MEDICAL EXPENDITURE RISK AND HOUSEHOLD PORTFOLIO CHOICE

Abstract

Medical expenses are an increasingly important contributor to household financial risk. We examine the effect of medical expenditure risk on the willingness of Medicare beneficiaries to hold risky assets. Using a discrete factor maximum likelihood method to address the endogeneity of insurance choices, we find that having a moderately protective Medigap or employer supplemental policy increases risky asset holding by 7.1 percentage points relative to those without supplemental coverage, while participation in a highly protective Medicare HMO increases risky asset holding by 13.0 percentage points. Our results highlight an important link between the availability of health insurance and financial behavior.

1. Introduction

As health care costs continue to rise, medical expenses have become an increasingly important contributor to financial risk. Medical expenses were cited in 62 percent of all personal bankruptcy filings in 2007 (up from 42 percent in 2001) and, astonishingly, three-quarters of medical debtors had health insurance (Himmelstein et al., 2005, 2009). Medical expenditure risk is especially important for older individuals who as they age face declining health. French and Jones (2004) estimate that one percent of the U.S. population will receive an age-65 shock to lifetime out-of-pocket healthcare costs of at least $43,500, and 0.1 percent will receive a shock of at least $125,000. Although nearly all Americans age 65 and older have Medicare coverage, benefit gaps—especially for catastrophic losses—place them at-risk for large out-of-pocket medical expenses.¹ Because of these potentially high costs, many individuals seek supplemental insurance, either through their former employers, a Medigap policy, or by enrolling in a Medicare HMO. These insurance arrangements offer different degrees of protection, but do not fully insure against the risk of large out-of-pocket medical expenses.

Because medical expenditure risk is not fully insurable and is largely beyond one’s control, it can be thought of as background risk. According to economic theory, when individuals face background risk, they should be less willing to bear other risks (Gollier and Pratt, 1996; Kimball, 1993; Pratt and Zeckhauser; 1987). For example, theory predicts that an exogenous increase in uninsurable medical expense risk would cause an individual to reduce his exposure to other risks, such as rate-of-return risk.

In this paper, we examine the effect of background risk on portfolio allocation by estimating the effect of exogenous medical expenditure risk on the decision to hold risky financial assets. In our analysis, variation in medical expenditure risk comes from the different supplemental insurance arrangements for Medicare beneficiaries; risk exposure is lowest in Medicare HMOs, moderate for those with employer insurance and Medigap policies, and highest for those who have no supplemental coverage. Because of the regulatory structure of the Medigap supplemental insurance market, most people make a one-time decision about supplemental insurance coverage when they enroll in Medicare at age 65. We measure portfolio outcomes subsequent to this decision, at an average age of 76, but in no case younger than age 67. Although simultaneity is not an issue, endogeneity may still arise through omitted variables that affect risky asset ownership and insurance choices (e.g., risk aversion). We control for the endogeneity of supplemental insurance choices by using a discrete factor maximum likelihood (DFML) method that allows for arbitrary correlation patterns in the unobserved heterogeneity affecting both ownership of risky assets and insurance choices. With the DFML method, the parameters of a discrete approximation to the joint distribution of the unobserved components are estimated simultaneously with all other parameters in the model, thus avoiding the need for stringent a priori distributional assumptions (Mroz, 1999). In addition, we make use of exogenous variation in supplemental insurance choices arising from the structure of non-Medicare HMO markets and from state insurance laws that limit the ways in which insurers can pool risks.

We find risky asset ownership rises as risk exposure decreases. Having either Medigap or employer supplemental insurance (moderate risk exposure) increases risky asset holding by 7.1 percentage points relative to having no supplemental coverage (high risk exposure). Medicare HMO participation (low risk exposure) increases risky asset holding by 13.0 percentage points compared to having no supplemental coverage. Given that just 50 percent of our sample holds risky assets, these represent economically important effects. We also present suggestive evidence that individuals in the middle third of the wealth distribution are most sensitive to background medical expenditure risk.

This research addresses an important yet understudied policy issue: How do public and private insurance programs affect risk-bearing generally? For example, it is well known that the elderly hold a disproportionate share of wealth in the U.S., and yet they invest relatively conservatively. If changes in medical expenditure risk affect their willingness to hold wealth in risky assets, reforms to the Medicare system could have important spillover effects on financial markets. Furthermore, as medical spending continues to absorb a larger fraction of household resources, the financial behavior of households will be increasingly distorted. Families with less wealth also tend to have less health insurance coverage; if they also invest in less risky assets, then their flatter wealth accumulation profiles will exacerbate the gap between high and low wealth households at older ages.

2. Theory and Evidence of Background Risk

In practice, individuals make economic decisions in an environment characterized by multiple risks. It makes intuitive sense that an individual facing one risk should be less willing to bear another risk, even if the two risks are independent. Theorists have alternately formalized this notion as proper risk aversion (Pratt and Zeckhauser, 1987), standard risk aversion (Kimball, 1993), and risk vulnerability (Gollier and Pratt, 1996). Each property entails slightly different restrictions on preferences and addresses different subclasses of random variables, but all yield the prediction that an unfair background risk makes individuals less willing to bear other independent risks.² Although the assumptions on preferences necessary to yield an unambiguous prediction are stronger than simply assuming risk aversion,³ the added restrictions are satisfied by a wide class of commonly used utility functions.

The first empirical investigations of background risk identified a small effect of background income risk on demand for risky assets (see e.g., Guiso et al., 1995, and Hochguertel, 2003). A related literature has found that precautionary saving is positively associated with both background income risk (Guiso et al., 1992; Lusardi, 1998; Carroll and Samwick, 1998; Gourinchas and Parker, 2001; Gollier, 2002; Cagetti, 2003) and medical expenditure risk (Kotlikoff, 1986; Levin, 1995; Palumbo, 1999; Pang and Warshawsky, 2010). ^4,5

Recent studies have examined the effect of health status on portfolio choices, where health status is viewed as an indicator of background health risk. Rosen and Wu (2004) first noted that older individuals who report themselves in fair or poor health choose safer portfolio allocations. Berkowitz and Qiu (2006) subsequently showed that once omitted variables biases are addressed, poor health affects portfolio choices only indirectly by reducing financial wealth. Consistent with this, Edwards (2008) found that individuals who assigned a higher probability to the possibility that medical expenses would exhaust their household savings in the next five years held lower risky portfolio shares. Later studies using panel methods to control for unobserved heterogeneity have consistently found either no direct effect or only a small direct effect of poor health on risky portfolio allocation (e.g., Coile and Milligan, 2009; Fan and Zhao, 2009; Cardak and Wilkins, 2009; and Love and Smith, 2010).⁶

Although health risk and medical expenditure risk are closely related, they are distinct sources of background risk. Medical expenditure risk is a function of not only health risk but also health insurance coverage; in fact, the relationship between health risk and medical expenditure risk is mediated by health insurance coverage. In models that included both health status and insurance coverage, Rosen and Wu (2004) and Edwards (2008) found that both variables retained independent effects on the demand for risky assets. This could arise if health risk has an indirect effect on portfolio behavior operating through the medical expenditure risk associated with a given level of insurance coverage, and a direct effect operating through the marginal utility of consumption or the rate of time preference (Edwards, 2008; Rosen and Wu, 2004).⁷ Although suggestive, in the U.S. context, an indicator variable for insurance coverage does not measure the causal effect of medical expenditure risk on portfolio choice since insurance coverage is an endogenous choice variable.

In general, we know quite little about the important question of how insurance coverage offsets background risk and in turn affects risk-bearing. Only two other studies offer some insight into this question. Cardak and Wilkins (2009) point to the presence of a universal health care system as an explanation for their finding that health status has no effect on risky asset holding among retired households in Australia. Atella, Brunetti and Maestas (2011) use the Survey of Health, Ageing and Retirement in Europe to show that health risk affects portfolio choices only in countries with less protective healthcare systems.

