# The Elasticity of Taxable Income and the Implications of Tax Evasion for Deadweight Loss

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2 alternative to earning \$1 of taxable income is to take 6 minutes of leisure time. 1 In Figure 1, at all points along the marginal cost curve to the left of Q*, 6 minutes of leisure are worth less than \$1 to the person. At all points along the marginal cost curve to the right of Q* in Figure 1, 6 minutes of leisure are worth more than \$1 to the person. So in the absence of taxes, the person chooses to earn a taxable income of Q*, at which point the marginal benefit of one more dollar of taxable income is just equal to the marginal cost of earning that dollar (that is, the 6 minutes of leisure the person has to give up to get the dollar is worth just a dollar). The person would not go beyond Q*, because beyond that point, the leisure given up is more valuable to the person, at the margin, than the additional \$1 of taxable income. Figure 1 The deadweight loss from a change in taxable income in response to taxation Marginal benefits and marginal costs (\$) Deadweight loss Marginal cost of taxable income = supply curve for taxable income = marginal benefit of next best alternative) \$1 \$(1-t) t Marginal social benefit of taxable income Qtax Q* Quantity of taxable income (\$) Now suppose the government imposes an income tax at a tax rate of t, say, 30%. In that case, the marginal private benefit to the individual of earning \$1 of taxable income is only \$(1-t), or \$0.70. When the tax is in effect, the person will only choose to earn taxable income up to the point where the marginal cost of earning that income (or in other words, the marginal benefit of the next best alternative) is \$(1-t). So in Figure 1, when the tax is in effect, the person chooses to earn an amount of taxable income equal to Qtax. For example, if the only alternative to earning taxable income is once again to take leisure, and the hourly wage before taxes is \$10 per hour, the person will choose leisure over work as soon as 6 minutes of leisure is worth \$0.70, which happens when taxable income is at Qtax. The deadweight loss caused by taxation is then the area of the gray shaded triangle in Figure 1 above. It represents the loss of economic surplus, in dollars, arising 1 If your wage is \$10 per hour, it takes 60 minutes / \$10 = 6 minutes to earn \$1. 2

3 from the fact that the tax induces people to switch away from something that in the absence of taxes was worth more to them (the taxable income) and towards something (in this example, leisure) that was would have been worth less to them in the absence of taxes. When the problem is framed in this way, it is easy to see how the responsiveness of overall taxable income to marginal tax rates could tell us about deadweight loss arising from all forms of behavior which change in response to taxation. All alternatives to earning taxable income can be thought of as involving some cost that makes them imperfect substitutes for taxable income. The height of the marginal cost curve at each point in Figure 1 can be thought of as the marginal benefit of the next best alternative to earning that particular dollar of taxable income, whatever that alternative might be. Consider some examples. One alternative to earning \$1 of taxable income might be to take the \$1 of labor compensation as a non-taxable fringe benefit (e.g., health insurance, or nicer office furniture) instead of as a taxable cash wage. An employer should be indifferent between providing you with \$1 of taxable cash wages or \$1 of non-taxable fringe benefits, because they each cost the employer \$1. But given the choice, an employee with a 30% marginal tax rate would prefer that the employer provide a fringe benefit that costs the employer \$1 as long as the marginal benefit of that fringe benefit to the employee is greater than \$0.70. So in Figure 1, the height of the marginal cost curve at a particular point might represent the marginal value of a non-taxable fringe benefit that costs the employer \$1 to provide, if that is the next best alternative to earning that particular dollar of taxable income. When the 30% tax is imposed, some of the foregone taxable income between Qtax and Q* represents switching from work to leisure, and some represents switching from cash wages to non-taxable fringe benefits. Both are sources of deadweight loss, in both cases the person is sacrificing taxable income that is worth a dollar to society (including both the benefit to the taxpayer and the value of the tax revenue going to the government) in order to substitute towards something that is worth less than a dollar. Consider another example. Suppose that one alternative to earning and reporting taxable income is to pay a fancy tax lawyer to help you take advantage of a complicated tax shelter that enables you to receive income without having to pay tax on it. This is an example of tax avoidance. Tax avoidance reduces the amount of taxable income you report to the tax authorities. The marginal benefit of shielding \$1 from taxation in this way is less than \$1, however, because it involves some real resource costs (for example, the opportunity cost of the time of the tax lawyer). So in Figure 1, the height of the marginal cost curve at a particular point might represent the marginal value of earning \$1 but shielding it from taxation through a tax shelter, if that is the next best alternative to that particular \$1 of taxable income. In our example, the person will choose to engage in the tax shelter as long as the net benefit to him or her from doing so (\$1 less the associated costs, such as paying the tax lawyer) is greater than \$0.70. Once again, this is a source of deadweight loss, as the person is switching from something that is worth \$1 3

