I. INTRODUCTION

Corruption is generally regarded to be a major impediment to economic development. However, economists have not been able to establish a robust negative correlation between various measures of corruption and economic growth in cross-country data (Svensson 2005). Svensson suggests that econometric problems and data limitations may make it impossible to identify the causal role of corruption in country-level studies.

This study develops a computational approach to identifying and quantifying the effects of corruption on growth. Computational general equilibrium models have long been used as a quantitative tool in many areas of economics (see the examples listed in the study by Kydland and Prescott 1996). We view this approach as complementary to other methods used to establish causality including econometrics with microeconomic and macroeconomic data, case studies, and historical analyses. Establishing causal mechanisms in economics is challenging and all types of evidence are needed in this effort.

Our focus is on the interaction among corruption, tax evasion, and a country's fiscal policy--including the possibility that corruption may have negative effects on growth that work through the determination of tax rates and public investment. We develop a dynamic quantitative theory where corruption, evasion, and fiscal policy are endogenously determined and where the macroeconomic characteristics of the economy are realistic. The goal of this study is to quantify the joint effects of corruption and evasion on fiscal policy and growth and to examine the consequences of various institutional changes designed to eliminate corruption and evasion.

There are three main components to the theory. First, there is an interaction between corruption and evasion with causation running in both directions. We introduce a "culture of corruption" effect where the average level of government corruption affects an individual's willingness to engage in illegal behavior--in particular a household's willingness to evade taxes and an individual government official's willingness to be corrupt. Slemrod (2003) emphasizes, and provides evidence for, the idea that tax evasion is affected by households' distaste for illegal activity and by their perceptions of government performance. Tax evasion, in turn, influences corruption by limiting the government's ability to raise funds that may be diverted for private use.

A culture of corruption effect is consistent with the data plotted in Figures 1 and 2. The figures are based on data from the World Values Survey (1980-2007). The survey asks households questions about their views on government performance and tax evasion. The public perception of government performance and the presence of corruption is plotted on the horizontal axis and public willingness to engage in evasion is plotted on the vertical axis. In both cases, there is a positive and statistically significant correlation between the public's concerns about their government and the public's willingness to evade taxes. (1) The correlations exhibited in Figures 1 and 2 are consistent with the studies by Johnson et al. (1999, figures 6-9), Uslander (2005, table 5.3), Aim and Torgler (2006), and Buehn and Schneider (2009, figure 2) who find a positive correlation between actual evasion and more objective measures of corruption that come from outside the country.

Second, we follow Tanzi and Davoodi (1997) and focus on the corruption associated with implementing public investment projects. There is evidence that large fractions of the budgets allocated for public school investments (Reinikka and Svensson 2004) and physical capital infrastructure (Olken 2007; Pritchett 1996, 2000; Tanzi and Davoodi 1997) are diverted to public officials for their private use. In the developing countries of Africa, corruption is negatively correlated with private investment but positively correlated with (measured) public investment (Baliamoune-Lutz and Ndikumana 2008). Much of the previous work on corruption focuses primarily on bribes that entrepreneurs must pay bureaucrats to avoid regulation. The corruption associated with public investment projects would appear to be at least as important for economic growth. (2)

Third, we examine how the presence of corruption and evasion affects the determination of a country's fiscal policy. In particular, we study how tax rates and public investment budgets are set when the government takes into account how its choices affect both corruption and tax evasion.

We quantify the theory by calibrating the model to match estimates of tax evasion in developing countries. We then test the model by checking its predictions across other dimensions: net tax rates, the corruption associated with public investment, and the correlation between corruption and tax revenue. We find that the model's predictions are quite reasonable, but only if the culture-of-corruption effect is included. Without the cultural effect of corruption, the predicted value for net tax rates is too high, the predicted value for corruption is too low, and the correlation between corruption and tax revenue is counterfactually positive.

For an intermediate tax evasion tax, we find that the presence of corruption and evasion increases the economy's tax rate 25%-85% and decreases steady-state worker productivity 10%-33% when compared to a baseline model without corruption and evasion. While evasion helps to limit taxation, corruption creates an incentive to increase tax revenues that can be diverted for private use. Unless aversion to illegal activity is comparatively low, and the response of evasion to the tax rate is comparatively high, the presence of corruption will dominate the restraint that evasion places on taxation and tax rates will be higher than in the baseline model. In addition to the effect on tax rates, corruption reduces the fraction of capital budgets that are actually invested. In our model, only 40%-60% of the capital budget is actually invested.

With much higher tax rates, and much lower public investment, one might expect a larger decline in output than 10%-33%. However, tax evasion is also high, as 33% of income goes untaxed in developing countries (a fact replicated in the model). The untaxed income increases the funds available for private investment, helping to mediate the negative effects of higher tax rates on private investment. In addition, if tax rates rise enough, total tax revenue need not fall dramatically and could even rise. The higher is tax revenue the greater are budgets for public investment. Larger investment budgets help keep public investment spending from falling dramatically as corruption steals away a portion of the budget. These offsets keep the negative effects on growth from being large and explain why it has been difficult to establish a significant negative correlation between corruption and growth in the cross-country data.

We end our analysis by considering how changes in certain exogenous features of the government affect equilibrium outcomes. We find that increasing the pay of government officials lowers both corruption and evasion with little associated rise in the economy's tax rate. The increased tax costs of raising the public official's wages are approximately offset by the reduced corruption and evasion that serves to raise tax revenue and public investment for a given tax rate. The rise in public capital accumulation leads to a rise in steady-state worker productivity. In fact, when public wages are sufficiently high, corruption and evasion can be completely eliminated and both private and public households are better off.

We also find that making tax evasion more difficult, without first addressing corruption, is a bad idea. Lower evasion causes tax rates and tax revenue to increase, creating greater opportunities to divert public funds resulting in more corruption. The reduction in private disposable income lowers private capital accumulation and the increase in corruption lowers public investment, causing worker productivity and the welfare of private households to fall. At the same time, cracking down on tax evasion may be welfare improving when checks on corruption are sufficiently strong. If diversion of public funds is difficult, then lower evasion and higher tax revenue may raise public investment significantly.

II. RELATED LITERATURE

This study relates corruption and evasion to fiscal policy and worker productivity. Thus, this work has connections to the corruption-evasion literature as well as the literatures explaining the size of government and the determinants of economic growth.

A. Corruption, Evasion, and Culture

The literature on corruption has primarily focused on bribes to public officials made by entrepreneurs in order to avoid taxation and regulation and to win public contracts (Becker and Stigler 1974; Besley and McLaren 1993; Henricks et al. 1999; Rose Ackerman 1975; Sanyal et al. 2000; Shleifer and Visny 1993). This literature has also been limited to a detailed microeconomic analysis of corruption.

As suggested by Tanzi and Davoodi (1997), and more recently and generally by Kaufmann (2010), there may be connections between corrupt activity by the government and various aspects of their fiscal policy, not working through bribes and "petty" corruption of bureaucrats, but through the formation of policies themselves or "grand" corruption. We focus on grand corruption in the present study within a dynamic general equilibrium model that can be used to examine the macroeconomic consequences of corruption.

The corruption literature has largely been developed independently from the literature on tax evasion. Exceptions include papers by Henricks et al. (1999), Sanyal et al. (2000), Choi and Thum (2005), and Dreher et al. (2005). Of particular interest are the papers by Choi and Thum (2005) and Dreher et al. (2005) where they consider how the decisions of entrepreneurs to produce in the underground economy limits the bribes charged by government regulators.

There is growing evidence that culture alters individual preferences and economic behavior (for surveys, see Guiso et al. 2006 and Fernandez 2010). We use a cultural mechanism to connect corruption and tax evasion. It is well known that the standard neoclassical approach to explaining tax evasion is incomplete: the predicted levels of tax evasion are too high and the responsiveness of tax evasion to the expected penalty is too weak (Andreoni et al. 1998; Erard and Feinstein 1994; Fischer et al. 1992; King and Sheffrin 2002; Orviska and Hudson 2002; Schneider and Klinglmair 2004; Slemrod 2003). The same authors reaching this conclusion stress that personal guilt, associated with the violation of social norms, plays a significant role in limiting tax evasion. Furthermore, the strength of the social norm in creating the personal guilt depends on perceptions of the government's performance, thereby explaining the strong empirical connection between mistrust of the government and tax evasion demonstrated in the introduction. Uslander (2005, 87) summarizes the causal connection that we attempt to model, "Countries with high levels of corruption also have higher levels of theft and tax evasion. People see corrupt regimes and believe it is acceptable to steal and especially to withhold their taxes." While this idea has intuitive appeal and is consistent with the strong correlation between corruption and tax evasion, to our knowledge, a cultural effect of corruption by public officials on the willingness of private households to evade taxation has never been formally modeled. (3)

The cultural effects of corruption are not limited to tax evasion alone. There is also evidence that the average level of government corruption in an economy affects the willingness of individual government officials to engage in corruption. There is experimental evidence that guilt affects corrupt behavior and that guilt may be influenced by cultural factors (Barr and Serra 2010; Robert and Arnad 2013; Schulze and Frank 2003). Perhaps more convincing is the now famous natural experiment identified by Fisman and Miguel (2007, 2008; chapter 4). They find that the corrupt behavior of government officials visiting the United States is highly correlated with the level of corruption in their home country. Their conclusion is that corrupt behavior is deeply engrained in culture and the standard prescriptions of economic reward and punishment may not be enough to root it out. For these reasons, we also consider a culture of corruption effect that extends to government officials themselves.

