Revenue-maximizing top earned income tax rate in the presence of income-shifting

The idea that lowering top marginal tax rates would increase tax revenue is often raised in the popular debate.

See, for example, http://www.forbes.com/sites/mikepatton/2012/10/15/dotax-cuts-increase-government-revenue/#29a1d8fb48a3.

We analyze this question in the context of Finland, which has one of the world’s highest marginal earned income tax rates on top earners. The Finnish income tax system is progressive, and the top marginal earned income tax rate (including employee social security contributions) was approximately 57% in 2015.

Throughout the article, we use the term “top tax rate” to refer to the marginal tax rate of top income earners.

Piketty et al. (2014) provide a theoretical framework for calculating the revenue-maximizing top tax rate in the presence of income-shifting, with top tax rate calculations for typical parameter values for the United States. Top tax rate calculations have also been provided for Sweden (Pirttila and Selin 2011b) and Denmark (Kreiner and Skov 2016), two other Nordic high tax countries. Riihela et al. (2014) provide an earlier discussion of top tax rates in the Finnish context. We contribute to this discussion by providing a careful and systematic account of the assumptions behind top tax rate calculations, illustrating how the appropriate choices of parameter values and calculation of the current top tax rate depend on the details of the tax system, and demonstrating how the choices made may affect policy conclusions. Another key feature of our analysis is that we explicitly account for the effect of income-shifting on the analysis of the revenue-maximizing top tax rate in a high tax country.

We demonstrate that policy conclusions—even the sign of the comparison between current and revenue-maximizing tax rates—depend critically on the assumptions made, for example, on how to calculate the current top marginal tax rate, or whether or not to account for income-shifting in the analysis. Therefore, the policy discussion revolving around top tax rates has little content unless the assumptions in the calcultions are made explicit. We find that the current top tax rate on earnings in Finland is likely to be below the revenue-maximizing rate.

The paper proceeds as follows. Section 2 sets out the theoretical background behind our calculations. Section 3 provides a discussion of the considerations that need to be taken into account when choosing parameter values in the Laffer curve calculations. Section 4 provides the results for our analysis of the Finnish case. Section 5 makes some further remarks on how the results should be interpreted in the context of making recommendations for tax policy.

The relationship between tax rates and tax revenue is described by the so-called Laffer curve. When taxation is at a moderate level, tax revenue is increasing in the tax rate. At high levels of the tax rate, the disincentive effects of taxation (e.g., because of reduced labor supply) may become so severe that tax revenue may start to fall if the tax rate was further increased. The Laffer curve is often discussed in the context of top incomes: as top incomes are often most heavily taxed, the Laffer curve considerations are likely to be particularly relevant at the top of the income distribution.

The revenue-maximizing tax rate for top incomes depends on how taxable income reacts to taxation (i.e., the elasticity of taxable income, ETI), as well as on the shape of the income distribution (e.g., the number of individuals in the top tax bracket). Following Piketty et al. (2014), consider the taxation of incomes (z) above a certain limit (z). It can be shown that the revenue-maximizing top tax rate is given by the following formula: tmax=11+a⋅<!-- ? -->e$$\begin{array}{} \displaystyle t^{max}=\frac{1}{1+a\cdot e} \end{array} $$(1)

where e=1−<!-- - -->tzdzd(1−<!-- - -->t)$\begin{array}{} \displaystyle e=\frac{1-t}{z}\frac{dz}{d(1-t)} \end{array} $ is the ETI in the top tax bracket with respect to the net-of-tax rate (1 − t) and a=zz−<!-- - -->z¯<!-- ? -->$\begin{array}{} \displaystyle a=\frac{z}{z-\bar z} \end{array} $ is the so-called Pareto-parameter that describes the relevant features of the income distribution. The revenue-maximizing top tax rate is decreasing in the responsiveness of incomes to taxation (captured by e) and the number of individuals who are affected by these adverse incentives (i.e., the thickness of the top tail of the income distribution, captured by a).

However, the formula presented in equation (1) for the revenue-maximizing income tax rate is applicable only under the assumption that the elasticity e consists of labor supply responses only. In general, the ETI captures all ways in which earned income responds to changes in the marginal earned income tax rate: in addition to changes in labor supply, it captures changes in tax avoidance and evasion, and in particular, it includes the reduction/increase in the earned income tax base caused by income-shifting, which we discuss below. Therefore, formula (1) is not fully applicable in a Nordic dual income system such as that of Finland or other tax systems in which possibilities for income-shifting are prevalent.