3. Medicare Supplemental Health Insurance

Nearly all Americans age 65 and older receive health insurance coverage through the Medicare program. Although Medicare coverage is fairly comprehensive, it has important gaps. Medicare did not cover prescription drugs until 2006 and has been slow to offer coverage for preventive care. It requires 20 percent coinsurance on most services and charges a deductible of $1132 for a single hospital stay of up to 60 days. For longer hospital stays, it applies an additional deductible of $283 per day during days 60–90 and $566 per day during days 91–150. After 150 days, the beneficiary is responsible for all costs.⁸

Because Medicare beneficiaries are still at risk for large out-of-pocket medical expenditures, many choose to purchase supplemental insurance policies known as Medigap plans. As the name suggests, Medigap plans are designed to fill the gaps in Medicare coverage. Since 1992, the federal government has required standardization of Medigap policies in 10 different plans ranging from Plan A, which covers coinsurance payments (but not deductibles), to Plan J, which covers coinsurance payments, deductibles, some prescription drugs and some kinds of preventive care.⁹ Medicare beneficiaries are guaranteed access to Medigap policies during a 6-month open enrollment period, which begins when the individual enrolls in Medicare Part B, usually at age 65.¹⁰ During this period, policies are either community- or age-rated; insurers are prohibited from either denying coverage or charging higher prices to those with pre-existing conditions. Once the open enrollment period has passed, insurers may take the individual’s health history into account in determining whether to offer coverage and at what price.¹¹

Another source of supplemental insurance comes through employers in the form of retiree health insurance. Employer supplemental policies generally offer more coverage at less cost than Medigap; for example, prior to 2006 virtually all retiree health plans offered by employers had prescription drug coverage (Kaiser, 2001). Although employer supplemental policies are not standardized, they operate under the same insurance model as Medigap, acting as secondary payer for Medicare-covered services. Some firms offer retirees a choice of either an employer-sponsored supplemental policy or a subsidy payment with which to purchase a Medigap policy.

Medicare HMOs offer a third way of filling the gaps in traditional fee-for-service Medicare. Whereas Medigap and employer-provided retiree health insurance act as secondary insurance, Medicare HMOs are an alternative to the traditional fee-for-service Medicare program. They provide the basic services of traditional Medicare as well as supplemental benefits such as lower copayments, unlimited hospitalization, prescription drugs, some preventive care, vision, and dental. Most HMOs require a modest or even no premium over and above the premium for Medicare Part B, but require individuals to obtain medical services from providers within the HMO’s network.¹² HMOs eliminate the need for a supplemental policy, and insurers are prohibited by law from selling Medigap policies to Medicare HMO enrollees. Finally, Medicaid provides supplemental insurance coverage for indigent Medicare beneficiaries who meet stringent asset and income limitations.

Table 1 shows supplemental insurance coverage rates in 2000 for Medicare beneficiaries in the Health and Retirement Study (HRS).¹³ The table shows that 15 percent of Medicare beneficiaries had no supplemental coverage of any kind (i.e., they had only Medicare Parts A and B), 16 percent were enrolled in a Medicare HMO, 33 percent had supplemental coverage through their employer, 29 percent had a Medigap policy, and 8 percent received supplemental coverage through Medicaid. From here forward we drop Medicaid recipients from our analysis since they do not generally invest in risky financial assets owing to the program’s strict asset limitations. Medicaid could still indirectly affect our analyses if high-risk individuals systematically spend down their risky assets to meet the program’s eligibility criteria, but we find little longitudinal evidence of this in the HRS.¹⁴

Table 1.

Health Insurance Coverage of Medicare Beneficiaries

Medicare A & B Only	14.8
Medicare HMO	16.2
Medicare + Individual Medigap Policy	28.5
Medicare + Employer Insurance	32.6
Medicare + Medicaid	8.0

Notes: Sample includes respondents in the 2000 wave of the HRS who were age 65 or older in 1998. N=8522

Table 2 shows a number of interesting differences in the mean characteristics of individuals across the insurance groups. Those without any supplemental coverage (Medicare A and B Only) tend to be somewhat older, have markedly low average education (10.6 years), are much more likely to be black and unmarried, and have low (non-capital) mean income and wealth ($220,591).¹⁵ Nearly 95 percent of those with Medigap coverage are white, and Medigap enrollees have the highest wealth ($467,611), followed by those with employer coverage ($400,515), and those enrolled in HMOs ($307,848). On most measures of socioeconomic status, HMO participants fall between the group with no supplemental coverage and the groups with either employer or Medigap coverage (e.g., they are more educated than the former, but less educated than the latter). Surprisingly those without any supplemental coverage are no more likely to have ever been diagnosed with a major health condition (defined as cancer, lung disease, heart disease, or stroke) and the groups show similar probabilities of having experienced a major health shock over the last two years.¹⁶ Nevertheless, those without supplemental coverage are much more likely than the other groups to report themselves in fair or poor health. Notably, reported rates of diabetes are somewhat higher in this group and suggest an elevated risk of diabetes-related complications.¹⁷

Table 2.

Sample Means by Insurance Status

	All	Medicare HMO	Medicare + Employer	Medicare + Medigap	Medicare A&B Only
Demographics
Age	75.7	75.0	74.8	76.4	77.3
Male	42.3	40.6	45.9	40.5	39.8
Years of Education	12.1	12.0	12.8	12.2	10.6
White	88.6	84.8	91.6	94.9	74.0
Black	6.9	7.4	5.5	2.8	17.4
Hispanic	3.1	6.2	1.5	1.5	6.5
Married	57.1	57.2	64.5	55.2	44.4
Completely Retired	84.1	83.7	85.7	81.6	85.9
Health Status
Ever Diagnosed with High Blood Pressure	55.4	55.2	56.9	54.4	54.1
Ever Diagnosed with Diabetes	15.4	16.8	15.2	14.0	17.0
Ever Diagnosed with Major Health Condition	51.6	50.2	51.7	53.2	49.8
Major Health Shock in Last 2 Yrs	11.9	12.0	11.1	12.8	11.8
Fair or Poor Health	28.2	28.3	24.7	27.1	37.5
Income and Wealth
Income (Non-Capital)	$37,860	$31,549	$44,756	$39,085	$27,204
Wealth	$376,100	$307,848	$400,515	$467,611	$220,591
Owns Any Risky Assets (%)	50.4	49.7	65.4	57.1	30.2
Median Value Risky Assets (if Own)	$80,000	$75,000	$89,000	$86,000	$53,000
Mean Value Risky Assets (if Own)	$251,436	$205,593	$230,090	$316,237	$220,180
No. of Observations	7774	1375	2751	2324	1324

Notes: Sample includes respondents in the 2000 wave of the HRS who were age 65 or older in 1998. Major health conditions are cancer, lung disease, heart disease, and stroke. Major health shock refers to onset of a major health condition. Completely Retired respondents include those who report themselves as completely retired and not working for pay, those who say they are “not in the labor force,” and those who report themselves as disabled. Wealth is defined as the sum of all assets including checking, savings and money market accounts, certificates of deposit, government savings bonds, treasury bills, stocks, mutual funds, bonds, IRA and Keogh accounts, housing, other real estate, collections, and vehicles, less mortgages, other home loans and all other debt. Risky assets are defined as stocks, bonds, and IRA and Keogh accounts.

4. Medical Expenditure Risk

Medicare HMO’s, which offer the most generous coverage, should be most protective a priori against out-of-pocket medical expense risk, followed by employer coverage and Medigap. It is not obvious whether employer supplemental plans should be more protective than Medigap plans because individual plans within both types can vary in generosity.

Table 3 shows the unadjusted distributions of annual out-of-pocket expenses by supplemental insurance status tabulated from pooled cross-sections of the 1999 and 2000 Medicare Current Beneficiary Survey (MCBS).¹⁸ Mean annual expenses are highest for those without any supplemental insurance ($2,066), and lowest for those enrolled in a Medicare HMO ($942). Those with Medigap pay on average $1,544 per year, while those with supplemental insurance from their employer pay on average $1,217. Examining different points of the distribution’s right tail, we note that those without any supplemental insurance always incur the most out-of-pocket expenses, reaching $31,751 at the 99^th percentile. In contrast, the 99^th percentile of expenses ranges from $9,750 for those with Medigap to $8,548 for those with employer insurance to $7,778 for those enrolled in a Medicare HMO.

