Kolmogorov–Smirnov type test for generated variables

Distribution homogeneity testing, particularly based on the Kolmogorov–Smirnov statistic, has been applied in various empirical studies. In empirical economic analysis, it is often the case that economic variables of interest are obtained as estimated values or residuals of preliminary model fits, called generated variables. In this paper, we extend the Kolmogorov–Smirnov type homogeneity test to accommodate such generated variables, and propose an asymptotically valid bootstrap inference procedure. A small simulation study illustrates that it is crucial for reliable inference to account for estimation errors in the generated variables. The proposed method is applied to compare the total factor productivities across different countries.