More precisely, in the presence of income-shifting, the ETI is not sufficient to measure the revenue (or welfare) losses from earnings taxation. This is because some of the tax revenue that is lost when the tax on earnings is increased is returned through the other tax base to which income is shifted. In this case, the revenue-maximizing top tax rate on earned income is given by tmax=1+t2⋅<!-- ? -->a⋅<!-- ? -->s⋅<!-- ? -->e1+a⋅<!-- ? -->e$$\begin{array}{} \displaystyle t^{max}=\frac{1+t_2\cdot a\cdot s\cdot e}{1+a\cdot e} \end{array} $$(2)

where t₂ is the marginal tax rate on the alternative tax base to which earnings can be shifted and s is the part of the total taxable income elasticity e that is due to this income-shifting behavior (Piketty et al. 2014; Saez et al. 2012). The analysis assumes that t₂ is fixed, that is, we consider the revenue-maximizing top earned income tax rate for a given level of the tax rate on the alternative tax base. Incomeshifting (s > 0, t₂ > 0) implies that the revenue-maximizing tax rate in equation (2) is higher than the benchmark case in equation (1).

As income-shifting possibilities are prevalent in the Finnish context, we use the case without income-shifting (corresponding to equation (1)) only as a benchmark. In most of the analysis, we use equation (2) to calculate the revenue-maximizing top earned income tax rate for Finland. Empirical evidence on the extent of incomeshifting in Finland is provided by Pirttila and Selin (2011a) and Harju and Matikka (2016).

We now turn to provide a roadmap of the considerations behind the choices of parameter values in the Laffer curve calculations. As we will argue, the assumptions made in the calucations have a crucial impact on the results of the analysis, and it is, therefore, important to make them explicit. For example, assumptions behind calculating the current effective top marginal tax rate are rarely discussed; but obviously, these assumptions affect the benchmark to which the revenue-maximizing tax rate is compared and thus may even affect the sign of the comparison. Without providing an explicit account of the assumptions made, it could even be argued that the calculations have little content when it comes to drawing policy conclusions.

We can now compare the current top earned income tax rate with the revenue-maximizing rate. Table 1 calculates the revenue-maximizing top tax rate for different parameter values. We start from a benchmark in which we assume that there is no income-shifting. This case is presented on the first row of Table 1. Given that this is only a benchmark, we consider only one value for the taxable income elasticity (Matikka 2016) in this case. When there is no income-shifting, assuming a modest elasticity (0.2) is reasonable. In this case, the revenue-maximizing top income tax rate would be 63%, which is very similar in size compared to the current top rate of 65%. (Note that all numbers refer to the effective marginal top tax rate that includes commodity taxation and empolyee social security contributions, as discussed earlier.)

Table 1

The revenue-maximizing top earned income tax rate for different parameter values.

Given the prevalence of income-shifting among top earners, it is important to calculate the revenue-maximizing income tax rate in such a way that income-shifting possibilities are taken into account. This is done on the remaining rows of Table 1. For example, for the ETI estimate of 0.2 from Matikka (2016) and making the assumption that income-shifting accounts for 50% of the overall response of top earners, the revenue-maximizing top earned income tax rate will be 75%. Therefore, the revenue-maximizing top tax rate for these parameter values is clearly higher than the current EMTR, 65%.

On the other hand, if the ETI at the top of the income distribution is considerably higher than that found in Matikka (2016), then the current top tax rate may be quite close to the revenue-maximizing one. For the current top tax rate to exceed the revenue-maximizing rate, the ETI would have to be above 0.42 (if the share of income-shifting in the ETI is 0.7) or above 0.35 (if the share of income-shifting is 0.5). Given that the ETI estimates in the relevant literature (e.g., those found for other Nordic countries) are below these numbers, it appears likely that the current top income tax rate is below the revenue-maximizing rate. It has to be kept in mind, however, that the above calculations are subject to considerable uncertainty, not least because of the uncertainty involved in estimates of e and s. Therefore, it is also possible that the current top tax rate may be close to the revenue-maximizing level.

