Inference for the Correlation Coefficient Between Potential Outcomes in the Gaussian Switching Regime Model

Abstract: We propose estimators of sharp bounds on the correlation coefficient between potential outcomes in the Gaussian switching regime model and develop an asymptotically uniformly valid and non-conservative confidence set for the true correlation coefficient. A boundary-interior-category selection procedure is proposed to deal with discontinuity of the pointwise asymptotic distribution of estimators of the sharp bounds. Our confidence set is easy to implement: it takes the form of a closed interval and its critical values have closed-form expressions. Simulation study reveals the better finite sample performance of our confidence set than the naive confidence set ignoring the discontinuity issue.