Optimal taxation and growth with public goods and costly enforcement

Abstract

This paper studies optimal direct and indirect taxation in an endogenous growth framework with a productive public good and costly tax collection. Optimal (growth-maximizing) tax rules are derived under exogenous collection costs. The optimal direct–indirect tax ratio is shown to be negatively related to the administrative costs of collecting these taxes, as documented in cross-country data. This result also holds under endogenous collection costs (with these costs inversely related to administrative spending on tax enforcement), but for these to generate significant effects on tax collection requires implausibly high degrees of efficiency in spending, or the allocation of a large fraction of resources to tax enforcement. Depending on how it is financed, the latter policy may entail adverse effects on growth. Improving ‘tax culture’ and the sense of civic duty through greater budgetary transparency may be a more effective policy to improve tax collection and promote economic growth.

Keywords:

• tax structure
• growth
• costly enforcement
• public goods

JEL Classification:

• E62
• H21
• O41

Acknowledgements

We are grateful to Sarantis Kalyvitis, an anonymous referee, and participants at various seminars for helpful comments.

Notes

 1. Adding revenue from seigniorage and trade duties, indirect tax revenue is more than twice as large (as a fraction of total revenue) in developing countries compared to developed countries, at 76% versus 35%.

 2. As argued by García-Peñalosa and Turnovsky (2005, 1052), abstracting from labor-leisure choices is a reasonable approximation when it comes to developing countries—particularly the poorest ones. Given the low levels of consumption to begin with in these countries, it is unlikely that much leisure is consumed. In addition, we do not discuss the composition of direct taxes.

 3. We could of course assume that the share of productive spending is also determined optimally; however, this issue has been discussed at length in the literature; see Agénor and Neanidis (2011) and the literature therein.

 4. Assuming that productivity-enhancing services are nonexcludable rules out the imposition of an explicit user fee by the government, as for instance in Ott and Turnovsky (2006). However, because we assume that the implicit rent generated by the public good accrues to the household, the direct tax rate can be thought of as playing in part the role of a user fee.

 5. In what follows, time subscripts are omitted for simplicity. Also, is used to denote the time derivative of any variable x.

 6. Productivity-enhancing services could be taken to affect also household utility. However, as demonstrated in the working paper of this article, this would complicate the analysis without altering the thrust of our results.

 7. To ensure that revenues from tax h are positive requires imposing .

 8. See for instance Turnosky (1996) for a model with government debt. However, in his model, debt plays no welfare-enhancing role. Ferreira (1999) and Holman and Neanidis (2006) develop endogenous growth models where public spending is financed by the inflation tax. In addition, given our focus on possible trade-offs between distortionary taxes, we do not account for lump-sum transfers.

 9. In addition, our aim is to explain an actual fact—greater reliance on consumption taxes, rather than subsidies (see Figure 1). Note also that the maximization problem with respect to is ill defined if . Intuitively, the reason for this is that in this case there are only benefits associated with a higher consumption tax rate; see the discussion at the end of the previous section.

10. Recall that , which is equal to , is the net elasticity of output with respect to productivity-enhancing public services. It reflects both the elasticity of output with respect to labor, , and the marginal benefits of a variety of public services—including infrastructure, education, and health—on productivity, . Using a standard value of 0.6, and assuming a value of (which may be on the low side for a low-income country if public services consist of health and education, in particular) gives .

11. The quantitative effect of and on illustrated in Table 2 is not very sensitive to the parameter values used for and , and neither is the pattern identified in the table. In addition, this pattern holds even though in some cases we have , that is, an enforcement technology that is relatively more efficient for collecting direct taxes.

12. Note that in Table 4, a doubling of the collection costs and (from 5 to 10) lead to a slight reduction in the direct-to-indirect tax revenue ratio, as defined in equation (21). The reason why this effect is not neutral is because the tax rates affect consumption and output through different channels, as discussed in previous sections.

13. These factors may include corrupt practices by tax officials, tax evasion by households, rules of punishment for bureaucrats and households who fail to abide by the tax law, and so on.

14. The simulation values are generated by assuming that the government determines the optimal values of both tax rates by maximizing total revenues, given by the right-hand side of equation (8), as a fraction of output.

15. Rewriting equation (23) as a monic polynomial, Descartes' rule of sign implies that this equation has either two positive real roots, or none at all, depending on parameter values. For obvious economic reasons, we focus on the first case and consider only bounded solutions, that is, .

16. From equation (8), it is possible to have with direct tax revenues remaining positive, given that .

17. Our analysis could be further extended by endogenizing tax culture through and . This could occur through civic education, where the introduction of courses at school in young age can stress the benefits of paying taxes as adults. This could lead to both lower tax evasion and higher tax revenues.

18. We would also expect to be substantially lower than , as a result of the ease with which consumption taxes can be raised. However, this inequality has no bearing on our results.

19. In the working paper version of this article (available upon request), it is shown that, with endogenous collection costs, an increase in the efficiency of the tax enforcement technology increases the growth-maximizing share of spending on tax enforcement.

20. We could also consider how tax inefficiency responds to the allocation of public spending on tax enforcement between the two taxes (), but we choose to treat both taxes with an equal weight; .

21. Note that in presenting the theoretical model, we imposed the restriction in equation (10)—which obviously does not hold in the context of the present exercise. A proper interpretation now is that represents the share of government spending allocated to unproductive items.

22. The pattern and the underlying intuition of the results displayed in Table 5 do not change even if we set as our starting point.

23. As there is no guidance in the literature on the magnitude of tax enforcement technology, , we experimented with various values, ranging from zero to a few thousands.

24. Note that the increase in is assumed to be financed by a cut in a category of government spending that has no output-enhancing effects. In terms of our model, this means that an increase in is not funded by an equivalent decrease in . Put differently, and in line with the discussion in footnote 21, we assume here that a fraction consists of unproductive spending. Otherwise, if public services are highly productive (that is, if is high), a shift in spending toward tax administration would also have a large, adverse effect on growth, as illustrated in a related context by Agénor and Neanidis (2011).

25. See Judd (1985) and Chamley (1986). Chari and Kehoe (1999) provide an overview of research on the issue of capital taxation. The Chamley-Judd result is derived under the assumption that households can fully insure against idiosyncratic risk. Some contributions have shown that if, by contrast, idiosyncratic risk is not insurable, positive capital taxation may be optimal. Even if insurance markets are complete, or equivalently households face no idiosyncratic risk, financial market frictions (in the form of borrowing constraints) may make the taxation of capital income desirable.

26. This result hinges upon the assumption that the accumulation of human capital requires the use of both human and physical capital. As the analysis in Milesi-Ferretti and Roubini (1998a, 1998b) indicates, the growth implications of factor income taxation in this type of models is sensitive to the technology in the human capital producing sector. If human capital is not a reproducible factor in production, the optimal tax on labor income may be zero.

27. This is also an important issue for industrial countries. For the United States, for instance, De Fiore (2000, 28) estimates that in the late 1990s collection costs accounted for 0.6% of revenues, whereas compliance costs amounted to 9.1%.