Identification of Regression Models With a Misclassified and Endogenous Binary Regressor

Abstract

We study identification in nonparametric regression models with a misclassified and endogenous binary regressor when an instrument is correlated with misclassification error. We show that the regression function is nonparametrically identified if one binary instrument variable and one binary covariate satisfy the following conditions. The instrumental variable corrects endogeneity; the instrumental variable must be correlated with the unobserved true underlying binary variable, must be uncorrelated with the error term in the outcome equation, but is allowed to be correlated with the misclassification error. The covariate corrects misclassification; this variable can be one of the regressors in the outcome equation, must be correlated with the unobserved true underlying binary variable, and must be uncorrelated with the misclassification error. We also propose a mixture-based framework for modeling unobserved heterogeneous treatment effects with a misclassified and endogenous binary regressor and show that treatment effects can be identified if the true treatment effect is related to an observed regressor and another observable variable.

Identifying program benefits when participation is misreported

“…Their estimator, the mismeasured robust local average treatment effect (MR-LATE), requires two binary proxies for the same treatment, which can be constructed using estimated treatments, different sources of treatment status, or multiple or repeated treatment measures. The flexibility and simplicity of MR-LATE makes it potentially easier for practitioners to adopt than alternative solutions that have been proposed in the literature (e.g., Battistin et al, 2014;Yanagi, 2018;DiTraglia and García-Jimeno, 2019;Kasahara and Shimotsu, 2021). 3 We focus on the IV estimand that captures the average causal effect on compliers (Imbens and Angrist, 1994).…”

“…3 More specifically, point identification of our target parameter(s) is achieved assuming resurvey data (Battistin et al, 2014), two instrumental variables (Yanagi, 2018), homogeneous treatment effects (DiTraglia and García-Jimeno, 2019), or a covariate satisfying an exclusion restriction from the misclassification (Kasahara and Shimotsu, 2021). A different line of research addresses the more general case of differential misclassification (e.g., Kreider et al, 2012;Nguimkeu et al, 2018;Ura, 2018;Jiang and Ding, 2020;Tommasi and Zhang, 2020).…”

Misclassification in Difference-in-differences Models

“…We situate our paper at the intersection of two strands of literature on difference-indifferences designs and measurement error. Our work is directly related to the longstanding literature on the identification of causal parameters when a binary treatment variable is misclassified (Aigner, 1973;Frazis and Loewenstein, 2003;Mahajan, 2006;Lewbel, 2007;Battistin and Sianesi, 2011;Kreider et al, 2012;Battistin, De Nadai, and Sianesi, 2014;Bollinger and van Hasselt, 2017;Chalak, 2017;Ura, 2018;DiTraglia and Garcia-Jimeno, 2019;Nguimkeu, Denteh, and Tchernis, 2019;Jiang and Ding, 2020;Tommasi and Zhang, 2020;Kasahara and Shimotsu, 2021;Acerenza, Ban, and Kédagni, 2021;Possebom, 2021). Although these studies and the additional papers cited therein cover many quasi-experimental designs, including instrumental variable models, they do not consider misclassification in the DID framework.…”

Identifying Program Benefits When Participation is Misreported

“…Their estimator, the mismeasured robust local average treatment effect (MR-LATE), requires two binary proxies for the same treatment, which can be constructed using estimated treatments, different sources of treatment status, or multiple or repeated treatment measures. The flexibility and simplicity of MR-LATE makes it potentially easier for practitioners to adopt than alternative solutions that have been proposed in the literature (e.g., Battistin et al, 2014;Yanagi, 2018;DiTraglia and García-Jimeno, 2019;Kasahara and Shimotsu, 2021). 3 We focus on the IV estimand that captures the average causal effect on compliers (Imbens and Angrist, 1994).…”

“…3 More specifically, point identification of our target parameter(s) is achieved assuming resurvey data (Battistin et al, 2014), two instrumental variables (Yanagi, 2018), homogeneous treatment effects (DiTraglia and García-Jimeno, 2019), or a covariate satisfying an exclusion restriction from the misclassification (Kasahara and Shimotsu, 2021). A different line of research addresses the more general case of differential misclassification (e.g., Kreider et al, 2012;Nguimkeu et al, 2018;Ura, 2018;Jiang and Ding, 2020;Tommasi and Zhang, 2020).…”