I am comparing the impact of weighting on Chi-square difference tests of some nested models (using DIFFTEST). I was wondering if anything is known about the reduction in power of the chi-square difference test by propensity weighting, e.g. due to reduced effective sample size.
Moreover, I am wondering, if there is a way to adjust the 'unweighted tests' to the weighted tests in terms of power, e.g. by randomly selecting a subset of observations which equals the effective sample size of the weighted test.