Multiple Dimensions of Private Information: Evidence from the … · 2008. 1. 30. · Multiple Dimensions of Private Information: Evidence from the Long-Term Care Insurance Market

Multiple Dimensions of Private Information: Evidence from theLong-Term Care Insurance Market

By AMY FINKELSTEIN AND KATHLEEN MCGARRY*

We demonstrate the existence of multiple dimensions of private information in thelong-term care insurance market. Two types of people purchase insurance: indi-viduals with private information that they are high risk and individuals with privateinformation that they have strong taste for insurance. Ex post, the former are higherrisk than insurance companies expect, while the latter are lower risk. In aggregate,those with more insurance are not higher risk. Our results demonstrate thatinsurance markets may suffer from asymmetric information even absent a positivecorrelation between insurance coverage and risk occurrence. The results alsosuggest a general test for asymmetric information. (JEL A82, G22, I11)

Theoretical research has long emphasized thepotential importance of asymmetric informationin impairing the efficient operation of insurancemarkets. Several recent studies in different in-surance markets, however, have found no evi-dence to support the central prediction of manyasymmetric information models that those withmore insurance should be more likely to expe-rience the insured risk.1

In this paper, we use a new method to test forthe presence of asymmetric information in thelong-term care insurance market in the UnitedStates. We use individuals’ subjective assess-

ments of the chance they will enter a nursinghome to show that, conditional on the insurancecompanies’ own assessment of the individuals’risk type, individuals have residual private in-formation that predicts their eventual risk.Moreover, this residual private information isalso positively correlated with insurance cover-age. Combined, these two findings provide di-rect evidence of asymmetric evidence in thelong-term care insurance market.

Yet despite this result, the same data provideno evidence of a positive correlation betweenindividuals’ insurance coverage and their riskexperience. A resolution of this apparent puzzlemay be that individuals have private informa-tion about a second determinant of insurancepurchase, their preferences for insurance cover-age, as well as private information about theirrisk type. If individuals with private informationthat they have strong tastes for insurance arelower risk than the insurance company wouldpredict, private information about risk type andprivate information about insurance preferencescan operate in offsetting directions to producean equilibrium in which those with more insur-ance are not more likely to experience the in-sured risk.

We provide some suggestive evidence of thenature of this offsetting private informationabout preferences in the long-term care insur-ance market. Specifically, we show that wealth-ier individuals and individuals who exhibitmore cautious behavior—as measured either by

* Finkelstein: Department of Economics, MassachusettsInstitute of Technology, E52-262F, 50 Memorial Drive,Cambridge, MA 02142, and National Bureau of EconomicResearch (e-mail: [email protected]); McGarry: Department ofEconomics, UCLA, 8283 Bunche Hall, Box 951477, LosAngeles, CA 90095-1477 (e-mail: [email protected]). Weare grateful to Daron Acemoglu, Doug Bernheim, JeffBrown, Pierre-Andre Chiappori, Raj Chetty, Janet Currie,David Cutler, David de Meza, Seema Jayachandran, JerryHausman, Ginger Jin, Larry Katz, Ben Olken, Sarah Reber,Casey Rothschild, Michael Rothschild, Bernard Salanie,Jesse Shapiro, Jonathan Skinner, Jonathan Wright, threeanonymous referees, and numerous seminar participants forhelpful comments and discussions. We are especially grate-ful to Jim Robinson for generously providing us with theactuarial model of long-term care utilization. Finkelsteinthanks the National Institute on Aging (NIA) (R01AG021900), and McGarry thanks the NIA (R01AG016593) for financial support.

1 See, e.g., John Cawley and Tomas Philipson (1999),Pierre-Andre Chiappori and Bernard Salanie (2000), andJames H. Cardon and Igal Hendel (2001).

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their investment in preventive health care or byseat belt use—are both more likely to havelong-term care insurance coverage and lesslikely to use long-term care; neither of thesecharacteristics is used by insurance companiesin pricing long-term care insurance.

Our findings have several important implica-tions for understanding the impact of asymmet-ric information on insurance markets. Theydemonstrate that the equilibrium in insurancemarkets with multiple types of correlated unob-served heterogeneity may look very differentfrom what standard unidimensional models ofasymmetric information about risk type alonewould predict. Because unobserved preferenceheterogeneity can offset the positive correlationbetween insurance coverage and risk occurrencethat private information about risk type alonewould produce, these findings also suggest thatthe widely used “positive correlation” test forasymmetric information can lead to incorrectconclusions.

This insight suggests an alternative approachfor testing for asymmetric information in insur-ance markets that we expect will have wideapplicability. Conditional on the information setused by the insurance company, the existence ofany individual characteristic that is observed bythe econometrician, but is not used by the in-surer, and is correlated with both insurancecoverage and risk occurrence, indicates thepresence of asymmetric information that affectsthe payoffs to the parties to the transaction.

Our evidence of preference-based selectionmay also provide a unifying explanation for thedisparities across different insurance markets inwhether the insured appear to be above averagein their risk type. For example, there is evidencefrom several different countries that annuitantsare longer lived (i.e., higher risk) than the gen-eral population while those with life insurance(which insures the opposite longevity risk) arealso longer lived (i.e., lower risk) relative to thegeneral population (Cawley and Philipson,1999; Finkelstein and James Poterba, 2002,2004; David McCarthy and Olivia S. Mitchell,2003). A possible explanation for the apparentselection differences between these markets isthat preference-based selection may operate inthe opposite direction for annuities and for lifeinsurance. Characteristics of the individual thatthe insurance company does not observe, such

as their level of caution or their wealth, may bepositively correlated with demand for bothforms of insurance, but negatively correlatedwith the life insurance risk of dying and posi-tively correlated with the annuity risk of living.Such an explanation would be consistent withthe existence of private information about risktype in both markets.

The remainder of the paper proceeds as fol-lows. In Section I, we provide some conceptualbackground on the empirical predictions madeby models of insurance markets with asymmet-ric information, as well as institutional back-ground on the private long-term care insurancemarket. Section II describes our data and out-lines our empirical approach. Section III pre-sents our findings. The final section concludes.

I. Background

A. Theoretical Effect of AsymmetricInformation on Market Equilibrium

Standard models of asymmetric informationconsider individuals who differ only in terms oftheir (privately known) risk type. A robust pre-diction of these models is that in equilibriumthere will be a positive correlation between theamount of insurance and the occurrence of therisky event (Chiappori and Salanie, 2000; Di-onne et al., 2001; Chiappori et al., forthcoming).This observation has motivated the standard testfor asymmetric information used in the litera-ture, which is to test for a positive correlationbetween the amount of insurance coverage andthe ex post occurrence of the (potentially) in-sured risk.2

This “positive correlation” can arise fromeither adverse selection or moral hazard, both ofwhich result in a market that is inefficient rela-tive to the first best. In the case of adverseselection, the insured is assumed to have ex ante

2 Of course, this prediction—and the appropriate empir-ical test of it—applies only to individuals who would betreated symmetrically by the insurance company (i.e.,placed in the same risk category and offered the same set ofinsurance contract options). Although we will not alwaysstate this qualification explicitly in our discussion, it isimplicitly always present. In the empirical work below, wetake great care to condition on the risk classification andoption set of the individual.

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private information about his risk type relativeto what the insurance company knows; thosewith private information that they are high riskselect contracts with more insurance than thosewith private information that they are low risk(see, e.g., Michael Rothschild and Joseph E.Stiglitz, 1976). In the case of moral hazard, thecausality is reversed and the informationalasymmetry occurs ex post: insurance coveragelowers the cost of an adverse outcome and thusincreases the probability or magnitude of therisk occurrence (see, e.g., Richard J. Arnott andStiglitz, 1988).

