Paper detail

On John's test for sphericity in large panel data models

This paper studies John&#39;s test for sphericity of the error terms in large panel data models, where the number of cross-section units $n$ is large enough to be comparable to the number of times series observations $T$, or even larger. Based on recent random matrix theory results, John&#39;s test&#39;s asymptotic normality properties are established under both the null and the alternative hypotheses. These asymptotics are valid for general populations, i.e., not necessarily Gaussian provided certain finite moments. A fantastic phenomenon found in the paper is that John&#39;s test for panel data models possesses a powerful dimension-proof property. It keeps the same null distribution under different $(n,T)$-asymptotics, i.e., the small or medium panel regime $n/T\to 0$ as $T\to \infty$, the large panel regime $n/T\to c \in (0,\infty)$ as $ T\to \infty$, and the ultra-large panel regime $n/T\to \infty (T^δ/n =O_p(1), 1<δ<2)$ as $T\to \infty$. Moreover, John&#39;s test is always consistent except under the alternative of bounded-norm covariance with the large panel regime $n/T\to c \in (0,\infty)$.