Table 3.

Distribution of Annual Out-of-Pocket Medical Expenses by Supplementary Insurance Status

		Percentile of OOP Expenses
	Mean	50th	90th	95th	99th
Medicare HMO	$942	$423	$1,883	$3,067	$7,778
Medicare + Employer Insurance	$1,217	$682	$2,575	$3,948	$8,548
Medicare + Individual Medigap Policy	$1,544	$973	$3,221	$4,657	$9,750
Medicare A & B Only	$2,066	$705	$3,869	$6,367	$31,751

Notes: Data are from the 1999 and 2000 MCBS Cost and Use files and are in 2000 dollars. Spending in 1999 is inflated to 2000 dollars using the consumer price index for medical care. Expenditures for inpatient services, outpatient services, home health care, medical equipment, prescription drugs, dental services, hospice care, skilled nursing facilities, and institutional care are included.

Another way to assess the degree of risk households face is to compare average annual out-of-pocket expenses to wealth. Median wealth in the 2000 wave of the HRS is $148,000, with an interquartile range of $46,300 to $362,000. The 95^th percentile of expenses for someone without supplemental coverage is 4 percent of median wealth and 13 percent of 25^th-percentile wealth. The 99^th percentile of expenses for someone without supplemental coverage is 21 percent of median wealth and 69 percent of 25^th-percentile wealth. These figures suggest medical expenditure risk is sizeable, especially considering that wealth is a stock, and medical expenses are a flow expenditure that is highly persistent over time (French and Jones, 2004).

Figure 1 shows the distribution of log out-of-pocket expenses for each of the four insurance groups. The superimposed reference distribution is a normal distribution with the same mean and variance as the empirical distribution for those without supplemental insurance (Medicare Parts A and B Only). Compared to those without supplemental insurance, the distributions of out-of-pocket expenses in the three supplemental insurance groups have noticeably less spread, and also less mass in the right tail. Although the distribution for Medicare HMO enrollees has more spread than the distributions for Medigap and employer insurance, the center of the distribution is noticeably lower. Pair wise Kolmogorov-Smirnov tests reject equality of the distributions.

Figure 1. Densities of Out-of-Pocket Medical Expenses by Supplementary Insurance Status.

Notes: Data are from the 1999 and 2000 MCBS Cost and Use files and are in 2000 dollars. Spending in 1999 is inflated to 2000 dollars using the consumer price index for medical care. Expenditures for inpatient services, outpatient services, home health care, medical equipment, prescription drugs, dental services, hospice care, skilled nursing facilities, and institutional care are included.

These descriptive statistics do not control for health status and other characteristics; however they make the basic point that individuals without any supplemental insurance are at significantly greater risk of large out-of-pocket medical expenses than are those with supplemental insurance.¹⁹ Even among those with supplemental insurance, the figures suggest variation across coverage types in line with the relative generosity of each type: HMO enrollees appear to be most protected, followed by those with employer insurance, and lastly those with Medigap policies.²⁰ The distributions for employer insurance and Medigap are most similar (though still statistically different from one another).

5. Household Portfolios of Older Americans

We next turn to an overview of the portfolio holdings of older Americans. We restrict our analysis to liquid financial assets since illiquid assets (such a primary home) are less readily adjustable to changes in background risk. We divide liquid assets into two categories: safe and risky.²¹ Safe assets are checking, saving, and money market accounts, certificates of deposit, government savings bonds, and treasury bills. Risky assets are stocks, bonds, and IRA and Keogh accounts.^22,23

Table 4 describes the household portfolios of HRS respondents in 2000 by supplemental insurance status. The left panel considers asset ownership, while the right panel shows portfolio shares. Generally, asset ownership of any type is lowest among the group without supplemental coverage (Medicare A and B Only) and highest among those with supplemental coverage through their employer. This pattern holds even among safe assets, where more than one-quarter of those without supplemental insurance do not own a checking, saving or money market account, compared to just six percent of those with employer coverage. The stock-holding puzzle is readily apparent: just 50 percent of the sample participates in the stock market. About one-third own stocks directly, whereas another one-third own stocks through an IRA. Bond ownership is relatively low, even among those with employer coverage. Turning to portfolio shares conditional on ownership, we note that checking, saving and money market accounts are the dominant liquid financial asset across all groups. Among those with no supplemental coverage, checking accounts comprise 61 percent of liquid assets, while among those with employer coverage they amount to 40 percent of liquid assets. Not only are those with employer coverage more likely to own risky assets, but they also invest the largest portfolio share in such assets (46 percent), followed by those with Medigap (42 percent), HMO enrollees (38 percent), and those without supplemental coverage (26 percent). The mean value of risky assets (among those who own them) is also highest among Medigap enrollees ($316,237), followed by those with employer coverage ($230,090), those with no supplemental coverage ($220,180), and HMO participants ($205,593) (See Table 2). Not surprisingly given the skew in asset distributions, median values are considerably lower in all groups. Still, median values are highest among those with employer ($89,000) and Medigap coverage ($86,000), followed by HMO participants ($75,000), and those with no supplemental coverage ($53,000).

Table 4.

Household Financial Portfolios in Liquid Assets

	Ownership					Portfolio Shares
	All	Medicare HMO	Medicare + Employer	Medicare + Medigap	Medicare A&B Only	All	Medicare HMO	Medicare + Employer	Medicare + Medigap	Medicare A&B Only
Full Sample
Safe Assets
Checking	84.7	87.5	93.6	89.1	73.6	46.7	49.0	40.2	40.0	60.8
CDs/T-bills	32.1	31.1	39.1	39.2	21.6	14.2	12.9	13.9	18.0	13.2
Risky Assets
Stocks	34.1	32.3	46.1	38.5	19.3	18.3	16.8	22.0	19.7	12.6
Bonds	9.6	8.0	12.8	11.9	5.3	2.2	1.8	2.4	2.9	1.6
IRA/Keogh Plans	34.5	35.6	45.2	39.2	16.9	18.6	19.4	21.6	19.5	11.7
Any Risky Assets	50.4	49.7	65.4	57.1	30.2	39.1	38.0	45.9	42.0	26.0
Bottom Wealth Tercile
Any Risky Assets	12.4	14.6	24.2	15.1	8.9	28.4	12.6	17.0	12.2	9.8
Middle Wealth Tercile
Any Risky Assets	48.4	45.7	56.5	49.5	32.7	33.3	32.2	36.5	33.7	24.8
Top Wealth Tercile
Any Risky Assets	83.9	82.6	87.7	83.3	75.9	60.4	60.8	62.7	60.5	51.9

Notes: Sample includes respondents in the 2000 wave of the HRS who were age 65 or older in 1998. The category denoted “Checking” also includes saving and money market accounts. Portfolio shares are computed conditional on ownership of any risky liquid assets.

Table 4 also shows that these portfolio composition patterns across insurance groups persist holding wealth constant: within each wealth tercile, risky asset ownership is highest among those with Medigap and employer policies, followed by those enrolled in Medicare HMOs, and lowest among those without any supplemental coverage.

Our analysis of out-of-pocket expenses showed that those without supplemental insurance are at most risk of realizing large out-of-pocket medical expenses. Those without supplemental insurance are also least likely to own risky assets, and conditional on ownership, hold the smallest share of their portfolios in risky assets. This is consistent with standard risk aversion—that those facing greater background risk reduce their exposure to avoidable risks. However, if we look within categories of supplemental insurance, we note that HMO’s offer the most protection followed by employer insurance and Medigap policies. By the logic of standard risk aversion, those in HMO’s should have the highest stock market participation rates, and the largest portfolio shares invested in risky assets. Instead, the descriptive statistics show that HMO participants are less likely than the two other groups to hold risky assets. The same pattern holds for portfolio shares. In the next section, we show that once we account for the endogeneity of insurance choices, this pattern reverses and a ‘dose-response’ relationship emerges. The reversal suggests that the descriptive statistics are biased down by a factor such as risk aversion, which increases the probability that individuals choose the most protective insurance policy and reduces the probability they invest in risky assets.

