Estimation of Matrix Exponential Unbalanced Panel Data Models with Fixed Effects: An Application to US Outward FDI Stock
提出一种矩阵指数非平衡面板数据模型的M估计方法，允许溢出效应、异质性和异方差，通过蒙特卡洛验证其有限样本性质，并应用于美国行业层面对外直接投资存量的第三国效应分析。
In this article, we consider a matrix exponential unbalanced panel data model that allows for (i) spillover effects using matrix exponential terms, (ii) unobserved heterogeneity across entities and time, and (iii) potential heteroscedasticity in the error terms across entities and time. We adopt a likelihood based direct estimation approach in which we jointly estimate the common parameters and fixed effects. To ensure that our estimator has the standard large sample properties, we show how the score functions should be suitably adjusted under both homoscedasticity and heteroscedasticity. We define our suggested estimator as the root of the adjusted score functions, and therefore our approach can be called the <i>M</i>-estimation approach. For inference, we suggest an analytical bias correction approach involving the sample counterpart and plug-in methods to consistently estimate the variance-covariance matrix of the suggested <i>M</i>-estimator. Through an extensive Monte Carlo study, we show that the suggested <i>M</i>-estimator has good finite sample properties. In an empirical application, we use our model to investigate the third country effects on the U.S. outward foreign direct investment (FDI) stock at the industry level.