Consistent Estimation Using Data From More Than One Sample

This paper considers the estimation of linear models when group average data from more than one sample is used. Conditions under which OL8 coefficient estimates are consistent are identified. The standard OL8 covariance estimate is shown to be inconsistent and a consistent estimator is proposed. Finally, since the conditions under which OL8 is consistent are quite restrictive, several estimators which are consistent in many cases where OL8 is not are developed. The large sample distribution properties and an estimator for the asymptotic covariance matrix for the most general of these alternative estimators is also presented. One important application of these findings is to estimating compensating wage differences. Past authors, beginning with Thaler and Rosen (1976) have argued that finer classification schemes would reduce errors-in-variable bias. The analysis presented here suggests that the opposite is true if finer classification results in fewer observations per classification. This could explain why authors using the broader (industry) classification schemes have found larger compensating differences and suggests that these estimates may be closer to the true values.