informal sector. Depending on which is greater, the agent will set at either its maximum or minimum value, implying either full or zero disclosure of her asset endowment and therefore either full or zero compliance with her tax obligations on asset income. The restriction A < rK + is relevant for the case in which F ( ) > G( ), where it is observed that an agent's expected utility is linearly increasing (decreasing) in up to (beyond) a critical level, max = rK+ A . The restriction implies that max > 1 which is not a feasible choice since the agent would be claiming to have more wealth than A -a claim that she would need to substantiate (but never could) when putting up her collateral.
In presenting the above results we have singled out two key parameters that may in ‡uence an agent's behaviour -namely, the cost of …nancial intermediation, , and the return on underground investment, . These are seen to impact on the expected gains and losses from the disclosure of wealth. In particular, we make the following observation.

Corollary 2
The marginal bene…t (cost) to an agent of disclosing more wealth is higher the lower (higher) is the cost of …nancial intermediation (return on underground investment).
Formally, F 0 ( ) < 0 and G 0 ( ) > 0. The e¤ect of is explained by the fact that a lower cost of intermediation makes the terms and conditions of loan contracts more attractive to agents. As such, agents have a stronger incentive to put up more collateral (i.e., to declare more wealth) in order to improve their chances of acquiring a loan. The e¤ect of is simply that a higher return from investing in the informal sector means a higher opportunity cost of investing in the formal sector. The incenive to do the former (i.e., to conceal more wealth) is therefore greater.

Aggregate Outcomes
The results obtained above establish conditions under which an individual agent will seek to evade some of her tax obligations. These conditions depend on economy-wide factors that are relevant to all agents. One of thesethe cost of intermediation -provides a measure of …nancial development. For the purposes of the present paper, we treat this as exogenous since our principal focus is on the causal role played by …nancial markets in governing events elsewhere in the economy. By contrast, the other economy-wide factor -the return on underground investment -is an outcome that we treat as being determined endogenously on the basis of the aggregate behaviour of individuals. The e¤ect of this is to introduce important interactions between agents, as 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 into that sector. One justi…cation for this is simply the existence of diminishing returns to informal productive activity: as more resources are devoted to such activity, the marginal gains from it decline. An alternative, more elaborate, motivation is as follows. Suppose that agents'subterfuge in concealing their income requires assistance from some other individuals who specialise in this type of practice. These individuals are experts at directing funds into areas where they are di¢ cult to trace by the government, such as the underground economy and overseas bank accounts. In return for this service an agent must pay a commission which increases with the total amount of funds being laundered because of the greater di¢ culty and greater costs of doing this. As before, the agent's net return on her own hidden income is lower the larger is the total amount of such income. Whichever way one chooses to motivate the assumption, the key implication is that there is an interdependence between individual and aggregate behaviour as any agent who participates in underground activity contributes to a small reduction in the rewards from this activity, an e¤ect that is translated into a large negative externality for all such participants, whose incentives to actually behave in this way are duly a¤ected. 13 We capture the above ideas as follows. Denote by 2 [0; 1] the fraction of agents who set = 0 so that the total volume of undeclared wealth invested in the shadow economy is A. Each agent then receives a black market return which is a decreasing function of these total hidden funds: that is, Given this, together with our previous results, we now proceed to determine the 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 discloses her initial wealth. Evidently, 0 > 1 . The corresponding marginal costs of disclosure are G( 0 ) and G( 1 ), where G( 0 ) > G( 1 ). Since the marginal bene…t of disclosure, F ( ), is a monotonically decreasing function, we may deduce 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 represent boundaries between regions where the incentive to conceal wealth and evade taxes is either present or absent. We are now in a position to establish our main result which we illustrate in Figure 2.