Recent theoretical work has enriched thesestandard asymmetric information models to al-low for private information about preferences aswell as about risk type. With these multipleforms of private information, a positive corre-lation between insurance coverage and risk oc-currence may be neither a necessary norsufficient condition for the presence of asym-metric information about risk type (MichaelSmart, 2000; Achim Wambach, 2000; David deMeza and David C. Webb, 2001; Bruno Jullienet al., 2002; Chiappori et al., forthcoming). Forexample, if unobserved preferences are posi-tively correlated with insurance demand andnegatively correlated with risk occurrence, thenthe correlation between insurance coverage andrisk occurrence in equilibrium can be negative,despite the presence of asymmetric informationabout risk type.3

Just as with a single dimension of privateinformation, an equilibrium with multiple formsof private information is unlikely to be efficientrelative to the first best. This result applies evenabsent a positive correlation between insurancecoverage and risk occurrence. Intuitively, con-sider the case in which private informationabout risk type and about risk preferences offseteach other to produce an equilibrium with nocorrelation between insurance coverage and riskoccurrence. In this case, one could well imaginetwo different groups of individuals purchasinga given insurance policy: low-risk, high-risk-

aversion individuals, and high-risk, low-risk-aversion individuals. If these groups pay thesame price for the insurance policy, but havedifferent expected costs, both cannot pay anactuarially fair price, and the quantity of insur-ance purchased by at least one group will there-fore not be first best. However, whether theequilibrium is inefficient relative to the second-best, or whether there is scope for Pareto im-provement for government intervention, variesacross models, just as in the case of unidimen-sional models of private information (Keith J.Crocker and Arthur Snow, 1985).4

B. Long-Term Care Expenditure Risk andPrivate Insurance

We focus on the long-term care insurancemarket for two main reasons. First, long-termcare expenditure risk is among the largest finan-cial risks faced by today’s elderly, making aninvestigation of this market of particular inter-est. Annual expenditures on long-term care inthe United States totaled $135 billion in 2004,comprising over 8.5 percent of total health ex-penditures, or roughly 1.2 percent of GDP (U.S.Congressional Budget Office, 2004). These ex-penses are distributed unevenly. For example,Christopher M. Murtaugh et al. (1997) estimatethat while 60 percent of individuals who reachage 65 will never enter a nursing home, one-fifth of those who do will spend at least fiveyears in the institution.

These figures suggest that there exist poten-tially large welfare gains from insurance to re-duce this expenditure risk. Yet most of the riskis uninsured. Only about 10 percent of individ-uals age 65 or older have private long-term careinsurance, and most of the private policies pro-vide only limited coverage (Health InsuranceAssociation of America (HIAA), 2000b; JeffreyR. Brown and Finkelstein, 2004a; Marc Cohen,2003). As a result, only 4 percent of expendi-tures are reimbursed by private insurers, whileone-third are paid for out of pocket (Congres-sional Budget Office, 2004; National Center forHealth Statistics, 2002).

3 Chiappori et al. (forthcoming) show that for there to beasymmetric information about risk type and no positivecorrelation between insurance coverage and risk occurrencerequires—if more than one type of contract is purchased—that there be not only an additional dimension of heteroge-neity but also a markup of price above expected claims.

4 For an example of an equilibrium with private infor-mation about risk type and risk preferences in which there isscope for Pareto improvement through government inter-vention, see de Meza and Webb (2001).

940 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2006

Second, the long-term care insurance market isunusual among insurance markets in the UnitedStates in that, during the period of our analysis,there was essentially no direct regulation of theprices charged or policies offered (National Asso-ciation of Insurance Commissioners, 2002a, 2002b;Stephanie Lewis et al., 2003). In a regulated mar-ket, it is more difficult to infer which aspects of theequilibrium are inherent to the market itself andwhich stem from regulatory constraints.5

The average age of purchase for long-termcare insurance is 67 (HIAA, 2000b). Once pur-chased, policies are guaranteed renewable forthe lifetime of the individual at a prespecifiedconstant nominal premium.

II. Empirical Approach

To investigate the nature of private informa-tion in the long-term care insurance market, wedraw on a rich dataset that contains the respon-dents’ own assessments of their nursing homerisk, as well as data on ex post risk occurrence,insurance coverage, precautionary activities,and a full set of health and demographic indi-cators that are sufficiently detailed to allow us toproxy the insurers’ risk categorization. Our em-pirical strategy proceeds in three simple steps.First, we demonstrate that individuals have pri-vate information about their risk type and thatthis private information is positively correlatedwith insurance coverage. Second, we show thatdespite this private information, the equilibriumdoes not exhibit the positive correlation be-tween insurance coverage and the use of long-term care predicted by unidimensional modelsof asymmetric information. These two sets offindings point mechanically to the existence of asecond form of unobserved heterogeneity—het-erogeneity in preferences—which offsets therisk-based selection and obscures the expectedpositive correlation between insurance coverageand risk occurrence. In the third step of theanalysis, we present direct evidence of the formof this offsetting preference-based selection.

A. Data

Our individual-level survey data are from theAsset and Health Dynamics (AHEAD) cohortof the Health and Retirement Study (HRS). Atbaseline this cohort is representative of the non-institutionalized population born in 1923 or ear-lier and their spouses. Appendix A providesmore detail on the data and our sample. Theaverage age of our respondents when we ob-serve them in 1995 is 78, and 11 percent havelong-term care insurance. These respondents arefollowed over time, allowing us to observe ac-tual nursing home use from 1995 to 2000. Six-teen percent of our initial community-basedsample enters a nursing home at some pointduring this five-year period.

Central to our analysis is a measure of indi-vidual beliefs about nursing home use. We takeadvantage of a question in AHEAD that directlyasks respondents about their perceived likeli-hood of nursing home use. The specific questionwe use from the 1995 survey is: “Of coursenobody wants to go to a nursing home, butsometimes it becomes necessary. What do youthink are the chances that you will move to anursing home in the next five years?” Individ-uals are asked to give a response on a scale ofzero to 100, which we rescale to be betweenzero and one. Their responses may reflect infor-mation about their health status and thus theirchance of needing nursing care. They may alsoreflect their alternatives to nursing care shouldthey need it, such as the willingness of a spouseor child to take care of them, or their insurancecoverage.

On several dimensions the subjective re-sponses to this question appear reasonable.Individual predictions appear to be correct onaverage; the average self-reported probabilityof nursing home use over the five-year periodis 18 percent, while 16 percent of the respond-ers actually enter a nursing home over thefive-year period. We also find that self-reported nursing home entry probabilities co-vary in sensible ways with known risk fac-tors; they are higher for women than for men,and increase monotonically with age and withdeteriorating health status. These results areconsistent with other work that has foundsensible covariance patterns for self-reportedmortality probabilities and characteristics

5 Although there is no direct regulation of prices orpolicies, the government is a major presence in long-termcare insurance provision through Medicaid, the public in-surance program for the indigent. In the empirical workbelow, we discuss how we account for the potential effectsof Medicaid.


such as the individual’s age or health status(Daniel S. Hamermesh, 1985; V. Kerry Smithet al., 2001; Michael D. Hurd and McGarry,2002).

