behavioral responses to taxation (e.g., Blundell and MaCurdy, 1999), we assume that income effects are negligible (so that _ξz_<sup>_u_=</sup><sup>_ξ_</sup> _z_<sup>_c_and</sup><sup>_ξ_</sup> _h_<sup>_u_=</sup><sup>_ξ_</sup> _h_<sup>_c_).27</sup> After briefly discussing what the baseline results imply about the drivers of income inequality, our main analysis concerns performing the inversion from labor supply decisions to primitives under different assumptions on the relevant elasticities, highlighting how deviations from the baseline estimates change our inference about the determinants of income inequality. We show that (1) larger differences between the income and hours elasticities with respect to the tax rate (i.e., larger effort elasticities) and (2) larger income effects will both lead us to infer that preference heterogeneity is increasingly important in driving income differences between rich and poor. We also discuss briefly at the end of this section how our findings change if allow for heterogeneity in the elasticity schedules (roughly in line with the findings of Gruber and Saez, 2002) and how we can account for labor market frictions using survey data on actual and preferred hours.

# **5.1 Data on Incomes and Hours Worked**

We will use data on incomes and hours worked from the American Time Use Survey (ATUS), which is a survey conducted on a subset of individuals who have participated in the CPS.<sup>28</sup> In addition to income data, the ATUS asks respondents to meticulously detail all of their activities on a particular (random) “diary day”. We then assume that this noisy “diary day” measure is representative of this individual’s average daily hours worked. We also do not have days worked per year, so we impute that all individuals work 250 days a year unless they report being part time and work _>_ 8 hours on their diary day, in which case we impute their days worked as 125. Our sample consists of all individuals reporting a positive income, thereby abstracting from the possibility of joint familial labor supply decisions. We show that our findings all hold with the smaller sample of single individuals, shown in Appendix C.3. We drop individuals who say they are involuntarily under-employed, hopefully mitigating the effect of labor supply frictions on our inferences. Our final sample from the ATUS then consists of data on (inflation adjusted) incomes and diary hours for 34,470 unique individuals from the years 2003-2015. See Appendix B for more detail on our sample construction.

Our measure of hours worked is noisy due to measurement and aggregation errors. Importantly, this noisy measure of hours worked is fine for our purposes so long as the noise is unbiased in the sense that the sample joint distribution of incomes and hours worked is representative of the true population joint distribution. Even if the sample

> 27We also assume that all individuals face a constant linear tax rate even though our method is easily adaptable to tax schedules with kinks, see Appendix A.4. This is for simplicity and consistency with the main body of the text and is likely inconsequential given the lack of bunching in the empirical income density.

> 28We discuss in Appendix B.2 why we do not use the hours worked measure from the CPS.

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