6. Research Design and Estimation Strategy

6.1 Sample

We begin with the nationally representative subsample of HRS respondents ages 65 and older in 1998. We require respondents to be present in both the 1998 and 2000 surveys; this permits us to model portfolio outcomes in 2000 using (in some cases) lagged variables from 1998. The HRS sample consists of respondents and their spouses (if married). Because portfolio outcomes are measured at the household level, we select just one spouse per household, choosing the spouse who is designated the “financial respondent” in the 1998 survey. Supplemental insurance participation is measured for that spouse, although there is high concordance in the insurance arrangements of spouses. We exclude business owners from the sample to eliminate potential biases due to background entrepreneurial income risk (Heaton and Lucas, 2000).

6.2 Extensive Margin

Demand for risky assets can be analyzed on the intensive margin—the share of assets held in risky assets—or the extensive margin—whether the individual owns any risky assets. Our analysis concentrates on behavior at the extensive margin (asset ownership). The extensive margin is interesting since it is the location of a persistent puzzle in empirical finance: why do so many households fail to hold risky assets at all? Known as the equity allocation (or stock-holding) puzzle, this is the microeconomic analog of the equity premium puzzle, and is viewed as a key issue in portfolio analysis (Campbell, 2006; Gollier, 2002; Haliassos and Bertaut, 1995; Miniaci and Weber, 2002). By focusing on the extensive margin, we also avoid difficult measurement issues associated with the intensive margin. One such issue is that the true riskiness of any given portfolio is unobservable in our data; two individuals with the same portfolio share in risky assets may yet have very different risk exposures if, for example, one holds lower-risk funds designed to produce income, while the other holds aggressive growth stocks. In addition, variation at the extensive margin represents actual behavior, whereas variation in portfolio shares reflects both active behavior and price changes. Finally, item non-response rates are dramatically lower for asset ownership than for asset values: just 6 percent of observations in our sample have an imputed value on any one of the liquid asset ownership items, compared to 32.8 percent of observations with an imputed value on at least one of the asset value variables used to compute portfolio shares.

6.3 Discrete Factor Maximum Likelihood Method

Our research design is cross-sectional; however, because of regulations governing the sale and purchase of Medigap plans, insurance choices are effectively predetermined relative to the portfolio outcomes we measure. Most people make a one-time supplementary insurance choice when they enroll in Medicare at age 65 (or when they first enroll in Medicare Part B), and relatively few change their supplementary insurance coverage after age 65.²⁴ Once the protected Medigap open enrollment period ends (six months after enrollment in Medicare Part B), access is no longer guaranteed and insurers may underwrite on the basis of health. As a result, in our sample supplemental insurance decisions were made at age 65, and portfolio outcomes are measured at ages 67 and older in 2000. Although there is no issue with simultaneity, omitted variable biases may yet arise if unobservable characteristics make some individuals more likely to hold risky assets and also more likely to purchase supplemental insurance or enroll in a Medicare HMO. To address this potential endogeneity problem, we jointly estimate equations for ownership of risky assets, supplemental insurance, and HMO participation, allowing for arbitrary correlation patterns in the unobserved heterogeneity across equations. In addition, we make use of exogenous variation in supplemental insurance choices arising from the structure of non-Medicare HMO markets and from state insurance laws that limit the ways in which insurers can pool risks.

Specifically, in our model we have three discrete endogenous variables: whether the individual owns any risky assets, whether the individual is enrolled in an HMO, and whether the individual holds a Medigap policy or supplemental insurance through an employer. We combine the Medigap and employer insurance choices since they are based on the same insurance delivery model (unlike HMOs), and offer a similar degree of protection against medical expenditure risk.

We employ a mixture maximum likelihood technique in which the distribution of the error terms are decomposed into correlated and uncorrelated components. The uncorrelated components are assumed to be independent and normally distributed. A discrete factor approximation for the correlated component enables identification of clustering in the unobserved components. Kiefer and Wolfowitz (1956) prove the consistency of this estimator. Monte Carlo experiments in a simultaneous equation setting demonstrate that these estimators compare favorably to maximum likelihood estimators under joint normality when the disturbances are joint normal, and outperform normal maximum likelihood when the disturbances are non-normal (Mroz, 1999). Using data from self-selected and randomly assigned populations, Goldman et al. (1998) show that such estimates can effectively recover the structural parameters of the underlying models.

Similar methods have been used to study patterns of unemployment duration (Heckman and Singer, 1984) and the effects of training on employment (Gritz, 1993). In a very similar application, Bhattacharya et al. (2003) estimate the impact of private and public insurance on mortality in an HIV-infected population.

Let $R_i^{*}$ represent an index function that measures individual i’s propensity to hold risky assets. Then we write:

$$R_i^{*}=c_1+{\gamma }_1·{\mathit{\text{supp}}}_i+{\gamma }_2·hm{o}_i+{\beta }_1\text{'}{X}_i+{\rho }_{\mathit{\text{risky}},i}-{\epsilon }_{\mathit{\text{risky}},i}$$ (1)

The vector X_i represents observed exogenous covariates that determine asset holdings, such as age, gender, and education. Asset holdings are also affected by insurance status, where supp_i denotes whether the individual holds Medigap or employer supplemental insurance, and hmo_i represents whether the individual is enrolled in a Medicare HMO. Asset holdings are also assumed to depend on an unobservable heterogeneity component ρ_risky,i. It is useful to think of this as unobserved financial sophistication or attitudes towards risk, and it is assumed to be orthogonal to the covariates X_i, but not necessarily to the insurance variables, supp_i and hmo_i. There is also a random error ε_risky,i that is uncorrelated with X_i and insurance status. We want to consistently estimate the parameters c₁, β₁, γ₁ and γ₂, after accounting for the heterogeneity.

We define R_i as an indicator variable that represents whether individual i holds any risky assets:

$$R_i=\{\begin{array}{cc}1\hfill & \text{if}{R}_{\mathrm{i}}^{*}>0\hfill \\ 0\hfill & \text{if}{R}_{\mathrm{i}}^{*}\le 0\hfill \end{array}$$ (2)

We assume ε_risky,i is distributed normally with zero mean and unit variance. This assumption implies a probit model for R_i, where the probability of holding risky assets, conditional on observed characteristics {supp_i,hmo_i, X_i} and unobserved characteristics ρ_risky,i is:

$$P[R_i=1|\{{\mathit{\text{supp}}}_i,hm{o}_i,X_i\},{\rho }_{\mathit{\text{risky}},i}]=\mathrm{\Phi }(c_1+{\gamma }_1·{\mathit{\text{supp}}}_i+{\gamma }_2·hm{o}_i+{\beta }_1\text{'}{X}_i+{\rho }_{\mathit{\text{risky}},i})$$ (3)

Here Ф(•) is the cumulative distribution function for the standard normal distribution.

We model insurance choices using the standard random indirect utility approach. Individuals choose among supplemental status j = {supplemental,hmo,none} on the basis of a random indirect utility function:

$$V_{j,i}^{*}=c_j+{\beta }_j\text{'}{Z}_{j,i}+{\rho }_{j,i}+{\epsilon }_{j,i}$$ (4)

Here Z_j,i represents variables that determine insurance status, including X_i as well as variables excluded from X_i; and ρ_j,i is an individual-specific random intercept that reflects the individuals’ propensity for insurance status j and is unobserved by the researcher. The parameters c_j and β_j are additional parameters to be estimated; and ε_j,i represents the orthogonal error term.