One well-known drawback with self-reported probabilities, however, is the pro-pensity of respondents to report round figuressuch as 0, 50, or 100 percent (Hurd and Mc-Garry, 1995; Li Gan et al., 2005). The pre-ponderance of focal responses suggests thatindividuals may not be comfortable reportingprobabilistic answers, and may not in facteven think in these terms. If individuals useprobabilistic information in making insurancepurchase decisions, but are unable to translatethese latent probabilities into numbers whenfaced with a survey question, our results arelikely to produce underestimates of the extentof the individual’s information.6

We supplement the AHEAD data with infor-mation obtained directly from insurance com-panies about the information they collect fromapplicants and their risk classification practices.We draw on the application forms used by sev-eral large long-term care insurance companieswhich reveal the set of individual characteristicsthe companies observe, and on the industry’sactuarial model of nursing home utilization,which itself is a function of these observedcharacteristics.

B. Econometric Approach

The first step of our analysis is to examinethe relationship between an individual’s be-liefs about his subsequent nursing home uti-lization, on the one hand, and his actualsubsequent nursing home utilization or hiscurrent long-term care insurance holdings, on

the other. We therefore estimate the followingtwo probits:

(1) Prob�CARE � 1� � ��X�1 � �2B�.

(2) Prob�LTCINS � 1� � ��X�1 � �2B�.

CARE is a binary variable for whether the in-dividual went into a nursing home in the fiveyears between 1995 and 2000. LTCINS is abinary variable for whether the individual haslong-term care insurance in 1995. The coeffi-cient of interest in each equation is that on B,the individual’s self-reported beliefs (measuredin 1995) of his probability of entering a nursinghome between 1995 and 2000. X is a vector ofcovariates to control for the risk classificationthat would be assigned to the individual byinsurance companies in 1995.7

The second step of our analysis is to imple-ment the standard positive correlation test forasymmetric information. To do so we employtwo approaches used in the literature (the resultsare quite similar across the two). In one ap-proach, we follow Chiappori and Salanie (2000)and estimate a bivariate probit of insurance cov-erage and risk occurrence, conditional on therisk classification variables (X). This is equiva-lent to estimating the probits in (1) and (2)simultaneously, with the beliefs variable (B)omitted from the regression. The key variable ofinterest is the correlation between the errorterms (�). A unidimensional model of asymmet-ric information predicts that residuals will bepositively correlated (� � 0) and an inability toreject the null hypothesis that � � 0 constitutesa failure to reject the null of symmetricinformation.8

Our second approach follows the work ofFinkelstein and Poterba (2004) and estimates aprobit model of nursing home use as a function6 Another interpretation of these focal responses is that

the responses may convey ordinal information about theirbeliefs of their risk (e.g., low, medium, or high) but notcardinal information about the scale. Almost 50 percent ofrespondents report a five-year nursing home entry probabil-ity of zero, and 14 percent report a 50-percent probability.The working paper version of this paper, therefore, reportsa parallel set of results to those shown here in which we usea set of indicator variables for low risk (reports of zeroprobability), medium risk (1–49 percent), and high risk(50–100 percent) to measure beliefs; the main findings ofthe paper are robust to this alternative parameterization ofindividuals’ beliefs (Finkelstein and McGarry, 2003).

7 Although we report results from estimating equations(1) and (2) independently, the findings are robust if weinstead estimate the equations simultaneously.

8 Chiappori and Salanie (2000) discuss several alterna-tive parametric and nonparametric approaches to imple-menting the test for residual correlation. In the interest ofspace we do not discuss and report them here, but we haveverified that our findings are robust to these alternativeapproaches.


of insurance coverage, controlling for risk clas-sification:

(3) Prob�CARE � 1� � ��X�1 � �2LTCINS�.

The positive correlation prediction is that �2 �0. Note that �2 does not have a causal interpre-tation. In a pure moral hazard model, the coef-ficient would represent the causal effect ofinsurance coverage on care utilization. In anadverse selection model, however, the causalityis reversed and private information about expectedcare utilization affects insurance demand.

In the final step in our empirical work, weprovide several examples of additional individ-ual characteristics that are not used in the insur-er’s risk classification, but that when added onthe right-hand sides of equations (1) and (2),have opposite signed relationships with CAREand with LTCINS.

C. Controlling for Risk Classification

Any analysis of private information, whetherthe approach we undertake in the first part ofour analysis or the standard positive correlationtest in our second step, requires that we condi-tion on the risk classification of the individualby insurance companies (X). This conditioningallows us to test for the existence of residualprivate information, which is the economicallymeaningful question.

Using insurance applications from five lead-ing long-term care insurance companies, wedetermined what individual characteristics in-surance companies observe. All of them collecta limited set of demographic information—age,gender, marital status, and age of spouse—aswell as similar and extremely detailed informa-tion on current health and on health history.This same information is observable in AHEAD,which collects extremely rich and detailed in-formation on current health and medical history,as well as standard demographic data. We cantherefore accurately replicate the insurer’s in-formation set.

Our preferred approach is to control for theinsurance companies’ actuarial prediction of theindividual’s risk type, because it is this measurethat is used to generate the price the individualis charged. We generated the insurance compa-nies’ prediction of the probability the individual

will go into a nursing home over a five-yearperiod using the same actuarial model that isemployed by many of the firms in the industry;the model and its pedigree are described indetail in James Robinson (1996), Robinson(2002), and Brown and Finkelstein (2004a).9

The predictions depend nonparametrically onthe individual’s age, sex, and membership inone of seven different health states (defined bythe number of limitations to instrumental activ-ities of daily living (IADLs), the number oflimitations to activities of daily living (ADLs),and the presence or absence of cognitive im-pairments). As noted, all of this information isavailable in the AHEAD. This measure pro-vides a parsimonious way of controlling fornonlinear (and nonparametric) interactions be-tween the observed characteristics of the indi-vidual used by the actuaries in pricing insuranceand care utilization.10

One potential issue with this approach is thatwe are implicitly assuming that none of theinformation that is collected by the insurancecompany, but omitted from the actuarial model,is used in pricing the policies. This assumptionappears broadly consistent with insurance com-pany practice. Companies offer age-specificprices with only two or three broad health-basedrate classifications within each age (Murtaugh etal., 1995; American Council of Life Insurers,2001; Weiss, 2002), and do not further adjustpremiums over time if the characteristics of theindividual change.11 However, we cannot rule-out the possibility that this information is some-how used by the insurance company indetermining which of the two or three broadhealth-based rate classifications to assign the

9 The model we use predicts care utilization for typicalindividuals in the population and makes no adjustment forpotential moral hazard effects of the insurance.

10 We also tried introducing the variables used in thisprediction directly into the regression in a fully flexible andinteracted manner. And we tried including indicator vari-ables for the decile of the insurance companies’ prediction.Both produced results that were virtually indistinguishablefrom those obtained using the prediction itself. We reportthe specification with the actuarial prediction directly on theright-hand side, since this single prediction of risk can becompared directly to the individual’s own prediction.

