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Research output: Working paper
Research output: Working paper
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TY - UNPB
T1 - Convergence Rates of GMM Estimators with Nonsmooth Moments under Misspecification
AU - Kang, David
AU - Lee, Seojeong
AU - Song, Juha
PY - 2025/5
Y1 - 2025/5
N2 - The asymptotic behavior of GMM estimators depends critically on whether the underlying moment condition model is correctly specified. Hong and Li (2023, Econometric Theory) showed that GMM estimators with nonsmooth (non-directionally differentiable) moment functions are at best n^(1/3)-consistent under misspecification. Through simulations, we verify the slower convergence rate of GMM estimators in such cases. For the two-step GMM estimator with an estimated weight matrix, our results align with theory. However, for the one-step GMM estimator with the identity weight matrix, the convergence rate remains √n, even under severe misspecification.
AB - The asymptotic behavior of GMM estimators depends critically on whether the underlying moment condition model is correctly specified. Hong and Li (2023, Econometric Theory) showed that GMM estimators with nonsmooth (non-directionally differentiable) moment functions are at best n^(1/3)-consistent under misspecification. Through simulations, we verify the slower convergence rate of GMM estimators in such cases. For the two-step GMM estimator with an estimated weight matrix, our results align with theory. However, for the one-step GMM estimator with the identity weight matrix, the convergence rate remains √n, even under severe misspecification.
KW - generalized method of moments
KW - non-differentiable moment
KW - nstrumental variables quantile regression
M3 - Working paper
T3 - Economics Working Papers Series
BT - Convergence Rates of GMM Estimators with Nonsmooth Moments under Misspecification
PB - Lancaster University, Department of Economics
CY - Lancaster
ER -