8 tax cut better off, without hurting anyone else, because tax revenues actually went up. We can see that personal income tax revenue in Russia did go up after the reform (Gorodnichenko et al. Table 1), but this is not convincing evidence because we need a counterfactual other things were changing over time in Russia that also affected incomes and tax revenues, so we need to know what would have happened to tax revenues in the absence of tax reform (the counterfactual), and we should only assign credit (or blame) to the reform for how tax revenues changed relative to that counterfactual. In the Gorodnichenko et al. study, the counterfactual is provided by observing changes in income among middle income people who did not experience large changes in tax rates. Their difference-in-differences estimates imply that taxable income went up by 19 percent more over time for the high-income treatment group who experienced the tax cut, compared to the middle-income control group that did not experience the tax cut (Table 10 of Gorodnichenko et al). To get a sense of the implications of this behavioral response for tax revenues, here is a rough back-of-theenvelope calculation. Consider someone who earns and reports 100,000 Rubles of taxable income before the reform. In the time before the reform, the tax was 13% of taxable income below 50,000 rubles, and 21% of taxable income above 50,000 Rubles, so this person would have paid 13%*50, %*50,000 = 17,000 rubles in tax. The estimates in Gorodnichenko et al. suggest that, holding other influences on income constant, the flat tax reform caused such a person to increase taxable income by 19%, to 119,000 rubles, all of which would be taxed at a flat rate of 13%. This produces tax revenue of 13%*119,000 Rubles = 15,470 rubles. This implies that even with the increased reporting of taxable income, the reform caused tax revenues collected from this person to decline by 17,000 15,470 = 1,530 rubles. That implies that there is a tradeoff here. The evidence suggests that the tax reform reduced tax evasion and reduced deadweight loss, so there were some benefits in terms of both efficiency and equity (i.e., better horizontal equity between evaders and non-evaders). But the reform also seems to have reduced tax revenues collected from high-income people relative to what would have been collected in the absence of the reform. The latter consequence is costly in terms of vertical equity (depending on one s philosophy of distributive justice) and in terms of ability to finance public goods. One way to put this in perspective is to figure out how much revenue would have been lost if there were no behavioral response. If we imposed a 13% tax rate on a taxable income of 100,000 rubles, it would have brought in 13,000 rubles in tax revenue, a decline of 4,000 rubles relative to the pre-reform progressive tax system. The behavioral response caused revenues for this person to decline by only 1,530. So the behavioral response to the tax reform caused tax revenue to decline by only 1,530 / 4,000 = 38% of the decline that would have happened had there been no behavioral response. This suggests that the reform did Russia some revenue, but not nearly as much as would have happened in the absence of the huge increase in income that largely reflected improved compliance. With that said, this is admittedly just a back of the envelope calculation. An accurate estimate of the revenue consequences of the Russian flat tax reform would require detailed microsimulation exercise, which takes into account the actual distribution of incomes and tax payments in Russia before and after the reform. 8

9 While the evidence Gorodnichenko et al. does suggest that the Russian flat tax involved a tradeoff (better efficiency and compliance, in exchange for reduced tax revenue from high income people), an econometric analysis of a Polish flat tax reform by Kopczuk (2012) suggests that the Polish reform may have been very close to a Pareto improvement, making those who got the tax cut better off while costing little or no revenue. Whether the behavioral response to taxation represents tax evasion or changes in real economic behavior can matter for other reasons as well. Slemrod (1994) points out one important reason why the policy implications might differ. If the reason people reduce their taxable incomes when marginal tax rates go up is that they are changing their real economic behavior (for example, working less), there is not much the government can do to avoid the deadweight loss from taxation except to lower marginal tax rates. So if this is what is going on, it suggests that the deadweight loss associated with taxation is unavoidable, and therefore we might want to reduce how much redistribution the government tries to do. The deadweight loss would imply that redistribution is economically costly, that there is an unavoidable leak in Okun s bucket, which reduces the optimal amount of redistribution (at least in a Utilitarian framework). If, however, the reason that people reduce their incomes when marginal tax rates go up is that they are engaging in more tax evasion or tax avoidance, then the government may have another alternative to reducing marginal tax rates that avoids some of the deadweight loss it could choose to do a better job of enforcing taxation, and reform the tax code to reduce opportunities for tax avoidance. In other words, maybe it could fix the leak in Okun s bucket. Improving tax administration involves real resource costs, so it does not necessarily enhance social welfare to do so, but it might. This also points out that the elasticity of taxable income is not some immutable behavioral parameter rather, it can be changed by public policy. A tax system that is well-enforced, with a broad base and few loopholes, deductions, and other opportunities for tax avoidance, will tend to involve a lower elasticity of taxable income. In that case, raising marginal tax rates to pay for public goods or redistribution would involve less deadweight loss, compared to doing so in the context of a tax system with a narrow base and lots of easy opportunities for evasion and avoidance. References Chetty, Raj "Is the Taxable Income Elasticity Sufficient to Calculate Deadweight Loss? The Implications of Evasion and Avoidance." American Economic Journal: Economic Policy 1, no. 2: Feldstein, Martin "The Effect of Marginal Tax Rates on Taxable Income: A Panel Study of the 1986 Tax Reform Act." Journal of Political Economy. 103, no. 3:

10 Feldstein, Martin Tax Avoidance and the Deadweight Loss of the Income Tax." Review of Economics and Statistics, 81(4): Gorodnichenko, Yuriy, Jorge Martinez-Vazquez, and Klara Sabirianova Peter "Myth and Reality of Flat Tax Reform: Micro Estimates of Tax Evasion Response and Welfare Effects in Russia." Journal of Political Economy. Vol. 117, no. 3. Kopczuk, Wojciech The Polish Business "Flat" Tax and its Effect on Reported Incomes: a Pareto Improving Tax Reform? Working Paper, Columbia University <http://www.columbia.edu/~wk2110/bin/polishflattax.pdf>. Saez, Emmanuel, Joel B. Slemrod, and Seth H. Giertz "The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review." Journal of Economic Literature. Vol. 50, No. 1, pp Slemrod, Joel "Fixing the Leak in Okun's Bucket: Optimal Tax Progressivity When Avoidance Can Be Controlled." Journal of Public Economics. 55, no. 1: Slemrod, Joel "A General Model of the Behavioral Response to Taxation." International Tax and Public Finance 8, no. 2:

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