Poisson-based expectile regression for nonnegative data with a mass point at zero

In many applications, the outcome of interest is nonnegative and has a mixed distribution with a long right-tail and a mass point at zero. Applications using this sort of data are typical in health and international economics but are also found in many other areas. The lower bound at zero implies that models for this kind of data are generally heteroskedastic, implying that the regressors will have different effects on different regions of the conditional distribution. The traditional way to learn about heterogeneous effects in conditional distributions is to use quantile regression. However, the conditional quantiles of outcomes of this kind cannot be given by smooth functions of the regressors because the mass point implies that some quantiles will be identically zero for certain values of the regressors. This complicates the estimation of quantile regressions for data of this kind and the interpretation of the estimated parameters. As an alternative, we can estimate Poisson-based expectile regressions using Efron’s (1992) asymmetric maximum- likelihood approach. After highlighting the problems that akict estimation of quantile regressions for this kind of data, we brieXy introduce expectile regression as introduced by Newey and Powell (1987) and show how they can be estimated with nonnegative data using Efron’s (1992) approach. We then introduce the appmlhdfe command and illustrate its use.