Cross-fitted empirical likelihood on semiparametric models

Summary We propose a new cross-fitted empirical likelihood (CFEL) inference procedure for low-dimensional parameters in the presence of complex, infinite dimensional nuisance parameters that may be estimated by modern machine-learning methods. Relying on the Neyman orthogonal moment condition and cross-fitting as a sample-splitting procedure, we show that our CFEL statistic is asymptotically pivotal under weak conditions often invoked in Wald-type approaches. Three examples show how these can be established using low-level conditions on the quality of the estimated nuisance parameters. Simulation evidence suggests that the Wald approach may undercover more compared to our CFEL approach, especially when the estimating equation is non-linear in the low-dimensional parameter and the first-step estimators have larger finite-sample estimation errors. We illustrate the value of our approach by revisiting the Pennsylvania Reemployment Bonus experiment, which studied the effect of cash bonuses on unemployment duration.