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Sequential and efficient GMM estimation of dynamic short panel data models

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journal contribution
posted on 2021-08-06, 02:02 authored by Fei Jin, Lung-fei Lee, Jihai Yu

This paper considers generalized method of moments (GMM) and sequential GMM (SGMM) estimation of dynamic short panel data models. The efficient GMM motivated from the quasi maximum likelihood (QML) can avoid the use of many instrument variables (IV) for estimation. It can be asymptotically efficient as maximum likelihood estimators (MLE) when disturbances are normal, and can be more efficient than QML estimators when disturbances are not normal. The SGMM, which also incorporates many IVs, generalizes the minimum distance estimation originated in Hsiao et al. . By focusing on the estimation of parameters of interest, the SGMM saves computational burden caused by nuisance parameters such as variances of disturbances. It is asymptotically as efficient as the corresponding GMM. In particular, the SGMM based on QML scores can generate a closed-form root estimator for the dynamic parameter, which is asymptotically as efficient as the QML estimator. Nuisance parameters can also be estimated efficiently by an additional SGMM step if they are of interest.

Funding

Fei Jin gratefully acknowledges the financial support from the National Natural Science Foundation of China (No. 71973030 and No. 71833004) and Program for Innovative Research Team of Shanghai University of Finance and Economics. Jihai Yu gratefully acknowledges the financial support from the National Natural Science Foundation of China (No. 71925006 and No. 92046021) and support from the Center for Statistical Science of Peking University and the Key Laboratory of Mathematical Economics and Quantitative Finance (Peking University), the Ministry of Education.

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