Joint with Kyungchul Song
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Abstract
Difference-in-differences (DiD) designs usually summarize treatment by an average effect, but many questions concern incidence: who gains, who loses, and whether losses on different outcomes are held by the same individuals. This paper shows how we can identify marginal and joint distributions of treatment effects among treated units using panel data. For treated units, the observed outcome change equals the individual treatment effect plus the untreated change the unit would have experienced absent treatment. A distributional version of parallel trends identifies the distribution of untreated changes from controls, while independence between untreated changes and treatment effects among treated units turns the observed treated-change distribution into a convolution. Deconvolution therefore recovers the treatment-effect distribution, including dependence across outcomes. We develop joint cumulative distribution function (cdf) estimators, uniform confidence bands, and falsification checks based on pre-treatment changes and characteristic-function restrictions. We apply the method to job displacement using Italian matched employer–employee data, asking whether losses in annual earnings, daily wages, and firm wage premia fall on the same workers. Earnings losses are widespread but only weakly related to daily-wage losses, suggesting that much of the earnings impact operates through reduced employment time rather than lower daily pay. Daily-wage losses, on the other hand, are closely bundled with losses in firm wage premia: among workers with wage losses, about 70 percent also lose firm premia, and the wage–premium rank correlation is 0.42. These results suggest that reallocation across employers is central to understand the unequal consequences of job displacement