Our model contains a mechanism by which tax evasion discourages corruption. Tax evasion limits the size of the budget that is managed by public officials. In our model, the fraction of the budget that is diverted for private use is increasing in the size of the budget--stealing a given share of the budget delivers a larger payoff, the larger is the budget. Thus, tax evasion creates a check on corruption similar to that found in the studies by Choi and Thum (2005) and Dreher et al. (2005).

B. Economic Growth

Corruption is commonly viewed as placing a drag on growth. Some initial evidence that tentatively supports this notion is provided by Mauro's (1995) cross-country study. Mauro's finding, while not conclusive, has served to motivate attempts to explain the negative correlation by introducing corruption into dynamic general equilibrium models (Barreto 2000; Brevik and Gartner 2008; Ehrlich and Lui 1999; James Ellis and Fender 2006; Mauro 2002) as we do in this paper. (4) Our approach is different from this literature because we include both private and public capital and both tax evasion and corruption. While tax evasion and corruption will reduce public investment, they may increase funds for private use and thereby raise private investment. To accurately quantify the effects of corruption and evasion on economic growth one needs to account for this possible substitution of private for public capital. In fact, we find only modest negative effects of corruption precisely because when corruption is high, so is tax evasion.

The emphasis on quantifying the effects of corruption and evasion is a second way that we differ from the theoretical literature. The goal in the literature is to qualitatively explain the negative correlation between corruption and growth. We attempt to identify the quantitative effect of corruption on growth by first calibrating our theory to match the estimated level of evasion in developing economies. We then generate predictions for net tax rates, corruption, and the correlation between corruption and tax revenue that can be compared against related stylized facts in order to gain confidence in the model's empirical relevance. Given that econometric and data problems may be particularly severe in the case of corruption, this alternative, less data intensive, quantitative approach appears justified.

Finally, the other papers in the literature assume that the government is entirely selfish. We assume that government officials have the same basic preferences as all other households. We include a case where households are motivated by both selfish and altruistic concerns.

This difference in modeling the government has important consequences for how tax policy is determined. For example, in the studies by James Ellis and Fender (2006) and Brevik and Gartner (2008), the selfish government is prevented from seizing the entire tax base, and giving up a chance for re-election, by a public that is willing tolerate a sufficiently high tax rate. The presence of a high tax rate encourages the government to curb its bad behavior so that it can run for re-election. If an exogenous event lowers the tax base, such as an exogenous change that increases tax evasion, the tax rate must rise in political equilibrium to compensate the selfish government for its loss in tax revenue. In our model, we find the opposite effect from a rise in tax evasion. Greater tax evasion reduces the benefit of high tax rates and corrupt behavior, causing reductions in both.

C. Size and Efficiency of Government

There is a literature analyzing how different political institutions (e.g., majority voting, representative democracies, strategic competition between parties, and centralized versus decentralized public good provision) affect the size of government and the impact of government policy on economic efficiency (see Battaglini and Coate 2007 for a recent contribution and literature review). This literature has not explored how corruption, and the related political institutions that foster or discourage it, affects fiscal policy and the size of government. A more recent work by Brevik and Gartner (2008) analyzes how tax evasion may check the behavior of an entirely selfish government. As mentioned above, their theory predicts that higher tax evasion leads to higher tax rates, although lower tax revenue.

We find that the joint presence of both corruption and evasion causes a rise in tax rates, but with a decline in tax revenue and the size of government. This result is consistent with the empirical literature that finds a robust inverse correlation between corruption and tax revenue (Johnson et al. 1999; Kaufmann 2010; Tanzi and Davoodi 1997). However, unlike Brevik and Gartner (2008), we find that institutional changes designed to reduce tax evasion alone will result in higher tax rates. In our model, tax evasion serves to reduce tax rates, corruption, and the size of government.

III. A BENCHMARK ECONOMY WITHOUT CORRUPTION-EVASION

For comparative purposes, this section develops a baseline model without corruption and evasion. The model is a standard overlapping-generations model of private capital accumulation that is extended to include a government sector that raises taxes to finance the salaries of public officials and public investment projects.

A. Private Households

There are N young households in each period. The households are standard two-period life-cycle savers. They work to earn wages ([w.sub.t]), consume ([c.sub.1t]), and save ([s.sub.t]) in the first period to finance second period retirementconsumption ([c.sub.2t+1]).

Household preferences are represented by the following utility function

(1) ln [c.sub.1t] + [beta]ln [c.sub.2t+1],

where [beta] is a parameter that gauges the relative weight placed on private future consumption. The household's lifetime budget constraint is given by

(2) [c.sub.1t] + [c.sub.2t+1]/(1 + [r.sub.t+1]) = (1 - [[tau].sub.t]) [w.sub.t],

where r is the rate of return to households saving, w is the wage rate, and [tau] is the tax rate on wage income. (5)

Maximizing Equation (1) subject to Equation (2) yields

(3a) [c.sub.1t] = (1 - [[tau].sub.t]) [w.sub.t]/(1 + [beta])

(3b) [c.sub.2t+1] = [beta](1 + [r.sub.t+1])[c.sub.1t].

The consumption equations imply that household saving can be written as

(3c) [s.sub.t] = [beta](1 - [tau].sub.t]) [w.sub.t]/(1 + [beta]).

B. Public Officials

There is a fixed number of public officials that set and carry out fiscal policy ([epsilon]N). The public officials are exogenously selected from the population of private sector households. The public officials have preferences that are identical to the private households, so the process through which they are selected is not important. The wage paid to public officials is proportional to the private sector wage, that is, the public official's wage is [[eta]w.sub.t] where [eta] is an exogenous parameter. Public officials pay taxes on their wages at the same rate as private sector households and work only when young. In the benchmark economy, the institutional parameters that characterize the government are then (1) the relative size of public employment ([epsilon]) and (2) the relative pay of public officials (q). (6)

The private choices of the public officials are of the same form as for private households

(4a) [c.sup.g.sub.1t] = (1 - [[tau].sub.t])[[eta]w.sub.t]/(1 + [beta])

(4b) [c.sup.g.sub.2t+1] = [beta](1 + [r.sub.t+1]) [c.sup.g.sub.1t],

(4c) [s.sup.g.sub.t] = [beta](1 - [[tau].sub.t]) [[eta]w.sub.t]/(1 + [beta]).

Collectively the public officials will also choose the current tax rate and next period's public capital ([G.sub.t+1]) to maximize ln [c.sup.g.sub.1t]; + [beta] [c.sup.g.sub.2t+1] subject to the government budget constraint,

[[tau.sub.t][w.sub.t](1 + [epsilon][eta])N = [eta][w.sub.t][epsilon]N + [G.sub.t+1],

where we assume, as in the case of private capital, that public capital depreciates fully after one period. Solving the government budget constraint for the tax rate gives us

(5) [[tau].sub.t] = [eta][epsilon]/(1 + [eta][epsilon]) + ([G.sub.t+1]/[w.sub.t]N(1 + [eta][epsilon])).

Note that because we do not include government transfers in the model, [tau] should be interpreted as the net tax rate--net of government transfers to private households.

C. Firms

Production takes place within standard neoclassical firms that combine physical capital and human capital to produce output from a Cobb-Douglas technology

(6) [Y.sub.t] = [K.sup.[alpha].sub.t] [([D.sub.t]N).sup.1-[alpha]].

