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Mathematical statistics --- -Data processing

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Econometrics --- Mathematical statistics --- Methodology

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This paper develops a framework to bound the welfare impacts of reforms to notches using two sufficient statistics: (1) the number of households bunching at the old notch who move toward the new notch, and (2) the number of households who "jump" down to the new notch. The bounds hold in a wide class of models, highlighting a new way to use reduced-form bunching evidence for welfare analysis without strong assumptions on the economic environment. These two statistics are estimated using a difference-in-difference strategy for a reform to the anti-poverty program Bolsa Familia, finding that the reform's marginal value of public funds lies between 0.90 and 1.12.

Mathematical statistics. --- Linear models (Statistics)

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Cluster analysis --- Mathematical statistics --- Pattern perception

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Probabilities. --- #WWIS:STAT --- 519.21 --- Probabilities --- 519.2 --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- 519.21 Probability theory. Stochastic processes --- Probability theory. Stochastic processes