A new Neyman-orthogonal estimator for the coefficients of interest in a high-dimensional ordinal logit model

This paper derives two new estimators for the coefficients of interest in a sparse, high-dimensional ordinal logit model that requires covariate selection. The new estimators for the coefficients of interest are robust to the covariate selection; estimators with this property are known as Neyman-orthogonal (NO) estimators. One of the new estimators is a cross-fitting version of the other. (Estimators that use cross-fitting are often called double machine learning estimators.) A further set of results relates NO estimators to stacked-moment-conditions estimators; these results are of independent interest and facilitate the construction of other NO estimators. The paper also derives a new selection algorithm for the covariates in an ordinal logit model that combines iterated sure independence screening with an ordinal-logit lasso. This algorithm uses newly derived estimators of the optimal lasso tuning parameters in an ordinal-logit lasso. Simulation results show that the new NO estimators perform well in finite samples when a naive post-selection estimator does not. An application to a unique administrative dataset with many student and class characteristics finds that tutoring increases the probability that a student gets a top grade and lowers the probability that a student fails.