The productivity index (D) is a function of disembodied technology (A) and public capital per adult worker (G/((1 + [epsilon])N)) and is given by

(7) [D.sub.t] = [A.sup.1-[mu].sub.t] [([G.sub.t]/((1 + [epsilon])N)).sup.[mu]],

where 0 < [mu] < 1 is a constant parameter. We assume that A progresses at the exogenous rate d. This specification captures the idea that public infrastructure raises the productivity of the private sector.

Firms operate in perfectly competitive factor and output markets. This implies the profit-maximizing factor mix must satisfy

(8a) [r.sub.t] + [delta] = [[alpha]g.sup.[mu](1 - [alpha]).sub.t][k.sup.[alpha]- 1.sub.t]

(8b) [w.sub.t] = (1 - [alpha]) [A.sub.t] [g.sup.[mu](1 - [alpha]).sub.t][k.sup.[alpha].sub.t],

where [delta] is the rate of depreciation on physical capital, which we take to be one for simplicity, g [equivalent to] G/A(1 + [epsilon]) N and k [equivalent to] K/AN.

D. Capital Market Equilibrium and Fiscal Policy

The capital stock rented to firms in period t + 1 must be accumulated as retirement savings by the private households and government officials,

[K.sub.t+1] = [Ns.sub.t] + [epsilon]N[s.sup.g.sub.t].

Using Equations (3c), (4c), and (8) gives us the transition equation for private capital intensity,

(9) [k.sub.t+1] = [beta](1 + [eta][epsilon])(1 - [[tau].sub.t])(1 - [alpha]) [k.sup.[alpha].sub.t] [g.sup.[mu](1 - [alpha]).sub.t]

E. Fiscal Policy

Public officials have identical preferences and opportunities, resulting in a common preferred tax rate. In voting on fiscal policy, whether it is the entire group of officials that vote or some subset, public officials will be in complete agreement. Finding the preferred tax rate of an individual official is then sufficient to determine the country's fiscal policy.

Using Equation (1) applied to public officials, along with Equations (8) and (9), we can write the objective function of a public official in terms of fiscal variables. Including only those components of the public official's preferences that are affected by their fiscal policy choices in period t gives us

(10) (1 + [beta])1n (1 - [[tau].sub.t]) + [beta][mu](1 - [alpha])1n [g.sub.t+1] + [beta]([alpha] - 1) 1n (1 - [[tau].sub.t]).

The first expression captures the negative effect of taxation on the lifetime wages and consumption of officials. The second expression represents a positive effect of public capital. Public capital raises the marginal product of private capital causing an increase in the return on private saving that raises second period consumption for public officials. The third expression gives a negative effect of private capital accumulation on the welfare of public officials. Private capital accumulation lowers the marginal product of private capital, the rate of return on savings, and second period retirement consumption.

Maximizing Equation (10) subject to government budget constraint given by Equation (5) yields the optimal fiscal policy (11a)

[g.sub.t+1] = B(1 - [alpha])[k.sup.[alpha].sub.t][g.sup.[mu](1 - [alpha]).sub.t]/(1 + [epsilon])(1 + d)

(11b) [[tau].sub.t] = ([eta][epsilon] + B)/(1 + [eta][epsilon]),

where 0 < B [[equivalent to] [beta][mu](1 - [alpha])/(1 + [beta][mu](1 - [alpha]) + [beta][alpha]) < 1.

The optimal fraction of pretax wages invested in public capital (B) is a constant that depends positively on the productivity of public capital ([mu]) and the value placed on the future state of the economy ([beta]). The optimal tax rate varies positively with the wage bill in the public sector ([eta][epsilon]) and the rate of investment in public capital (B).

F. Calibrating the Benchmark Economy

We now calibrate the steady state of the model so that we can make quantitative comparisons between the corruption and no-corruption economies.

To calibrate the benchmark no-corruption model, we start with conventional estimates for the output elasticities of private and public capital: [alpha] = 0.33, [mu] = 0.30 (see, e.g., Mourmouras and Rangazas 2009 for a survey of the evidence on these parameters).

Assuming that each period in the model lasts 20 years and the annualized growth in labor productivity due to exogenous technological change is 2%, we have d = [(1.02).sup.20] - 1 = 0.4859. This parameter setting is motivated by the fact that the average country growth rate from 1961 to 2011, taken over a large cross-section of countries, was about 2% (Im and Rosenblatt 2013). In addition, the average growth rate over this period did not vary much across countries with different income levels (there has been no convergence on average). For a quick visual confirmation of this last point, see figure 3.6 in the study by Jones and Vollrath (2013). Overall, the data give the appearance of countries with different steady states but common growth rates. We follow this interpretation by assuming that countries are comparatively rich because of high levels of TFP (D) and strong government institutions that prevent corruption.

We assume an annual time discount rate of 4% as is commonly used in calibration experiments (see, e.g., Prescott 1986). This implies [beta] = 0.442, leading to an annualized rate of return on private capital of 4.2%.

OECD countries, although not completely devoid of corruption, have comparatively low corruption and we use them to form reasonable targets for net tax revenue (or the government purchase share) and the public employment share in the no-corruption case. The average for both these values in OECD countries is about 15% (OECD 2011). These targets lead us to set [epsilon] = 0.15. Finally, we initially assume [eta] = 1. For these parameter setting, we compute an optimal tax value of [tau] = 0.19.

IV. AN ECONOMY WITH CORRUPTION AND EVASION

We now introduce the possibility that households will engage in illegal activity. Each public official manages a public sector investment project. They consider the possibility of diverting public funds, earmarked to finance investment projects, for their own private use. In addition, each private household now considers hiding income from the government to avoid taxation. In general both activities are costly because resources are lost in attempting to conceal the illegal actions. The stronger are the government's detection institutions, the more resources are lost in avoiding detection.

However, the empirical literature indicates tax evasion cannot be explained by the detection of illegal activity alone and that tax payer guilt plays role. To capture this result, we assume households experience a loss in utility, "guilt" from violating a social norm, when evading taxes. Furthermore, as empirical work suggests, the strength of the guilt associated with tax evasion varies inversely with the average level of corruption by government officials.

Our approach builds on the growing literature that examines the culture determinants of individual preferences. Much of the work on culture uses the framework developed by Cavalli-Sforza and Feldman (1981). They organize cultural influences on individual preference formation along three lines of transmission: vertical--parents influence their children preferences, oblique--the parent's entire generation influence children's preferences, and horizontal--a generation influences individuals from that same generation.

Vertical transmission is often modeled as parents investing time to influence the time preference and risk version of their children (Bisin and Verdier 2001: Doepke and Zilibotti 2014; Klasing and Milinois 2014). In some cases, the preferences and behavior of the parent's entire generation exert an external influence on the parent's attempt to form their children's preference, an oblique transmission mechanism (Saez-Marti and Sjogren 2008).

The model in the present study follows more closely the research focusing on the horizontal transmission of culture on preferences. Lindbeck et al. (1999) assume that individuals receiving a pecuniary gain from welfare programs also experience a disutility from living on public transfers rather than their own work. Culture enters because the disutility or stigma from public transfers is weaker the greater is the number of individuals in the society who receive government welfare. Fernandez (2010) assumes that a woman's disutility for work is a function of the mean disutility for work by women in the society. In this way, a woman's preference for work is affected by the labor force participation rate of women in the economy. Butler et al. (2012) argue that standard pecuniary preferences need to be augmented with a moral cost function. Based on experimental evidence, they propose a moral cost function that is a decreasing function of the deviation of an individual's behavior from what society expects from him. Similar to the approach of these authors, we assume there is a disutility associated with illegal behavior. The horizontal cultural transmission enters our model because we further assume that the average amount of corruption in society influences the individual's disutility associated with their own illegal behavior.

A. Private Choices

The preferences of private households and public officials are written as

1n [c.sub.1t] + [beta] 1n [c.sub.2t+1] - [[phi]v.sup.2.sub.t]/[2[bar.u].sup.- [kappa].sub.t]

and

1n [c.sup.g.sub.1t] + [beta] 1n [c.sup.g.sub.2t+1] - [[phi]u.sup.2.sub.t]/[2[bar.u].sup.-[lambda].sub.t],

where [phi], [lambda], and [kappa] are nonnegative preference parameters. The illegal activity of private households is measured by v, the fraction of their income that is not reported for tax purposes. The illegal activity of public officials is measured by u, the fraction of the public investment budget that is diverted for private use. The last term in each expression captures the "guilt" or direct disutility of engaging in illegal activity. (7)

Higher values of [phi] imply a stronger distaste for illegal activity. The disutility of illegal activity is also affected by the average level of corruption among government officials. The greater is the average level of corruption the less guilt an individual experiences from their own illegal activity. We refer to this as the "culture of corruption" (COC) effect.

