Nonseparability without Monotonicity: The Couterfactual Distribution M-Estimator for Causal Inference

40 Pages Posted: 11 Dec 2018

See all articles by Nir Billfeld

Nir Billfeld

University of Haifa

Moshe Kim

University of Haifa - Department of Economics

Date Written: November 18, 2018

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.

Keywords: Nonparametric, Counter factual distribution, Reproducing kernel, Non separable error, Nonmonotonic

JEL Classification: C01, C14, C26

Suggested Citation

Billfeld, Nir and Kim, Moshe, Nonseparability without Monotonicity: The Couterfactual Distribution M-Estimator for Causal Inference (November 18, 2018). Available at SSRN: https://ssrn.com/abstract=3286538 or http://dx.doi.org/10.2139/ssrn.3286538

Nir Billfeld

University of Haifa ( email )

Mount Carmel
Haifa, 31905
Israel

Moshe Kim (Contact Author)

University of Haifa - Department of Economics ( email )

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

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