The calculation of likelihood functions of many econometric models requires the evaluation of integrals without analytical solutions. Approaches for extending Gaussian quadrature to multiple dimensions discussed in the literature are either very specific or suffer from exponentially rising computational costs in the number of dimensions. We propose an extension that is very general and easily implemented, and does not suffer from the curse of dimensionality. Monte Carlo experiments for the mixed logit model indicate the superior performance of the proposed method over simulation techniques.JEL codes: C15, C35, C63

Early results on the Medicare Part D prescription drug program, from a survey of people age sixty-five and older who were interviewed just before enrollment started and just after it ended, indicate that Medicare has met its target of 90 percent coverage. Enrollment rates in vulnerable subpopulations-poor health, low income, or cognitive impairment-are almost high enough to offset lower rates of other coverage. However, sizable numbers of elderly people remain uncovered, contrary to their self-interest. Seniors give Part D mixed reviews, and majorities are less satisfied with Medicare and with the government as a result of their experience with this program. [Health Affairs 25 (2006): w344-w354; 10.1377/hlthaff.25.w344] E n r o l l m e n t i n t h e f i r s t o u t pat i e n t d ru g coverage benefit in Medicare's history began 1 January 2006, following the passage of the Medicare Prescription Drug, Improvement, and Modernization Act (MMA) of 2003. A much-publicized enrollment deadline passed 15 May 2006, after which most seniors face penalties for late enrollment. This paper presents early results on the demographics of enrollment in the Medicare Part D prescription drug program, based on the Retirement Perspectives Survey (RPS) conducted by our research group before and after the enrollment deadline. closed.2 Respondents were asked about their Part D knowledge and intentions in the first interview and about their enrollment-process choices and opinions in the second interview. We present results primarily from a core of 1,571 respondents who were age sixty-five and older in May 2006, were eligible for Part D, were interviewed in both waves, and had no item nonresponse on key variables.The RPS was administered to a panel of subjects enrolled by Knowledge Networks, a commercial survey firm. Panel members were representative of the U.S. resident population in terms of demographics and socioeconomic status, and sample weighting was used to adjust for subsequent nonresponse.3 They were interviewed using supplied Web TV hardware. Respondents are somewhat more computer-literate than the underlying population: About half of the panel members use the Internet, compared with about a third in the corresponding population. 4 Panel members were compensated for participation. In addition to questions about Medicare Part D, each RPS interview contained questions and embedded experiments regarding health status and conditions, long-term care choices, prescription drug use and cost, and attitudes toward risk. 5Additional socioeconomic and demographic variables were provided by Knowledge Networks as background on panel members. We also constructed a simple index of cognitive impairment. Study ResultsOf the 35.84 million people age sixty-five and older who reside in the United States and are eligible for Medicare Part D, data from the Centers for Medicare and Medicaid Services (CMS) suggest that as of 14 June 2006, 24.67 million (68.9 percent) were enrolled in Part D, 8.50 million (23.7 percent) had other credita...

Medicare Part D provides prescription drug coverage through Medicare approved plans offered by private insurance companies and HMOs. In this paper, we study the role of current prescription drug use and health risks, related expectations, and subjective factors in the demand for prescription drug insurance. To characterize rational behavior in the complex Part D environment, we develop an intertemporal optimization model of enrollment decisions. We generally find that seniors' choices respond to the incentives provided by their own health status and the market environment as predicted by the optimization model. The proportion of individuals who do not attain the optimal choice is small, but the margin for error is also small since enrollment is transparently optimal for most eligible seniors. Further, there is also evidence that seniors over-react to some salient features of the choice situation, do not take full account of the future benefit and cost consequences of their decisions, or the expected net benefits and risk properties of alternative plans.

We study the Medicare Part D prescription drug insurance program as a bellwether for designs of private, non-mandatory health insurance markets, focusing on the ability of consumers to evaluate and optimize their choices of plans. Our analysis of administrative data on medical claims in Medicare Part D suggests that fewer than 25 percent of individuals enroll in plans that are ex ante as good as the least cost plan specified by the Plan Finder tool made available to seniors by the Medicare administration, and that consumers on average have expected excess spending of about $300 per year, or about 15 percent of expected total out-of-pocket cost for drugs and Part D insurance. These numbers are hard to reconcile with decision costs alone; it appears that unless a sizeable fraction of consumers place large values on plan features other than cost, they are not optimizing effectively.