The political economics of redistribution, inequality and tax avoidance

See Borck (2007) for a survey and further references and Strulik (2007) for a critical review of cross-sectional studies that find both supporting and contradicting evidence regarding a positive relationship between income inequality and redistribution.

See also Slemrod (2007), who estimates that the US income tax gap in 2001 amounts to a total of $345 billion, which equals more than 15 % of the estimated actual tax liability.

Similarly, Sandford et al. (1989) and OECD (2013) highlight the economic significance of these costs relative to other public costs.

See also Borck (2004), Borck (2009) and Traxler (2009b) for models with illegal tax evasion instead of legal avoidance.

See Traxler (2012) for an exception. His analysis, however, focuses on the welfare implications when there is sequential majority voting over enforcement and taxes, and does not explicitly consider the relationship between income inequality and redistribution. By contrast, as will be further explained below, our paper focuses on structure-induced equilibrium rather than sequential majority voting. In Sect. 4.5, however, we also study the case where enforcement is set by the government, which in turn brings the analysis closer to the one in Traxler (2012).

It is important to note that our results are not limited to the case of tax avoidance. Rather, as shown in Online Appendix A, they readily carry over to the case of tax evasion. Hence, our model can as well be interpreted as a reduced form analysis of risky evasion activities (Cowell 1990). More precisely, Cowell (1990) shows how the standard portfolio selection approach to tax evasion can be reconciled with the one adopted in the present paper, in which a so-called cost-of-concealment function is specified a priori. However, neither Cowell (1990) nor the aforementioned papers about tax evasion explicitly consider the relationship between income inequality and redistribution in the politico-economic context, which is the aim of the present paper.

Enforcement expenditures encompass any administrative costs that broaden the tax base (Traxler 2012). However, they may also be interpreted as reflecting real enforcement costs, such as auditing expenditures, when considering tax evasion activities. Clearly, the specific kind of any avoidance/evasion activity determines how costly it is for the government to enforce taxation. For example, costs can be extremely high when enforcement requires international cooperation (in case of international income shifting or off-shore tax evasion) or if lobbyism and political constraints prevent the government from effectively closing tax loopholes (such as the exemption for fringe benefits) and reforming the tax system.

According to theory, however, outcomes should be affected by changes in the median to mean income ratio. More precisely, the Meltzer–Richard hypothesis states that, whenever the median voter’s income is less than the mean income, the decisive median voter will support redistributive income taxation. Hence, a more uneven income distribution (i.e., a higher mean-to-median income ratio) is associated with higher taxes. Yet, different measures of income inequality tend to be correlated over time. Corcoran and Evans (2010), e.g., show that, in the United States, both the mean to median income ratio and the Gini coefficient increased quite uniformly over time from 1970 to 2000. See also Cowell (2009) for an extensive treatment of alternative approaches to measuring income inequality.

See also the large literature on the taxable income elasticity surveyed by Saez et al. (2012), which typically finds large behavioral responses to tax changes by top income earners.

Her findings, which are based on numerical simulations, point to a non-monotonic relationship between inequality and redistribution. See also Lee and Roemer (1999).

See Online Appendix A for an extension to the case of tax evasion. There it is shown that the qualitative results hold equally in this case.

Note further that \(K_{ay}\) may be positive or negative. Slemrod (2001), e.g., assumes that higher income makes avoidance less costly and therefore more attractive at the margin, i.e., \(K_{ay}<0\), which is consistent with empirical evidence in Lang et al. (1997).

The assumption that the government incurs convex costs in order to ensure a certain level of tax compliance is in line with the literature on optimal taxation; see also Slemrod and Yitzhaki (1987).

The description of the voting game follows Bethencourt and Galasso (2008).

See Galasso (2008) and Nuscheler and Roeder (2013) for similar characterizations.

It is straightforward to show that our qualitative results carry over to the case where \(Z(y)\) is monotonically increasing and \(K_e(a^*,e,y)\) is monotonically decreasing in \(y\). The difference, however, is that richer individuals would then prefer a higher level of tax enforcement as marginal costs of enforcement are decreasing with income. As a result, we are left with an additional offsetting (rather than reinforcing) effect if income inequality increases; see the discussion after proposition 2.

Note that the denominator in both expressions equals the second-order conditions for \(\tau\) and \(e\), which we assume to hold in the following. See Online Appendix B.