Proof. Suppose, …rst, that > 1 , in which case F ( ) < G( 1 ) < G( 0 ). Consider a pro…le of behaviour where all agents choose = 0 so that = 1 (corresponding to = 1). Since F ( ) < G( 1 ), no agent has an incentive to deviate from this choice. To establish that this is a unique equilibrium, consider the opposite pro…le where all agents choose = 1 so that = 0 (corresponding to = 0). Since F ( ) < G( 0 ), it is optimal for each agent to deviate from this choice, implying that = 0 cannot exist as an equilibrium. Next, suppose that < 0 , in which case F ( ) > G( 0 ) > G( 1 ). By a similar argument, there is a unique equilibrium in which all agents set = 1: no agent has an incentive to deviate from this (since F ( ) > G( 0 )), whilst each agent has an incentive to deviate from = 0 if all other agents are choosing = 0 (since F ( ) > G( 1 )). Finally, suppose that 2 ( 0 ; 1 ), in which case G( 1 ) < F ( ) < G( 0 ). If all agents were to choose = 0, then it would be optimal for each one to deviate and set = 1 (since G( 1 ) < F ( )). Likewise, if all agents were to choose = 1, then it would be optimal for each one to deviate and set = 0 (since F ( ) < G( 0 )). Thus, neither = 1 nor = 0 can exist as an equilibrium. Consider, however, a 2 (0; 1) such that . Then there exists a unique value of this which supports an equilibrium with F Based on the above, we are led to distinguish between three types of regime for an economy: the …rst -a low …nancial development regime -is one in which the incidence of tax evasion is always at its maximum ( = 1) for any given value of above the higher threshold value, 1 ; the second -a high …nancial development regime -is one in which the incidence of tax evasion is always at its minimum ( = 0) for any given value of below the lower threshold value, 0 . And the third -an intermediate …nancial development regime -is one in which the incidence of tax evasion is somewhere in between its maximum and minimum ( 2 (0; 1)), and decreases monotonically as decreases within the interval of the thresholds from 1 to 0 . The intuition is as follows.
Each agent chooses to disclose or conceal her initial wealth according to whether F ( ) > G( ) or F ( ) < G( ). Whichever of these conditions holds depends on the level of …nancial development and the return on undergound investment: the higher is the former (i.e., the smaller is ) the better are the terms and conditions of loan contracts (an inducement to disclosure), whilst the higher is the latter (i.e., the greater is ) the more attractive is participation in the informal sector (an inducement to concealment). For any > 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 her wealth, even if she is faced with the lowest possible return on underground investment as a result of all other agents concealing their wealth. As such, each and every agent chooses to evade taxes in a unique equilibrium from which there is no incentive to deviate. Conversely, for any < 0 , we have F ( ) > G( 0 ) > G( 1 ). In this instance the level of …nancial development is so high that an agent is always better o¤ by declaring her wealth, even if she could earn the the highest possible return in the informal sector due to all other agents declaring their wealth. Consequently, the only equilibrium from which defection will not occur is one in which each and every agent chooses not to evade taxes. Contrasting these scenarios is the case of 2 ( 0 ; 1 ), for which we have G( 1 ) < F ( ) < G( 0 ). In this intermediate range of …nancial development the bene…ts from declaring and concealing wealth exactly o¤set each other in an equilibrium where some agents evade taxes and others do not. The fraction of tax evaders is the value of that satis…es F ( ) = G( ), where = b ( ). Since F 0 ( ) < 0, G 0 ( ) > 0 and b 0 ( ) < 0, a lower value of requires a lower value of so as to preserve the marginal agent's indi¤erence between compliance and non-compliance in tax regulations. 14 It is worth mentioning that similar results could be obtained using an alternative version of the model based on agent heterogeneity, rather than diminishing returns to black market investment. Suppose, for example, that agents are di¤erentiated according to di¤erences in their costs of concealing wealth, which may be re ‡ected in di¤erent net returns from concealment (i.e., di¤erences in ), or di¤erent disutilities from some personal guilt, moral shame and social stigma attached to such behaviour. This heterogeneity may be captured in a distribution of G( ), the marginal cost of wealth disclosure. For any given , one could then identify a b G( ) which satisi…es F ( ) = b G( ) and which de…nes the critical agent for whom it just pays to set = 1. All other agents with G( ) < b G( ) would also be setting = 1, whilst all others with G( ) > b G( ) would be setting = 0. As decreases (causing F ( ) to increase), b G( ) would increase, meaning that = 1 would be chosen by an increasing proportion of the population.
