Second-Order Least Squares Method for Dynamic Panel Data Models with Application

Abstract

Management of financial risks and sound decision making rely on the accurate information and predictive models. Drawing useful information efficiently from big data with complex structures and building accurate models are therefore crucial tasks. Most commonly used methods for statistical inference in dynamic panel data models are based on the differencing transformation of data. However, differencing data may cause substantial loss of information, and therefore the subsequent analysis may fail to capture important features in the original level data. This point is demonstrated by a real data example where we use a semiparametrically efficient estimation method on the level data to reach a more favorable model. In particular, we study a second-order least squares approach which is based on the first two conditional moments of the response variable given the explanatory variables. This estimator is root-N consistent and its asymptotic variance reaches a lower bound semiparametric efficiency. Monte Carlo simulations show that this estimator performs favorably in finite sample situations compared to the first-differenced GMM and the random effects pseudo ML estimators. We also propose a new diagnostic test to check the working moments assumption based on the proposed estimator. A real data application is presented to further demonstrate the usage of this method.