Nonseparability Without Monotonicity: The Couterfactual Distribution Estimator for Causal Inference
33 Pages Posted: 20 Mar 2019
Date Written: February 13, 2019
Nonparametric identification strategy is employed to capture causal relationships without imposing any variant of monotonicity existing in the nonseparable nonlinear error model literature. Monotonicity may fail to exist for fundamental reasons related e.g., to the strategic behavior of economic agents or to a multidimensional utility which is neither monotonic nor scalar. Thus, the monotonicity-based estimators might be severely biased as shown here in comparative Monte Carlo simulations. We offer a two-step M-Estimator in which causality is preserved by uncovering the latent counterfactual distribution of the dependent variable, reflecting random assignment of the treatment, imitating a "natural experiment". The offered estimator is based on a resolution dependent reproducing kernel rather than on the bandwidth-dependent classical kernel, attesting to very high accuracy. Further, this estimator is induced by a biorthogonal wavelet and thus, less sensitive to bandwidth choice. Asymptotic properties are established.
Keywords: Nonparametric, Counter factual distribution, Reproducing kernel, Nonseparable error, Nonmonotonic
JEL Classification: C01, C14, C26
Suggested Citation: Suggested Citation