Since the commonly available time series on micro units are typically quite short, this paper considers a different estimation of linear panel data models where the unobserved individual effects are permitted to have time-varying effects on the response variable. We allow flexible possible correlations between included regressors and unobserved individual effects, and the model can accommodate both time varying and time invariant covariates. The quasi-maximum likelihood method is then proposed to obtain the estimates, which are easily executed by a simple iterative method. Two types of approaches to estimate the covariance matrix are introduced. The large sample properties are established when \(n\rightarrow \infty \) and T is fixed. The estimates are efficient when both the individual effects and random errors follow normal distributions. Simulation studies show that our estimates perform well even when the correlations between the regressors and unobserved individual effects are misspecified. The proposed method is further illustrated by applications to a real data.

由于微型单位的常用时间序列通常很短，因此本文考虑了线性面板数据模型的不同估计，其中允许未观察到的个体效应对响应变量产生时变效应。我们允许包含的回归变量和未观察到的个体效应之间存在灵活的可能相关性，并且该模型可以适应时变和时变协变量。然后提出了拟最大似然方法来获得估计，这很容易通过简单的迭代方法执行。介绍了两种估计协方差矩阵的方法。当\(n\rightarrow \infty \)和T是固定的。当个体效应和随机误差都服从正态分布时，估计是有效的。模拟研究表明，即使在回归量和未观察到的个体效应之间的相关性被错误指定时，我们的估计也表现良好。通过对真实数据的应用进一步说明了所提出的方法。