In summary, our analysis is able to explain the observed negative relationship between the level of …nancial development and the incidence of tax evasion. When the former is su¢ ciently low or su¢ ciently high, the latter is at its maximum or at its minimum; when the former is somewhere in between, the latter is somewhere in between and decreases monotonically as the e¢ ciency of …nancial markets improves. To the extent that …nancial development occurs endogenously as the economy, in general, develops, tax evasion may be a temporary phenomenon that a government might be willing to live with, especially if the costs of mitigating it are high. On the other hand, an economy that staggers in its process of development may …nd itself permanently deprived of tax revenues that could otherwise be put to good causes. According to our analysis, …nancial development serves to combat the incentives to engage in tax evasion only above some threshold level: if this threshold is not reached, then the underground economy will continue to thrive against a backdrop of …nancial repression.

Conclusions
The existence of a shadow economy has potentially serious implications for economic performance and public policy. Activities conducted in this sector are neither protected nor regulated in the same way that applies to activities in the formal sector. Growth prospects can be compromised by encumbrances to doing business due to the lack of social infrastructure. Public …nances can su¤er as the tax base shrinks, thus weakening the government's capacity to generate revenue. And policy makers'assessments and recommendations can be 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 nontrivial concern and an important task is to understand what factors might in ‡uence it.
Informality in an economy is a re ‡ection of individuals'incentives to conceal their activities or circumstances. This may take various forms, ranging from full participation in the underground sector (e.g., working exclusively in the shadow labour market) to more subtle clandestine practices (e.g., misreporting income and hiding invesments). In this paper we have focused on the latter by considering a situation in which individuals may choose to conceal their true wealth status for the purpose of tax evasion. Our central concern has been to study how the temptation to engage in such behaviour might be in ‡uenced by conditions in …nancial markets from which individuals acquire loans to undertake business ventures. The crux of our analysis is that, in the presence of …nancial market imperfections (i.e., asymmetric information), the amount of wealth disclosed by an individual a¤ects the terms and conditions 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 …nancial markets, as represented by a lower cost of …nancial intermediation. In spite of its simplicity, the model produces a rich variety of outcomes as a result of the mutual interaction between individual decision making and the aggregate economic environment. In particular, we are led to distinguish between three types of …nancial development regime with the implication that the fraction of tax-evading agents declines as the economy moves from a low, through an intermediate, to a high development regime. This negative relationship between the incidence of tax evasion (or size of the underground sector) and the level of …nancial development accords well with empirical evidence. Figure 1 is based on a regression using annual data for 114 countries (including both developed and developing countries) over the period 1999-2005. The regression equation is speci…ed as SE it = 0 + 1 RF it + 2 RQ it + 3 T B it + 4 P C it + 5 RW it + " it ; where the notation and data are summarised as follows: SE -shadow economy, measured by the average size of the underground economy as a percentage of GDP (source: Schneider 2007); RF -regulatory freedom, measured by the average scores on the regulatory freedom index (source: Heritage Foundation Freedom in the World Indicators); RQ -regulatory quality, measured by the average scores on the regulatory quality index (source: World Bank Governance Indicators); T B -tax burden, measured by the average scores on the …scal freedom index (source: Heritage Foundation Freedom in the World Indicators); P C -public sector corruption, measured by the average scores on the corruption perception index (source: Transparency International); RW -rule of law, measured by the average scores on the rule of law index (source: World Bank Governance Indicator).
i -country index.
The residuals from the above regression are plotted against the following indicators of …nancial development: Domestic credit to the private sector, measured by the average overall amount of domestic credit provided to private borrowers as a percentage of GDP (source: World Bank Development Indicators).
Domestic credit provided by the banking sector, measured by the average overall amount of domestic credit provided by private deposit institutions as a percentage of GDP (source: World Bank Development Indicators).
Liquid liabilities (M3), measured by the average amount of outstanding liquid liabilities of the banking system as a percentage of GDP (source: World Bank Development Indicators).