Minimum distance estimation of covariance structures
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Speakers |
Lorenzo Cappellari, University of Warwick
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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.
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