As a natural outgrowth of the proliferation of large scale empirical analyses, there is an increased interest in unifying the results of related regression analyses. In particular, when similar models have been estimated under a variety of circumstances, it is often desirable to explain any differences in results. However, systematically analyzing such differences is often difficult because new statistical problems are introduced when once relates a series of different estimated relationships. The specific case of efficiently estimating a regression model which has an estimated regress coefficient as the dependent variable is developed here.