In empirical economics the robustness of an estimated coefficient to specification changes is usually inferred from the fact that the estimate does not change too much across the considered models. However, this decision is subjective. The focus of this paper therefore is a test of the difference between two coefficients from two potentially non-nested models to be statistically different from zero.
The test can be classified as a sensitivity testing tool used to identify the proper empirical model specification for a given purpose. In particular, it might be used to answer the question whether including further control variables significantly changes the magnitude of the estimated coefficient of interest. A closed-form solution for the variance of this difference would require a consistent estimate of the covariance between the estimated coefficients in addition to the estimated coefficients’ standard errors. In order to minimize necessary parametric assumptions we propose to bootstrap the difference directly to obtain a valid confidence interval. This procedure leads to a nonparametric test in the sense that it does not use any test distribution. Furthermore, the test can be applied to nested and to non-nested models. It is possible to test for equality of two coefficients from variables that are common in both models, and for variables, where each appears in only one model. We start by proving that the bootstrap succeeds in asymptotically mimicking the dis- tribution of the estimated difference under minimal assumptions. Afterwards, we show which correlations determine the difference between the estimates of the considered coefficients. Using Monte Carlo simulations we are then able to show that our testing procedure does not seem to suffer from size distortions. The bootstrap coefficient test across potentially non-nested models also performs well with respect to its power.