Welfare Analysis of Changing Notches: Evidence from Bolsa Família

We develop a framework to bound the welfare impacts of arbi-trarily large reforms to notches using two sufficient statistics:the change in the number of households locating below the newnotch and the change in the number of households locatingbelow the old notch. Our bounds hold in a wide class of models,highlighting a new way to use reduced-form bunching evidencefor welfare analysis without making strong assumptions on theeconomic environment. We estimate these two statistics using adifference-in-difference strategy for a reform to the anti-povertyprogram Bolsa Fam ́ılia, finding that the reform’s MVPF is between 0.90-1.12.