GMM under finite-population asymptotics: instrumental variables and regression adjustment

Haruo Kakehi, Yukitoshi Matsushita and Taisuke Otsu

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Abstract: This paper extends the finite-population asymptotic framework of Abadie et al. (2014,2020) to the generalized method of moments (GMM) estimator for moment condition models. Motivating examples include instrumental variable regressions and regression adjustments under randomized controlled trials. We establish consistency and asymptotic normality of the GMM estimator and propose conservative variance estimators. We also study GMM weighting, misspecification, and over-identification testing under finite-population asymptotics. Notably, even though the optimally weighted GMM estimator is infeasible under finite-population asymptotics, the regression adjustment estimator in a randomized controlled trial is shown to be asymptotically equivalent to the optimally weighted GMM estimator. A simulation study and real data application illustrate the usefulness of our GMM theory.

Date: 2026-10
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2610.15168

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