Haruo Kakehi, Yukitoshi Matsushita and Taisuke Otsu

Published 8 January 2026

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This paper extends the finite-population asymptotic approach by 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 study asymptotic properties of the GMM estimator and propose conservative variance estimators. Notably, even though the optimally weighted GMM estimation is infeasible under the 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 empirical example illustrate usefulness of our GMM theory.