11 According to our conversations with industry actuar-ies, insurance companies collect more detailed informationthan they currently use in order to build a detailed claimsdatabase for future improvements in actuarial modeling.


individual to, or whether the company agreesto insure the individual in the first place.Therefore, we also present results from analternative approach, which we term the “ap-plication information” specification. In thisspecification, we attempt to control for every-thing insurance companies observe about the in-dividual. We include a full set of single year ofage dummies, all of the demographic informa-tion that insurance companies collect in theirapplications (sex, marital status, and age ofspouse), and over 35 indicator variables foreach of the detailed current health and healthhistory characteristics collected by any insur-ance company.12 To be conservative, we alsoinclude indicator variables for the household’sincome quartile and asset quartile, even thoughwe found only one company that collected anyfinancial information.13 Finally, to allow forpossible nonlinearities among these variouscharacteristics, we also include a complete setof two-way and three-way interactions betweenage, sex, and the health variables that are in-cluded in the actuarial model (ADLs, IADLs,and cognitive impairment). The “application in-formation” specification thus invokes a morefinely defined categorization of risk than insur-ance companies likely use in pricing.14

III. Results

A. Private Information about Risk Type andIts Relation to Insurance Coverage

Table 1 reports the marginal effects fromprobit estimation of equation (1) of the relation-ship between beliefs and subsequent nursinghome use. The results in column 1 indicate thatindividual beliefs about the likelihood of enter-ing a nursing home are a statistically significant,positive predictor of subsequent nursing homeexperience. Our finding of a relationship be-tween risk perception and actual risk of nursinghome use complements similar findings formortality risk (e.g., Smith et al., 2001; Hurd andMcGarry, 2002).

The results in column 2 indicate that, perhapsnot surprisingly, the insurance companies’ pre-diction is more highly correlated with subse-quent nursing home use than is the individual’s.Comparing columns 1 and 2, we see that a10-percentage-point increase in the self-reported probability of nursing home use is as-sociated with a 0.9-percentage-point increase ineventual use, whereas a 10-percentage-point in-crease in the insurer’s prediction is associatedwith a 4-percentage-point increase in eventualuse. This is not, however, the relevant metric fortesting for asymmetric information; as long asthe individual has residual private information—conditional on the menu of choices offered bythe insurance company—asymmetric informa-tion can operate as in the theoretical models.15

Indeed, most importantly, columns 3 and 4indicate that, controlling for the insurer’s riskclassification, individual beliefs remain a posi-tive and statistically significant predictor of sub-sequent nursing home use. Individuals thusappear to have residual private informationabout their risk type.16

12 These indicator variables are: limitations with respect toeach of five activities of daily living (bathing, eating, dressing,toileting, and walking across a room) and two instrumentalactivities of daily living (grocery shopping and managing med-ication); use of each of five devices (a wheelchair, walker,crutches, cane, and oxygen); low-body-mass index; high-body-mass index; whether the respondent is incontinent, uses pre-scription drugs regularly, smokes, is depressed, has a drinkingproblem, suffers from cognitive impairment; whether the re-spondent has or had diabetes, diabetes treated with insulin,kidney failure associated with diabetes, a stroke, a heart con-dition, medication for a heart condition, a heart attack, conges-tive heart failure, high blood pressure, hip fracture, lungdisease, cancer, psychiatric problems, arthritis, prior nursinghome use, prior home health care, or has been injured in afall. Finkelstein and McGarry (2003) provide summary sta-tistics for these covariates. Appendix A provides a descrip-tion of the construction of some of the variables.

13 This company asked only whether the individual hadless than $30,000 in financial assets, presumably to screenfor likely Medicaid eligibility.

14 To deal with the issue that insurance companies denycoverage to some observably poor-health individuals, wecollected information from applications and underwritingguides on criteria used to deny coverage; all of these criteriaare included in the “application information” specification.In the sensitivity analysis below we also show that the

results are robust to excluding individuals who might havebeen denied coverage based on these criteria.

15 See Meglena Jeleva and Bertrand Villeneuve (2004)for analysis of a market equilibrium when insurance com-panies are better at predicting risk than consumers, butconsumers have residual private information about risk.

16 The small R-squared of the regression analysis, evenwith the extremely detailed controls in column 4, suggeststhat there is a large amount of genuine uncertainty aboutsubsequent nursing home use, and thus a potentially largevalue of insurance that covers this risk.


Table 2 reports the results from estimatingthe relationship between beliefs and insurancecoverage in equation (2). The results indicatethat individuals who believe that they are ofhigher risk are also more likely to have insur-ance. By contrast, the insurance company’s pre-diction of the individual’s risk is negativelyrelated to insurance coverage; this is consistentwith the results below that, in fact, on averagerisk type and insurance coverage are negativelycorrelated. It also supports our use of the insur-ance company prediction as a proxy for insur-ance pricing; conditional on the individual’s riskassessment, a higher insurance company predic-

tion implies a higher price relative to the individ-ual’s perception of an actuarially fair price, andtherefore reduces the probability of purchase.

Taken together, the results in Tables 1 and 2indicate that individuals have residual privateinformation that predicts their risk type and ispositively correlated with insurance ownership.This provides direct evidence of asymmetricinformation. It does not, however, allow us todistinguish between ex ante private information(adverse selection) and ex post private informa-tion (moral hazard). Other empirical evidencesuggests that demand for nursing home use isrelatively price inelastic (David Grabowski and

TABLE 1—RELATIONSHIP BETWEEN INDIVIDUAL BELIEFS AND SUBSEQUENT NURSING HOME USE

No controls(1)

Control for insurancecompany prediction

Control forapplicationinformation

(4)(2) (3)

Individual prediction 0.091*** 0.043** 0.037*(0.021) (0.020) (0.019)

Insurance company prediction 0.400*** 0.395***(0.020) (0.021)

pseudo-R2 0.005 0.097 0.099 0.183N 5,072 5,072 5,072 4,780

Notes: Reported coefficients are marginal effects from probit estimation of equation (1). Dependent variable is an indicatorfor any nursing home use from 1995 through 2000 (mean is 0.16). Both individual and insurance company predictions aremeasured in 1995. Heteroskedacticity-adjusted robust standard errors are in parentheses. ***, **, * denote statisticalsignificance at the 1-percent, 5-percent, and 10-percent level, respectively. Column 4—which includes controls for “appli-cation information”—includes controls for age (in single year dummies), sex, marital status, age of spouse, over-35 healthindicators, and a complete set of two-way and three-way interactions for all of the variables used in the insurance companyprediction (age dummies, sex, limitations to activities of daily living, limitations to instrumental activities of daily living, andcognitive impairment); see text for more details.

TABLE 2—RELATIONSHIP BETWEEN INDIVIDUAL BELIEFS AND INSURANCE COVERAGE

No controls(1)

Control for insurancecompany prediction

Control forapplicationinformation

(4)(2) (3)

Individual prediction 0.086*** 0.099*** 0.083***(0.017) (0.017) (0.016)

Insurance company prediction �0.125*** �0.140***(0.023) (0.023)

pseudo-R2 0.007 0.010 0.019 0.079N 5,072 5,072 5,072 4,780

Notes: Reported coefficients are marginal effects from probit estimation of equation (2). Dependent variable is an indicatorfor whether individual has long-term care insurance coverage in 1995 (mean is 0.11). Both individual and insurance companypredictions are measured in 1995. Heteroskedacticity-adjusted robust standard errors are in parentheses. ***, **, * denotestatistical significance at the 1-percent, 5-percent, and 10-percent level, respectively. Column 4—which includes controls for“application information”—includes controls for age (in single year dummies), sex, marital status, age of spouse, over-35health indicators, and a complete set of two-way and three-way interactions for all of the variables used in the insurancecompany prediction (age dummies, sex, limitations to activities of daily living, limitations to instrumental activities of dailyliving, and cognitive impairment); see text for more details.