Individuals choose the insurance status that maximizes their indirect utility. We assume that ε_j,i are independently and identically distributed according to the Type II extreme value distribution. This distributional assumption and normalizing {c_none, β_none, ρ_none,i} to zero yields a multinomial logit model for insurance choice:

$$\text{Pr}[{\mathit{\text{supp}}}_i=1|{\mathrm{Z}}_{\mathrm{j},\mathrm{i}},{\rho }_{\mathit{\text{supp}}},{\rho }_{hmo}]=\frac{\text{exp}(c_{\mathit{\text{supp}}}+{\beta }_{\mathit{\text{supp}}}\text{'}{Z}_{\mathit{\text{supp}},i}+{\rho }_{\mathit{\text{supp}},i})}{1+\sum _{j\ne \mathit{\text{none}}}\text{exp}(c_j+{\beta }_j\text{'}{Z}_{j,i}+{\rho }_{j,i})}$$ (5)

$$\text{Pr}[hm{o}_i=1|{\mathrm{Z}}_{\mathrm{j},\mathrm{i}},{\rho }_{\mathit{\text{supp}}},{\rho }_{hmo}]=\frac{\text{exp}(c_{hmo}+{\beta }_{hmo}\text{'}{Z}_{hmo,i}+{\rho }_{hmo,i})}{1+\sum _{j\ne \mathit{\text{none}}}\text{exp}(c_j+{\beta }_j\text{'}{Z}_{j,i}+{\rho }_{j,i})}$$ (6)

To complete the model and allow for correlation between asset holdings and insurance choices, we need to assume a joint distribution for the unobserved heterogeneity vector ρ = (ρ_risky, ρ_supp, ρ_hmo). Our approach is semi-parametric. Let k = 1,…,K index the number of discrete heterogeneity factors (points of support)—intuitively, there are K types of people that occur with probabilities p_k. The effect of being a certain type has different effects on each outcome. For example, there is a p₁ probability that a person will be of the first type, which would imply realizations of ${\rho }_{\mathit{\text{risky}}}^1$ for the propensity to hold risky assets, ${\rho }_{\mathit{\text{supp}}}^1$ for the propensity to have supplemental insurance, and ${\rho }_{hmo}^1$ for the propensity to be in a Medicare HMO.

This discrete factor distributional approach has several advantages over specifying a continuous parametric density for the unobserved heterogeneity vector. First, an incorrect specification of the parametric density function might lead to inconsistent parameter estimates. The discrete factor density allows us to approximate any underlying distribution of heterogeneity. In fact, Monte Carlo studies show that discrete factor distributions with two to four points of support adequately model many distributions (Heckman, 2001; Mroz, 1999). Second, discrete factor models are computationally simpler than parametric models as they avoid multiple numerical integration in the construction of the likelihood function.

Since all three outcome equations have intercept terms, we normalize the mean of the heterogeneity distribution for each equation to be zero. This implies that one point of support in each equation is not “free,” but is determined by a combination of the other points. Thus our distributional assumption on the unobserved heterogeneity adds 4(K−1) additional parameters. The resulting variance-covariance matrix for the unobserved heterogeneity may be written as:

$$\mathit{\text{Var}}({\mathrm{\rho }}_{\mathit{\text{risky}}},{\mathrm{\rho }}_{\mathit{\text{supp}}},{\mathrm{\rho }}_{hmo})=\left[\begin{array}{ccc}\sum _k{p}_k{\left({\mathrm{\rho }}_{\mathit{\text{risky}}}^k\right)}^2\hfill & \sum _k{p}_k{\mathrm{\rho }}_{\mathit{\text{risky}}}^k{\mathrm{\rho }}_{\mathit{\text{supp}}}^k\hfill & \sum _k{p}_k{\mathrm{\rho }}_{\mathit{\text{risky}}}^k{\mathrm{\rho }}_{hmo}^k\hfill \\ & \sum _k{p}_k{\left({\mathrm{\rho }}_{\mathit{\text{supp}}}^k\right)}^2\hfill & \sum _k{p}_k{\mathrm{\rho }}_{\mathit{\text{supp}}}^k{\mathrm{\rho }}_{hmo}^k\hfill \\ \hfill & \hfill & \sum _k{p}_k{\left({\mathrm{\rho }}_{hmo}^k\right)}^2\hfill \end{array}\right]$$ (7)

This model not only allows non-zero covariance across asset holdings and insurance propensities but also allows non-zero covariance between the propensities to have supplemental and HMO insurance. Thus our model relaxes the independence of irrelevant alternatives assumption of the standard multinomial logit model and allows a more general variance-covariance matrix. The key correlations in our model may thus be written as:

$$\mathit{\text{Corr}}({\rho }_{hmo},{\rho }_{\mathit{\text{risky}}})=\frac{\sum _k{p}_k{\rho }_{hmo}^k{\rho }_{\mathit{\text{risky}}}^k}{\sqrt{\sum _k{p}_k{\left({\rho }_{hmo}^k\right)}^2\sum _k{p}_k{\left({\rho }_{\mathit{\text{risky}}}^k\right)}^2}}$$ (8)

$$\mathit{\text{Corr}}({\rho }_{\mathit{\text{supp}}},{\rho }_{\mathit{\text{risky}}})=\frac{\sum _k{p}_k{\rho }_{\mathit{\text{supp}}}^k{\rho }_{\mathit{\text{risky}}}^k}{\sqrt{\sum _k{p}_k{\left({\rho }_{\mathit{\text{supp}}}^k\right)}^2\sum _k{p}_k{\left({\rho }_{\mathit{\text{risky}}}^k\right)}^2}}$$ (9)

$$\mathit{\text{Corr}}({\rho }_{\mathit{\text{supp}}},{\rho }_{hmo})=\frac{\sum _k{p}_k{\rho }_{\mathit{\text{supp}}}^k{\rho }_{hmo}^k}{\sqrt{\sum _k{p}_k{\left({\rho }_{\mathit{\text{supp}}}^k\right)}^2\sum _k{p}_k{\left({\rho }_{hmo}^k\right)}^2}}$$ (10)

The model is estimated using maximum likelihood. We have six possible outcomes for the dependent variables: a person can either hold or not hold risky assets, denoted by R_i, while being in one of three insurance states. (“None” refers to the case where the individual is covered by Medicare Parts A and B only and is denoted by (1-supp)(1-hmo)). To construct the contribution to the likelihood function for each individual, we first obtain the likelihood of observing that value of the dependent variables conditional on a realization k of the unobserved heterogeneity ${\rho }^k=({\rho }_{\mathit{\text{risky}}}^k,{\rho }_{\mathit{\text{supp}}}^k,{\rho }_{hmo}^k)$. We then sum over all the possible realizations to obtain the contribution of individual i to the likelihood function:

$$l_i=\sum _k{p}_k{\left(\text{Pr}\right[R_i=1|{\rho }_{\mathit{\text{risky}}}^k])}^{R_i}\times {(1-\text{Pr}[R_i=1|{\rho }_{\mathit{\text{risky}}}^k])}^{1-R_i}\times {\left(\text{Pr}\right[{\mathit{\text{supp}}}_i=1|{\rho }_{\mathit{\text{supp}}}^k,{\rho }_{hmo}^k])}^{{\mathit{\text{supp}}}_i}\times {\left(\text{Pr}\right[hm{o}_i=1|{\rho }_{\mathit{\text{supp}}}^k,{\rho }_{hmo}^k])}^{hm{o}_i}\times {(1-\text{Pr}[{\mathit{\text{supp}}}_i=1|{\rho }_{\mathit{\text{supp}}}^k,{\rho }_{hmo}^k]-\text{Pr}[hm{o}_i=1|{\rho }_{\mathit{\text{supp}}}^k,{\rho }_{hmo}^k\left]\right)}^{(1-{\mathit{\text{supp}}}_i)(1-hm{o}_i)}$$ (11)

Finally we obtain the weighted log-likelihood function by summing the log-likelihood across individuals:

$$\text{ln}(\mathrm{\Gamma })=\sum _{i=1}^N{w}_i\text{ln}(l_i),$$ (12)

where Γ is the vector of model parameters, w_i are the analytic sample weights and N is the sample size. Because it is difficult to interpret the magnitude of the parameter estimates directly, we also report the mean predicted probabilities and marginal effects. Marginal effects are computed by constructing predicted differences in each respondent’s probability of holding supplemental insurance (compared to Medicare Parts A and B only) and being in a Medicare HMO (compared to Medicare Parts A and B only), and then averaging over respondents.

