Inference for the correlation coefficient between potential outcomes in the Gaussian switching regime model

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.