If financial development attenuates MB and/or intensifies MC, then financial de-velopment leads to a decrease in p∗. Intuitively, this case arises when a marginal crease in the unit cost of banking transactions induces individuals to increase their de-posits in banks to a large extent. Obviously, this increases the government tax revenues to a great extent. To keep the budget balanced, the government reduces its revenues from penalties by reducing the probability of tax detection. According to Propositions 3 and 4, a decrease in p∗leads to an increase in τ∗and hence a decrease in β∗. Though a decrease in p∗leads to a decrease in β∗, the overall effect of a decrease in δ on β∗is not negative. This is because, as shown in eq. (10a) above, a decrease in δ also directly increases β∗. If this direct effect from δ outweighs the one from a decrease in p∗ on β∗, then the optimal tax compliance β∗ can be increased as a result of a decrease in δ.39 In this case, we can derive a conclusion that a decrease in δ is associated with an increase in β∗, implying that developing countries with a higher δ should adopt a policy of tax enforcement that leads to severe tax evasion and hence a larger size of the informal sector (i.e., a lower β∗). By assuming that the direct effect from δ outweighs
39If this direct effect fromδ is outweighed, then a decrease in δ will lead to a decrease in β∗. This implies that developing countries should adopt a policy of tax enforcement that leads to more tax compli-ance and a smaller size of the informal sector. This case, however, is not consistent with recent empirical studies.
the one from p∗ on β∗in Case 2, we reach the following conclusion from Cases 1 and 2:40
Proposition 5 If µ is large enough, countries with a less-developed financial sector should adopt a policy of tax enforcement that leads to more severe tax evasion and a larger size of the informal sector.
4. C AL IBRATIO N
Since the equilibrium tax rate τ∗is too complicated to derive, we are not able to obtain an analytical solution for the optimal β∗. To obtain a more concrete image of our results, we calibrate the model by adopting values of parameters from recent studies.
Consider the following values for the model parameters. First, the income share of capital α is set equal to 0.92, as in Turnovsky (2000). Moreover, the cost parameter of tax detection f0is equal to 0.0082, the fixed penalty rate π is equal to 1.5, and the cost parameter of tax evasion h0is equal to 0.2.41 All of these are taken directly from Chen (2003). Since the government size in developing countries is between 20% and 30% of GDP, the share of government expenditure θ is set equal to 0.25. If we view each period in the two-period-lived OLG model as 30 years, then the discount factor η is set equal to 0.4, implying that the discount factor for each year is about 97%. We also set µ = 0.8 in the benchmark case, implying that, except the initial generation, the utility of each generation is discounted at 80% in the welfare function. The value of 120 for A is chosen to yield reasonable figures of economic growth.42 Note that the value of λ is not available from the literature. In order to satisfy the condition of λ+ δ − 1 > 0 for any possible value of δ, we set λ = 0.95.
Due to the nature of tax evasion, data related to tax evasion are difficult to ob-tain, because they usually escape normal statistical registration and documentation.
Recently, Beck et al. (2014) employ a large data set from World Bank-IFC to measure
40We calibrate our model with a relatively high value ofµ (i.e., µ = 0.8) in the next section. We also calibrate the case of a lower value ofµ (µ = 0.5). We find that our conclusions still hold for µ = 0.8 or µ = 0.5. Results are available upon request.
41The cost parameter of tax evasionh0in the benchmark case of Chen (2003) is equal to 0.15. Since we consolidate costs of tax evasion and participation in the informal sector, we assume thath0is equal to 0.2 in the benchmark case. Note that Chen (2003) also changesh0from 0.15 to 0.39.
42Note thatβ∗andp∗are independent ofA.
the degree of tax evasion. The data set is a set of firm-level surveys containing more than 64,000 firm observations across 102 countries over the period 2002 to 2010. From this data set, they construct a tax evasion ratio, which is equal to one minus the share of sales reported for tax purpose. We calibrate our model to yield values of 1− β∗that are consistent with the tax evasion ratios reported by Beck et al. (2014). According to Table 1 of Beck et al. (2014), the tax evasion ratio ranges from 68% in Gambia to less than 4% in Ireland, indicating that the values of 1− β∗ should lie between 0.04 and 0.68. Since the purpose of our study is to examine the relationship between tax eva-sion and financial development, we should consider values of δ that can yield values of 1− β∗in a range of 0.04 and 0.68. Given the above parameter values, we find that 1− β∗ is equal to 0.684 if δ= 0.47. Moreover, if δ = 0.078, then 1 − β∗is equal to 0.04. Consequently, we should consider δ in a range of 0.078 and 0.47.