Note that such extreme outcomes are very common in the politico economic literature on tax avoidance/evasion, see Roine (2006), Traxler (2009b) or Borck (2009). The intuition behind the non-existence of an interior equilibrium in the present model is that voters will prefer \(\tau =e=0\) if enforcement is very expensive and ineffective so that the costs of enforcement and increasing avoidance activities exceed additional tax revenues from higher taxes (in this case the required \(\tau\) for supporting a desired level of \(e\), would be higher than the \(\tau\) that the median voter would choose, this is, \(\bar{\tau }(e)>\tau (e)\) for all \(e\) and where \(\bar{\tau }(e)\) is the inverse function of \(e(\tau )\)). By contrast, if enforcement is very cheap and effective in generating tax revenues and tax avoidance is thus low, voters will prefer \(\tau =1\) and the corresponding maximum level of enforcement (in this case \(\bar{\tau }(e)<\tau (e)\) for all \(e\)).

The latter assumption implies that \(\frac{d\tau (e)}{de}>0\) and \(\frac{de(\tau )}{d\tau }>0\).

More precisely, Lee and Roemer (1999) consider a model in which the existence of incomplete credit markets implies that, in equilibrium, poorer households may prefer lower tax rates if they do not invest into private education and are thus unable to benefit from complementarities arising in the joint provision of public and private investments in education. Similarly, Freitas (2012) emphasizes the importance of the tax mix between direct and indirect taxes when there is an informal sector and individuals may evade taxation by supplying labor to this sector.

Similarly, an increase in income inequality affects the politically chosen level of tax enforcement as follows: A poorer median voter prefers a higher level of enforcement, i.e., \(de/dy_m>0\), and a higher tax rate, which in turn makes enforcement more attractive, i.e., \(\frac{de}{d\tau }\frac{d\tau }{dy_m}>0\). These positive effects have to be balanced with the potentially offsetting tax base effect in order to determine the overall effect of rising inequality on the level of tax enforcement.

See also Yitzhaki (1979) and Wilson (1989) for similar arguments.

There is also a recent literature studying the impact of income inequality on the level of public debt, see, e.g., Azzimonti et al. (2014) and references therein. These studies find that governments choose higher levels of public debt when inequality increases.

See also Besley and Persson (2014) who find a strong negative relationship between the size of the informal sector and the level of income taxation and argue that this is due to a large elasticity of taxable income which in turn implies a significant loss of tax revenue when raising taxes.

This view is also supported by recent evidence in Kleven and Waseem (2013) who find that the majority of the population in Pakistan is relatively unresponsive to tax incentives.

See, e.g., Casaburi and Troiano (2013) for a first attempt in this direction.

Note that this specification assumes that a higher income makes avoidance less costly and therefore more attractive at the margin, i.e., \(K_{ay} < 0\). The example could be extended, however, to allow for a specification implying \(K_{ay}>0\). This would not affect the qualitative results. Note further that we assume the cost function to be convex in \(e\), so that every dollar spent on tax enforcement must be more productive than the one before. This would, e.g., be the case if tax enforcement is characterized by some administrative fixed costs. However, enforcement spillovers may also account for this pattern. The importance of such spillovers has, e.g., recently been emphasized by Rinke and Traxler (2011) and Galbiati and Zanella (2012).

It is straightforward to show that the monotonicity conditions (the assumptions of proposition 1) are satisfied so that a unique equilibrium does exist.

Note that the existence of an interior equilibrium further requires \(\delta \ne \eta\) which we assume to hold throughout the remaining analysis.

The tax base effect can further be illustrated as follows: In fact, it is easy to prove that the net effect on the aggregate level of tax avoidance resulting from an increase in income inequality turns out to be positive. Let \(\widetilde{a}\) be the aggregate amount of tax avoidance,In equilibrium, we havewithThus, the positive effect of the tax rate on the aggregate level of tax avoidance outweighs the negative effect through an increase in the level of tax enforcement.

Available at census.​gov/​hhes/​www/​income/​data/​historical/​index.​html.

See data from the IRS at www.​irs.​gov/​uac/​Tax-Stats-2. Data on GDP are taken from the Worldbank; see data.​worldbank.​org/​.

Data on the costs of tax collection are taken from the IRS, available at www.​irs.​gov/​uac/​Tax-Stats-2.

It can be shown that the qualitative results remain unchanged if the timing of events is reversed.

Note that Borck (2004) and Traxler (2009a) do not explicitly address the relationship between tax avoidance and income inequality within this framework. Note further that Traxler (2009a) characterizes the voting equilibrium with general functional forms. In order to illustrate that our main result carries over to such a framework, however, we stick to the simple functional forms of the preceding subsection.

From Eq. 33 is straightforward to see that \(\frac{\partial \widehat{e}}{\partial \tau }>0\).