Moment Forests

When constructing empirical models, researchers must make decisions about which variables to include, how those variables relate to the outcome variable, and how that mapping varies across units in the population. Additional decisions are made in conducting robustness checks or analyzing heterogeneity or multiple outcomes. Estimates from the selected models often do not account for the search process or correlations across models, and may depend on ad hoc choices made in the selection process. We propose a new methodology, the moment forest, that allows parameters in a broad class of moment-based models to vary across groups of observations on the basis of observable characteristics. A two step estimation process first assigns observations to groups with common parameters, and then estimates an empirical model within each group. We prove the consistency of this estimator and show that standard rates of convergence apply under weak regularity conditions. Our results are applicable to an enormous range of empirical settings, including linear regression, randomized controlled trials with multiple arms or multiple outcomes, regression discontinuity designs, and a wide variety of structural models. Monte Carlo evidence demonstrates the excellent small sample performance and faster-than-parametric convergence rates of the model selection step. We showcase our approach by estimating heterogeneous treatment effects in a regression discontinuity design in a development setting.