Testing for the equality of maximum-likelihood regression coefficients between two independent equations

Consider the case where one obtains maximum-likelihood estimates of regression coefficients for the respective populations from which each of two large independent samples is drawn. A question sometimes asked about the results of such an analysis is whether there is a difference between a coefficient in one population, theta(a), and the same coefficient in another population, theta(b). In this paper, we evaluate the performance of two test statistics that have been used to address this problem. Our results suggest that one statistic produces valid conclusions, while the other fails.