2SLS and IV Estimation of Dynamic Panel Models with Heterogeneous Trend*
研究了当个体数N和时间T都趋于无穷时，动态面板数据模型中两阶段最小二乘和简单工具变量估计的渐近性质，发现不同去趋势方法会导致估计量有偏或无偏。
Abstract In this paper, we consider two‐stage least squares (2SLS) and simple instrumental variable (IV) type estimation of dynamic panel data models with both individual‐specific effects and heterogeneous time trend when both N and T tend to infinity. We consider the forward orthogonal deviations (FOD) proposed by (Hayakawa, et al. Econometric Reviews, 2019. Vol. 38, pp. 1055–1088) and the double first difference (2FD) to remove both the individual‐specific effects and heterogeneous trend. As the main theoretical contribution, we establish the asymptotic properties of the 2SLS estimation of the lag coefficient and find that the 2SLS estimation using FOD and optimal 2SLS estimation using 2FD are asymptotically biased of order , while the 2SLS based on 2FD using non‐optimal weighting matrix is asymptotically biased of order . We also establish the asymptotic unbiasedness of the simple IV estimation using first differenced lagged dependent variable as instrument, and establish the invalidity of using level lagged dependent variable as instrument for the simple IV estimation. Monte Carlo simulations confirm our findings in this paper.