income tax returns.<sup>2</sup> The data are based on a random sample of tax records led during a particular calendar year. Importantly for our analysis, high-income returns are over-sampled, and we use the appropriate sampling weights to adjust for this. Following Piketty and Saez (2007a) and the literature using tax records more generally, the unit of analysis is a tax unit as dened under US tax law. We thus include singles and married couples without adjusting for dierences in tax unit size.<sup>3</sup> Not every tax unit les a tax return; historically there were high exemption levels and income taxes only applied to the most auent taxpayers. We ignore the non-ling issue in this paper because we would have to make an arbitrary assumption about the income composition of the non-lers. Furthermore, this is unlikely to aect our results, since the fraction of lers is quite high and stable over the period of analysis (94% on average, compared with 9% before World War II). The PUFs are subject to some adjustments, especially at the top, that try to minimize the risk that individual taxpayers can be identied (Winglee et al., 2002). As a result, an observation in the PUF never contains all the information on a tax return, and may include information from other returns. Further information is provided in Appendix A.3, where we also show some robustness checks.

Income is dened as (taxable) gross market income, as reported on federal income tax returns.<sup>4</sup> We follow Piketty and Saez (2007b), Piketty et al. (2018) and Saez and Zucman

> 2Like other papers using these data (e.g. Saez and Zucman, 2016 or Piketty et al., 2018), we exclude the micro data for 1960, since it contains fewer tax return variables. There exist no PUFs for 1963 and 1965. More information on these data is available at http://users.nber.org/~taxsim/gdb/.

> 3Our results are robust to including only tax units that have two adults. Between the 1960s and 2000s, the average tax unit size declined from 2.6 to almost 2 persons. The proportion of married tax units declined by 10pp in the whole population but slower at the top of the distribution (Saez, 2004). Lakner (2014) shows that the trend in top shares is robust to accounting for tax unit size. Piketty et al. (2018) also nd very similar trends for tax units and adults. Tax units tend to be smaller than households; Hungerford (2010) estimates 75% of households to have one tax unit, and another 17% to have two tax units.

> 4We exclude any income that is not taxable (e.g. non-taxable fringe benets such as health insurance), since it is not reported on the tax return. Imputing such non-taxable incomes from the US Current Population Survey does not have a large eect on top income shares (Bivens and Mishel, 2013; CBO, 2012). We also exclude non-market or transfer income such as Social Security and unemployment insurance benets. Since the PUFs do not capture all tax liabilities (e.g. exclusion of state and local taxes), we focus on gross incomes, like Piketty and Saez (2007a) and most of the literature on top incomes. It is also unclear how to split total federal income taxes between capital and labor without additional imputations. Finally, our analysis uses income that is observed from tax records (like Piketty and Saez, 2007a), which does not match national income (like Piketty et al., 2018) or macro totals in the nancial accounts (like Saez and Zucman, 2016) (also see Figure A.5).

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