in one of the world’s largest cash transfer programs, Bolsa Fam ́ılia (BF). BF is a Brazilian anti-poverty program that started in 2003 and gave benefits to around 14 million households as of 2014 (Gazola Hellmann, 2015). Eligibility for BF benefits is based on self-reported household income, likely generating substantial scope for misreporting given that approximately 50% of economically active individuals work in the informal sector (Henley, Arabsheibani and Carneiro, 2009). Importantly, the BF schedule features a pronounced notch that was expanded in June 2014. Prior to June 2014, households reporting a per-capita income below the extreme-poverty threshold of R$70 per-month were eligible for an unconditional monthly benefit of R$70 per-month, whereas households reporting an income above this threshold were not.<sup>3</sup> In June 2014, both the eligibility threshold and benefit were raised by 10%: the eligibility threshold increased from R$70 per-capita, per-month to R$77 per-capita, per-month, while the unconditional benefit increased from R$70 per-month to R$77 per-month.

We have access to administrative data spanning December 2011 to September 2016 from Cadastro Unico,<sup> ́</sup> which is the Brazilian government’s national registry used to determine eligibility for all federal social welfare programs. Using this data, we seek to estimate the number of original bunching households who move towards the new notch and the number of households jumping down to the new notch as a result of the reform. The number of bunching households is simply equal to the reduction in the bunching mass at the old notch (as a result of reform), while the number of jumping households is equal to the increase in the bunching mass at the new notch less the reduction in the bunching mass at the old notch (as a result of the reform). However, when looking at the raw data, there are clear time trends in the number of households locating at the old and new notch in the pre-reform period. Thus, our identification challenge is to understand how the number of households reporting incomes at the old and new notch would have evolved in the post-reform period had the reform not occurred.

At a high level, our identification strategy is based on the following insight: the incentives to report an income at and above the original notch are affected by the reform, but the incentives to report an income below the original notch are unaffected by the reform. Hence, we can use portions of the reported income distribution below the original notch as control groups for underlying time trends in the reported income distribution at and above the original notch. To do so, we use a generalized difference-in-difference strategy as employed in, for example, Wolfers (2006) or Mora and Reggio (2013). A standard difference-in-difference estimator requires that the control groups and treatment groups have “parallel trends” pre-reform that would have persisted in the post-reform period had the reform not occurred. Similarly, the generalized difference-indifference estimator requires that there exist stable relationships, which are well approximated by relatively low order polynomials, between treatment and control groups which existed pre-reform that would have persisted in the post-reform period had the reform not occurred. In our setting, we discretize the reported income distribution into bins, using bins below the original notch as control bins while using bins that include the original and new notches as treatment bins. We then use the estimated relationships between treatment and control bins in the pre-reform period to create counterfactuals for how the treatment bins would have evolved absent the reform. Fundamentally, there are complex structural relationships between the number of people reporting in each income bin; these relationships are determined by how the true income distribution is evolving over time, how the true income distribution is mapped to the reported income distribution, as

> 3. BF also includes a conditional variable benefit for households with children. To receive this variable benefit, households must make specified health and education investments in their children and have a reported per-capita income below the “poverty threshold” (which is higher than the extreme-poverty threshold). We restrict our attention to the _unconditional_ component of BF in this paper.

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