On Causal Inference with Model-Based Outcomes

Dmitry Arkhangelsky, Kazuharu Yanagimoto and Tom Zohar

No 12686, CESifo Working Paper Series from CESifo

Abstract: We study the estimation of causal effects on group-level parameters identified from microdata (e.g., child penalties). We demonstrate that standard one-step methods (such as pooled OLS and IV regressions) are generally inconsistent due to an endogenous weighting bias, where the policy affects the implicit weights (e.g., altering fertility rates). In contrast, we advocate for a two-step Minimum Distance (MD) framework that explicitly separates parameter identification from policy evaluation. This approach eliminates the endogenous weighting bias and requires explicitly confronting sample selection when groups are small, thereby improving transparency. We show the MD estimator performs well when parameters can be estimated for most groups, and propose a robust alternative that uses auxiliary information in settings with limited data. To illustrate the importance of this methodological choice, we evaluate the effect of the 2005 Dutch childcare reform on child penalties and find that the conventional one-step approach yields estimates that are substantially larger than those from the two-step method.

Keywords: causal inference; model-based outcomes; GMM; minimum distance; child penalty (search for similar items in EconPapers)
JEL-codes: C13 C14 C21 J13 J16 (search for similar items in EconPapers)
Date: 2026
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