Abstract

The commonly used 1-step and 2-step System GMM estimators for the panel AR(1) model are inconsistent under mean stationarity when the ratio of the variance of the individual effects to the variance of the idiosyncratic errors is unbounded when $N\to \infty .$ The reason for their inconsistency is that their weight matrices select moment conditions that do not identify the autoregressive parameter. This paper proposes a new 2-step System estimator that is still consistent in this case provided that $T>3.$ Unlike the commonly used 2-step System estimator, the new estimator uses an estimator of the optimal weight matrix that remains consistent in this case. We also show that the commonly used 1-step and 2-step Arellano-Bond GMM estimators and the Random Effects Quasi MLE remain consistent under the same conditions. To illustrate the usefulness of our new System estimator we revisit the growth study of Levine et al. (2000 Levine, R., Loayza, N., Beck, T. (2000). Financial intermediation and growth: causality and causes. Journal of Monetary Economics 46(1):31–77. doi:https://doi.org/10.1016/S0304-3932(00)00017-9[Crossref], [Web of Science ®] , [Google Scholar]).

摘要

面板 AR(1) 模型常用的 1 步和 2 步系统 GMM 估计量在平均平稳性下不一致，当个体效应的方差与异质误差方差的比值是无限时$ñ\to \infty .$它们不一致的原因是它们的权重矩阵选择了不能识别自回归参数的矩条件。本文提出了一种新的两步系统估计器，在这种情况下仍然是一致的，前提是$吨>3.$与常用的两步系统估计器不同，新估计器使用在这种情况下保持一致的最优权重矩阵的估计器。我们还表明，常用的 1 步和 2 步 Arellano-Bond GMM 估计量和随机效应准 MLE 在相同条件下保持一致。为了说明我们的新系统估计器的有用性，我们重新审视了 Levine 等人的增长研究。( 2000 Levine, R. , Loayza, N. , Beck, T. ( 2000 )。金融中介和增长：因果关系和原因。货币经济学杂志46(1): 31 – 77。doi：https://doi.org/10.1016/S0304-3932(00)00017-9 [Crossref]、[Web of Science®]  、[Google Scholar]）。