Before we examine the relationship between financial development and tax eva-sion, we first examine the relationship between the probability of p and τ∗, β∗, g∗, and W∗, respectively, for a given δ. This can confirm the existence of the optimal prob-ability of tax detection. For this purpose, we choose δ = 0.3, which is in the range of 0.078 and 0.47. Results are presented in Figure 5. As shown in part (A) of Figure 5, an increase in p reduces the equilibrium tax rate τ∗ (Proposition 3) for given other parameters. On the other hand, an increase in p increases β∗(Proposition 4) as shown in part (B) of Figure 5. From parts (C) and (D) of Figure 5, the optimal probability of tax detection that maximizes social welfare is equal to 0.735, and the corresponding economic growth rate is equal to 1.676.
We now turn our attention to examining the effects of financial development, measured by a decrease in δ from 0.47 to 0.078 on β∗, τ∗, p∗, g∗, and W∗, where g∗ and W∗ are economic growth and social welfare when p is optimally chosen. We report the results in Table 1.
Some interesting results are obtained from Table 1. First, financial development in the formal financial sector, represented by a decrease in δ from 0.47 to 0.078 is associated with a decrease in p∗, an increase in τ∗, and hence a decrease in 1− β∗, implying that financial development is associated with a policy of tax enforcement that leads to more tax evasion. This corresponds to Case 2, which we discussed above.
Hence, countries with a more developed financial sector should adopt a policy of tax detection that leads to less-severe tax evasion, more tax compliance (a higher β∗), and a smaller size of informal financial sector. This conclusion provides a theoretical explanation for why developing countries with a less-developed financial sector have
0.50
a larger size of informal sector and more severe tax evasion.
Second, a decrease in δ from 0.47 first leads to a decrease in economic growth, un-til δ reaches 0.275, from where a further decrease in δ leads to an increase in economic growth.43 This implies that there exists a threshold effect of financial development on economic growth or a nonlinear relationship between financial development and economic growth. This threshold effect has been discovered by many recent studies.
Bose and Cothren (1996), for example, present a model with asymmetric informa-tion in which lenders may induce self-selecinforma-tion either by rainforma-tioning and/or screening a fraction of borrowers. While there is no cost associated with rationing borrowers, screening is costly. In this setting, there are two opposite effects of a decrease in the screening cost, which can be viewed as financial development, on capital investment and economic growth. First, it induces the lender to screen more borrowers and hence
43As an alternative view from Table 1, the impact of financial development in the formal financial sector, measured by a decrease inδ, may be ambiguous or insignificant on economic growth when δ >
0.15, because a decrease in δ may lead to a decrease or an increase in economic growth. Nevertheless, whenδ < 0.15 a further decrease in δ significantly enhances economic growth. This implication is consistent with empirical studies presented below.
Table 1) Effects of a Decrease in δ on β∗, τ∗, p∗, g, and W : The Case of α= 0.92
δ 1− β∗ τ∗ p∗ g∗ W∗
0.470 0.684 0.198 0.936 1.796 12.539
0.450 0.656 0.207 0.895 1.767 12.094
0.425 0.621 0.216 0.853 1.737 11.635
0.400 0.586 0.224 0.819 1.713 11.281
0.375 0.548 0.230 0.791 1.696 11.031
0.350 0.512 0.236 0.769 1.684 10.882
0.325 0.473 0.240 0.750 1.677 10.831
0.300 0.434 0.244 0.735 1.676 10.875
0.275 0.393 0.247 0.722 1.680 11.012
0.250 0.352 0.249 0.712 1.689 11.237
0.225 0.309 0.251 0.704 1.703 11.549
0.200 0.265 0.252 0.697 1.722 11.942
0.175 0.221 0.253 0.692 1.745 12.414
0.150 0.176 0.2542 0.687 1.774 12.960
0.125 0.130 0.2547 0.684 1.808 13.576
0.100 0.083 0.2551 0.681 1.847 14.258
0.078 0.042 0.2554 0.679 1.891 15.000
enables more borrowers to obtain credit. Second, screening more borrowers implies that a larger amount of resources are lost, which is detrimental to capital investment and economic growth. Bose and Cothren (1996) demonstrate that a decrease in δ may decrease economic growth initially.44 Only when δ falls below a threshold level will a decrease in δ lead to an increase in economic growth. In Deidda and Fattouh (2002), financial intermediation enables individuals to diversify risk so that savings could be more productive. However, transactions in financial intermediation incur fixed costs.
