Two-Stage Residual Inclusion Estimation in Health Services Research and Health Economics.

OBJECTIVES: Empirical analyses in health services research and health economics often require implementation of nonlinear models whose regressors include one or more endogenous variables-regressors that are correlated with the unobserved random component of the model. In such cases, implementation of conventional regression methods that ignore endogeneity will likely produce results that are biased and not causally interpretable. Terza et al. (2008) discuss a relatively simple estimation method that avoids endogeneity bias and is applicable in a wide variety of nonlinear regression contexts. They call this method two-stage residual inclusion (2SRI). In the present paper, I offer a 2SRI how-to guide for practitioners and a step-by-step protocol that can be implemented with any of the popular statistical or econometric software packages. STUDY DESIGN: We introduce the protocol and its Stata implementation in the context of a real data example. Implementation of 2SRI for a very broad class of nonlinear models is then discussed. Additional examples are given. EMPIRICAL APPLICATION: We analyze cigarette smoking as a determinant of infant birthweight using data from Mullahy (1997). CONCLUSION: It is hoped that the discussion will serve as a practical guide to implementation of the 2SRI protocol for applied researchers.

Emergency room visits and hospitalizations among participants with spinal cord injury.

BACKGROUND: Literature examining emergency room visits (ERV) and emergency room related hospitalizations (ERH) after spinal cord injury (SCI) is limited. OBJECTIVE: Identify (1) the annual frequency of ERV and ERH and (2) their likelihood as a function of demographic, injury, and socioeconomic characteristics. METHODS: Participants (n = 1,579) with SCI completed mailed self-report questionnaires. RESULTS: 37% reported at least one ERV, with an average of 85 ERV per 100 participants. 19% reported at least one ERH and an average of 33 ERH annually per 100 participants. A greater likelihood of ERV was observed among non-whites, those with more severe SCI, less education, and lower income. Among those with at least one ERV, greater risk of ERH was observed among non-Hispanic whites, those with more severe SCI, lower education, and higher age. CONCLUSIONS: ERV are common after SCI and should be accounted for when predicting SCI related expenses. Those with the most severe SCI and those in the oldest age group were most likely to be hospitalized after an ERV.

U.S. alcohol affordability and real tax rates, 1950-2011.

BACKGROUND: The affordability of alcoholic beverages, determined by the relationship of prices to incomes, may be an important factor in relation to heavy drinking, but little is known about how affordability has changed over time. PURPOSE: To calculate real prices and affordability measures for alcoholic beverages in the U.S. over the period from 1950 to 2011. METHODS: Affordability is calculated as the percentage of mean disposable income required to purchase 1 drink per day of the cheapest spirits, as well as popular brands of spirits, beer, and wine. Alternative income and price measures also are considered. Analyses were conducted in 2012. RESULTS: One drink per day of the cheapest brand of spirits required 0.29% of U.S. mean per capita disposable income in 2011 as compared to 1.02% in 1980, 2.24% in 1970, 3.61% in 1960, and 4.46% in 1950. One drink per day of a popular beer required 0.96% of income in 2010 compared to 4.87% in 1950, whereas a low-priced wine in 2011 required 0.36% of income compared to 1.05% in 1978. Reduced real federal and state tax rates were an important source of the declines in real prices. CONCLUSIONS: Alcoholic beverages sold for off-premises consumption are more affordable today than at any time in the past 60 years; dramatic increases in affordability occurred particularly in the 1960s and 1970s. Declines in real prices are a major component of this change. Increases in alcoholic beverage tax rates and/or implementing minimum prices, together with indexing these to inflation could be used to mitigate further declines in real prices.

What U.S. data should be used to measure the price elasticity of demand for alcohol?

This paper examines how estimates of the price elasticity of demand for beer vary with the choice of alcohol price series examined. Our most important finding is that the commonly used ACCRA price data are unlikely to reliably indicate alcohol demand elasticities-estimates obtained from this source vary drastically and unpredictably. As an alternative, researchers often use beer taxes to proxy for alcohol prices. While the estimated beer taxes elasticities are more stable, there are several problems with using taxes, including difficulties in accounting for cross-price effects. We believe that the most useful estimates reported in this paper are obtained using annual Uniform Product Code (UPC) "barcode" scanner data on grocery store alcohol prices. These estimates suggest relatively low demand elasticity, probably around -0.3, with evidence that the elasticities are considerably overstated in models that control for beer but not wine or spirits prices.

