面板数据双因素误差回归模型序列相关和随机效应的联合LM检验

对面板数据双因素误差回归模型构造了检验序列相关和随机效应的一种联合LM检验，发现该LM统计量也是检验联合假设H0：σμ^2=λ=0的Baltagi-Li LM统计量和检验假设H0：σv^2=λ=0的Breusch-Pagan-LM统计量之和。当面板数据的个体数N充分大时，该联合LM统计量的渐近分布是χ^2（3）分布；无论双因素误差面板数据回归模型的剩余误差项是AR（1）过程还是MA（1）过程，联合LM检验是相同的，即对随机效应和一阶序列相关的联合LM检验是独立于序列相关的形式。

A Joint LM Test of Serial Correlation and Random Effect in Two-Way Error Component Models of Panel Data

On account of two - way error component models of panel data, this paper has built up a joint LM test of serial correlation and random effect. It is found that the joint LM statistic is equal to the sum of the Baltagi - Li＇ s LM statistic testing joint null hypothesis H0：σμ^2=λ=0 and the Breusch - Pagan＇ s LM statistic testing null hypothesis H0：σv^2=λ=0 . The LM statistic has also a limiting chi- squared distribution with degrees of freedom equal to 3 for larger individual number N of panel data under the joint null hypothesis. Otherwise, the joint LM test statistic is the same whether the residual disturbances follow an AR（1） or an MA（1） process, i.e. the joint LM test is independent of the form of serial correlation.