A symmetric treatment of preferences across private households and public officials has an intuitive appeal. Similar to tax evasion, given the comparatively low expected penalty, it is difficult to explain why there is not more corruption (Lambsdorff et al. 2005, 3). Furthermore, the average behavior of the government could set a social norm by which all individuals judge their own illegal actions, both tax evasion and corruption, as indicated in the literature review. In this sense, private households and government officials are the same "type."

In our baseline case, we take a parsimonious approach where [lambda] is either equal to [kappa] (perfect symmetry of the cultural effect) or [lambda] = 0 (no cultural effect on corruption). Rather than consider a range of values for [kappa], we use the parameter simply to turn the COC effect on and off. With [kappa] = 0 there is no cultural effect (serving as a baseline comparison) and with [kappa] = 1 the average level of corruption lowers the individual's distaste for illegal conduct (as indicated by the data). Calibration exercises are used to test whether this parsimonious approach is sufficient to replicate key features of the data.

The private household maximizes utility subject to the lifetime budget constraint

[c.sub.1t] + [c.sub.2t+1]/(1 + [r.sub.t+1]) = (1 - [[tau].sub.t]) + [w.sub.t] (1 - [v.sub.t]) + [[theta].sup.[tau]][w.sub.t][v.sub.t],

where [[theta].sup.[tau]] is a parameter, that lies between 0 and 1, reflecting the fraction of unreported income that the household can recover for private use. The parameter captures the traditional monetary deterrent to tax evasion. The more difficult it is to hide income from the government, the less of it can be recovered and used, thus lowering the benefit of evasion. (8)

The maximization problem generates the following equations for tax evasion and private household saving

(12a) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

(12b) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Evasion is increasing in [[tau].sub.t] and [[theta].sup.[tau]]. (9) Evasion is also increasing in [bar.u] if [kappa] [not equal to] 0. In fact, as [bar.u] goes to zero, so does v. If the government officials are not corrupt, then they will act in the private household best interests (as they have the same preferences), so there is no motivation for private household to evade taxes. (10) The term (1 + [beta])/[phi] is a measure of "greed" because it is a measure of the value of consumption relative to the disutility of being dishonest. Tax evasion is increasing in greed, other things constant.

Next, we move to the behavior of the public official. In the case of uncoordinated or decentralized corruption, each public official takes the average level of corruption, the tax rate, and the total public investment budget as given when making their private choices. (11) The public official's private choices now include what fraction of their project budget to divert for their own private use. The budget allocated to each public official is [[??].sub.t+1]/[epsilon]N, where [[??].sub.t+1] is the amount of recorded or planned investment and not the actual investment. The officials maximize utility subject to the public budget and their private lifetime budget constraint, [c.sup.g.sub.1t] + [c.sup.g.sub.2t+1] / (1 + r) = [eta] (1 - [[tau].sub.t]) [w.sub.t] + [[theta].sup.g][u.sub.t] ([[??].sub.t+1]/[epsilon]N), where [[theta].sup.g] is a parameter, that lies between 0 and 1, reflecting the fraction of diverted public funds that the official can recover for private use. The parameter captures the effect of institutional safeguards that make it difficult to steal public funds and use them openly without detection, working like the standard monetary deterrent to illegal activity. We assume that public officials do not have the opportunity to avoid taxation on their official salary but, of course, they pay no taxes on the income they obtain by diverting funds from public investment projects.

The maximization problem generates the following equations for corruption and the public official's private saving

(13a) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

(13b) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

As with evasion, corruption is increasing in [[tau].sub.t] and [[theta].sup.g]. The larger is the budget that the official manages, relative to his official after-tax wage, the more tempting it is to be corrupt. This is also why corruption is decreasing in [eta][epsilon]--the larger is the official wage (increasing in [eta]) relative to the official's budget (decreasing in the number of officials or [epsilon]), the less corruption. An increase in the official's wage raises consumption and lowers the value of additional consumption gained by diverting public funds. However, the larger is the size of the public budget, the greater is the benefit of diverting a higher fraction of it. Thus, the greater is the number of officials, the smaller is each official's budget and the lower is corruption. Note that, other things constant, tax evasion lowers corruption because it reduces the size of the official's budget. In this way, evasion places a check on corruption.

The negative effect of tax evasion on corruption ([u.sub.t]) occurs because the marginal value of the stolen income is smaller, the smaller is the discretionary budget relative to legal income. The underlying positive relationship between the discretionary budget and the rate of corruption implies that growth in the relative size of government, Wagner's Law, leads to more corruption unless institutions are developed that make illegal activity more costly. Thus, in our theory, economies do not "grow out of corruption" without institutional improvement (see, also, footnote 7).

One can imagine theories where larger government budgets lead to falling corruption rates, as the weaker income effect of greater stolen funds lowers the marginal value of corrupt activity. However, these theories imply that larger governments automatically become less corrupt, without the need for institutional improvement. We find this approach less appealing because there are examples of richer countries, with comparatively large government sectors, that continue to struggle with significant corruption problems.

B. Corruption and Evasion for a Given Tax Rate

To build intuition about the microeconomic behavior and provide the foundation for the complete solution of the model, we first solve for the level of corruption and evasion for a given tax rate. Begin by writing out the government budget constraint to establish a connection between tax evasion, tax revenue, and the budget available for public investment, (14)

[[??].sub.t+1] = [[tau].sub.t] ([w.sub.t] (1 - [v.sub.t]) N + [eta][w.sub.t][epsilon]N) - [eta][w.sub.t][epsilon]N

The government budget constraint implies that [[??].sub.t+1]/[w.sub.t][epsilon]N = [[tau].sub.t]((1 - [v.sub.t])/[epsilon] + [eta]) - [eta]. Substituting this expression into Equation (13a), noting that [u.sub.t] = [[bar.u].sub.t] in both Equations (12a) and (13a), and then solving for [u.sub.t] in Equation (13a), gives evasion and corruption with and without the COC effect (15a)

[v.sub.t] = (1/2)[[square root of ([T.sup.2] + (4(1 + [beta])[u.sub.t]/[phi]))] - T],

(15b) [u.sub.t] = (1 + [beta])/[phi] ([eta][epsilon] (1 - [[tau].sub.t]) /[[theta].sup.g] ([[tau].sub.t] (1 - [v.sub.t]) - (1 - [[tau].sub.t])[eta][epsilon])).

(15a') [v.sub.t] = (1/2) [[square root of ([T.sup.2] + (4(1 + [beta])/[phi]))] - T],

(15b') [u.sub.t] = (1/2) [[square root of ([[GAMMA].sup.2] + (4(1 + [beta])/[phi]))] - [GAMMA]].

These equations allow us to solve for v and u conditional on a given value for [tau]. Note that for a given [tau], the solutions for v and u are independent of time. So if the tax rate is stationary so are the rates of corruption and evasion (conditional on the institutional parameters [eta], [epsilon], [[theta].sup.[tau]], [[theta].sup.g]).

Next, we examine the effects of corruption and evasion on the economy's growth by examining how corruption affects public and private capital accumulation. The actual investment in public capital is the accounting measure [[??].sub.t+1] minus the budget funds consumed by the government officials. Subtracting the portion of the capital budget that is consumed by government officials from Equation (14), and de-trending by dividing by [A.sub.t+1], gives us the transition equation for public capital intensity in the presence of corruption and evasion,

(16a) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

For a given tax rate, corruption and evasion both serve to shift the transition equation for public capital downward.

The private saving functions for private households and public officials, given by Equations (12b) and (13b), can be used to derive the transition equation for private capital,

(16b) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

While corruption and evasion reduce funds available for public investment, for a given tax rate, they increase funds available for private investment. Thus, the overall effect of corruption and evasion on growth is not clear. In addition, we have not yet determined how the presence of corruption and evasion will affect the tax rate chosen by the public officials.

C. Corruption, Evasion, and the Tax Rate

As in the benchmark economy, because all public officials are identical, the preferred tax rate maximizes the representative public official's welfare. The optimal tax rate takes into account tax rate effects on private choices, whether made by private households or public officials. The effects on private choices now include how the tax rate alters corruption and evasion.

The representative government official's preferences, including only those terms that are influenced by the choice of the current period tax rate, can be written as

(17) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The first term gives the effect of tax rates and tax revenue on the private income and consumption of the government official. The second term is the disutility of being corrupt. The third term gives the effect of taxation working through public investment. A higher tax rate increases next period's public capital and raises the welfare of a generation-t official because it raises the marginal product and the rate of return to private capital. The last term gives the effect of taxation working through private investment. A higher tax rate lowers next period's private capital stock and raises welfare because it raises the marginal product and the rate of return to private capital.

