Estimation of Limited Dependent Variable Models With Dummy Endogenous Regressors - Simple Strategies for Empirical Practice

Sep 4, 2026

Applied economists face challenges when binary endogenous regressors appear in models with binary and nonnegative outcomes. The article argues that difficulties in limited dependent variable settings stem from emphasizing structural parameters rather than causal effects. Once the estimand is the causal treatment effect, several practical approaches become available, including conventional two-stage least squares, multiplicative conditional-mean models, linear approximations to nonlinear causal models, distribution-effect modeling, and quantile regression. Examples using multiple births illustrate effects on employment status and hours.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages28

Reading Time1 h 11 min

AccessFree to download

Introduction

Causal effects vs structural parameters

Identification and instrumental variables

Estimation strategies for endogenous binary regressors

Applications and empirical illustrations

Journal of Business & Economic Statistics ISSN: 0735-0015 (Print) 1537-2707 (Online) Journal homepage: [https://www.tandfonline.com/loi/ubes20](https://www.tandfonline.com/loi/ubes20) Estimation of Limited Dependent Variable Models With Dummy Endogenous Regressors Simple Strategies for Empirical Practice Joshua D Angrist To cite this article: Joshua D Angrist (2001) Estimation of Limited Dependent Variable Models With Dummy Endogenous Regressors, Journal of Business & Economic Statistics, 19:1, 2-28, DOI: 10. 1198/07350010152472571 To link to this article: [https://doi.org/10.1198/07350010152472571](https://doi.org/10.1198/07350010152472571) Published online: 01 Jan 2012. | Submit your article to this journal | | --- | | Article views: 2162 | | View related articles | | Citing articles: 523 View citing articles | Full Terms & Conditions of access and use can be found at [https://www.tandfonline.com/action/journalInformation?journalCode=ubes20](https://www.tandfonline.com/action/journalInformation?journalCode=ubes20) Editor’s Note. This article is the JBES 1999 Invited Lecture at the Joint Statistical Meetings, August 1999, in Baltimore, Maryland. Estimation of Limited Dependent Variable Models With Dummy Endogenous Regressors: Simple Strategies for Empirical Practice Joshua D. Angrist Department of Economics, Massachusetts Institute of Technology, Cambridge, MA 02142-1347, and National Bureau of Economic Research, Cambridge, MA ([angrist@mit.edu](angrist@mit.edu)) Applied economists have long struggled with the question of how to accommodate binary endogenous regressors in models with binary and nonnegative outcomes. I argue here that much of the dif􀂎 culty with limited dependent variables comes from a focus on structural parameters, such as index coef􀂎 cients, instead of causal effects. Once the object of estimation is taken to be the causal effect of treatment, several simple strategies are available. These include conventional two-stage least squares, multiplicative models for conditional means, linear approximation of nonlinear causal models, models for distribution effects, and quantile regression with an endogenous binary regressor. The estimation strategies discussed in the article are illustrated by using multiple births to estimate the effect of childbearing on employment status and hours of work. KEY WORDS: Instrumental variables; Labor supply; Sample selection; Semiparametric methods; Tobit. Econometric models with dummy endogenous regressors capture the causal relationship between a binary regressor and an outcome variable. A canonical example is the evaluation of training programs, in which the binary regressor is an indicator for those who were trained and outcomes are earnings and employment status. Other examples include treatment effects in epidemiology and health economics, effects of union status, and the effects of teen childbearing on schooling or labormarket outcomes. All of these problems have a treatmentcontrol 􀂏 avor. The notion that treatment status is “endogenous” re􀂏ects the fact that simple comparisons of treated and untreated individuals are unlikely to have a causal interpretation. Instead, the dummy endogenous-variable model is meant to allow for the possibility of joint determination of outcomesand treatment status or omitted variables related to both treatment status and outcomes. The principal challenge facing empirical researchers conducting studies of this type is identi􀂎cation. Successful identi􀂎cation in this context usually means 􀂎 nding an instrumental variable (IV) that affects outcomes solely through its impact on the binary regressor of interest. For better or worse, however, the formal discipline of econometrics is not much concerned with the “􀂎 nding instruments problem”; this is a job left to the imagination of empirical researchers. This division of responsibility reminds me a little of Steve Martin’sold joke about “how to make a mill

FAQs

What problem does the article address in models with binary endogenous regressors and limited dependent variables?

It addresses how to handle binary endogenous regressors in settings with binary and nonnegative outcomes, where standard comparisons can fail to deliver causal interpretations.

Why does the article claim many LDV difficulties are “more apparent than real”?

It argues that the main issue is a counterproductive focus on structural parameters instead of directly interpretable causal effects.

Which estimation approaches does the article discuss once the target is the causal treatment effect?

It discusses two-stage least squares, multiplicative models for conditional means, linear approximations to nonlinear causal models, models for distribution effects, and quantile regression with an endogenous binary regressor.

Sep 4, 2026

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