TIME AND RISK PREFERENCES IN THE COVERAGE. W. DAVID BRADFORD, PH.D. Department of Public Administration and Policy, University of Georgia.

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1 TIME AND RISK PREFERENCES IN THE CHOICE OF HEALTH INSURANCE COVERAGE W. DAVID BRADFORD, PH.D. Department of Public Administration and Policy, University of Georgia JAMES F. BURGESS, JR., PH.D. Department of Health Policy and Management, Boston University 3Center for Organization, Leadership and Management Research, VA Background Relatively little is known about how individual level time and risk preferences affect selection of insurance options. Conceptually, the productivity of health care, and thus the demand for health insurance, should vary with past behaviors and expectations about the future. Insurance options differ across groups that may have very differenttimetime andrisk preferences: The Medicare population faces a reasonably structured set of choices that varies largely by location. The under 65 age population obtains health insurance from more heterogeneous sources. 1

2 Background Time and risk preferences are considered a fundamental characteristic of economic behavior. Standard utility theory has strong predictions about the effect of different rates of discounting and risk aversion on behavior. Higher rates of discounting will lead individuals to more strongly shift consumption of economic goods to the present. Greater levels of risk aversion should lead individuals to opt for more complete insurance coverage. Unexplored Dynamic Issues Patients who discount the future more heavily should be less likely to demand health insurance that covers primary preventative health care. But if so, high discounting imply past neglect of primary prevention will raise the likelihood of disease. Increased clinical need may outweigh the economic tendency toward delaying costs. Despite the potential importance of time discounting effects on the demand for health insurance, the issue has not been heavily studied to date. 2

3 Goals Contribute to the literature that investigates whether time and risk preferences are determined by time varying events and personal characteristics. Conceptually characterize the dynamic relationships between time and risk preferences and insurance choices. Empirically evaluate how time and risk preferences affect choices for full vs. incomplete insurance coverage for the under aged 65 population. CONCEPTUAL CONSIDERATIONS 3

4 Static Insurance Choice Consider a simple model of insurance demand, such as put forward in Feldman and Dowd (1991) and Cutlerand Zeckhauser (2000). Individuals maximize utility across a numeraire good, Y, facing the risk of illness,, and medical costs, m, if ill The individual can purchase actuarially fair insurance where the price = m, and have a certain utility of Static Insurance Choice Equating utility with insurance (no risk) with an approximation of utility without insurance (but around income of Y ) yields the value of insurance This is the standard result that as the (Arrow Pratt) coefficient of absolute risk aversion increases (as U (.) /U (.) gets larger in absolute value) then the value of insurance should rise. We need to contemplate how this standard relationship changes when dynamic considerations are taken into account. 4

5 Dynamic Issues in Insurance Choice Risk Aversion Greaterrisk risk aversion means higher likelihood of complete coverage in the current year which implies higher demand for covered health services in the current year. This, however, lowers the probability of illness in future years. Thus, we may in principle assume that (R) and that (. )/ R < 0. Dynamic Issues in Insurance Choice Risk Aversion Under these assumptions, the Taylor series expansion around Y ρ(t) becomes and the present value of insurance is 5

6 Dynamic Issues in Insurance Choice Risk Aversion Now, the choice depends on The sign is indeterminate, since the first term in brackets (D) is positive and the second two terms are negative. The net result depends upon two things: the rate at which the probability of illness with and without insurance diverge, and the relative magnitudes of the individual s (always positive) discount rate and (always negative) ratio of risk aversion. As risk aversion increases, and the person builds health capital from continued investments in current health, the probability of becoming sick in the future falls, conditional on effects of general aging which can be mitigated by these investments. Dynamic Issues in Insurance Choice Risk Aversion Thus: as risk aversion increases a person s demand for current insurance and so current health care increases; as a very risk averse person builds health capital over time, the probability of becoming sick falls, which reduces the current demand for insurance. It is possible that the associated reduction in static demand from past health investments will offset the increasein static demand from current risk aversion. We expect to see that the demand for full insurance has a concave (inverted U )relationship to R, which suggests the probability of less comprehensive (or no) insurance has a convex. 6

7 Dynamic Issues in Insurance Choice Discounting Future outcomes are "future" in large part because We can't have them now, and Things at a temporal distance are less predictable than things temporally proximate. In other words, the future is risky and the further in the future something is, the riskier it is. Behaviorally, then, if a person is very risk averse then her valuation of temporally distant benefits should be lower than a person who is not very risk averse. DATA AND EMPIRICAL MODEL 7

8 Data: Waves of the HRS Questions about time preferences were asked of around 1200 randomly selectedrespondents to the HRS in Questions about risk preferences are asked periodically in the core of the HRS survey to all respondents We examine the impact of time and risk preferences measured in 2004 on the insurance choices made in 2006 and 2008, in order to avoid issues of simultaneity. After matching across all three waves, and eliminating a few outliers (e.g., over 65 years old, but no Medicare) we arrive at a final sample of 854 respondents. 8

9 Time Preference Questions Risk Preference Questions 9

10 Risk Preference Questions 10

11 Empirical Relationship Between Time Preferences and Insurance Choice Empirical Relationship Between Risk Aversion and Insurance Choice 11

12 Empirical Specification Discount and Risk Models Assume underlying latent variables Estimate models using grouped (interval) regression Each is a function of individual characteristics in 2004 Empirical Specification Insurance Choice Multinomial probit regressions for insurance choices (None=0, FFS=1, HMO=2) Where D i,2004 are subjective discount rate variables, R i,2004 are coefficient of relative risk aversion variables C i,2004 represent lagged expenditures on health care H it represent contemporaneous health state measures X it represent contemporaneous other characteristics of the individual, such as age, gender, race, income, and so forth. 12

13 RESULTS Selected Parameters from Time and Risk Aversion Models Grouped Regression Models 13

14 Selected Parameters from Time and Risk Aversion Models Grouped Regression Models 14

15 Multinomial Probit for Insurance Choice, 2006 Multinomial Probit for Insurance Choice,

16 Conclusions We find that time and risk preferences are determined by time varying events and personal characteristics. Thus, rather than bi being fixed endowments time and risk ik preferences may be directly malleable. We find some evidence that preferences for insurance coverage do depend upon individual s rates of discounting the future There is little evidence that aversion to risk is an important attribute of choice on this extensive margin. These time responses are consistent with a theoretical description that assumes dynamic effects of health choices on health expectations yield non linear effects. Conclusions When designing insurance benefit structures and policies that independently affect coverage, policy makers often consider the consequences on health. Our results suggest that policy considerations should be significantly more comprehensive. If health affects time and risk preferences, then the dynamic impact on insurance decisions and future health outcomes are potentially large. In addition, the spillover effects from insurance policy decisions to other aspects of life (e.g., savings rates, educational attainment, and addictive behaviors) may themselves become first order considerations. 16