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Empirical Economics

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19-01-2021

Cross-sectional quasi-maximum likelihood and bias-corrected pooled least squares estimators for short dynamic panels

Authors: In Choi, Sanghyun Jung

Published in: Empirical Economics | Issue 1/2021

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Abstract

This paper proposes new estimators for the panel autoregressive (PAR) model of order 1 with short time dimensions and large cross sections. These estimators are based on the cross-sectional regression model using the first time series observations as a regressor and the last as a dependent variable. The regressors and errors of this regression model are correlated. The first estimator is the quasi-maximum likelihood estimator (QMLE). The second estimator is the bias-corrected pooled least squares estimator (BCPLSE) that eliminates the asymptotic bias of the pooled least squares estimator by using the QMLE. The QMLE and BCPLSE are extended to the PAR model with endogenous regressors. The QMLE and BCPLSE provide consistent estimates of the PAR coefficients for stationary, unit root and explosive PAR models and consistently estimate the coefficients of endogenous regressors. Their finite sample properties are compared with those of some other estimators for the PAR model of order 1. This paper’s estimators are shown to perform quite well in finite samples.

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But they can also be subject to the weak instrument problem as reported in Hayakawa (2007) and Bun and Windmeijer (2010).

In practice, we can demean \(\{y_{iT}\}\) and \(\{y_{1i}\}\) to make this assumption plausible.

Model (6) is also used in Choi (2019) to devise unit root tests for dependent and heterogeneous micro-panels.

In fact, the QMLE of \(\alpha \) behaves strangely at \(T=2\) according to our simulation.

We assumed \(\mathrm{Var}(u_{it})=\sigma _{\mathrm {u}}^{2}\,\)for every i and t for this estimator.

The previous versions of this paper also considered Han and Phillips’ (2010) first difference least squares estimator. But we found that it performs worse than PFAE in finite samples.

Simulation results assuming normal distributions are available from the authors upon request. AH tends to outperform the rest in this case, which reflects the fact that AH is the MLE under the assumption of normality.

This method of proof was inspired by Bai and Li (2012).

\(\sqrt{N}\left( \hat{\alpha }-\alpha ^{*}\right) \) can be shown to be \(O_{p}(1)\ \)using the first and second derivatives of \(l(\alpha ;\hat{\omega }_{22},\hat{\lambda },\hat{\zeta })\) in the conventional way.

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Title: Cross-sectional quasi-maximum likelihood and bias-corrected pooled least squares estimators for short dynamic panels
Authors: In Choi
Sanghyun Jung
Publication date: 19-01-2021
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 1/2021
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-020-02007-x

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