A Consistent Heteroskedasticity‐Robust LM‐Type Specification Test for Semiparametric Models
提出一种半参数回归模型的异方差稳健LM型设定检验，能检测多种偏离原假设的情况，统计量基于受限模型估计且渐近标准正态，应用于环境恩格尔曲线发现收入与排放关系可能为二次型但形状随其他变量变化。
ABSTRACT This article develops a heteroskedasticity‐robust Lagrange Multiplier‐type specification test for semiparametric regression models. The test is able to detect a wide class of deviations from the null hypothesis. The test statistic is based on the estimates from the restricted semiparametric model, can be computed in a regression‐based way, and is asymptotically standard normal under the null. I apply the test to Environmental Engel Curves and find that while the relationship between income and emissions may be quadratic, its shape changes with other variables in the model. Monte Carlo studies suggest that my test controls size well, has good power, and is fairly robust to the tuning parameter choice.