Jonathan Gruber, 2005); we therefore suspect—but cannot directly corroborate—that at leastsome of what we are detecting reflects ex anteprivate information.17

We now turn to an examination of what theresults from the standard positive correlationtest would suggest about asymmetric informa-tion in this market. This test also does notdistinguish between adverse selection andmoral hazard.

B. Long-Term Care Insurance andLong-Term Care Use

The standard test for residual asymmetric in-formation, based on a positive correlation be-

tween insurance coverage and risk occurrenceconditional on insurance company risk classifi-cation, has been applied across a variety ofinsurance markets with differing results. In thecase of health insurance, David Cutler andRichard Zeckhauser (2000) review an extensiveliterature that tends to find evidence of thispositive correlation. The positive correlationalso appears in annuity markets (Finkelstein andPoterba, 2002, 2004; McCarthy and Mitchell,2003). Several papers, however, find no evi-dence of a positive correlation in life insurancemarkets (Cawley and Philipson, 1999; Mc-Carthy and Mitchell, 2003) or in automobileinsurance markets (Chiappori and Salanie,2000; Georges Dionne et al., 2001; and Chiap-pori et al., forthcoming).

Table 3 shows the results of this standard testin the long-term care insurance market. The toprow shows the correlation of the residuals froma bivariate probit of long-term care insuranceand nursing home use, as in Chiappori andSalanie (2000). The bottom row shows the mar-ginal effect from probit estimation of nursinghome use on long-term care insurance (equation(3)), as in Finkelstein and Poterba (2004). Bothapproaches yield the same findings. With nocontrols for the insurers’ information set, therelationship between coverage and risk occur-rence is negative and statistically significant.This finding is consistent with other aggregatedata on relative rates of nursing home use for

17 Our findings also raise the question of why insur-ance companies do not collect additional information toreduce the informational advantage of the consumer. Ouranalysis suggests the answer may be that the collection ofadditional available information is unlikely to reduce theconsumers’ residual private information. We added ad-ditional control variables in equations (1) and (2) for allthe information we can observe in the AHEAD that theinsurance companies do not collect—including the num-ber, sex, and proximity of the individual’s children; theindividual’s race, religion, and education; information ona spouse’s health; and individual investments in a varietyof potentially risk-reducing behaviors (described in moredetail in Section IIIC). Although jointly statistically sig-nificant, these additional control variables did not atten-uate either the magnitude or statistical significance of thecoefficient on the individual’s prediction.

TABLE 3—THE RELATIONSHIP BETWEEN LONG-TERM CARE INSURANCE AND NURSING HOME ENTRY

No controls(1)

Controls for insurancecompany prediction

(2)

Controls for applicationinformation

(3)

Correlation coefficient frombivariate probit ofLTCINS and CARE

�0.105*** �0.047 �0.028

(p � 0.006) (p � 0.25) (p � 0.51)Coefficient from probit of

CARE on LTCINS�0.046*** �0.021 �0.014

(0.015) (0.016) (0.016)N 5,072 5,072 4,780

Notes: Top row reports the correlation of the residual from estimation of a bivariate probit of any nursing home use(1995–2000) and long-term care insurance coverage (1995); p values are given in parentheses. Bottom row reports marginaleffect on indicator variable for long-term care insurance in 1995 from probit estimation of equation (3). The dependentvariable is an indicator variable for any nursing home use from 1995 through 2000; heteroskedacticity-adjusted robuststandard errors are in parentheses. For all rows, control variables are described in column headings; see text for moreinformation. ***, **, * denote statistical significance at the 1-percent, 5-percent, and 10-percent level, respectively. Meansof CARE and LTCINS are 0.16 and 0.11, respectively.


the insured and general population (Society ofActuaries, 2002). When we control for the in-surance companies’ risk classification in col-umns 2 and 3, as required by the positivecorrelation test, we are unable to reject the nullhypothesis of zero correlation.

Proper implementation of the positive corre-lation test requires that we examine insurancedemand among individuals who face the sameset of possible insurance contracts. The controlsfor risk classification—and hence the premiumthe insurer would offer the individual—repre-sent an important component of this choice set.They may not, however, fully capture all deter-minants of the individual’s choice set. Wetherefore use two approaches to verify that ourfailure to reject the null hypothesis of symmet-ric information with the positive correlation testis not an artifact of our inability to controlcompletely for the options offered to theindividuals.

First, we implement the positive correlationtest in a more homogenous subsample of indi-viduals who are likely to face the same optionset. We identified two additional characteristicsof the individual that are particularly likely toaffect his effective choice set: his wealth, andthe presence of certain adverse health condi-tions.18 The public long-term care insuranceprovided by Medicaid offers a substitute forprivate insurance; indeed, Brown and Finkel-stein (2004b) estimate that Medicaid may havesubstantial crowd-out effects on demand forprivate long-term care insurance. However, be-cause Medicaid requires that individuals ex-haust virtually all of their financial assets beforeit will cover long-term care expenses, Medicaidis a substantially better option for lower-wealthindividuals. In addition, individuals with someobservably very poor health conditions are oftendenied insurance coverage, at least by the largelong-term care insurance companies (Murtaugh

et al., 1995; Weiss, 2002).19 For such individ-uals, simply controlling for the price they wouldface, if they were to be offered coverage, mayproduce misleading results. We therefore re-implement the positive correlation test limitingour analysis to the 20 percent of individualswho are in the top quartile of the wealth distri-bution and who have none of the health condi-tions that could trigger a denial.20 Consistentwith the better option set available to the health-ier and wealthier subsample, 17 percent of ourselected sample have long-term care insurance,compared to only 11 percent of the total sample.Table 4 shows the results from implementingthe positive correlation test on this much morehomogenous subsample. There is again no evi-dence of a positive correlation between cover-age and nursing home use. Indeed, there is nowstatistically significant evidence of a negativecorrelation.21

Second, to identify more precisely the op-tions that individuals face and the policies theychoose, much of the existing literature testingfor asymmetric information has relied on pro-prietary data provided by insurance companiesthemselves. These data typically include theindividual’s risk classification as assigned bythe company, details about the policy he hasselected from the menu of available policies,and his ex post risk experience (see, e.g., Chiap-

18 For other forms of health insurance, whether thecurrent or former employer of the individual or hisspouse offers insurance can be an essential element of theoption set. Although the group long-term care insurancemarket began to grow in the early to mid-1990s and iscurrently about 20 percent of the total market, it wasvirtually nonexistent at the time the elderly individuals inour data would have been in the workforce (HIAA,2000a, 2001).

19 An examination of applications from the major long-term care insurance companies and several of their under-writing guides indicates that coverage is often denied toindividuals who have limitations with respect to any ADLs(bathing, eating, dressing, toileting, walking, and maintain-ing continence), use mechanical devices (wheelchair,walker, crutches, quad cane, oxygen), or suffer from cog-nitive impairment. All of these factors are controlled for inour “application information” specification. The practice ofdenying observably high-risk individuals coverage is com-mon in other insurance markets as well. It may reflect issuesof reputation or brand name, greater concerns about asym-metric information for individuals of higher observable risk,or lower variability in care utilization for these individuals.

20 This approach is likely to yield an overestimate of thenumber of ineligible individuals, because individuals clas-sified as ineligible in 1995 may have been previously eli-gible for insurance. We use this overly inclusive definitionto be sure that the remaining sample would have beeneligible for insurance coverage.