Thus, the presence of financial intermediation may first lower economic growth, un-til the income of the economy reaches a threshold level.45 Empirical evidence that
44See also Hung and Cothren (2002) and Hung (2005). In these models, financial development may first benefit consumption borrowing, which crowds out capital investment and economic growth. The positive correlation between financial development and economic growth can be obtained only when financial development reaches a threshold level.
45It is generally believed that the level of financial development is positively correlated with income
confirms the existence of the threshold effects of financial development and economic growth can be found in De Gregorio and Guidotti (1995), Odedokum (1996), Deidda and Fattouh (2002), and Rioja and Valev (2004).46
While our model obtains a nonlinear relationship between financial development and economic growth, the mechanism underlying this relationship is totally different from recent studies. By integrating tax evasion with financial dualism, a decrease in δ also leads to two opposite effects on economic growth in our model. First, a decrease in δ induces the agents to allocate more savings into the formal financial sector. This is detrimental to capital investment and economic growth, because the efficiency of banks is less than that of ROSCAs. Second, financial development directly enhances the efficiency of capital investment (through banks), which leads to an increase in economic growth. Table 1 implies that the first (second) effect dominates the second (first) for higher (lower) values of δ.
Finally and more importantly, Table 1 indicates that countries with severe tax evasion can have growth performance similar to that of countries with less-severe tax evasion. For example, the growth rate when δ = 0.47 (less-developed financial sector) and hence 1− β∗ = 0.684 (severe tax evasion) is roughly equal to the one when δ = 0.125 (more-developed financial sector) and 1− β∗ = 0.130 (less-severe tax evasion).
This result captures the growth performance of the Asian tigers in the 1980s and 1990s well, as countries with a less-developed financial sector and severe tax evasion (such as Taiwan and Korea) can have growth performance similar to that of countries with a more developed financial sector and less severe tax evasion (such as Hong Kong and Singapore).
5. DISC US SION
Several aspects of our modeling strategy merit comments. First, we abstract from issues related to tax evasion of labor incomes in this model. Tax evasion of labor in-comes can be introduced by assuming that young agents may underreport their labor incomes to the tax authority or allocate some labor into production in the informal
level. Given this, Deidda and Fattouh’s (2002) model implies a nonlinear relationship between financial development and economic growth.
46While different techniques of estimation in these studies may lead to different conclusions, these stud-ies generally conclude that there is a nonlinear relationship between financial development and economic growth.
sector. This consideration, however, will only complicate our analyses without adding new insights. Recall that the purpose of this paper is to illustrate a possibility that it may be optimal for developing countries to adopt a looser policy of tax enforcement.
As we have shown, this possibility hinges on the two following facts: First, a young agent may deposit a fraction of savings in ROSCAs for the purpose of evading tax on capital incomes. Second, ROSCAs may be more efficient than banks in facilitating capital investment. The fraction of young agents’ savings deposited in ROSCAs, how-ever, is determined by the costs and benefits of doing so. The costs include the rate of returns from deposits on banks and the possibility of concealing capital incomes from being audited. On the other hand, the benefits are the possibility of evading taxes on capital incomes. Obviously, whether the young agent can evade taxes on labor incomes or not plays no role in influencing the costs and benefits of this decision.47
Second, our model has a feature that the choice of deposits in ROSCAs is equiv-alent to the choice of tax evasion. Again, we make this assumption to simplify our analysis. We may, as an alternative, separate this decision into two distinct decisions such that young agents determine the fraction of savings deposits in ROSCAs at pe-riod t and underreport capital incomes (derived from banks and ROSCAs) to the tax authority at period t+ 1. Following Gordon and Li (2009), the government can access banks’ records of agents and use them to enforce tax payment. By contrast, the govern-ment does not have any control on ROSCAs, so taxes on capital incomes derived from ROSCAs are evadable. Given this, the old agent at period t+ 1 will report all capital incomes derived from banks but underreport those derived from ROSCAs. As a ra-tional agent, the young agent, who decides the fractions of savings deposited in banks and ROSCAs at period t, will take this disparity of tax evasion on capital incomes in the next period into account. Specifically, suppose that the government announces that the probability of tax detection p will be increased in the next period (i.e., at period t+ 1), which will induce the (old) agent to report a greater fraction of capital incomes derived from ROSCAs to the tax authority. Knowing that he will be forced to report more capital incomes derived from ROSCAs at the next period, the agent will reduce the fraction of savings deposited in ROSCAs at period t, because deposits in ROSCAs
47The presence of tax evasion of labor incomes will change the amount of after-tax labor incomes and hence savingsSt. The fraction of savings deposited in ROSCAs, however, is not affected by the amount ofSt. Note that tax evasion is less severe in wages and salaries, as both are covered by withholding (Clotfelter, 1983). By contrast, the reporting rate of capital incomes is much smaller. This may give an alternative reasoning that considering tax evasion on capital incomes seems more important. We also thank an anonymous referee for bringing this point to our attention.
