Minimum distance estimation of covariance structures

Covariance structure analysis of panel data has the aim of decomposing the total variation of individual time-series processes into a persistent component (representing variation between individual processes) and volatility (i.e. variation within an individual time process). Examples in the economics literature are dynamic analyses of wage inequality, where permanent variance represents dispersion due to persistent workers' characteristics (say individual unobserved ability), while transitory variance captures volatility due to wage shocks, which washes out after few periods. The simplest case of such models is given by the error specification of a `random effect' panel equation. More realistic specifications allow for some dynamics within the permanent component, say a random walk, and some form of autocorrelation within the transitory component, say some low-order ARMA. The pioneering work of Chamberlain (1984) shows how the parameters of these processes can be estimated by imposing restrictions on the empirical second moments, using Minimum distance (GMM) estimation. This talk shows how such estimator can be implemented following a two step procedure. Firstly, second and fourth sample moments are computed from data levels using the code covar. Secondly, it is shown how STATA's non-linear least squares (nl) can be used to impose the restrictions implied by the theoretical model. It is also shown how to use the fourth moments matrix to correct standard errors for the presence of heteroscedasticity and autocorrelation in empirical second moments. Empirical illustrations are provided.

References

Chamberlain, G. 1984. Panel Data. In Handbook of Econometrics, vol 2, ch. 22, Griliches Z. and Intriligator M.D. (eds.), North–Holland.