21 We verified that the point estimates in Tables 1 and 2were not sensitive to the same sample restriction, althoughin a few specifications standard errors increased to the pointwhere statistical significance no longer obtained.


pori and Salanie, 2000; or Finkelstein and Pot-erba, 2004). To implement this alternativeapproach, we obtained proprietary data from alarge long-term care insurance company whichcontain all of the information used in similaranalyses, including the individual’s choice fromthe menu of contracts, his exact risk classifica-tion, and his ex post risk experience.22 Thisanalysis complements the analysis with theAHEAD data because it allows us to examinethe relationship between the quantity of insur-ance coverage (conditional on having insur-ance) and risk occurrence. Using these data, weonce again fail to reject the null hypothesis ofno positive correlation. The data and resultsfrom this exercise are described more fully inAppendix B.

We also undertook numerous additional testsof robustness in the AHEAD data, many ofwhich we present in detail in the working paperversion (Finkelstein and McGarry, 2003). Forexample, we verified that the positive correla-tion does not manifest itself in other measuresof care utilization such as the intensity of careuse (i.e., number of nights in a nursing home),or home health care use. We also verified thatthe positive correlation does not emerge if the

relationship between insurance coverage andrisk occurrence is analyzed over a longer timehorizon than the five-year period studied here.Finally, although policies once purchased areguaranteed renewable for life, some individualsstop paying their premiums and thereby forfeitsome or all of their potential future nursinghome benefits; we therefore verified that theresults are unaffected by excluding from thesample the 10 percent of insured individuals in1995 who subsequently report having droppedtheir insurance coverage.23

The results presented in Tables 1 and 2 pointto the presence of asymmetric information, eventhough the results in Tables 3 and 4 indicate thatthe standard positive correlation test is unable toreject the null of symmetric information. Thissuggests that our beliefs-based test may be amore discerning test for asymmetric informa-tion than the standard positive correlation test.Moreover, as noted previously, because our be-liefs measure is a highly imperfect proxy for anindividual’s private information, our findings inTables 1 and 2 likely understate the amount ofprivate information in this market.

Nonetheless, a natural question is whether theprivate information we detected in Tables 1 and2 is sufficiently large that we should have ex-

22 The downside to these data is that they do not containthe rich information on individuals’ beliefs about their risktype or about other characteristics not used by the insurancecompany which are critical for our analysis.

23 Finkelstein et al. (2005) provide a more detailed dis-cussion of this dropping behavior as well as an empiricalexploration of some of the factors that may be behind it.

TABLE 4—RELATIONSHIP BETWEEN LTCINS AND CARE(Sample restricted to individuals with same choice set)

No controls(1)

Controls for insurancecompany prediction

(2)

Controls for applicationinformation

(3)

Correlation coefficient from �0.123* �0.122* �0.191**bivariate probit ofLTCINS and CARE

(p � 0.08) (p � 0.10) (p � 0.017)

Coefficient from regression �0.032* �0.028* �0.033**of CARE on LTCINS (0.018) (0.015) (0.012)

N 1,504 1,504 1,438

Notes: Sample is limited to individuals in the top quartile of the wealth and income distribution and who have none of thehealth characteristics that might make them ineligible for private insurance. Top row reports the correlation of the residualfrom estimation of a bivariate probit of any nursing home use (1995–2000) and long-term care insurance coverage (1995);p values are given in parentheses. Bottom row reports marginal effect on indicator variable for long-term care insurance in1995 from probit estimation in equation (3). The dependent variable is an indicator variable for any nursing home use from1995 through 2000; heteroskedacticity-adjusted robust standard errors are in parentheses. For all rows, control variables aredescribed in column headings; see text for more information. ***, **, * denote statistical significance at the 1-percent,5-percent, and 10-percent level, respectively. Means of CARE and LTCINS are 0.09 and 0.17, respectively.


pected to obtain a positive correlation betweeninsurance coverage and long-term care use inthe absence of any offsetting selection. A sim-ple decomposition suggests that this is indeedthe case. Specifically, we used the results fromestimating equation (2) to decompose long-termcare insurance coverage into the portion ex-plained by individual beliefs and a residual thatis not explained by these beliefs. We then rees-timated the nursing home utilization equation(3) substituting these two components of long-term care insurance for the LTCINS variable. Indoing so we found a positive and statisticallysignificant relationship between nursing homeutilization and the portion of insurance cover-age predicted by individual beliefs, with a co-efficient of around 0.5 when controls for riskclassification are included. This suggests thatthe relationship between nursing home utiliza-tion and insurance coverage would indeed bepositive in the absence of any offsetting selec-tion effects. The next section presents moredirect evidence of the existence of these offset-ting selection effects.

C. Private Information about Preferencesfor Insurance

Our finding that insured individuals are nomore likely to enter a nursing home than indi-viduals without insurance might ostensiblyseem at odds with our finding that individualshave private information about their risk typethat is positively correlated with insurance cov-erage. A natural reconciliation of these two setsof results, however, is the existence of other(unobserved) characteristics of the individualthat are positively correlated with insurancecoverage but negatively related to insuranceuse. These factors must be items that are omit-ted from the pricing formulas used by insurancecompanies and that have the opposite correla-tion with insurance coverage and care utiliza-tion. We now turn to an empirical examinationof what some of these offsetting preference-based factors might be.

It is worth noting at the outset that if individ-uals’ self-reported beliefs are a sufficient statis-tic for their private information and if individualsefficiently incorporate all available informationwhen forming their beliefs, then conditional onthese beliefs other characteristics of the individ-

ual should have no predictive power in explain-ing subsequent utilization. In practice, however,our belief measures are likely to be an imperfectproxy for individuals’ beliefs. Moreover, evi-dence from Smith et al.’s (2001) study of beliefformation about mortality prospects suggeststhat in fact individuals do not efficiently incor-porate all available information in forming andupdating their beliefs.

We focus on two potential dimensions ofoffsetting preference-based selection—wealthand cautiousness—which have previously at-tracted theoretical attention (de Meza andWebb, 2001; Bruno Jullien et al., 2002). Neitherof these factors is used by insurance companiesin pricing long-term care insurance.

As we noted earlier, Medicaid offers a sub-stantially better substitute for private insurancefor lower-wealth individuals. This makes itlikely that an individual’s wealth—a factor notused in pricing private policies—may be animportant source of preference heterogeneity inprivate insurance demand. The top panel ofTable 5 reports the results of adding indicatorvariables for the individual’s financial netwealth quartile to equations (1) and (2). Indi-viduals in higher wealth quartiles are less likelyto go into a nursing home (odd columns) butmore likely to have long-term care insurance(even columns).

We measure an individual’s cautiousness byhis investment in risk-reducing activities. Weobserve, in 1995, whether the individual under-took various gender-appropriate preventivehealth care measures in the previous two years.These activities are: whether the individualhad a flu shot, had a blood test for cholesterol,checked her breasts for lumps monthly, had amammogram or breast x-ray, had a Papsmear, and had a prostate screen. The medianindividual undertakes two-thirds of gender-relevant activities; 7 percent report doingnothing and 30 percent report engaging in allrelevant activities. The insurance companyapplications we reviewed did not solicit anyof this information.

