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.

中文翻译：

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具有异构趋势的动态面板模型的 2SLS 和 IV 估计*

在本文中，我们考虑了动态面板数据模型的两阶段最小二乘法 (2SLS) 和简单工具变量 (IV) 类型估计，当N和T 都趋于无穷大时，具有个体特定效应和异质时间趋势。我们考虑 (Hayakawa, et al. Econometric Reviews, 2019. Vol. 38, pp. 1055–1088) 和双重一阶差分 (2FD) 提出的前向正交偏差 (FOD) 来消除个体特定效应和异质性趋势。作为主要的理论贡献，我们建立了滞后系数的 2SLS 估计的渐近性质，并发现使用 FOD 的 2SLS 估计和使用 2FD 的最优 2SLS 估计是渐近偏置的，而基于 2FD 的 2SLS 使用非最优加权矩阵是阶次渐近偏置的。我们还建立了使用一阶差分滞后因变量作为工具的简单IV估计的渐近无偏性，并建立了使用水平滞后因变量作为简单IV估计工具的无效性。Monte Carlo 模拟证实了我们在本文中的发现。