Some futher notes concerning the above calculations are in order. First, as mentioned earlier, we have included consumption taxes in calculating the current top tax rate. As consumption taxes affect work incentives, in our view, it is advisable to take consumption taxes into account in the calculations. However, to our knowledge, none of the ETI estimates in the literature actually take into account consumption taxes. While there are good reasons for this practice in the ETI literature, for example, ensuring that ETI estimates are more comparable across countries, it implies that there is somewhat of a discrepancy between the EMTR used in our calculations and the ETI estimates. To eliminate the discrepancy, existing ETI estimates should be revised downwards.

This is because baseline tax rates including consumption taxes are higher than the baseline tax rates used in the ETI studies—and therefore, baseline net-of-tax rates including consumption taxes are correspondingly lower. Hence, a 1% change in the baseline net-of-tax rates in the ETI studies corresponds to a more than 1% change in the netof-tax rate including consumption taxes. A 1% change in net-of-tax rates including consumption taxeswould, therefore, lead to a smaller response than those typically estimated in ETI studies.

Finally, we have not accounted for the possibility of tax-motivated emigration in our calculations. If high taxes were to cause a significant proportion of high-income individuals to emigrate, this would call for lower tax rates at the top (Brewer et al. 2010). There is relatively little empirical evidence on the effects of taxation on migration decisions to date (Kleven et al. 2014). Piketty and Saez (2013) conclude that the migration elasticity is likely to be fairly low in most countries. Furthermore, in Finland, the migration elasticity is likely to be lower than that in many other countries because of the relatively low fraction of foreigners (whose migration elasticity is likely to be higher than that of natives) in the population. The effect of migration on optimal top tax rates is, therefore, likely to be fairly limited in practice, even though its importance may increase if labor markets become more integrated internationally.

In this paper, we have discussed the role of income-shifting in evaluating the revenue-maximizing top tax rate on earned income. Taking into account income-shifting from the earned income tax base to the more leniently taxed capital income tax bases increases the estimate for the revenue-maximizing rate. Under reasonable assumptions on overall tax elasticities estimated for Finland and other Nordic countries, income-shifting responses imply that the current top tax rates are below the revenue-maximizing rates.

However, it is important to note that the Laffer curve calculations do not imply that top earned income tax rates should be increased. First, the analysis was conducted keeping the capital income tax rate fixed. When tax rates on both earned income and capital income can be adjusted, income-shifting considerations are typically regarded as providing an argument for moving the two tax rates closer together: the two rates should be closer to each other than they would be if income-shifting was not a concern (Piketty and Saez 2013). It should also be noted that the extent of income-shifting is not completely beyond the control of policy-makers. Rather, income-shifting or tax avoidance in general are to some extent determined by the features of the tax system (Piketty et al. 2014) and the efficiency of tax collection can be improved by limiting the opportunities for tax avoidance if the costs of combatting avoidance are not too high. From this perspective, the capital income tax rate (in particular taxation of dividends) and the top earned income tax rate in Finland are still quite far apart.

If capital income and earned income have the same taxable income elasticity, the two tax rates should be equalized to maximize tax revenue (Piketty et al. 2014; Piketty and Saez 2013). This also assumes that shifting and labor supply elasticities are homogeneous within the population. Recent research has argued that a gap between the two tax rates might be optimal if individuals who engage in income-shifting also have more elastic labor supply (Selin and Simula 2017). More generally, taking into account considerations beyond income-shifting, there is no unanimity in the literature on whether the tax rates should be identical. See, for example, Diamond and Saez (2011) for a policy-oriented discussion on capital income taxation.

Finally, it needs to be stressed that the above discussion relates to tax revenue maximization only. However, the objective of the government should be to maximize the welfare of citizens, not tax revenue. The analysis is, nevertheless, also relevant for discussions about welfare, as the revenue-maximizing tax rate provides an upper bound for the welfare-maximizing tax rate: increasing tax rates above the Laffer rate would make no sense, because it would make taxpayers worse off (because of lower disposable income) and also would reduce tax revenue (as we would be on the downward sloping part of the Laffer curve). Therefore, it is clear that tax rates should, in most cases, be lower than and never exceed the revenue-maximizing rate.

The revenue-maximizing tax rate and the optimal tax rate are equal only if the social welfare weight of top income earners is zero, as in the Rawlsian social welfare criterion. This type of situation may also arise in the context of utilitarianism. Roughly speaking, this would occur if the marginal utility of money goes to zero when income is very high. See, for example, Diamond and Saez 2011, p. 169 for a discussion.