RAND Health Insurance Experiment Research Articles

A flexible copula regression model with Bernoulli and Tweedie margins for estimating the effect of spending on mental health.

We develop a flexible two-equation copula model to address endogeneity of medical expenditures in a distribution regression for health. The expenditure margin uses the compound gamma distribution, a special case of the Tweedie family of distributions, to account for a spike at zero and a highly skewed continuous part. An efficient estimation algorithm offers flexible choices of copulae and link functions, including logit, probit and cloglog for the health margin. Our empirical application revisits data from the Rand Health Insurance Experiment. In the joint model, using random insurance plan assignment as instrument for spending, a $1000 increase is estimated to reduce the probability of a low post-program mental health index by 1.9 percentage points. The effect is not statistically significant. Ignoring endogeneity leads to a spurious positive effect estimate.

Correcting for transitory effects in RCTs: Evidence from the RAND Health Insurance Experiment

AbstractTemporary randomized controlled trials are susceptible to transitory effects that would not result from a permanent treatment. We find a large and statistically significant “deadline effect”—a surge in spending in the final treatment year—in the RAND Health Insurance Experiment, identified by random allocation to three‐ or five‐year enrolment terms. Participants facing lower coinsurance rates show larger spending surges. Partialing out the price–deadline interaction reduces in magnitude estimates of the permanent price elasticity of drug spending (and in some specifications of outpatient and supplies spending). This implies higher optimal coinsurance rates and illustrates the importance of experimental design to identifying parameters of interest in randomized controlled trials.

Family health spillovers: evidence from the RAND health insurance experiment

I study how family spillovers shape healthcare consumption through two main sources: a learning channel whereby family members share information about their health insurance and the effectiveness of healthcare, and a behavioral channel whereby risk perception and habits are shared and transmitted. I exploit two types of sudden health shocks to identify a causal effect operating through each channel: a spouse’s non-fatal heart attack or stroke and a severe injury to a child. I incorporate these shocks into an event-study framework to quantify the effect of spillovers on healthcare consumption of a non-injured adult family member. I find a significant behavioral spillover effect of an increase of more than 200% in medical expenditure of preventive care over a four-year horizon. Moreover, I find a strong and persistent learning spillover that amounts to an average increase of more than 150% in medical expenditure relative to prior to the health shock, and I demonstrate that this effect promotes health investment. While the first result is in line with previous findings in the literature, the second is novel.

Two-part quantile regression models for semi-continuous longitudinal data: A finite mixture approach

This article develops a two-part finite mixture quantile regression model for semi-continuous longitudinal data. The proposed methodology allows heterogeneity sources that influence the model for the binary response variable to also influence the distribution of the positive outcomes. As is common in the quantile regression literature, estimation and inference on the model parameters are based on the asymmetric Laplace distribution. Maximum likelihood estimates are obtained through the EM algorithm without parametric assumptions on the random effects distribution. In addition, a penalized version of the EM algorithm is presented to tackle the problem of variable selection. The proposed statistical method is applied to the well-known RAND Health Insurance Experiment dataset which gives further insights on its empirical behaviour.

The Design of the RAND Health Insurance Experiment: A Retrospective.

This article, prepared as part of a special issue on multiarmed experiments, describes the design of the RAND Health Insurance Experiment, paying particular attention to the choice of arms. It also describes how the results of the Experiment were used in a simulation model and, looking back, how the design might have differed, and how the results apply today, 4 decades after the Experiment was conducted.

Semiparametric models and inference for the effect of a treatment when the outcome is nonnegative with clumping at zero.

The outcome in a randomized experiment is sometimes nonnegative with a clump of observations at zero and continuously distributed positive values. One widely used model for a nonnegative outcome with a clump at zero is the Tobit model, which assumes that the treatment has a shift effect on the distribution of a normally distributed latent variable and the observed outcome is the maximum of the latent variable and zero. We develop a class of semiparametric models and inference procedures that extend the Tobit model in two useful directions. First, we consider more flexible models for the treatment effect than the shift effect of the Tobit model; for example, our models allow for the treatment to have a larger in magnitude effect for upper quantiles. Second, we make semiparametric inferences using empirical likelihood that allow the underlying latent variable to have any distribution, unlike the original Tobit model that assumes the latent variable is normally distributed. We apply our approach to data from the RAND Health Insurance Experiment. We also extend our approach to observational studies in which treatment assignment is strongly ignorable.

