Testing for sphericity in panels

This manuscript considers locally best invariant tests for sphericity in heterogeneous panel models. The associated test statistics take the form of a weighted sum of individual test statistics, each of which is a quadratic form in a spherical random vector under the null. An exact integral expression for the distribution of such a weighted sum, and hence the null distribution of the test, is provided, valid for any size of the cross-sectional and time series dimensions. Addressing the need to quickly compute approximate p-values in empirical work, a highly accurate saddlepoint approximation is also derived, which offers a substantial improvement over the normal approximation in applications where the cross-sectional dimension is small. A panel stationarity test serves as a numerical example.