income inequality in the U.S. Using several labor supply elasticity estimates and using data on incomes and hours worked from the American Time Use Survey, we apply our method to recover individual productivities and preferences.<sup>5</sup> We begin with a baseline set of elasticity parameters taken as averages from a number of labor supply studies discussed in Chetty (2012). Under the baseline elasticities, we infer high income people actually have lower average preferences for consumption compared to middle income people. Essentially, the baseline labor supply elasticities imply that high income people should work substantially more than low income individuals; because we observe a relatively flat hours gradient over the income distribution, we infer that high income people have, on average, lower preferences for consumption relative to leisure. However, we then vary the elasticity parameters and show that we will infer preferences are increasingly important in driving income inequality if we use (1) a larger difference between the income and hours elasticities and/or (2) larger income effects to recover individual productivities and preferences. Thus, a larger difference between the income and hours elasticities and larger income effects imply that more of the difference in incomes between rich and poor is due to preferences.

Finally, to highlight how our findings on the determinants of income inequality change our understanding of the welfare benefits of redistribution, we simulate optimal tax schedules that account for both productivity and preference heterogeneity driving inequality. While the general methodology to recover determinants of income inequality devised in this paper is free of normative assumptions, for the purpose of welfare calculations, we adopt the normative stance developed in Fleurbaey and Maniquet (2006) in which differences in productivities merit redistribution whereas differences in preferences do not merit redistribution. We simulate optimal tax schedules, accounting for both productivity and preference heterogeneity, under different values of the relevant labor supply elasticities and compare these schedules to the optimal tax schedules in which all income inequality is due to productivity heterogeneity as in Mirrlees (1971) or Saez (2001).

Under our baseline elasticity estimates from Chetty (2012), we find that optimal tax rates are actually slightly higher than the Mirrleesian reference case in which all income inequality is due to productivity heterogeneity. Essentially, the elasticity estimates from Chetty (2012) imply that high income individuals actually have lower preferences for consumption, on average, than middle income individuals. Therefore, high taxes are even more desirable than in the Mirrleesian benchmark. However, this finding is sensitive to the elasticity estimates used to recover individual productivities and preferences. We find that a larger difference between the income and hours worked elasticities and larger income effects both imply lower tax rates relative to the Mirrleesian optimal tax schedule.

> 5Because the literature has not reached a consensus on the magnitudes of the different labor supply elasticities, and because current data provides imperfect measurements of hours worked, our empirical application aims to investigate how changing labor supply elasticities affects the relative importance of productivities vs. preferences in driving income inequality.

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