Distributional conformal prediction.

We propose a robust method for constructing conditionally valid prediction intervals based on models for conditional distributions such as quantile and distribution regression. Our approach can be applied to important prediction problems, including cross-sectional prediction, k-step-ahead forecasts, synthetic controls and counterfactual prediction, and individual treatment effects prediction. Our method exploits the probability integral transform and relies on permuting estimated ranks. Unlike regression residuals, ranks are independent of the predictors, allowing us to construct conditionally valid prediction intervals under heteroskedasticity. We establish approximate conditional validity under consistent estimation and provide approximate unconditional validity under model misspecification, under overfitting, and with time series data. We also propose a simple "shape" adjustment of our baseline method that yields optimal prediction intervals.

Financial incentives and physician prescription behavior: Evidence from dispensing regulations.

In many health care markets, physicians can respond to changes in reimbursement schemes by changing the volume (volume response) and the composition of services provided (substitution response). We examine the relative importance of these two behavioral responses in the context of physician drug dispensing in Switzerland. We find that dispensing increases drug costs by 52% for general practitioners and 56% for specialists. This increase is mainly due to a volume increase. The substitution response is negative on average, but not significantly different from zero for large parts of the distribution. In addition, our results reveal substantial effect heterogeneity.