Individuals who invest more in such pre-ventive activities may also be more riskaverse and thus place a higher value on in-surance (de Meza and Webb, 2001). How-ever, more cautious individuals are notnecessarily more risk averse; preventive ac-


tivity affects the mean as well as the varianceof the risk distribution (see, e.g., Dionne andEeckhoudt, 1985, and Jullien et al., 1999).Thus the sign of the correlation between cau-tious behavior and insurance coverage is anempirical question. The results in Table5, panel B, indicate that individuals who un-dertake a greater fraction of potential preven-tive health activities (i.e., more cautiousindividuals) are in fact more likely to owninsurance; they are also less likely to enter anursing home.24

One interpretation of the negative relation-ship between preventive health behaviors andnursing home use is that the preventive behav-

iors endogenously lower the individual’s risktype by forestalling or preventing nursing homeadmissions. For example, flu shots reduce therisk of pneumonia which is a nontrivial contrib-utor to nursing home use among the elderly. Wealso find, however, that individuals who investmore in our measured preventive health activi-ties are substantially less likely to have a hipfracture (another important contributor to nurs-ing home use), yet none of the measured activ-ities themselves would be expected to affectbone density or agility. We therefore suspectthat these preventive health activities are corre-lated with other health investments that them-selves cause lower rates of institutionalization.It is also possible that these preventive healthactivities proxy for other unmeasured preference-related characteristics that themselves have acausal effect on nursing home utilization. Wefind, for example, that individuals who engage

24 We verified that these results are robust instead tomeasuring preventive health activity subsequent to the in-surance contracting in 1995 (i.e., over the period 1998–2000).

TABLE 5—PREFERENCE-BASED SELECTION

No controlsControl for insurancecompany prediction

Control for applicationinformation

NH Entry(1)

LTCInsurance

(2)NH Entry

(3)

LTCInsurance

(4)NH Entry

(5)

LTCInsurance

(6)

Panel A: WealthTop wealth quartile �0.095*** 0.150*** �0.038** 0.131*** �0.018 0.139***

(0.013) (0.020) (0.014) (0.020) (0.015) (0.022)Wealth quartile 2 �0.073*** 0.104*** �0.025* 0.089*** �0.013 0.092***

(0.013) (0.020) (0.014) (0.020) (0.014) (0.020)Wealth quartile 3 �0.030** 0.062*** 0.0004 0.052*** 0.006 0.057***

(0.015) (0.020) (0.016) (0.019) (0.015) (0.020)Bottom wealth quartile (omitted) — — — — — —Individual prediction 0.086*** 0.089*** 0.042** 0.098*** 0.035* 0.086***

(0.021) (0.017) (0.020) (0.017) (0.019) (0.017)

Panel B: Preventive health activityPreventive activity �0.106*** 0.066*** �0.054*** 0.052*** �0.016 0.016

(0.0118) (0.017) (0.018) (0.017) (0.019) (0.017)Individual prediction 0.095*** 0.082*** 0.047** 0.095*** 0.037* 0.082***

(0.021) (0.017) (0.020) (0.017) (0.020) (0.017)

Panel C: Seat belt useAlways wear seatbelt �0.059*** 0.053*** �0.031** 0.048*** �0.018 0.029***

(0.014) (0.010) (0.013) (0.010) (0.012) (0.010)Individual prediction 0.092*** 0.084*** 0.044** 0.097*** 0.038* 0.082***

(0.021) (0.017) (0.020) (0.017) (0.019) (0.016)

Notes: Table reports marginal effects from probit estimation of equations (1) and (2). Additional controls are given in columnheadings; see text for more information. In panel A, omitted wealth category is quartile 4. For panel A, income controls areomitted from the “application information” controls since they are highly multi-collinear with assets. In panel B, “preventiveactivity” measures the proportion of gender-appropriate preventive health behaviors undertaken; all estimates in panel Binclude an additional control for gender. Heteroskedacticity-adjusted robust standard errors are in parentheses. ***, **, *denote statistical significance at the 1-percent, 5-percent, and 10-percent level, respectively.


in more preventive health activity tend system-atically to overestimate their risk probabilityrelative to actual experience. This suggests theexistence of an unobserved “pessimism” factor;Kostas Koufopoulos (2003) conjectures thatpessimism simultaneously increases demand forinsurance and demand for risk-reducing activi-ties, which lower risk type.25

One concern with our findings, however, isthat preventive health measures may themselvesbe determined by insurance coverage or healthstatus. We suspect this is unlikely, as everyonein our sample is covered by Medicare (whichcovers the expenses from these preventivehealth measures at least to some extent), virtu-ally our entire sample of elderly individuals hasseen a doctor in the last two years, and ouranalysis includes detailed controls for healthstatus. As a further check, however, we turn toa different type of precautionary behavior that isless likely to be affected by health status orhealth insurance coverage: seat belt use. Theresults in panel C of Table 5 indicate that indi-viduals who report that they always wear theirseat belt in a car (which 77 percent do) are alsoless likely to go into a nursing home and morelikely to own insurance.26

Interestingly, other than preventive activityand wealth, the characteristics of the individualthat we can measure and that insurance compa-nies do not use in pricing appear to have thesame correlation with insurance coverage andrisk occurrence. For example, individuals withmore children are both less likely to have insur-ance and less likely to use nursing home care.The same is true for non-whites relative towhites, Hispanics relative to non-Hispanics, andless educated individuals relative to moreeducated.

IV. Conclusion

In this paper we document the existence ofmultiple forms of private information in an in-

surance market, and demonstrate how thesefactors can have offsetting effects on the corre-lation between insurance coverage and risk oc-currence, thus invalidating the standard test ofasymmetric information. Our empirical workfocuses on the private long-term care insurancemarket, but the ideas we develop have broaderapplicability.

We begin by using data on self-assessmentsof nursing home risk, along with elaborate con-trols for the risk classification used by the in-surance company, to demonstrate directly thatprivate information about risk type exists, and ispositively correlated with insurance coverage.We then show that despite this private informa-tion, insurance coverage and risk occurrence arenot positively correlated, and thus the standardtest of asymmetric information fails to reject thenull of symmetric information. We reconcilethese findings by presenting evidence of a sec-ond type of heterogeneity—heterogeneity inpreferences for insurance—that offsets the se-lection based on private information about risk.For example, we find that both wealthier indi-viduals and individuals who behave more cau-tiously in terms of preventive health activities orseat belt use are both more likely to own insur-ance and less likely to use long-term care; thesefactors are not used by insurance companies inpricing insurance.

Our findings highlight that when individualshave private information about risk preferencesas well as risk type, an asymmetric informationequilibrium in an insurance market can lookvery different from the standard theoretical casewith heterogeneity in risk type alone. As in thestandard unidimensional case, the equilibriumwith multiple forms of private information isunlikely to be efficient relative to the first besteven if the market does not appear “adverselyselected” in aggregate. An unanswered ques-tion, however, and an important avenue for fur-ther work, is under what conditions this addeddimension of heterogeneity reduces or increasesthe efficiency cost of asymmetric informationabout risk type.

It is worth noting that although preference-based and risk-based selection act in offsettingdirections in the long-term care insurance market,they may reinforce each other in other insurancemarkets. Indeed, in a recent paper, Alma Cohenand Liran Einav (2005) provide evidence that risk

25 See also Arnold Chassagnon and Villeneuve (2005)for the characteristics of equilibrium with adverse selectionas well as heterogeneity in pessimism.

26 To verify that the variation in seat belt use does notmerely reflect differences in state laws (or the enforcementof these laws) requiring seat belt use, we verified that theresults are robust to including state fixed effects.


type and risk aversion are positively correlated inthe automobile insurance market. Differencesacross insurance markets in the relationship be-tween preference-based selection and actual riskmay therefore provide a potential unifying expla-nation for the apparent differences across insur-ance markets in whether the insured are above-average in their risk type.

