Nonseparability Without Monotonicity: The Couterfactual Distribution Estimator for Causal Inference

Abstract

Nonparametric identification strategy is employed to capture causal relationships without imposing any variant of monotonicity existing in the nonseparable nonlinear error model literature. This is important as when monotonicity is applied to the instrumental variables it limits their availability and when applied to the unobservables it can hardly be justified in the non-scalar case. Moreover, in cases where monotonicity is not satisfied the monotonicity-based estimators might be severely biased as shown in comparative Monte Carlo simulation. The key idea in the proposed identification and estimation strategy is to uncover the counterfactual distribution of the dependent variable, which is not directly observed in the data. We offer a two-step M-Estimator based on a resolution-dependent reproducing symmetric kernel density estimator rather than on the bandwidth-dependent classical kernel and thus, less sensitive to bandwidth choice. Additionally, the average marginal effect of the endogenous covariate on the outcome variable is identified directly from the noisy data which precludes the need to employ additional estimation steps thereby avoiding potential error accumulation. Asymptotic properties of the counterfactual M-Estimator are established.