Consumerism Made Real

Consumerism Made Real

Estimating Poisson pseudo-maximum-likelihood rather than log-linear model of a log-transformed dependent variable

Purpose The purpose of this study is to account for a recent non-mainstream econometric approach using microdata and how it can inform research in business administration. More specifically, the paper draws from the applied microeconometric literature stances in favor of fitting Poisson regression with robust standard errors rather than the OLS linear regression of a log-transformed dependent variable. In addition, the authors point to the appropriate Stata coding and take into account the possibility of failing to check for the existence of the estimates – convergency issues – as well as being sensitive to numerical problems. Design/methodology/approach The author details the main issues with the log-linear model, drawing from the applied econometric literature in favor of estimating multiplicative models for non-count data. Then, he provides the Stata commands and illustrates the differences in the coefficient and standard errors between both OLS and Poisson models using the health expenditure dataset from the RAND Health Insurance Experiment (RHIE). Findings The results indicate that the use of Poisson pseudo maximum likelihood estimators yield better results that the log-linear model, as well as other alternative models, such as Tobit and two-part models. Originality/value The originality of this study lies in demonstrating an alternative microeconometric technique to deal with positive skewness of dependent variables.

A Qualitative Synthesis of the Effects of Rising Cost-Sharing Requirements in the United States

In diesem Beitrag evaluiere und synthetisiere ich Ergebnisse aus zehn Jahren qualitativer Forschung zu den Effekten steigender Selbstbeteiligungsanforderungen in der Gesundheitsversorgung. Wahrend das Gros an Forschung in diesem Feld quantitativ ausgerichtet war und ist, will ich mit meiner Analyse dazu beitragen, die Perspektiven und Erfahrungen der Patient/innen und der Dienstanbieter/innen nachzuvollziehen. Ein Ergebnis ist, dass steigende Selbstbeteiligungsanforderungen viele Amerikaner/innen veranlassen, auf Gesundheitsdienstleistungen zu verzichten. Dies gilt auch fur medizinisch erforderliche Behandlungen fur sie selbst und fur ihre Familienmitglieder, und zwar auch im Falle von der Mittelklasse zugehorigen Familien, bei denen Angehorige in regularen Arbeitsverhaltnissen stehen und versichert sind. Zweitens zeige ich, dass diese Anforderungen zu Konfusion, Sorge, Stress und einer allgemeinen Angstlichkeit aufseiten der Patient/innen beitragen. Meine Befunde sind komplementar zu denen aus dem RAND Health Insurance Experiment, einer grosen experimentellen Studie zu Gesundheitskosten und der Nutzung von Gesundheitsdienstleistungen, die von 1974 bis 1982 durchgefuhrt wurde, um die Effekte von Krankheitsfolgekosten nachvollziehen zu konnen. Diese Befunde sind kritisch, weil aufseiten einiger politischer Entscheidungstrager/innen eine weitere Steigerung der Selbstbeteiligung unterstutzt wird. Ich diskutiere auch Grenzen und mogliche Folgerichtungen solcher Untersuchungsansatze.

Intertemporal substitution in health care demand: Evidence from the RAND Health Insurance Experiment

Nonlinear cost-sharing in health insurance encourages intertemporal substitution because patients can reduce their out-of-pocket costs by concentrating spending in years when they hit the deductible. We develop a test for intertemporal substitution and apply it to data from the RAND Health Insurance Experiment, where people were randomly assigned either to a free care plan or to a cost-sharing plan which had coinsurance up to a maximum dollar expenditure (MDE). Hitting the MDE—leading to an effective price of zero—has a bigger effect on health care demand than does being in free care, because people who hit the MDE face low current prices but high future prices, and so stock up on health care. As a result, short-lasting price changes induce nearly twice as big a response as do long-lasting changes. These findings help reconcile disparate estimates of the price elasticity of demand for health care in the existing literature. Failing to account for intertemporal substitution can lead researchers to overstate cost savings from high deductible health plans by 20% or more.

