that the reform was welfare improving as long as the government values giving R$0.90 to BF households in a non-distortionary manner more than spending R$1 on their next best alternative. On the other hand, the reform was welfare decreasing if the government values spending R$1 on their next best alternative more than giving R$1.12 to BF households in a non-distortionary manner.<sup>42</sup> But what is the government’s best alternative use of funds? In general, this is a difficult question to answer. Lindert et al. (2007) show that BF performs better (in terms of targeting performance) than other anti-poverty programs in both Brazil and other countries in Latin America; this suggests that there is not a better alternative anti-poverty program that the government could finance. Instead, for expositional simplicity we assume that the next best use of funds is a non-distortionary UBI. Under this assumption, we can perform a conservative back-of-the-envelope calculation to argue that the 2014 BF reform was almost certainly welfare improving. Suppose the government is utilitarian and that the true income distribution is log-normal with parameters taken from the World Bank’s PovcalNet database for Brazil in 2016.<sup>43</sup> Conservatively, we assume that the BF household per-capita income distribution matches the distribution for the bottom 50% of income earners in Brazil.<sup>44</sup> Moreover, we assume utility of consumption is CRRA: _u_ ( _c_ ) = _c_<sup>1</sup><sup>_−γ_</sup> _/_ (1 _− γ_ ). Based on these assumptions, the government prefers giving R$0.90 (in a non-distortionary manner) to BF households more than spending R$1 on a non-distortionary UBI as long as _γ >_ 0 _._ 14. While estimates for _γ_ vary widely, typically estimates fall between 1 and 10 (Outreville, 2014). Alternatively, if _γ_ = 1 (i.e., _u_ ( _c_ ) = log( _c_ )), giving R$0.90 (in a non-distortionary manner) to BF households yields equivalent welfare gains to spending R$1.50 on a non-distortionary UBI. Thus, if the next best alternative policy is a non-distortionary UBI and the government is utilitarian, the BF reform was almost certainly welfare improving. This finding contributes to the debate around targeted vs. universal transfers in developing settings (Hanna and Olken, 2018): we find that even in a setting with a highly pronounced notch and substantial scope for misreporting, the efficiency cost generated by behavioral responses is simply not large enough to outweigh the equity gain associated with increased benefit generosity targeted to poor households (relative to a universal transfer).

Finally, when calculating our bounds for the MVPF, we have ignored any potential fiscal externalities when determining the total cost of the reform (i.e., we have ignored the impact that behavioral responses have on other components of the government budget). There is evidence to suggest that some beneficiaries partially substitute formal sector employment for informal sector employment to become eligible for the BF benefit (as informal income is less easily verified making misreporting less costly; see De Brauw et al. (2015)). While it is easier to evade taxes in the informal sector, it is unlikely that this behavioral response will affect tax revenues as BF beneficiaries are almost certainly sufficiently poor so as to be exempt from income 42. Technically, the reform is welfare improving as long as the government values spending R$1 on their next best alternative less than splitting R$0.90 (in a non-distortionary manner) among the mechanical, threshold, bunching, and jumping households, where the split is determined by the lower bounds on each group’s WTP for the reform. Similarly, the reform is welfare decreasing if the government values spending R$1 on their next best alternative more than splitting R$1.12 (in a non-distortionary manner) among the mechanical, threshold, bunching, and jumping households, where the split is determined by the upper bounds on each group’s WTP for the reform.

43. In 2016, the mean per-capita income in Brazil was R$615.32 and the Gini coefficient was 0.533; these parameters fully pin down the income distribution if we assume log-normality.

44. Bastagli (2008) finds that of all transfers paid in 2004, 91% went to households in the bottom 50% of the income distribution. Alternatively, Lindert et al. (2007) suggests even better targeting performance, finding that 94% of all benefits go to the bottom 40%. Notably, transfers are not evenly distributed across the bottom 50% of households: the poorest households within this group receive more (e.g., Bastagli (2008) finds that the bottom 20% of the income distribution receive 50% of BF transfers, while Lindert et al. (2007) report that the bottom 20% receive 73% of BF transfers). Thus, we believe the assumption that the income distribution of BF households is the same as the income distribution for the bottom 50% of income earners in Brazil is highly conservative.

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