Note that Equations (15) and (17) indicate that the optimal tax rate will be constant across time, as in the case without corruption and evasion. Our assumptions imply the rates of taxation, evasion, and corruption are independent of capital intensities, TFP (the exact level of D), and per capita income. It is only the quality of government institutions (captured by [[theta].sup.[tau]], [[theta].sup.g], [eta], and [epsilon]) that determine these key variables. Weak institutions will cause high levels of taxation and corruption resulting in low steady-state capital intensities and persistently low income levels. Thus, countries will not fully develop without institutional improvements. The economy in Section III is "rich" because it has a superior steady state resulting from its institutional control over corruption (and possibly from high levels of TFP). We believe the data, reported in the calibration portion of Section III, support our decision to focus on steady-state differences across countries.

It is not possible to derive an analytical expression for the optimal tax rate. We calibrate the model and attempt to find a numerical solution. We start by focusing on a developing economy without institutional checks on corruption and evasion. In our model, this is captured by assuming that [[theta].sup.[tau]] = [[theta].sup.g] = [eta] = 1. For parameters other than [phi], we use the calibration from the no-corruption benchmark model. In our central corruption case, we calibrate cp to target a value of v equal to 1/3. The target is an intermediate value for evasion based on available estimates of the relative size of the shadow economy. LaPorta and Schleifer (2008; Table 1) estimate the shadow economy is between 20% and 43% of total GDP or total income for lower- and middle-income countries. Schneider (2012) estimates that the shadow economy is 26%-29% of GDP for 116 developing economies and 33%-38% for 25 transition economies. Given the range of estimates, we also adjust cp to match a low target for v of 25 and a high target of 40%.

Once the model is calibrated, we attempt to find the optimal tax rate by first substituting Equations (15) and (16) into Equation (17), and then by searching over a range of tax rates to find the one that maximizes Equation (17). For our calibration, Equation (17) is strictly concave in the tax rate. Given the optimal tax rate, the evolution of the economy is given by Equations (16a) and (16b), the transition equations for public and private capital. Under all the calibrations we examined, the dynamic system converged monotonically to a unique steady state. (12)

Table 1 presents calibrations and predictions of the model with and without the COC effect. We focus first on our central case with the intermediate target for evasion. With a COC effect on both individual tax evasion and individual corruption ([kappa] = [lambda] = 1), to match the evasion target of 1/3 requires setting [phi] = 1.1. The implied tax rate associated with this calibration is 35%. Net tax rates of this magnitude are common in developing countries (Mourmouras and Rangazas 2007). In contrast, without a COC effect ([kappa] = [lambda] = 0), a much higher value of [phi], and a much higher tax rate of 87%, is required to meet the target for v. With a COC effect on tax evasion only, [kappa] = 1 and [lambda] = 0, the tax rate is again reasonable at 29%. (13)

Comparing corruption across the three calibrations for the intermediate target, we see that when [kappa] = [lambda] = 1, corruption is 57%--more than half the investment budget is consumed by public officials. This value could be reduced by lowering [[theta].sup.g], but the estimate is quite reasonable without further adjustment of parameters. Evidence from the study by Tanzi and Davoodi (1997) suggests diverted cost overruns of almost exactly this magnitude on public investment projects in Italy. Reinikka and Svensson (2004) document that about 85% of funds allocated for public school projects were diverted for private use. More comprehensively, Pritchett (1996, 2000) provides evidence indicating that less than half of public investment budgets are actually invested in developing countries.

Note that without the COC effect, [kappa] = [lambda] = 0, the predicted level of corruption would be too low, less than 40%. Given that [[theta].sup.g] is set at its highest value, no adjustment can be made to improve the match by raising corruption above 40%. With a COC effect on tax evasion only, the corruption rate reaches 68%. This high value for the corruption rate could be reduced by lowering [[theta].sup.g], so this prediction alone does not reject the [kappa] = 1 and [lambda] = 0 calibration. We need to consider the model's match to another stylized fact to determine the preferred specification. For this purpose, we focus on the relationship between government quality and tax revenue.

The empirical literature estimates an inverse correlation between corruption and tax revenue (Johnson et al. 1999; Kaufmann 2010; Tanzi and Davoodi 1997). We vary [[theta].sup.g] to simulate the correlation between corruption and tax revenue. We find that, over the range of [[theta].sup.g] that generates positive corruption rates, tax revenue falls with corruption. The decline in tax revenue is caused by a decline in the tax base due to a rise in evasion and a decrease in wages as capital accumulation falls with higher corruption.

This result is displayed in Figure 3 where tax revenue is plotted against the range of [[theta].sup.g] values that generates positive corruption. One can imagine a cross-section of governments with different institutional quality; the higher the value of [[theta].sup.g], the lower the quality. Consistent with empirical estimates, when [kappa] = [lambda] = 1, the model predicts that worker productivity and tax revenue fall as [[theta].sup.g] increases. In our model, tax revenue falls when [[theta].sup.g] increases primarily because greater corruption causes significant increases in tax evasion. This result depends critically on the presence of the COC effect.

In contrast, when we set [kappa] = [lambda] = 0 and thus eliminate the COC effect, tax evasion shows little response to changes in corruption and tax rates. The comparatively low responsiveness of evasion to corruption and tax rates without a COC effect causes tax revenue to increase with the level of corruption. Even in the case with a COC effect on tax evasion only, [kappa] = 1 and [lambda] = 0, the model is unable to generate inverse relationship between tax revenue and government quality. Thus, in terms of predictions regarding tax rates, corruption levels, and the relationship between tax revenue and government quality, the preferred calibration is clearly [kappa] = [lambda] = 1.

Moving to the cases with the low and high evasion targets, we see patterns that are similar to the case with the intermediate target (note that we needed to scale the common value of [kappa] and [lambda] down to 0.75 to match the high evasion target). Without a COC effect, the predicted tax rates are again unreasonably high. With the symmetric COC effect for evasion and corruption, the result in Figure 3 holds for the low evasion target but not strictly for the high evasion target. For the high evasion target, the relationship between [[theta].sup.g] and tax revenue is negative only for values of [[theta].sup.g] above 0.65. For values below 0.65, tax revenue varies little with government quality.

The break in the strictly negative relationship between corruption and tax revenue caused us to look at a full range of evasion targets between

0.20 and 0.40. We found that for evasion targets between 0.20 and 0.38, the result in Figure 3 holds across all values of [[theta].sup.g], but only when we assume the symmetric COC specification. The relationship exhibited in Figure 3 breaks down for high evasion targets, above 0.38, when the values of [[theta].sup.g] are sufficiently low. Overall, with a symmetric COC effect, the inverse relationship is predominantly negative across a wide range of values for evasion and government quality. There is certainly no prediction of a strongly positive relationship across the entire range of evasion targets and ([[theta].sup.g]-values. For this reason, we focus on the calibration with a symmetric COC effect for the remainder of our analysis.

D. Corruption, Evasion, and Output

We now examine the effect of corruption on economic growth. Table 2 reports the percentage change in output as one goes from the no-corruption benchmark economy to the economy with corruption for our three evasion targets. In order to isolate the effects of evasion and corruption per se, we also include cases where we alter kappa and lambda to keep the tax rate as close to 0.35 as possible across our three evasion targets. In the low-evasion case, the highest tax rate we could calibrate was 0.30.

Again, start with the intermediate case. Here we find a 9% decline in output from introducing corruption. With much higher tax rates and substantial government corruption, one might expect a larger decline in output than 9%. However, tax evasion is also high as 33% of income goes untaxed. The untaxed income increases the funds available for private investment, helping to mediate the negative effects of higher tax rates on private capital accumulation. In addition, much of higher tax rate actually increases the funding for public investment, despite tax evasion. The extra funds serve to offset the rise in the fraction of the budget that is diverted for private use. The share of income that is invested in public capital only falls to 2.2% of output from a value of 2.8% without corruption. Thus, neither private capital nor public capital falls dramatically.

The absence of a large negative output effect holds up as we vary the evasion target. In fact, for the high evasion target, the output effect is slightly positive. This happens because while evasion and corruption are high in that case, the tax rate is quite high at 51%. The government collects enough revenue so that public investment is higher than in the no-corruption case, leading to a small increase in output. When we alter the values of kappa and lambda to keep the tax rate from rising above 0.35, the output effect becomes negative. With the same rate of corruption, the tax rate in this case does not rise enough to generate an increase in public investment. Note, in general, that lower tax rates tend to generate larger declines in output. The rise in corruption reduces public investment when tax revenue does not rise sufficiently.

