Who wins, who loses? Identification of conditional causal effects, and the welfare impact of changing wages

Abstract

The incidence of tax and other policy changes depends on their impact on equilibrium wages. In a standard model of labor supply, the impact of wage changes on a worker’s welfare equals current labor supply times the induced wage change. Worker heterogeneity implies that wage changes vary across workers. In this context, in order to identify welfare effects one needs to identify the causal effect of policy changes on wages conditional on baseline labor supply and wages.This paper characterizes identification of such outcome-conditioned causal effects for general vectors of endogenous outcomes. Even with exogenous policy variation, outcome-conditioned causal effects are only partially identified for outcome vectors of dimension larger than one. We provide assumptions restricting heterogeneity of effects just enough for point-identification and propose corresponding estimators.This paper then applies the proposed approach to analyze the distributional welfare impact (i) of the expansion of the Earned Income Tax Credit (EITC) in the 1990s, using variation in state supplements in order to identify causal effects, and (ii) of historical changes of the wage distribution in the US in the 1990s. For the EITC, we find negative welfare effects of depressed wages as a consequence of increased labor supply, in particular for individuals earning around $20,000 per year. Looking at historical changes, we find modest welfare gains rising linearly with earnings.