On Causal Inference with Model-Based Outcomes

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• github.com/kazuyanagimoto/unitdid
  OfficialIn papernone★ 7

Abstract

We study a causal inference problem with group-level outcomes, which are themselves parameters identified from microdata. We formalize these outcomes using population moment conditions and demonstrate that one-step Generalized Method of Moments (GMM) estimators are generally inconsistent due to an endogenous weighting bias, where policy affects the implicit GMM weights. In contrast, two-stage Minimum Distance (MD) estimators perform well when group sizes are sufficiently large. While MD estimators can still be inconsistent in small groups due to a policy-induced sample selection, we demonstrate that this can be addressed by incorporating auxiliary population information. An empirical application illustrates the practical importance of these findings.

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