The relatively modest effect of corruption on output may help explain why it has been difficult to uncover a statistically significant negative correlation in cross-country data (Svennson 2005). In Section VI, we will see that this quantitative result is somewhat sensitive to the precise specification of the cultural effect. However, we find the conclusion that the output loss from corruption is not large is robust.

V. THE EFFECTS OF INSTITUTIONAL CHANGE

Having demonstrated the negative effects of corruption and evasion on fiscal policy and growth, we now examine how changes in institutions might improve the situation. The initial calibration was for a situation with no particular safeguards against corruption and evasion--public officials are able to fully utilize whatever funds they divert, tax evaders can do the same with their unreported income, and public officials receive the same pay as those in the private sector. Table 3 considers the steady-state effects of changing laws so as to discourage corruption and evasion. In particular, we consider new laws and enforcements that make it more difficult to keep diverted and unreported income hidden, causing [[theta].sup.[tau]] and [[theta].sup.g] to fall by 10%, and a new policy that raises the pay of public officials by 10%.

Table 3 reports the results of comparative static experiments for our intermediate evasion case. The results are not sensitive to the exact targeting of evasion and taxation, so we do not generally report the comparative static exercises for all parameter settings. However, because of the potentially controversial nature of the result associated with the evasion crackdown, we report the outcome for that experiment across all parameter settings in Table 4.

A. Increasing the Public Official's Wage

A 10% increase in the government official's wage lowers corruption and, through the COC effect, tax evasion falls as well. Despite the increase in pay to officials, the tax rate only rises slightly. This is due to the decline in corruption, which allows government investment to rise without an increase in taxation. The rise in investment causes worker productivity to rise by about 4% in the long run.

In the approaches based on the study by Becker and Stigler (1974), wage premiums will only encourage good behavior by officials if they are accompanied by monitoring (e.g., Di Telia and Schargrodsky 2003). The bad behavior is deterred by high wages only if the official faces a threat of being caught and fired. In our model, the high wages increase consumption and lower the benefit of gaining additional consumption through corrupt behavior. This reduces the utility gain from corruption without lowering the utility loss associated with illegal actions. Thus, higher wages reduce corruption without the need for monitoring. In our model corruption falls because with higher wages there is less need, and thus less will, to steal (regardless of the threat of being caught). Of course, increasing the threat of being caught would help reduce corruption as well. The two policies will reinforce each other because the officials have more to lose if they are caught and fired when their salary is higher. Because of these reinforcing "carrot and stick" effects, it is likely that the most efficient way to stop corruption would include both tougher laws/better detection and higher pay.

The fact that a rise in public sector wages has positive effects on worker productivity naturally leads to the possibility of an optimal public sector wage premium. Figure 4 plots the steady-state utility of private households and public officials as a function of the public sector wage premium, [eta].

A public wage premium of about 1.6 drives corruption and evasion to zero. After this point, further increases in the public wage premium serve only to raise tax rates and lower private household's welfare. The public officials continue to gain from further wage premium increases beyond the value that maximizes private welfare. Thus, while a wage premium can be justified, there is also a possibility that the wage premium will be set too high by the public officials.

Increasing the number of public officials, and thereby reducing the size of the budget under the control of any one official, would have an effect on corruption similar to increasing a given official's wage. In both cases, the relative value of the income gained through corrupt actions would fall leading to a reduction in corruption (see Equation (13a)). However, increasing the number of officials is more costly to the economy because it lowers the relative size of the work force engaged in production. A decrease in the relative size of the productive work force reduces output per person, public investment per person, and, indirectly, private capital per worker. To see this, note that the transition equation for public capital per person, Equation (16a), is a decreasing function of e for a given value of [eta][epsilon]. For this reason, attacking corruption by offering higher wages is clearly superior to increasing the number of officials and reducing their individual responsibilities. Thus, it would be optimal to reduce public sector employment to some minimal level needed to operate the government, and then use the public sector wage premium to help control corruption.

B. Reducing the Benefits of Illegal Activity

We can also examine the effects of lowering [[theta].sup.[tau]] and [[theta].sup.g]--although the model does not specify the costs of these changes, so the analysis cannot be as complete as for the policy of raising public sector wages.

A 10% decline in the official's ability to use diverted funds lowers corruption and evasion as well. In addition, in part because there is no explicit cost associated with reducing [[theta].sup.g] the optimal tax remains approximately constant. The resulting increase in output per worker is almost 6%. If reducing [[theta].sup.g] is associated with a one-time cost, say investing in a new accounting system that improves the tracking of public funds, then this may be less expensive than permanently raising the wages of public officials.

Turning to [[theta].sup.[tau]], we see that a 10% decline in the private household's ability to use unreported income causes a more than unitary elastic decline in evasion. The reduction in the "fiscal discipline" provided by evasion causes corruption and tax rates to rise. The rise in tax rates and in corruption reduces capital accumulation and

causes steady-state output to fall by almost 8%. The rise in corruption reduces public investment and the increased taxation reduces private investment. So cracking down on evasion is a bad idea without also cracking down on corruption because evasion provides a check on the selfish motives of public officials. Table 4 reveals that this result holds across the range of calibrations that were used in Table 2.

The negative outcome from reducing the benefits of tax evasion creates a link between corruption and the shadow economy similar to that suggested by Choi and Thum (2005). They argue that entrepreneurs may avoid the need to pay bribes to public officials by moving to the unregulated underground economy. The threat of exit to the underground economy places a constraint on bribes that public officials attempt to collect. We show that, in a similar way, tax evasion can constrain the corrupt behavior of public officials and the tax rates chosen by the government. Thus, in both cases the shadow economy plays a useful role in constraining government behavior.

VI. ROBUSTNESS CHECKS

In this section, we report on how the results are affected when we try some natural deviations from our baseline modeling assumptions.

A. Alternative Specifications of the Cultural Effect

We considered two other specifications of the cultural effect. The first specification uses an index of all illegal activity-both evasion and corruption-rather than using corruption alone as the source of the cultural externality. This specification could not match the facts as well as the specification with corruption alone, unless the weight placed on evasion was much smaller than the weight placed on corruption. Thus, the corruption-only specification serves as a good approximation to this more general specification.

We considered a second specification where the cultural externality is captured by the term 1 + [bar.u] instead of [bar.u]. The motivation of this specification is that it allows evasion to be positive even when corruption is zero. With this specification it is more difficult to match the data--some adjustment to the cost of evasion ([[theta].sup.[tau]]) is necessary to match lower evasion targets. However, for the baseline intermediate case, the specification allowed for a reasonable fit to the data and introduced somewhat different predictions than the specification reported in the text.

With [beta] = 0.442, [epsilon] = 0.15, [kappa] = [lambda] = 1, and a target of v = 0.33, the predicted values for u and x are 0.39 and 0.24. The predictions for corruption and taxes are on the low side but not unreasonable. This specification was able to replicate the stylized facts that tax revenue and worker productivity are inversely related to rising corruption, as [[theta].sup.g] increases, similar to Figure 3. Overall, the fit is good enough to take this specification seriously for the intermediate case.

Similar to the results from Table 2, cases with low tax rates and high corruption rates generate the largest decline in output. The lower tax rate (0.24 vs. 0.35) generates less tax revenue than in the baseline case and as a result the investment budget is lower, leading to less of a revenue-offset for the rise in corruption. In fact, here revenue falls. As a consequence, public investment falls more dramatically when corruption is introduced, resulting in a larger reduction in steady state output; a 31 % decline rather than the 9% decline in the baseline case.

Most other conclusions are not affected by this alternative specification but the conclusion regarding when it is welfare improving to crackdown on evasion is now more nuanced. Figure 5 presents numerical computations related to preventing tax evasion under the alternative specification. When corruption is high ([[theta].sup.g] is closer to one) cracking down on tax evasion reduces workers' productivity for the same reasons as in our main specification. However, when the government is less corrupt, a reduction in tax evasion may increase worker productivity. This happens because in lower corruption environments more of the increased tax revenue is invested in public capital. Changing 0T from 1 (no checks on tax evasion) to 0.9 is beneficial for the economy if not more than 70%-80% of assets stolen by bureaucrats can be recovered for private consumption and investment (i.e., when [[theta].sup.g] is around 0.75). The benefits of reducing tax evasion further get smaller: reducing [[theta].sup.[tau]] from 0.9 to 0.81 improves workers' productivity only if [[theta].sup.g] is smaller than 0.45. Thus, this specification clarifies that the negative results of cracking down on evasion are more likely when government corruption is unchecked.