6.4 Selecting the Number of Points of Support

To select the number of points of support in the heterogeneity distribution (K), we use an upwards testing criterion suggested by Mroz and Zayats (2008). This involves sequential comparisons of models with 2 v. 1 point, 3 v. 2 points, etc. until a likelihood ratio chi-square test comparing the two models indicates that the null hypothesis—that the simpler model is the true model—is not rejected at a significance level of 25 percent or greater. The simpler model always has 4 fewer parameters, so we use a chi-square distribution with 4 degrees of freedom. Appendix Table 1 shows results from the upwards testing procedure, which indicates that K=2 points of support is the preferred model in this application.²⁵

6.5 Exclusion Restrictions

In addition to the functional form assumptions described in Section 6.3, we also make use of exogenous policy variation by applying two exclusion restrictions, one for each endogenous variable in equation (1). The vector of exogenous variables Z _j,i in equation (4) includes X_i plus two variables that are excluded from X_i: 1) an indicator for a state law limiting the structure of risk pooling by insurers in the respondent’s state; and 2) non-Medicare HMO market penetration in the respondent’s county. Currently, ten states limit the risk pooling options available to insurance companies: seven states require mandatory community rating and another three states prohibit insurers from using attained age rating.²⁶ Under community rating, all individuals are in the same risk pool regardless of age, and all pay the same premium. Under age-based rating, individuals are pooled with others of the same age (either current age or age at buy-in), and premiums typically increase with age. Consequently, age-65 premiums for community-rated policies are higher than age-65 premiums under age-based rating methods, and demand for supplemental insurance at age 65 should be lower in states that prohibit age-based rating. Note that this variation arises because of differences in the structure of risk pooling, not the riskiness (e.g., health status) of the insured pool itself. Such insurance regulations have arisen in response to concerns that individuals, initially attracted to low age-65 premiums for attained age policies, did not fully understand that their premiums would rise (potentially dramatically) with age.

Non-Medicare HMO market penetration is useful identifying variation for Medicare HMO participation because Medicare HMOs have historically entered markets in which the parent firm was already operating an HMO. We computed county-level non-Medicare HMO market penetration in 1998 from the 2003 Area Resource File. Market penetration is defined as the percent of population under age 65 enrolled in an HMO.

7. Estimation Results

7.1 DFML Model of Risky Asset Ownership

In Table 5, we present coefficient estimates for the three-equation DFML model in which we account for the endogeneity of insurance status. For comparison, we also show coefficient estimates for a single-equation probit model in which we do not account for the endogeneity of insurance status. While the coefficient estimates are not directly comparable across the Probit and DFML specifications because of their different error variance normalizations,²⁷ one can compare signs, coefficient ratios, and predicted probabilities. In the probit model (col. 1), the coefficient on supplemental insurance is positive and statistically significant, while the HMO coefficient is about half the size of the supplemental insurance coefficient and just under the threshold for statistical significance at the 5 percent level. Although the coefficients suggest that both supplemental insurance coverage and HMO participation increase demand for risky assets, they also suggest that supplemental insurance does so relatively more than HMO participation, even though, as we showed earlier, supplemental insurance is less protective against medical expenditure risk.

Table 5.

Covariate Parameters of Probit and Discrete Factor Maximum Likelihood Models of Risky Asset Ownership

	Single-Equation Probit Model	Three-Equation Discrete Factor Model
Covariate	Asset Ownership (1)	Asset Ownership (2)	Supp. Insurance (3)	HMO Participation (4)
Supplemental Insurance	0.272 (0.065)	0.279 (0.073)
HMO Participation	0.145 (0.079)	0.512 (0.193)
Mandatory Community Rating in State	--	--	−.226 (0.098)	1.402 (0.388)
Non-Medicare HMO Market Share in County	--	--	0.003 (0.004)	0.153 (0.020)
Demographics
Age	−.120 (0.071)	−.125 (0.071)	−.080 (0.126)	−.047 (0.416)
Age Squared/1000	0.629 (0.453)	0.661 (0.455)	0.425 (0.796)	−.223 (2.658)
Female	−.011 (0.052)	−.008 (0.052)	0.134 (0.104)	−.047 (0.312)
HS Grad/GED	0.222 (0.058)	0.224 (0.058)	0.365 (0.106)	−.041 (0.332)
Some College	0.298 (0.069)	0.298 (0.070)	0.338 (0.138)	0.105 (0.421)
College or More	0.477 (0.080)	0.480 (0.080)	0.481 (0.169)	0.391 (0.508)
Black	−.474 (0.104)	−.482 (0.104)	−.906 (0.146)	0.268 (0.613)
Hispanic	−.447 (0.161)	−.463 (0.162)	−1.221 (0.252)	1.126 (0.917)
Other Races	−.304 (0.202)	−.281 (0.204)	−.815 (0.326)	−3.077 (1.075)
Divorced	−.055 (0.092)	−.057 (0.092)	0.308 (0.182)	−.269 (0.538)
Widowed	−.156 (0.064)	−.159 (0.064)	0.316 (0.131)	−.476 (0.368)
Never Married	0.155 (0.131)	0.170 (0.132)	0.506 (0.249)	−2.450 (0.855)
Household Size	−.131 (0.027)	−.136 (0.027)	−.023 (0.045)	0.272 (0.156)
Health Status 2 Years Ago
High Blood Pressure	0.016 (0.047)	0.014 (0.048)	0.095 (0.093)	0.284 (0.284)
Diabetes	−.079 (0.060)	−.085 (0.060)	0.028 (0.119)	0.643 (0.393)
Cancer	0.104 (0.058)	0.102 (0.058)	0.210 (0.122)	0.296 (0.351)
Lung Disease	−.211 (0.070)	−.207 (0.071)	−.126 (0.134)	−.897 (0.421)
Heart Disease	0.049 (0.049)	0.051 (0.049)	0.217 (0.098)	−.001 (0.291)
Stroke	−.117 (0.070)	−.117 (0.070)	−.338 (0.126)	−.534 (0.416)
Psychiatric Problems	−.046 (0.068)	−.050 (0.068)	0.161 (0.135)	0.288 (0.399)
Arthritis	0.039 (0.049)	0.036 (0.049)	0.213 (0.094)	0.541 (0.286)
Health Shock in Last 2 Years	0.005 (0.062)	0.003 (0.062)	0.070 (0.124)	0.140 (0.355)
Fair or Poor Health	−.195 (0.053)	−.194 (0.053)	−.055 (0.101)	−.062 (0.307)
Ratio Subj. Survival Prob. to Life Table Prob.	−.006 (0.006)	−.006 (0.006)	−.017 (0.011)	0.000 (0.031)
Income and Wealth 2 Years Ago
Non-Capital Income Quintile 2	−.230 (0.094)	−.236 (0.094)	−1.108 (0.193)	0.028 (0.601)
Non-Capital Income Quintile 3	−.142 (0.081)	−.143 (0.082)	−.914 (0.179)	−.064 (0.549)
Non-Capital Income Quintile 4	−.056 (0.078)	−.057 (0.078)	−.322 (0.183)	−.011 (0.529)
Non-Capital Income Quintile 5	0.022 (0.077)	0.018 (0.078)	−.069 (0.187)	0.268 (0.475)
Wealth Decile 2	0.840 (0.167)	0.839 (0.168)	0.901 (0.187)	1.150 (0.671)
Wealth Decile 3	0.951 (0.177)	0.937 (0.177)	1.052 (0.221)	2.654 (0.822)
Wealth Decile 4	1.424 (0.173)	1.419 (0.174)	1.532 (0.226)	2.122 (0.789)
Wealth Decile 5	1.647 (0.175)	1.639 (0.176)	1.293 (0.232)	2.099 (0.810)
Wealth Decile 6	2.028 (0.178)	2.031 (0.179)	1.484 (0.249)	1.813 (0.850)
Wealth Decile 7	2.293 (0.181)	2.300 (0.182)	1.602 (0.259)	1.555 (0.867)
Wealth Decile 8	2.392 (0.184)	2.398 (0.185)	1.490 (0.268)	1.287 (0.859)
Wealth Decile 9	2.690 (0.192)	2.693 (0.193)	1.674 (0.292)	2.031 (0.968)
Wealth Decile 10	3.302 (0.213)	3.327 (0.216)	1.503 (0.301)	0.875 (0.947)
ASINH Pension Wealth	0.054 (0.020)	0.059 (0.021)	0.148 (0.034)	−.460 (0.225)
Held Long-Term Care Insurance	0.175 (0.070)	0.181 (0.070)	0.587 (0.170)	0.381 (0.438)
Owned Home	−.458 (0.074)	−.448 (0.075)	−.360 (0.146)	−1.278 (0.483)
Subj. Prob(Leave Bequest)	0.169 (0.068)	0.158 (0.068)	0.159 (0.152)	0.866 (0.440)