incur transaction costs. Consequently, an increase in p at period t+ 1 will result in a higher fraction of reported capital incomes at period t+ 1 and a lower fraction of savings deposited in ROSCAs at period t. In our current model, both are equivalent to a higher value of β∗. Consolidating these two different decisions into one, however, can simplify our analysis without losing generality.
Third, one may think that the integration of the choices of deposits in ROSCAs and tax evasion may not be consistent with reality. Indeed, the majority of tax evasion in developing countries is due to their industrial structure of small retail business and small manufacturing, rather than ROSCAs.48 Nevertheless, we think that our model is consistent with the majority of tax evasion in developing countries, since agents who intend to engage in small business and manufacturing usually seek external funding from informal financial institutions. Tang (1995), for example, provides a comprehen-sive survey on the roles of informal financial institutions in developing countries with a focus on Taiwan. Specifically, credit markets in developing countries are segmented, as large-scale firms seek external financing from banks while small-scale ones borrow from informal financial institutions. More recently, Beck et al. (2008), using a firm-level survey database covering 48 countries, confirm that small firms use significantly more informal finance than large firms, especially in countries with underdeveloped financial markets. Moreover, they find that small firms, even with access to informal and other financing, still face severe financial constraints.49 Given that the majority of tax evasion in developing countries is by small-scale firms which obtain loans from ROSCAs, our setting in which capital incomes derived from deposits in ROSCAs are tax evadable should be consistent with reality.
Our model also abstracts from the possibility that government spending may facil-itate private production as in Chen (2003), who adds tax evasion into Barro (1990) and examines the effects of tax evasion on the optimal tax rate, the optimal share of gov-ernment public spending, and economic growth. By optimizing individual’s behavior of tax evasion, Chen (2003) finds that tax evasion has a negligible effect on economic growth if the degree of externality of public spendings is less than 0.2, which seems to be consistent with some empirical studies.50 Note that a lower degree of the
ex-48We thank an anonymous referee for raising this point.
49This implies that the amount of loans offered in credit markets (through formal or informal institu-tions) is determined by the supply side, not the demand side of small firms. Thus, this paper focuses on deposits in informal financial institutions (the supply side of loans), not the demand side of loans from small firms.
50Various conclusions regarding the degree of externality of public spending are obtained by recent
ternality of public spending actually implies that government spending is relatively unimportant to output production and hence economic growth. From this, the effects of tax evasion on economic growth, through influencing government tax revenues and hence spending, are also unimportant. It should be noted that a small degree of the externality of public spending in Barro (1990) implies that private capital investment is the key impetus to output production and hence economic growth. In other words, if the degree of externality of government spending is small, we should focus on how tax evasion directly influences capital investment, instead of emphasizing how tax evasion affects government tax revenues and spendings. Consequently, we do not consider the possibility that government spending may facilitate private production.
Our analysis focuses on the optimal probability of tax detection. As stated, Chen (2003) examines the optimal tax rate with the presence of tax evasion. In the literature of tax evasion, however, both the tax rate and the optimal probability of tax detection have been the central issues of investigation. Without considering the productive role of government spending, it should be noted that the tax rate and the optimal proba-bility of tax detection are actually interrelated under the balanced government budget.
Indeed, as we have seen from eq. (17), an increase in the optimal probability of tax detection leads to a decrease in the tax rate for a given constant share of government useless spending. In fact, our conclusions will not change if we derive an optimal tax rate first and allow eq. (17) to determine the optimal probability of tax detection.
Since our purpose is to illustrate the possibility that it may be optimal for developing countries to adopt a looser or stricter policy of tax enforcement, we choose to obtain the optimal probability of tax detection, instead of the optimal tax rate.
It may be worth comparing our model with Chen (2003). The focus of Chen (2003) is the optimal tax rate and optimal government spending. The probability of
It may be worth comparing our model with Chen (2003). The focus of Chen (2003) is the optimal tax rate and optimal government spending. The probability of