Pediatric palliative care: describing hospice users and identifying factors that affect hospice expenditures.

OBJECTIVE: Each year approximately 50,000 children die. These children could benefit from pediatric palliative care, and hospice is one important provider of palliative care. However, little information exists to understand pediatric hospice care. This study seeks to describe Medicaid pediatric hospice and nonhospice users and to identify factors that affect hospice expenditures. DESIGN: Analyses of Medicaid administrative data and death certificate data. PARTICIPANTS: A total of 1527 children in Florida Medicaid program. RESULTS: Few children in the sample used hospice services (11%) and the dominant location of death was home for hospice users (55%). Descriptive analyses show that pediatric hospice users had higher inpatient, outpatient, emergency department, and pharmacy expenditures than nonhospice users. Regression results suggest that black non-Hispanic, Hispanic, and children of other races had $730 to $880 fewer hospice expenditures than Whites. Higher hospice expenditures ($970) were associated with longer enrollment spans. CONCLUSIONS: Descriptive analyses suggest that there are differences between pediatric hospice and nonhospice users. Minority race/ethnicities, as well as shortened Medicaid enrollment spans, are both associated with decreased hospice expenditures. Information from this study can be used to develop interventions aimed at increasing the prevalence of and reducing inequalities in hospice care.

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 $16 (p<.001). The residual inclusion IV model prediction was that each additional prescription fill reduced hospital spending by $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 use of linear instrumental variables methods in health services research and health economics: a cautionary note.

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. PRINCIPAL 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.

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.

Care-giver advice as a preventive measure for drinking during pregnancy: zeros, categorical outcome responses, and endogeneity.

We conduct an empirical investigation of the impact of prenatal care-giver advice on alcohol consumption by pregnant women. In the design of the model and estimator, we pay particular attention to three aspects of the data. First, a large proportion of pregnant women do not drink at all. To accommodate this aspect of the sample we base the essential formulation of the model on the modified version of the two-part approach of Duan et al. (Journal of Business and Economic Statistics 1983; 1: 115-126.) suggested by Mullahy (Journal of Health Economics 1998; 17: 247-281.). Second, in the survey that we analyze (the 1988 National Maternal and Infant Health Survey - NMIHS), respondents were only required to report their consumption up to a specified range of values (e.g. 1-2 drinks per week, 2-5 drinks per week, and so on). For this reason, the model is cast in the grouped regression framework of Stewart (Review of Economic Studies 1983; 50: 141-149.). Third, the binary physician advice variable is likely to be endogenous and the econometric specification explicitly accounts for this possibility. To summarize the results, we find that failing to account for endogeneity leads to the counterintuitive conclusion that advice has a positive and statistically significant influence on drinking during pregnancy. When the model is extended to allow for potential endogeneity, we find that advice has a negative and statistically significant impact.

Estimating the effects of prescription drug coverage for Medicare beneficiaries.

OBJECTIVE: To identify the effect of insurance coverage on prescription utilization by Medicare beneficiaries. DATA SOURCES/STUDY SETTING: Secondary data from the 1999 Medicare Current Beneficiary Survey (MCBS) Cost and Use files, a nationally representative survey of Medicare enrollees. STUDY DESIGN: The paper uses a cross-sectional design with (1) a standard regression framework to estimate the impact of prescription coverage on utilization controlling for potential selection bias with covariate control based on the Diagnostic Cost Group/Hierarchical Condition Category (DCG/HCC) risk adjuster, and (2) a multistage residual inclusion method using instrumental variables to control for selection bias and identify the insurance coverage effect. DATA COLLECTION/EXTRACTION METHODS: Data were extracted from the 1999 MCBS. Study inclusion criteria are community-dwelling MCBS respondents with full-year Medicare enrollment and supplemental medical insurance with or without full-year drug benefits. The final sample totaled 5,270 Medicare beneficiaries. PRINCIPAL FINDINGS: Both the model using the DCG/HCC risk adjuster and the model using the residual inclusion method produced similar results. The estimated price elasticity of demand for prescription drugs for the Medicare beneficiaries in our sample was -0.54. CONCLUSIONS: Our results confirm that selection into prescription coverage is predictable based on observable health. Our results further confirm prior estimates of price sensitivity of prescription drug demand for Medicare beneficiaries, though our estimate is slightly above prior results.