Estimation Techniques

The TSCSREG Procedure

Estimation Techniques

If the effects are fixed, the models are essentially regression models with dummy variables corresponding to the specified effects. For fixed effects models, ordinary least squares (OLS) estimation is best linear unbiased.

The other alternative is to assume that the effects are random. In the one-way case, ${E({\ssbeleven {\nu}_{i}})=0}$ , ${E({\ssbeleven {\nu}^2_{i}})= {\sigma}^2_{{\nu} }}$ , and

${E({\ssbeleven {\nu}_{i}{\nu}_{j}})=0}$ for ${i {\neq} j}$ , and ${{\nu}_{i}}$ is uncorrelated with ${{\epsilon}_{it}}$ for all i and t. In the two-way case, in addition to all of the preceding, E(e_t) = 0, ${E({\ssbeleven e^2_{t}})= {\sigma}^2_{e} }$ , and

E(e_t e_s) = 0 for ${t {\neq} s}$ , and the e_t are uncorrelated with the ${{\nu}_{i}}$ and the ${{\epsilon}_{it}}$ for all iand t. Thus, the model is a variance components model, with the variance components ${ {\sigma}^2_{{\nu}} }$ and ${ {\sigma}^2_{e}}$ , as well as ${ {\sigma}_{{\epsilon}}^2}$ , to be estimated. A crucial implication of such a specification is that the effects are independent of the regressors. For random effects models, the estimation method is an estimated generalized least squares (EGLS) procedure that involves estimating the variance components in the first stage and using the estimated variance covariance matrix thus obtained to apply generalized least squares (GLS) to the data.

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