Random Forest Estimation of the Ordered Choice Model

In econometrics so-called ordered choice models are popular when interest is in the estimation of the probabilities of particular values of categorical outcome variables with an inherent ordering, conditional on covariates. In this paper we develop a new machine learning estimator based on the random forest algorithm for such models without imposing any distributional assumptions. The proposed Ordered Forest estimator provides a flexible estimation method of the conditional choice probabilities that can naturally deal with nonlinearities in the data, while taking the ordering information explicitly into account. In addition to common machine learning estimators, it enables the estimation of marginal effects as well as conducting inference thereof and thus providing the same output as classical econometric estimators based on ordered logit or probit models. An extensive simulation study examines the finite sample properties of the Ordered Forest and reveals its good predictive performance, particularly in settings with multicollinearity among the predictors and nonlinear functional forms. An empirical application further illustrates the estimation of the marginal effects and their standard errors and demonstrates the advantages of the flexible estimation compared to a parametric benchmark model.