Optimal taxation and insurance using machine learning — Sufficient statistics and beyond

How should one use (quasi-)experimental evidence when choosing policies such as tax rates, health insurance copay, unemployment benefit levels, and class sizes in schools? This paper suggests an approach based on maximizing posterior expected social welfare, combining insights from (i) optimal policy theory as developed in the field of public finance, and (ii) machine learning using Gaussian process priors. We provide explicit formulas for posterior expected social welfare and optimal policies in a wide class of policy problems.The proposed methods are applied to the choice of coinsurance rates in health insurance, using data from the RAND health insurance experiment. The key trade-off in this setting is between transfers toward the sick and insurance costs. The key empirical relationship the policy maker needs to learn about is the response of health care expenditures to coinsurance rates. Holding the economic model and distributive preferences constant, we obtain much smaller point estimates of the optimal coinsurance rate (18% vs. 50%) when applying our estimation method instead of the conventional “sufficient statistic” approach.

The medical assistance system and inpatient health care provision: Empirical evidence from short-term hospitalizations in Japan.

This paper uses two nationally representative sets of medical claims data from medical assistance and universal public health insurance systems to examine how medical assistance system assignment affects short-term inpatient health care provision. In Japan, the medical assistance system, which is part of a public assistance system, provides medical care services for its beneficiaries without imposing any financial burdens, such as copayments or advance premium payments. These circumstances can lead to inpatient costs, as physicians may provide more treatments because there is a financial incentive. Because the assignment of public assistance in Japan is not random but is subject to means testing by the local government, I employ the instrumental variable model to control the potential correlation. I find that medical expenditure is significantly higher for medical assistance patients than for universal public health insurance patients, with an arc elasticity of approximately 0.20. This elasticity is slightly greater than that found for inpatient care in the randomized RAND Health Insurance Experiment and recent empirical studies on low-income populations. In addition, the elasticities for patients who receive medication, treatment and surgery are greater.

Price elasticities of pharmaceuticals in a value based-formulary setting.

Empirical estimates of price elasticities of demand (PED) for pharmaceuticals suggest that they are relatively price inelastic. However, in many settings, a medication and its substitutes and complements face simultaneous differential changes in prices that affect the observed "composite" PED. We exploit an implementation of a value-based formulary (VBF) that utilized drug-specific incremental cost-effectiveness ratios (ICERs) to inform drug copayments, resulting in increases in copayments for some medications and decreases in copayments for others. We first show theoretically that by changing the price of a medication and its substitute in opposite directions, VBF designs can leverage cross-price effects to increase the range of composite PEDs. We then empirically estimate PED and welfare effects using a consumer surplus approach. Overall PED was -0.16, similar to the RAND Health Insurance Experiment estimate. However, there was substantial dispersion of PED across the VBF copayment tiers ranging from -0.09 to -0.87 with a statistically significant trend aligned with the levels of value as reflected by the ICER estimates (p<0.001). The net welfare increase was $147,000 for the cohort or $28 per member over the postpolicy year. Further experimentations of VBF designs with alternative cost-effectiveness thresholds, copayment levels and value definitions could be quite promising for improving welfare.

Health insurance and the demand for medical care: Instrumental variable estimates using health insurer claims data

This paper takes a different approach to estimating demand for medical care that uses the negotiated prices between insurers and providers as an instrument. The instrument is viewed as a textbook “cost shifting” instrument that impacts plan offerings, but is unobserved by consumers. The paper finds a price elasticity of demand of around −0.20, matching the elasticity found in the RAND Health Insurance Experiment. The paper also studies within-market variation in demand for prescription drugs and other medical care services and obtains comparable price elasticity estimates.