Notes: Standard errors shown in parentheses. N=4708. Sample includes one respondent per household from the 2000 wave of the HRS who was age 65 or older in 1998. Probit Log L=−2134, DF Log L=−5768. Specification also includes a constant, the average Medicare expenditure in respondent’s county, county population, and two dummies for missing values on subjective probability questions. “Subj. Prob(Leave Bequest)” is the respondent’s self-assessed probability of leaving a bequest of $100,000 or more in 1998. “Ratio Subj. Survival Prob. to Life-Table Prob.” is the respondent’s self-assessed probability of surviving 10 years divided by the corresponding life table probability for someone of the same age and sex. See Table 6 for DFML distributional parameters.

In sharp contrast, the HMO coefficient in the DFML model (col. 2) is nearly twice the size of the supplemental insurance coefficient, implying that once we account for the endogeneity of insurance status, individuals enrolled in more protective HMO plans have greater demand for risky assets than those enrolled in less protective supplemental insurance plans. Both coefficients are statistically significant. The difference in relative magnitudes across the two models indicates that in the probit model the HMO coefficient is biased downward relative to the supplemental insurance coefficient; but once we address this endogeneity bias, the data support the more refined hypothesis that variation in risk should relate negatively to variation in the demand for risky assets. A plausible omitted factor is unobservable risk aversion;²⁸ risk averse individuals should prefer protective HMOs over supplemental insurance or no such plan and also demand fewer risky assets. Bias could also arise through compensatory behavior if people in less generous plans intentionally reduce their out-of-pocket expenses (by foregoing discretionary care or selecting less expensive treatment options), and consequently have higher demand for risky assets.

The DFML model includes extensive controls for demographic characteristics, health and longevity risk, and income and wealth. We model health risk at the household level by including indicators for whether the respondent or, if married, the respondent’s spouse, has ever been diagnosed with a chronic disease (i.e., high blood pressure, diabetes, cancer, lung disease, heart disease, stroke, psychiatric problems, or arthritis), as well as an indicator for self-reported fair or poor health. We account for the health of spouses to capture risk sharing within married households. To mitigate potential endogeneity of health status, we use two-year lags of the health variables from the 1998 survey. We also include an indicator for having had a serious health shock between 1998 and 2000, which we define as onset of cancer, lung disease, heart disease, or stroke. In the risky asset ownership equation (col. 2), our measure of overall health status—the indicator for self-reported fair or poor health—is negative and highly significant, which is consistent with the notion that a perception of elevated background health risk should reduce exposure to avoidable risks. Conditional on perceived health status, having been diagnosed with a serious health condition is also negatively related to ownership of risky assets (col. 2), though only the coefficient on lung disease is statistically significant.²⁹ The health shock coefficient is not statistically different from zero, which may indicate that people take time to adjust their portfolios in response to changes in background health risk. We also control for subjective life expectancy, measured as the ratio of the respondent’s self-reported probability of surviving 10 years to the life-table probability for an individual of the same age and sex. The coefficient is negative but statistically insignificant.

To control flexibly for wealth and income, we include a set of indicators for wealth decile and non-capital income quintile. To mitigate simultaneity bias, we use their two-year lagged values. As expected, wealth is positively and significantly related to ownership of risky assets, with the coefficients increasing monotonically with each decile. Conditional on wealth, the non-capital income coefficients are mostly negative and insignificant. Although the value of housing is included in total wealth, we include a separate dummy for lagged home ownership, since home ownership itself is a form of background risk.³⁰ Consistent with this interpretation, home ownership is negatively correlated with risky asset holding. The specification also includes pension wealth, a variable not typically found in empirical studies of portfolio choice, but especially relevant for portfolio choice by the elderly since pension wealth, in particular defined benefit pension wealth, represents a guaranteed annuity which is generally considered a “safe” asset. Pension wealth was constructed using respondent answers to questions about receipt of private pension and Social Security benefits, and for coupled households reflects the pension wealth of the couple.³¹ Consistent with the proposition that a safe asset should raise risk tolerance, pension wealth is positively (and significantly) correlated with holding risky assets.³² Bequest motives may also be important. To capture these, we take advantage of subjective probability questions in the HRS that ask respondents to rate the probability they will leave a bequest of $100,000 or more. Not surprisingly, those with a higher probability of leaving a large bequest are more likely to own risky assets. Finally, the future risk of needing long-term care may also be an important background risk, and consistent with theory, we find that those with (lagged) long-term care insurance are more likely to hold risky assets.³³

Table 5 also shows the effect of the excluded variables in the supplemental insurance and HMO equations in the DFML model. In the supplemental insurance equation (col. 3), the indicator for mandatory community rating in the respondent’s state is negative, as expected, and statistically significant. In the HMO participation equation (col. 4), the non-Medicare HMO market share in the respondent’s county is positive and statistically significant. Interestingly, the mandatory community rating indicator is positive and statistically significant in the HMO equation, indicating substitution toward Medicare HMOs in states with mandatory community rating. The pattern of coefficients on the other exogenous variables in the supplemental insurance and HMO participation equations presents a story similar to the descriptive statistics in Table 2.

Table 6 presents the estimated distributional parameters of the DFML model, which were estimated simultaneously with the coefficients in Table 5. Shown are estimates of the six points of support, $({\rho }_{\mathit{\text{risky}}}^1,{\rho }_{\mathit{\text{risky}}}^2),({\rho }_{\mathit{\text{supp}}}^1,{\rho }_{\mathit{\text{supp}}}^2)$, and $({\rho }_{hmo}^1,{\rho }_{hmo}^2)$, and two probabilities p₁ and p₂. The estimated probabilities imply two types with fairly even shares of the distributional mass, at 45.5 and 54.5 percent. As shown in equations (8)–(10), the DFML model has three implied correlations between the unobserved heterogeneity components in each equation. The correlation in the unobservable components of risky asset ownership and Medicare HMO participation is negative at −0.25, pointing to an unobserved factor like risk aversion that is negatively correlated with risky asset ownership and positively correlated with HMO participation, or, alternatively, compensatory behavior to avoid high out-of-pocket expenditures that is positively correlated with risky asset ownership and negatively correlated with HMO participation. This makes sense in light of the downward bias in the HMO coefficient (relative to the supplemental coefficient) in the probit model compared to the DFML model. The correlation in the unobservable components of risky asset ownership and supplemental insurance is close to zero, indicating little bias in the supplemental insurance coefficient in the probit model.³⁴ Finally, the correlation between the unobservables in the supplemental insurance and HMO equations is near zero.

Table 6.

Distributional Parameters of DFML Model

Parameter	Estimate	St. Err.
${\rho }_{\mathit{\text{risky}}}^1$	−0.284	(0.134)
${\rho }_{\mathit{\text{risky}}}^2$	0.237	(0.112)
${\rho }_{\mathit{\text{supp}}}^1$	0.035	(0.507)
${\rho }_{\mathit{\text{supp}}}^2$	−0.029	(0.424)
${\rho }_{hmo}^1$	10.136	(1.898)
${\rho }_{hmo}^2$	−8.469	(1.651)
p1	0.455	(0.028)
p2	0.545	(0.028)
corr(ρhmo,ρrisky)	−0.250
corr(ρsupp,ρrisky)	−0.008
corr(ρsupp,ρhmo)	0.032

Notes: Table presents estimated distributional parameters of the DFML model with two points of support reported in Table 5. Also shown are the implied correlation coefficients. See text for definitions.