B. Public Concern for the Economy as a Whole

We introduce a type of altruism where households, some of which are public officials, have concerns about the current and future state of the economy and not only their private consumption. We characterize the concern for the economy as a whole by introducing the average level of worker productivity during both periods of the household's life ([y.sub.t], [y.sub.t+1]) into the utility function. (14)

The preferences of private households and public officials are written as

ln [c.sub.1t] + [beta] ln [c.sub.2t+1] + [gamma] (ln [y.sub.t] + [beta] ln [y.sub.+1]) - [phi] [v.sup.2.sub.t]/2[[bar.u].sup.[kappa].sub.t]

and

ln [c.sup.g.sub.1t] + [beta] ln [c.sup.g.sub.2t+1] + [gamma] (ln [y.sub.t] + [beta] ln [y.sub.+1]) - [phi] [u.sup.2.sub.t]/2[[bar.u].sup.[lambda].sub.t],

where [gamma] is positive when the altruistic concern is present. The parameter [phi] can be set to 0 to establish the no-corruption benchmark with altruism.

Our entire working paper, Ivanyna et al. (2013), is devoted to analyzing the altruistic case. We conduct the same analysis provided here and reach essentially the same conclusions. Thus, our results are not sensitive to the government having altruistic concerns about the economy's performance beyond those captured by the concern over their own consumption.

C. Corruption and Taxation in an Open Economy

Throughout we have assumed a closed economy. Opening the economy to capital flows will not affect the rates of taxation, corruption, or evasion. This is a corollary of the fact that these behaviors are not affected by capital intensities or per capita income (see the discussion from Section IV.C). Any inflow or outflow of capital in an open economy will leave taxation, corruption, and evasion unchanged.

If we extend the analysis to consider an income tax, rather than a wage tax, opening the economy will generally affect these behaviors. However, the direction of the effects is ambiguous.

To see why opening the economy may be important, we introduce an income tax into a simplified version of the model from Section IV, where [[theta].sup.[tau]] is set sufficiently low to eliminate tax evasion (v = 0). Begin with a closed economy and levy an income tax on both wages and capital income. The return to capital is now redefined as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. By taxing capital income, the tax base has expanded and tax revenue will increase. For analytical purposes it is convenient to eliminate this pure revenue effect. We assume the revenue collected from capital income is used for purposes that are exogenous to the model (say, national defense). As a result, any difference in outcomes will not simply be due to a direct expansion of the budget for the

public officials. We take this approach for three reasons. First, it allows us to focus on other differences between taxing income and taxing wages. Second, it facilitates comparison to our existing equilibria where revenue is collected from labor income only. Finally, expanding the budget because of a broader tax base increases corruption, other things constant. As we will see, corruption will be excessive in an open economy even without a larger budget.

Notice that because the interest rate does not affect saving, evasion, or corruption, the household solutions remain the same. In addition, note that the income tax does affect the welfare of all households, including public officials. However, the income tax rate that affects the public officials who choose tax rates in period t is actually [[tau].sub.t+1]. This future tax rate is chosen by the next generation of public officials, so the current generation takes [[tau].sub.t+1] as given when they decide the income tax in period t. This all means that when current period public officials maximize their welfare by choosing the current period income tax rate, it will be equivalent to choosing the current period tax rate on wage income only. Therefore, none of the key behaviors are affected by assuming income over wage taxation in a closed economy, again provided that the budget in Equation (14) does not expand directly with the tax base.

However, in an open economy the income tax can lead to different behavior then we see under a wage tax. It is natural to assume that the poor economy is a "small" open economy. This means that the policy choices of the country in period t will not affect [r.sub.t+1] because capital flows will ensure that this return is always equal to the world after-tax rate of return, which is exogenous to the country. The inability to influence next period's return to private capital, with this period's policy choices, eliminates the last two terms of the closed economy objective function for choosing tax rates given by Equation (17). In a closed economy, these two terms exert an ambiguous effect on the tax rate, so moving to an open economy and eliminating them makes it impossible to make a qualitative prediction on how tax rates and corruption will be affected.

There is a second change that comes from opening the economy. The current income tax rate now affects current period private capital intensity. This effect is due to the standard assumption that capital flows across borders equate the after-tax rate of return in each period. A higher income tax rate causes outflows of existing domestic capital, lowering current period wages and household welfare. The effect on capital flows adds the term (1 + [beta])[alpha]/1 - [alpha]) ln (1 - [[tau].sub.t]) to Equation (17). This term raises the cost of taxation and, if it dominates the ambiguous impact of eliminating the last two terms, opening the economy will lower tax rates and corruption. In this sense, an open economy "substitutes" for tax evasion in disciplining government behavior. (15)

To get an initial gauge of the quantitative importance of the open economy mechanism on taxes and corruption, we conduct the following numerical experiment. We use the same parameters as in the baseline model of Section IV, with the exception that we set [[theta].sup.[tau]] sufficiently low that it wipes out tax evasion. The world after-tax interest rate is set to equal that of the rich country from Section III. We then compute the equilibrium in a perfectly open economy by making the adjustments to the policy maker's objective function that were discussed above. Finally, we compare the equilibrium tax rates and corruption rates to the Section IV closed-economy equilibrium with tax evasion. Will the open economy, without tax evasion, be as effective as evasion in a closed economy in checking high taxes and corruption rates?

We find that when we attempt to compute the open economy equilibria without evasion, the corruption rate is forced to a corner at one. While the open economy can potentially create incentives that keep taxation in check, it dramatically weakens the incentive to restrain from corruption. This happens even though the tax rate itself is not high--a tax rate of 30% was enough to push corruption to the limit. With no tax evasion, a tax rate of 30% is effectively higher than the 35% tax rate from our central closed-economy case with a tax evasion rate of 33%. The effective tax rate for revenue purposes is just 23.5% in that case. So, we find that an open economy does not lower the tax rate enough to substitute for the discipline provided by the presence of tax evasion.

VII. CONCLUSION

This study provides a quantitative theoretical analysis of how corruption and tax evasion interact with each other and with the setting of fiscal policy in developing countries. Our focus is on the determination of the labor income tax rate and the level of public investment. Corruption tends to force the tax rate up because corrupt officials want to divert some government revenue earmarked for investment for their own private use. Evasion tends to force the tax rate down because evasion lowers the government's ability to raise revenue at higher tax rates. We find that when the model is calibrated to match typical evasion levels found in developing countries, along with other macroeconomic characteristics, the combined presence of corruption and evasion causes the net tax rate to be significantly higher than in a baseline model with no corruption and evasion. The predicted levels of corruption and the net tax rates are similar to those found in many poor developing countries.

The rise in corruption lowers the government revenue that is actually invested in public capital and the rise in the tax rate reduces private investment, causing a drop in worker productivity. However, the drop is not large, which helps explain why it has been so difficult to establish a statistically significant correlation between corruption and growth in cross-country studies.

We consider the effect of making various institutional changes aimed at reducing corruption or evasion. We find that reducing the ability of the private households to evade taxation can be a bad idea if corruption is not first addressed. Reducing evasion raises tax revenue and increases the budgets of public officials. An increase in budget size leads officials to become more corrupt, diverting larger fraction of the budget for private use. Public investment declines and worker productivity falls.

We find that increasing the pay of public officials can serve to reduce corruption and evasion, with only a slight rise in the tax rate. The reduction in corruption and evasion increases the government revenue for a given tax rate. This effect frees enough government revenue to pay for the increase in public sector wages with only a slight increase in the tax rate. With the decline in corruption, funds available for public investment are increased. The rise in public sector investment causes an increase in worker productivity and this effect dominates the rise in the tax rate, causing steady welfare of private households to rise. While the result provides some justification for offering a public sector wage premium, especially when combined with some increase in monitoring, public officials will choose a wage premium that is too high from the perspective of private households. Thus, public sector pay will tend to be too high when the ability of public officials to set their own wages goes unchecked.

