Considerations on Partially Identified Regression Models

Motivated by Manski and Tamer (2002) and especially their partial identification analysis of the regression model where one covariate is only interval-measured, we offer several contributions. Manski and Tamer (2002) propose two estimation approaches in this context, focussing on general results. The modified minimum distance (MMD) estimates the true identified set and the modified method of moments (MMM) a superset. Our first contribution is to characterize the true identified set and the superset. Second, we complete and extend the Monte Carlo study of Manski and Tamer (2002). We present benchmark results using the exact functional form for the expectation of the dependent variable conditional on observables to compare with results using its nonparametric estimates, and illustrate the superiority of MMD over MMM. For MMD, we propose a simple shortcut for estimation.

Keywords: partial identification, true identified set, superset, MMD, MMM, estimation

JEL Classification: C01, C13, C40

Suggested Citation: Suggested Citation

Cerquera, Daniel and Laisney, Francois and Ullrich, Hannes and Ullrich, Hannes, Considerations on Partially Identified Regression Models (March 30, 2012). Working Papers of BETA (Bureau d'Economie Théorique et Appliquée) No. 2012-07, ZEW - Centre for European Economic Research Discussion Paper No. 12-024, Available at SSRN: https://ssrn.com/abstract=1975022 or http://dx.doi.org/10.2139/ssrn.1975022