A Difference in Copayment and the Physician Agency Problem: Empirical Evidence from Japan

I use two nationally representative sets of medical claim data from the Ministry of Health, Labour, and Welfare in Japan to examine how medical assistance system assignment affects beneficiary utilization of short-term inpatient health care. Since assignment of public assistance by local government is not random but is subject to means testing, I estimate instrumental variable models to control for this endogeneity. I find that monthly medical expenditure is significantly higher for medical assistance patients than that for universal public health insurance patients, but its implied price elasticity ranges from -0.158 to -0.081, which is equivalent to or slightly lower than the elasticity for the RAND health insurance experiment and for the recent Japanese studies. If the effect of patients with high medical expenditure is excluded, the price elasticity becomes more inelastic. However, there is no significant difference in length of hospital stay between medical assistance and health insurance patients. These findings imply that the medical assistance patients are provided with more intensive inpatient treatments than health insurance patients during short-term hospitalization.

Can European Countries Improve Sustainability of Health Care Financing through Patient Cost-Sharing?

Rising health care cost and resource constraints confront policy makers with the challenge to ensure the financial sustainability of health care systems, without jeopardizing the main health system objectives. To respond to this challenge, many European countries have introduced patient payments for publicly financed health care services (patient cost-sharing) (1–4). The potential of patient cost-sharing to contribute to the sustainability of the health care system relies on two elements. First, cost-sharing generates additional sources of funding. Hence, through cost-sharing, some of the health care cost might be shifted from public budgets to patients. Second, cost-sharing has the potential to improve efficiency in publicly financed health care, as it is expected that patients, when faced with the price of health care services, reduce the utilization of unnecessary and low-value health care (5, 6). It is also expected that this could slow the growth of health care costs. However, opponents of cost-sharing question the potential of cost-sharing to improve efficiency and instead point to its potentially negative effects on equity in health care. This is documented by evidence, among them the best known is the RAND health insurance experiment (7, 8). Whether the potential of cost-sharing can be realized without threatening equity and consumers financial protection depends on various context-specific factors as well as on the design of the cost-sharing systems applied by European countries.

Copayments and the evidence-base paradox.

From 1971 to 1982, the RAND Health Insurance Experiment (HIE) in the United States randomly allocated families to health insurance plans with zero, 25%, 50% or 95% copayments.2 The study found that “Cost sharing in general had no adverse effects on participant health”. This finding might support a copayment. However, the study also provides evidence against copayments by emphasising the finding that “The poorest and sickest 6 percent of the sample at the start of the experiment had better outcomes under the free plan for 4 of the 30 conditions measured”.

40 years of training physician-scientists: a journey from clinical pearls to evidence-based practice and policies.

During the past 4 decades, the training of physician-scientists has been driven by the information needs of clinicians; policymakers; and, more recently, patients who have voiced a strong desire to move from case-based, opinion-driven clinical care to practice informed by evidence. Thought leaders, primarily from the fields of internal medicine, epidemiology, and public health, proposed that this task could best be accomplished by developing researchers grounded in clinical medicine but armed with the skills needed to ask and answer the most pressing clinical and health care delivery questions in medicine. One long-lasting result was the Clinical Scholars Program (CSP), initially funded by the Carnegie Corporation and the Commonwealth Foundation and later by the Robert Wood Johnson Foundation (RWJF) (1).

Life or Debt: Underinsurance in America

Life or Debt: Underinsurance in America

Estimation of a regression spline sample selection model

It is often the case that an outcome of interest is observed for a restricted non-randomly selected sample of the population. In such a situation, standard statistical analysis yields biased results. This issue can be addressed using sample selection models which are based on the estimation of two regressions: a binary selection equation determining whether a particular statistical unit will be available in the outcome equation. Classic sample selection models assume a priori that continuous regressors have a pre-specified linear or non-linear relationship to the outcome, which can lead to erroneous conclusions. In the case of continuous response, methods in which covariate effects are modeled flexibly have been previously proposed, the most recent being based on a Bayesian Markov chain Monte Carlo approach. A frequentist counterpart which has the advantage of being computationally fast is introduced. The proposed algorithm is based on the penalized likelihood estimation framework. The construction of confidence intervals is also discussed. The empirical properties of the existing and proposed methods are studied through a simulation study. The approaches are finally illustrated by analyzing data from the RAND Health Insurance Experiment on annual health expenditures.