SPECIFICATION OF VARIANCE MATRICES FOR PANEL DATA MODELS

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