SPECIFICATION OF VARIANCE MATRICES FOR PANEL DATA MODELS

Many regression models have two dimensions, say time (t = 1, . . . ,T ) and households (i = 1, . . . , N), as in panel data, error components, or spatial econometrics. In estimating such models we need to specify the structure of the error variance matrix Ω, which is of dimension T N ×T N. If T N is large, then direct computation of the determinant and inverse of Ω is not practical. In this note we define structures of Ω that allow the computation of its determinant and inverse, only using matrices of orders T and N, and at the same time allowing for heteroskedasticity, for householdor station-specific autocorrelation, and for time-specific spatial correlation.