Testing Exogeneity of Multinomial Regressors in Count Data Models: Does Two-stage Residual Inclusion Work?

Abstract

We study a simple exogeneity test in count data models with possibly endogenous multinomial treatment. The test is based on Two Stage Residual Inclusion (2SRI). Results from a broad Monte Carlo study provide novel evidence on important features of this approach in nonlinear settings. We …nd di¤erences in the …nite sample performance of various likelihood-based tests under correct speci…cation and when the outcome equation is misspeci…ed due to neglected over-dispersion or nonlinearity. We compare alternative 2SRI procedures and uncover that standardizing the variance of the …rst stage residuals leads to higher power of the test and reduces the bias of the treatment coe¢ cients. An original application in health economics corroborates our …ndings.JEL Classi…cation: C12, C31, C35, I11

The Influence of Increasing Levels of Provider-Patient Discussion on Quit Behavior: An Instrumental Variable Analysis of a National Survey

“…We applied a two-stage residual inclusion (2SRI) method, an established method for producing consistent estimators for nonlinear parametric models [30,31]. In the first stage, the provider-patient discussion was modeled as a function of the IV and the aforementioned covariates using a multinomial logistic regression.…”

“…In the second stage, the individual dichotomized outcome variable was predicted as a function of the exposure variable, all covariates, and the standardized residuals obtained from the first stage using a binomial logistic regression. The standard errors of two-stage estimators were calculated by implementing a bootstrap method with 500 repetitions [30,31].…”

Treatment effects beyond the mean using distributional regression: Methods and guidance

“…Wooldridge [54] recommended includingξ u nonlinearily and/or interactions with X e , X o in (34) to improve the approximation. Furthermore, a simulation study on different 2SRI settings suggested standardizing the variance of the first stage residuals [56].…”

An Econometric Analysis Of Health Care Utilization In Kenya

“…The 2SRI method is applicable when there are regressors in a nonlinear model that are correlated with unobserved (latent) variables, and these unobservables also influence the outcome variable. In the context of linear models, instrumental variable (IV) methods represent the established solution to the problem of endogeneity of regressors (Geraci, Fabbri and Monfardini, 2012). For example, the conventional Two-Stage Least Squares (2SLS) method is based on the assumption that the regression relationship of the outcome variable on the treatment variable and the observable confounders is linear.…”