Robust ranking of happiness outcomes: a median regression perspective

Ordered probit and logit models have been frequently used to estimate the mean ranking of happiness outcomes (and other ordinal data) across groups. However, it has been recently highlighted that such ranking may not be identified in most happiness applications. We suggest researchers focus on median comparison instead of the mean. This is because the median rank can be identified even if the mean rank is not. Furthermore, median ranks in probit and logit models can be readily estimated using standard statistical softwares. The median ranking, as well as ranking for other quantiles, can also be estimated semiparametrically and we provide a new constrained mixed integer optimization procedure for implementation. We apply it to estimate a happiness equation using General Social Survey data of the US.