Nonseparability Without Monotonicity: The Couterfactual Distribution Estimator for Causal Inference

33 Pages Posted: 20 Mar 2019

See all articles by Nir Billfeld

Nir Billfeld

University of Haifa

Moshe Kim

University of Haifa - Department of Economics

Date Written: February 13, 2019

Abstract

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

Billfeld, Nir and Kim, Moshe, Nonseparability Without Monotonicity: The Couterfactual Distribution Estimator for Causal Inference (February 13, 2019). Available at SSRN: https://ssrn.com/abstract=3343438 or http://dx.doi.org/10.2139/ssrn.3343438

Nir Billfeld (Contact Author)

University of Haifa ( email )

Mount Carmel
Haifa, 31905
Israel

Moshe Kim

University of Haifa - Department of Economics ( email )

Haifa 31905
Israel
(972) 4 8240115 (Phone)
(972)4-8240059 (Fax)

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