REGULARIZED ESTIMATION OF DYNAMIC PANEL MODELS
针对动态面板模型中矩条件过多导致小样本偏差大的问题，提出了三种正则化方案来改进一步GMM估计量，并给出了数据驱动的调参方法，适用于收入动态等实证研究。
In a dynamic panel data model, the number of moment conditions increases rapidly with the time dimension, resulting in a large dimensional covariance matrix of the instruments. As a consequence, the generalized method of moments (GMM) estimator exhibits a large bias in small samples, especially when the autoregressive parameter is close to unity. To address this issue, we propose a regularized version of the one-step GMM estimator using three regularization schemes based on three different ways of inverting the covariance matrix of the instruments. Under double asymptotics, we show that our regularized estimators are consistent and asymptotically normal. These regularization schemes involve a tuning or regularization parameter which needs to be chosen. We derive a data-driven selection of this regularization parameter based on an approximation of the higher-order mean square error and show its optimality. As an empirical application, we estimate a model of income dynamics.