# On the Behavior of the GMM Estimator in Persistent Dynamic Panel Data Models with Unrestricted Initial Conditions

41 Pages Posted: 23 Feb 2012 Last revised: 4 Apr 2016

See all articles by Kazuhiko Hayakawa

## Kazuhiko Hayakawa

Hiroshima University

## Shuichi Nagata

Kwansei Gakuin University - School of Business Administration; Kwansei Gakuin University - Department of Mathematical Sciences

Date Written: June 24, 2013

### Abstract

This paper investigates the behavior of the first-difference(FD) GMM estimator for dynamic panel data models when the persistency of data is (moderately) strong and the initial conditions are unrestricted. We show that both the initial conditions and the degree of persistency affect the rate of convergence of the GMM estimator under a local to unity system where the autoregressive parameter is modeled as $\alpha_N=1-c/N^p$, where $N$ is the cross-sectional sample size and $0 < p < \infty$. One of the most important implications is that the FD-GMM estimator can be consistent even when persistency is strong if mean-{\it non}stationarity is present. This result is in sharp contrast to the well known weak instruments problem of the FD-GMM estimator which arises under mean-stationarity. We then conduct a simulation and confirm that the derived asymptotic results approximate the finite sample behavior well. Since these results are for the AR(1) case, we also provide extensive simulation results for the models with an exogenous variable, and obtain similar results. Finally, we provide an empirical illustration that supports the theoretical results and confirm that the FD-GMM estimator can precisely estimate the coefficients even when persistency is strong if mean-nonstationarity is present. Also, we obtain a lesson that reducing the number of instruments as a strategy to mitigate the finite sample bias is not always useful.

Keywords: dynamic panels, GMM, initial conditions, weak instruments

Suggested Citation

Hayakawa, Kazuhiko and Nagata, Shuichi, On the Behavior of the GMM Estimator in Persistent Dynamic Panel Data Models with Unrestricted Initial Conditions (June 24, 2013). Available at SSRN: https://ssrn.com/abstract=2009015 or http://dx.doi.org/10.2139/ssrn.2009015