Joseph V. Terza

Two-stage residual inclusion estimation: addressing endogeneity in health econometric modeling.

The paper focuses on two estimation methods that have been widely used to address endogeneity in empirical research in health economics and health services research-two-stage predictor substitution (2SPS) and two-stage residual inclusion (2SRI). 2SPS is the rote extension (to nonlinear models) of the popular linear two-stage least squares estimator. The 2SRI estimator is similar except that in the second-stage regression, the endogenous variables are not replaced by first-stage predictors. Instead, first-stage residuals are included as additional regressors. In a generic parametric framework, we show that 2SRI is consistent and 2SPS is not. Results from a simulation study and an illustrative example also recommend against 2SPS and favor 2SRI. Our findings are important given that there are many prominent examples of the application of inconsistent 2SPS in the recent literature. This study can be used as a guide by future researchers in health economics who are confronted with endogeneity in their empirical work.

Estimating count data models with endogenous switching: Sample selection and endogenous treatment effects

Count data regression models are extended to account for endogenous switching and its two most common incarnations, viz., endogenous dummy variables (treatment effects) and sample selection. Fully parametric and partially parametric versions of the extended model are discussed. In the parametric version of the model, a full information maximum likelihood (FIML) approach to estimation is introduced. Under the correct model specification the FIML estimator is efficient but computationally burdensome. For the relatively robust partially parametric version of the model I develop a two-stage method of moments (TSM) estimator. The TSM estimator is a nonlinear least-squares analog to the popular Heckman (1976, 1979) estimator and therefore avoids the computational requirements of FIML estimation. A nonlinear weighted least-squares (NWLS) estimator is offered for the fully parametric case. The NWLS estimator is computationally efficient relative to FIML estimation, and statistically efficient relative to the TSM estimator. For illustrative purposes the TSM and NWLS estimators are applied to the estimation of a regression model with household trip frequency as the dependent variable and a potentially endogenous dummy variable indicating vehicle ownership among the regressors.

Applying the risk/use equilibrium: use medicinal nicotine now for harm reduction

Both the recent Institute of Medicine (IOM) report1 and the article by Henningfield and Fagerstrom2 in this issue of Tobacco Control consider the value of adding harm reduction products to the main public health strategies for dealing with tobacco use—prevention, cessation, and protection of non-smokers from tobacco smoke pollution.3 4 Harm reducing products are those that lower total tobacco caused morbidity and mortality, even though these products might involve continued exposure to one or more tobacco related toxicants. The IOM committee developed a testing strategy to assess which products (tobacco or pharmaceutical) are truly harm reducing, along with surveillance and regulatory principles for the protection of public health. Henningfield and Fagerstrom2 discussed the possible benefits from an uncontrolled harm reduction “intervention” in Sweden involving Snus (Swedish moist snuff) and to some extent nicotine replacement pharmaceuticals or medicinal nicotine (MN). It will take years, if ever, before any battery of IOM-type tests will be in place. Given the probability of legal and political battles, the final form of testing and regulation may be far from adequate, leading to further decades of the promotion of ostensibly reduced risk products falsely reassuring tobacco users. Cigarette smoking remains the single leading preventable cause of death in most developed countries5 and a major cause of current and future deaths in developing countries.6 For health, non-smokers should never start smoking, and current smokers should become former smokers as soon as possible. Harm reduction, if done well, offers additional promise. Once it was hoped that lower tar cigarettes would have harm reducing properties and be good for the publics health,7but, on current evidence, they have been a public health disaster.8-11 One harm reduction strategy is to alter cigarettes to try to reduce or eliminate toxic ingredients. Such altered …

Assessing the Impact of Drug Use on Hospital Costs

OBJECTIVE To assess whether outpatient prescription drug utilization produces offsets in the cost of hospitalization for Medicare beneficiaries. DATA SOURCES/STUDY SETTING The study analyzed a sample (N=3,101) of community-dwelling fee-for-service U.S. Medicare beneficiaries drawn from the 1999 and 2000 Medicare Current Beneficiary Surveys. STUDY DESIGN Using a two-part model specification, we regressed any hospital admission (part 1: probit) and hospital spending by those with one or more admissions (part 2: nonlinear least squares regression) on drug use in a standard model with strong covariate controls and a residual inclusion instrumental variable (IV) model using an exogenous measure of drug coverage as the instrument. PRINCIPAL FINDINGS The covariate control model predicted that each additional prescription drug used (mean=30) raised hospital spending by

Earnings among people with spinal cord injury.

16 (p<.001). The residual inclusion IV model prediction was that each additional prescription fill reduced hospital spending by

Parametric Nonlinear Regression with Endogenous Switching

104 (p<.001). CONCLUSIONS The findings indicate that drug use is associated with cost offsets in hospitalization among Medicare beneficiaries, once omitted variable bias is corrected using an IV technique appropriate for nonlinear applications.

The Determinants of Escape Clause Petitions

OBJECTIVE To identify differences in conditional and unconditional earnings among participants with spinal cord injury (SCI) attributable to biographic, injury, educational, and employment factors by using a 2-part model (employment, earnings). DESIGN A secondary analysis of cross-sectional survey data. SETTING A Midwestern university hospital and a private hospital in the Southeastern United States. PARTICIPANTS All participants (N=1296) were adults between the ages of 18 and 64 who had a traumatic SCI at least 1 year before study initiation. INTERVENTIONS Not applicable. MAIN OUTCOME MEASURES Earnings were defined by earnings within the previous 12 months and were measured by a single categoric item. Conditional earnings reflect the earnings of employed participants, whereas unconditional earnings reflect all participants with

Factors associated with labor force participation after spinal cord injury

0 in earnings recorded for those unemployed. RESULTS Sex and race were significantly related to conditional earnings, even after controlling for educational and vocational variables. Additionally, conditional earnings (employed participants only) were related to 16 or more years of education, number of years employed, the percentage of time after SCI spent employed, and working in either government or private industry (not self-employed or family business). There was a greater number of significant variables for unconditional earnings, largely reflective of the influence of the portion employed (those not working having

U.S. Alcohol Affordability and Real Tax Rates, 1950–2011

0 in earnings). CONCLUSIONS Efforts to improve employment outcomes should focus on facilitating return to work immediately after injury, returning to preinjury job, maintaining regular employment, and working for placement in government or private industry. Special efforts may be needed to promote vocational outcomes among women and nonwhites.

Estimation of policy effects using parametric nonlinear models: a contextual critique of the generalized method of moments

Based on the insightful work of Olsen (1980) for the linear context, a generic and unifying framework is developed that affords a simple extension of the classical method of Heckman (1974, 1976, 1978, 1979) to a broad class of nonlinear regression models involving endogenous switching and its two most common incarnations, endogenous sample selection and endogenous treatment effects. The approach should be appealing to applied researchers for three reasons. First, econometric applications involving endogenous switching abound. Secondly, the approach requires neither linearity of the regression function nor full parametric specification of the model. It can, in fact, be applied under the minimal parametric assumptions—i.e., specification of only the conditional means of the outcome and switching variables. Finally, it is amenable to relatively straightforward estimation methods. Examples of applications of the method are discussed.