This paper reexamines the seminal Lagrange multiplier test for cross-section independence in a large panel model where both the number of cross-sectional units n and the number of time series observations T can be large. The first contribution of the paper is an enlargement of the test with two extensions: firstly the new asymptotic normality is derived in a simultaneous limiting scheme where the two dimensions (n, T) tend to infinity with comparable magnitudes; second, the result is valid for general error distribution (not necessarily normal). The second contribution of the paper is a new test statistic based on the sum of the fourth powers of cross-section correlations from OLS residuals, instead of their squares used in the Lagrange multiplier statistic. This new test is generally more powerful, and the improvement is particularly visible against alternatives with weak or sparse cross-section dependence. Both simulation study and real data analysis are proposed to demonstrate the advantages of the enlarged Lagrange multiplier test and the power enhanced test in comparison with the existing procedures.
翻译:本文在大型面板模型中重新审查了剖面独立的显性拉格朗乘数测试,该模型的跨部门单位数量n和时间序列观测T数量都可能很大。本文的第一个贡献是扩大了测试,增加了两个扩展:首先,新的无症状正常性是在同时限制办法中产生的,其中两个维度(n、T)往往不尽相同大小;其次,结果适用于一般误差分布(不一定正常)。本文的第二个贡献是新的测试统计,其依据是OSLS残余的交叉关系第四强力之和,而不是在Lagrange乘数统计中使用的正方形。这一新的测试通常更为有力,对于依赖性弱或稀疏的跨部的替代物,其改进尤为明显。提议进行模拟研究和实际数据分析,以证明扩大的拉格朗乘数测试和与现有程序相比较的增强能力测试的优势。