The Use of Linear Instrumental Variables Methods in Health Services Research and Health Economics: A Cautionary Note

Abstract

Objective. To investigate potential bias in the use of the conventional linear instrumental variables (IV) method for the estimation of causal effects in inherently nonlinear regression settings. Data Sources. Smoking Supplement to the 1979 National Health Interview Survey, National Longitudinal Alcohol Epidemiologic Survey, and simulated data. Study Design. Potential bias from the use of the linear IV method in nonlinear models is assessed via simulation studies and real world data analyses in two commonly encountered regression setting: (1) models with a nonnegative outcome (e.g., a count) and a continuous endogenous regressor; and (2) models with a binary outcome and a binary endogenous regressor. Principle Findings. The simulation analyses show that substantial bias in the estimation of causal effects can result from applying the conventional IV method in inherently nonlinear regression settings. Moreover, the bias is not attenuated as the sample size increases. This point is further illustrated in the survey data analyses in which IV-based estimates of the relevant causal effects diverge substantially from those obtained with appropriate nonlinear estimation methods. Conclusions. We offer this research as a cautionary note to those who would opt for the use of linear specifications in inherently nonlinear settings involving endogeneity.Key Words. Econometrics, nonlinear models, health economics When analyzing data with the goal of informing health policy, the ability to draw true causal inference from the estimation results is of paramount importance. The typical health policy analysis focuses on identifying the effect that a variable, over which there exists some degree of policy control (x p --henceforth the policy variable), has on an outcome of some policy interest (y--the outcome variable). Empirical analyses that offer estimates of mere associations between x p and y are of little value to policy makers. Estimating the desired causal effect of x p on y is not straightforward and is particularly r Health Research and Educational Trust DOI: 10.1111/j. 1475-6773.2007.00807.x 1102 difficult in the context of nonexperimental (survey) data. In observational surveys respondent behavior, as manifested in the value of y, can be influenced by a myriad of stimuli aside from the policy variable x p . Such alternative influences on y will obfuscate causal inference if they are also correlated with x p . If not properly taken into account, this will lead to bias in conventional estimation of causal effects. 1 For example, Mullahy (1997) posits that an individual's habit stock, accumulated over previous periods of smoking, will have an effect on current cigarette demand. 2 We might observe, for instance, that individuals with higher habit stocks have greater demands for cigarettes. Interpreting such an observation, as indicative of the causal effect of habit stock on current cigarette smoking will, however, be upward biased if ''healthminded'' individuals tend to smoke less both currently and in the past.Some co...

Does the Extension of Primary Care Practice Opening Hours Reduce the Use of Emergency Services?

“…Unfortunately, the linear IV estimator (2SLS) has severe drawbacks in this framework. Terza, Bradford and Dismuke (2008) show that addressing endogeneity by applying conventional linear IV methods that ignore the non-linear specification of the relationship of to an endogenous regressor, and a set of additional confounders, can lead to biased estimates of the causal effect in question. Mullahy (1997) and Terza, Basu and Rathouz (2008), among others, have suggested alternative estimators in order to deal with endogeneity in count/exponential regression models.…”

Instrumental Variable Analysis in Epidemiologic Studies: An Overview of the Estimation Methods

“…The advantage of 2SRI over 2SLS is that 2SLS is only consistent when the second-stage model is linear, whereas this restriction does not hold for 2SRI [43,51]. Moreover, this method shows more precise estimates than 2SPS [52].…”

“…In the first-stage, a nonlinear least squares method (NLS) or any other consistent estimation technique is used to estimate the relation between the IVand exposure [43]. Then, the predicted exposure status from the first-stage model replaces the observed exposure as the principal covariate in the second-stage model on the outcome [43,44].…”

The Effects of Market Structure and Payment Rate on the Entry of Private Health Plans into the Medicare Market

“…Following Amel and Liang (1997), we proxy expected market structure with a measure of observed structure: contemporaneous product-level HHI. Consistent with the recent work on the effect of commercial health insurance market structure on premiums (Dafny, Duggan, and Ramanarayanan 2009) and the quantity of hospital services used (Bates and Santerre 2008), we account for the endogeneity of market structure with a twostage residual inclusion (2SRI) instrumental variables approach (Terza, Basu, and Rathouz 2008;Terza, Bradford, and Dismuke 2008), computing standard errors via bootstrapping (Efron 1979).…”