Because the coefficient estimates give little sense of the economic importance of the estimated coefficients, we present in Table 7 the coefficients and predicted marginal effects of HMO participation and supplemental insurance (compared to enrollment in Medicare Parts A and B only) across model specifications. The top panel shows results for the full estimation sample, while the lower panels show results for subsamples defined by wealth tercile. Row 1 shows the key coefficients from the probit model in Table 5, and the implied marginal effects (standard errors in parentheses, obtained by the delta method). Row 2 shows that the DFML model in Table 5 predicts that those with supplemental insurance are 7.1 percentage points more likely to hold risky assets than those with Medicare Parts A and B only. Those in a Medicare HMO are 13.0 percentage points more likely to own risky assets, substantially larger than the estimated 3.8 percentage points implied by the probit model that did not account for the endogeneity of insurance, and consistent with a dose-response relationship between background medical expenditure risk and financial risk. Table 7 also shows that the key coefficients and marginal effects do not change when we omit the set of controls for health risk; when we reclassify bonds as safe assets, the marginal effect of supplemental coverage stays the same while the effect of HMO coverage increases.

Table 7.

Coefficients and Marginal Effects for Full Sample and for Wealth Terciles

	Coefficients		Marginal Effects
Model	Supp. (1)	HMO (2)	Supp. (3)	HMO (4)
Sample: All
Probit	0.272	0.145	0.070	0.038
(Table 5, Col. 1)	(0.065)	(0.079)	(0.055)	(0.056)
DFML	0.279	0.512	0.071	0.130
(Table 5, Cols. 2–4)	(0.073)	(0.193)	(0.057)	(0.068)
DFML, No Health Controls	0.288	0.529	0.073	0.135
	(0.071)	(0.190)	(0.051)	(0.063)
DFML, Bonds Classified Safe	0.316	0.767	0.077	0.198
	(0.079)	(0.261)	(0.054)	(0.081)
Sample: Top Wealth Tercile
DFML	0.208	0.085	0.046	0.020
	(0.160)	(0.248)	(0.083)	(0.102)
Sample: Middle Wealth Tercile
DFML	0.321	0.887	0.103	0.286
	(0.116)	(0.347)	(0.098)	(0.120)
Sample: Bottom Wealth Tercile
DFML	0.425	2.743	0.002	0.122
	(0.216)	(1.132)	(0.140)	(0.143)

Notes: Reference category for coefficients and marginal effects is group with no HMO or supplemental insurance. Marginal effects were computed by constructing probability differences for each observation, and averaging over observations in estimation sample. Standard errors (in parentheses) obtained using the delta method. The 33rd and 66th percentiles of the net worth distribution are $61,661 and $223,528, respectively.

Finally, we investigate whether the response to background medical expenditure risk varies with wealth. The lower portion of Table 7 presents coefficient estimates and marginal effects for the DFML specification in Table 5, estimated separately for respondents in each wealth tercile. The pattern of differences across groups is interesting; although a loss in precision means group differences are only suggestive. The marginal effect of HMO coverage in the top wealth tercile (household wealth greater than $223,528) is only 2 percentage points (not statistically significant), suggesting that this group is less responsive to background medical expenditure risk, perhaps because the potential wealth loss is a much smaller share of total wealth even in the absence of more protective HMO coverage. In sharp contrast, the middle wealth tercile (household wealth between $61,661 and $223,528) appears highly responsive to changes in background medical expenditure risk—more protective HMO coverage leads to a statistically significant 28.6 percentage point increase in risky asset ownership. Interestingly, the bottom wealth group (below $61,551) is in between—HMO coverage leads to a 12.2 percentage point (not statistically significant) increase in risky asset ownership. The estimated marginal effect of supplemental insurance coverage varies across groups, though to a lesser degree. The finding that the wealthiest respondents are least sensitive to background medical expenditure risk is consistent with the property of standard risk aversion or decreasing absolute prudence, which describes a precautionary saving motive that decreases as wealth rises. However, while we find that the wealthiest are the least sensitive, we also find that the least wealthy are not the most sensitive. The diminished sensitivity of the bottom group relative to the middle group could be due to the implicit availability of Medicaid for individuals with low assets, or it could reflect lower financial literacy among the least wealthy. Overall, this pattern suggest that medical expenditure risk is most salient for individuals in the middle of the wealth distribution, who have only a moderate amount of wealth available to use as a buffer against unexpected medical expenditures and yet perhaps too much wealth to make Medicaid a reasonable option. An important caveat is that this pattern could also be due to functional form differences in the predicted probabilities across wealth groups, rather than real economic effects.

8. Conclusion

Our results offer evidence in support of the theoretical implications of background risk. We find that individuals who face lower medical expenditure risk, as measured by their enrollment in a Medicare HMO or a supplemental insurance policy, are more likely to hold risky financial assets, accounting for the endogeneity of insurance status by using a discrete factor approximation of the unobserved heterogeneity. Our results suggest that simple probit estimates that do not account for the endogeneity of insurance choices may be biased by a factor such as unobserved risk aversion, and that the bias can be quite large.

Consistent with the evidence that HMOs offer the most protection against catastrophic medical expenses, the marginal effect of HMO participation on ownership of risky assets is larger than the effect of supplemental insurance. We find that HMO participation increases risky asset holding by 13.0 percentage points relative to those enrolled in Medicare Parts A and B only, whereas supplemental insurance increases risky asset holding by 7.1 percentage points. We also present suggestive evidence that the responsiveness to background medical expenditure risk may vary by wealth level. For example, the wealthiest one-third of respondents is least sensitive, while the middle one-third is highly sensitive; the bottom third is moderately sensitive. We speculate that the heightened sensitivity to medical expenditure risk among the middle wealth group could reflect their position of having, on the one hand, relatively limited wealth to use as a buffer against unexpected medical expenditures (compared to the top wealth group) and, on the other hand, relatively too much wealth (compared to the bottom wealth group) to make Medicaid a reasonable option. This finding is only suggestive since we cannot rule out the possibility that the differences in marginal effects are driven by group differences in the functional forms of the underlying predicted probabilities.

Given that just 50 percent of our sample holds risky assets, our estimated marginal effects represent sizable effects in percent terms; however, it makes perhaps more sense to evaluate the magnitude of these effects in terms of the degree of risk reduction they reflect. We calculate that supplemental insurance plans lower both the expected value and standard deviation of out-of-pocket expenditures by roughly 10 percent on average (controlling for detailed health status and socioeconomic status). HMO plans also lower the standard deviation by about 10 percent, but they lower the expected value of out-of-pocket expenditures by roughly 20 percent. Thus, the relatively large point estimates we obtain seem plausible in light of the significant amount of risk reduction embodied in each insurance scheme.

Our results suggest that reforms to the Medicare system that appreciably change the degree of medical expenditure risk older households face have the potential to affect demand for risky assets in the economy.

Appendix Table 1

Results of Upwards Testing to Select Number of Points of Support in Distribution of Unobserved Heterogeneity

			P-val for LR	Predicted Probabilities of Holding Risky Assets by Insurance Type			Marginal Effects
Model	Support Points	Ln(L)	Test~χ2(4)	Supp.	HMO	None	Supp.-None	HMO-None
Probit (Indep. Errors)	1	−5817		0.507	0.475	0.437	0.070	0.038
				(0.037)	(0.039)	(0.039)	(0.055)	(0.056)
Discrete Factor	2	−5768	0.00	0.491	0.550	0.420	0.071	0.130
				(0.039)	(0.050)	(0.041)	(0.057)	(0.068)
Discrete Factor	3	−5768	0.99	0.491	0.545	0.423	0.069	0.123
				(0.039)	(0.053)	(0.041)	(0.057)	(0.068)

Notes: This table reports results of upwards testing to select the number of points of support for the distribution of unobserved heterogeneity. The reported P-value is for a likelihood ratio chi-square test (df=4) comparing the indicated model against a model with one fewer point of support (four fewer estimated parameters). The null hypothesis--that the simpler model is the true model--is not rejected when the test statistic is not statistically significant at the 25% level or greater (Mroz and Zayats (2008)). The box highlights the preferred model as a result of the upwards testing procedure.