In future work, we plan to refine our estimates by making several extensions to the model. First, we will include an expanded set of fiscal policy variables, such as public debt and capital income taxation. These extensions increase the motivation for extending the analysis to allow for international borrowing by the government and for private capital flows across countries (see Section VI.C for a start). Also, making a distinction between high-level officials who vote on fiscal policy and lower-level nonvoting bureaucrats would help to identify the separate effects of administrative and political corruption.

doi: 10.1111/ecin.12228

ABBREVIATIONS

COC: Culture of Corruption

OECD: Organization for Economic Co-operation and Development

TFP: Total Factor Productivity

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(1.) The evidence for a "culture of corruption" effect is also present at the individual level within countries. We run regressions of tax evasion on "confidence in government" at the individual level for each country and each year. Of 138 country-year pairs, the estimate of the association between "cheating on taxes" and "no confidence in government" is positive and significant in 82 cases. Only in 19 cases is the point estimate negative, just 6 of these are significant. The association is strongest in Croatia (0.85) and Belarus (0.81) in Europe; China (0.45) and Viet Nam (0.39) in Asia; Mali (0.38) and Uganda (0.34) in Africa; and Peru (0.21) and Argentina (0.18) in Latin America.

(2.) In practice, it may be difficult to decompose the negative effects of total corruption according to whether the corruption is bribes to bureaucrats or corruption associated with high public officials and policy makers. Bribes, diversion of public funds for private use, and policy choices are likely to be interconnected.

(3.) Mauro (2002) discusses possible effects of average corruption on individual corruption that works through the probability of being caught and punished. Our effect works independently of the probability that corruption or evasion is detected. There is also a new literature on the intergenerational transmission of values in general that could be used to further endogenize the willingness to engage in illegal activities (see Tabellini 2008; and the references therein).

(4.) There is a separate literature that introduces tax evasion into growth theory in the absence of corruption (Chen 2003; Dzhumashev and Gahramanov 2010).

(5.) We assume that interest income is not taxed to avoid the problem of time inconsistency when choosing the optimal tax on capital income (Kydland and Prescott 1977). We plan to address capital taxation in future work. We do discuss an income tax, without allowing for separate tax rates on labor and capital income, in Section VI.

(6.) For tractability, some features of the government must be taken as given in our analysis. However, we eventually discuss how changes in exogenous features of the government affect the results and even go as far as to indicate what may be considered the optimal levels of r| and e. In addition, note that when [eta] = 1, the households are indifferent about working in the public or private sectors. However, this is not necessarily true after we introduce corruption and evasion. In the presence of corruption and evasion, we find that public officials are better off than private households as long as [eta] [greater than or equal to] 1 (even though we assume that public officials cannot avoid taxes on their official salaries). Thus, everyone would want a government job.

(7.) We assume that the fraction of money stolen generates the disutility rather than absolute amount. This specification will generate fractions of income that go unreported and fraction of public budgets that are diverted for private use that are independent of the level of income. This allows us to focus on institutional determinants of corruption because increases in income alone will not alter the rate of illegal activity.

(8.) One can interpret 0T as the fraction of the before-tax market wage that a worker can earn in the untaxed underground economy. To see this, let the technology used in the untaxed sector be the same as in the taxed sector except that the productivity index for labor is [[theta].sup.[tau]][D.sub.t], rather than [D.sub.t]. This captures the idea that the government could lower access to productive public services for firms in the underground economy and thus lower the productivity of labor there. In this case, the profit maximizing wage offered in the untaxed sector is [[theta].sup.[tau]][w.sub.t], where we have used the fact that if the return to capital is untaxed, then the capital to effective labor ratio must be equal in each sector. As the government clamps down on the untaxed sector by making it more difficult for those firms to use productive public services, [[theta].sup.[tau]] falls and the relative wage earned in the underground economy falls as well.

(9.) Schneider and Enste (2000) and Johnson, Kaufmann, and Zoido-Lobaton (1998,1999) provide evidence that higher tax rates increase the underground economy and tax evasion.

(10.) In Section VI.A, we consider an alternative specification of preferences where evasion can occur in the absence of corruption.

(11.) We did not consider the case of centralized corruption, where both corruption and tax rates are chosen jointly by all public officials, but this might be an interesting extension.

(12.) As explained, because the rates of taxation, evasion, and corruption do not vary with capital intensities, the transition is not particularly interesting.

(13.) With no COC effect, in order to generate observed levels of tax evasion, the aversion to engage in illegal activity must be comparatively high. When the aversion to engage in illegal activity is high, evasion is not very responsive to tax rate increases and the government can set high tax rates without concerns that evasion will lower the tax base. Thus, to match the observed evasion levels requires unrealistically large tax rates. When the COC effect is present, the level of tax evasion varies with corruption. The corruption-evasion interaction makes each variable more responsive to changes in parameters and helps target observed evasion levels without assuming a high degree of aversion to illegal activity. The corruption-evasion interaction and the lower aversion to illegal activity makes evasion more responsive to tax rates and causes the government to set much more reasonable tax rates.

(14.) For our purposes, this altruistic specification can be shown to be equivalent to a specification used in the vast literature on fertility and development where parents choose between the quantity and quality of children. The quality of children is measured by the children's adult wage, similar to our specification that uses the average product of labor of future generations. See Galor (2005) for a survey. So one can interpret our specification as one where households have intergenerational altruism measured by a concern for the quality of their children's employment opportunities.

(15.) We thank a referee for suggesting that we think about this possibility.

MAKSYM IVANYNA, ALEXANDROS MOUMOURAS and PETER RANGAZAS *

* We thank Jay Choi, Hamid Davoodi, Chris Ellis, Gareth Myles, John Wilson, and the participants of the JPET workshop on Governance and Political Economy for their useful comments.

Ivanyna: Economist, Joint Vienna Institute, Vienna, 1070, Austria. Phone 0043-1-798-9495, Fax 0043-1-798 0525, E-mail mivanyna@jvi.org

Moumouras: Division Chief, Asia and Pacific Department, International Monetary Fund, Bethesda, MD 20817. Phone 202-623-5402, E-mail amourmouras@gmail.com Rangazas: Professor, Department of Economics, IUPUI, Indianapolis, IN 46202. Phone 317-437-6403, Fax 317-274-0097, E-mail prangaza@iupui.edu

TABLE 1
The Need for a Culture-of-Corruption Effect

           [kappa] =             v = 0.25           [kappa] = 1,
         [lambda] = 1     [kappa] = [lambda] = 0    [lambda] = 0

[phi]        0.82                   17                  0.72
[tau]        0.26                  0.92                 0.21
u            0.44                  0.28                 0.51

           [kappa] =             v = 0.33           [kappa] = 1,
         [lambda] = 1     [kappa] = [lambda] = 0    [lambda] = 0

[phi]         1.1                  8.8                   1.0
[tau]        0.35                  0.87                 0.29
u            0.57                  0.39                 0.68

           [kappa] =             v = 0.40          [kappa] = 0.75,
        [lambda] = 0.75   [kappa] = [lambda] = 0    [lambda] = 0

[phi]         1.8                  5.0                   1.5
[tau]        0.51                  0.75                 0.40
u            0.60                  0.49                 0.73

TABLE 2
Output Effects

                v = 0.25         v = 0.33         v = 0.40
             ([tau] = 0.26)   ([tau] = 0.35)   ([tau] = 0.51)

% [DELTA]y        -16               -9              8.7

                v = 0.25         v = 0.33         v = 0.40
             ([tau] = 0.30)   ([tau] = 0.35)   ([tau] = 0.35)

% [DELTA]y       -14.5              -9              -19

Note: The table gives the percentage change in steady-
state output across the corruption and no-corruption cases
with different evasion and tax rate targets.

TABLE 3
Comparative Steady States

Parameter
Changes                       % [DELTA]u   % [DELTA]v   % [DELTA][tau]

Rise in [eta]                   -11.0         -9.3            0.3
Fall in [[theta].sup.g]          -9.2         -9.3           -1.4
Fall in [[theta].sup.[tau]]      18.5         -5.1            4.3

Parameter
Changes                       % [DELTA]REV   % [DELTA]y

Rise in [eta]                     12.1           5.8
Fall in [[theta].sup.g]            8.0           5.6
Fall in [[theta].sup.[tau]]       -1.9          -7.9

Note: The table gives the percentage in the variable
associated with a 10% change in the parameter indicated.

TABLE 4
Output Effect from Evasion Crackdown

                 v = 0.25         v = 0.33         v = 0.40
              ([tau] = 0.26)   ([tau] = 0.35)   ([tau] = 0.51)

% [DELTA]y         -13              -7.9             -1.1

                 v = 0.25         v = 0.33         v = 0.40
              ([tau] = 0.30)   ([tau] = 0.35)   ([tau] = 0.35)

% [DELTA]y        -12.4             -7.9             -4.0

Note: The table gives the percentage change in steady-
state output that results from a 10% reduction in [[theta].sup.[tau]
when [[theta].sup.g] is maintained at one.