Finally, our analysis suggests a more robustapproach to testing for asymmetric informationin insurance markets than the widely used “pos-itive correlation” test. Moreover, it is possible toimplement this test without the rich data onsubjective beliefs available in the HRS. Specif-ically, the econometrician can reject the nullhypothesis of symmetric information if, condi-tional on the information used by the insurer insetting prices, she observes some other charac-teristic of the individual that is correlated withboth insurance coverage and ex post risk occur-rence that is unknown (or unused) by the in-surer. There are many examples of informationnot priced by insurance companies that theeconometrician may observe in survey data,such as wealth which is not priced for annuities,occupation which is often not priced for autoinsurance, and preventive health measureswhich are often not priced for health insurance.These types of disparities between the infor-mation collected and used by the insurancecompany and that available to the econometri-cian suggest that this test may find widespreadapplicability.

APPENDIX A: THE AHEAD SAMPLE AND

VARIABLE DEFINITIONS

Sample definition: Our sample is drawn fromthe original AHEAD cohort of the HRS. TheAHEAD is a representative sample of individ-uals born in 1923 or earlier, and their spouses.The AHEAD respondents were interviewed in1993, 1995, 1998, and 2000. We restrict ouranalysis to data from 1995 to 2000, as 1995 isthe first year in which we have a reliable mea-sure of long-term care insurance (see below).We exclude the 3 percent of original respon-dents who were in a nursing home in 1995. Wealso exclude from our analysis the approxi-mately 13 percent of the 1995 respondents forwhom the interview was completed by a proxy

respondent; these individuals are not asked thequestion about self-reported beliefs of nursinghome use that is central to our analysis. Ouranalyses that do not use this beliefs variable arerobust to including the proxy interviews (seeFinkelstein and McGarry, 2003, for these re-sults). Non-death (i.e., “real”) attrition is justover 4 percent from 1995 to 2000. All of ourestimates from the AHEAD data are weightedusing the 1995 household weights.

Measuring long-term care insurance: We mea-sure individuals’ insurance coverage in 1995,the first wave for which reliable information isavailable. Our indicator variable LTCINS iscoded 1 if the individual answers yes to thefollowing question:

R15: Aside from the government pro-grams, do you now have any insurancewhich specifically pays any part of long-term care, such as personal or medicalcare in the home or in a nursing home?

Although a few papers have used answers toquestions about long-term care insurance in the1993 wave (see, e.g., Frank A. Sloan and Ed-ward C. Norton, 1997, or Jennifer M. Mellor,2001) we are uncomfortable with this measure.In that year the survey asked specifically abouta variety of types of health insurance and thenasked if the respondent had any (other) type ofinsurance:

R6. Do you have any (other) type ofhealth insurance coverage?R7. What kind of coverage do you have?Is it basic health insurance, a supplementto Medicare (MEDIGAP) or to otherhealth insurance, long-term care insur-ance, or what?

The question thus does not specifically targetlong-term care insurance coverage. It yields anestimated coverage rate of just over 2 percent,substantially below what other analyses haveindicated for this time period. By contrast, thereported coverage rate using the 1995 measure(10 percent) matches other existing estimates(see, e.g., Cohen, 2003, and citations therein).Our concern about the accuracy of the 1993long-term care insurance measure was corrobo-rated in email correspondence with David Weir,Assistant Director of HRS (April 2002).


Construction of Some of the Health MeasuresCollected by Insurance Companies

Cognition: We follow Kahla M. Mehta et al.(2002) who work specifically with AHEAD anddefine an individual as cognitively impaired ifhe has a score of 8 or less (out of 35) on theTelephone Interview for Cognitive Status (TICS).

Depression: We again follow Meta et al.(2002) and define depression as a score of 3 orgreater (out of 8) on the CES-D8.

Drinking problem: We define a drinking prob-lem as 3 or more drinks per day.

Assets: Household assets are defined as totalbequeathable assets (including housing wealthbut not Social Security or defined benefit pen-sion wealth) less debts.

APPENDIX B: THE POSITIVE CORRELATION TEST

APPLIED TO PROPRIETARY COMPANY DATA

An alternative way of implementing the pos-itive correlation test that more closely mirrorsthe existing literature is to use administrativedata from a specific insurance company on thecontracts chosen by individuals and their expost risk experience. Such data provide moredetailed information on the coverage choicesmade than is available in the AHEAD. These datahave the added advantage that all individuals facethe same set of product choices, at least within thecompany studied, and the risk classification andpremium assigned to each individual can be ob-served directly. We therefore obtained such adataset and verified that, as in the AHEAD data,there is no evidence of a positive correlation be-tween insurance coverage and risk occurrence inthe insurance company data.

Our data consist of all private long-term careinsurance policies sold by a large U.S. privatelong-term care insurance company from Janu-ary 1, 1997, through December 31, 2001. Wealso observe all claims incurred through De-cember 31, 2001. The company is among thetop-five companies in this market.

Although these data come from a single com-pany, they appear comparable to the broadermarket on a variety of dimensions. These in-

clude the average age at purchase, the gendermix of the purchasers, the average daily benefit,and the average length of the benefit period.27 Inaddition, this particular company has experi-enced similar growth rates in policy sales to theindustry as a whole over our sample period(Life Insurance and Market Research Associa-tion, 2001). Finally, the company follows thestandard risk classification practices of the in-dustry (see, e.g., American Council of Life In-surers, 2001; Weiss, 2002), and varies thepremium based on the date of purchase, theindividual’s age at purchase, and three health-based risk classifications: preferred, standard, orsubstandard. However, there are a few dimen-sions along which the company differs from theindustry average. Almost all of the policies soldcover both home care and nursing home care,whereas in the industry as a whole only aboutthree-quarters of recent policies do (HIAA,2000b). In addition, the policies tend to havelarger deductibles than industry averages.

To test the positive correlation prediction, weexamine the relationship between the quantity ofinsurance purchased and subsequent nursinghome utilization. Long-term care policies typi-cally have a deductible equal to a specified num-ber of days. The relevant risk for the insurancecompany is the risk that the individual stays in anursing home beyond the length of the deductible;we observe nursing home use in these data only ifit exceeds the length of the deductible and resultsin a claim. The modal deductible in the sample is100 days. We therefore define a “failure” in ourhazard model as at least 100 continuous days ofnursing home care and restrict the sample to the94 percent of policies that have a deductible of100 days or less (and were issued at least 100 daysbefore the end of the sample period). Of oursample, 87 percent have a deductible equal toexactly 100 days. The average failure rate in oursample, 0.3 percent, is quite low, but is consistentwith market-wide and population statistics onrates of nursing home utilization of 100 days ormore (Society of Actuaries, 1992, 2002).28

27 Finkelstein and McGarry (2003) provide summarystatistics for these data in Table 1. HIAA (2000b) providescomparable industry-wide statistics.

28 Conditional on entering a nursing home, stays of morethan 100 days are quite common (Dick et al., 1994; Kemperand Murtaugh, 1991; and Murtaugh et al., 1997).


We estimate a proportional hazard model ofthe relationship between policy characteristicsand a measure of nursing home utilization (thefailure rate):

(4) ��t, xi , �, �0� � exp�x�i��0�t�.

The proportional hazard model assumes that thehazard at time t, �(t, xi, �, �0), can be decom-posed into a baseline hazard �0(t) and a “shiftfactor” exp(x�i�) which represents the propor-tional shift in the hazard caused by the vector ofexplanatory variables xi with unknown coeffi-cients �.

Specification of the baseline hazard �0(t) is akey issue in estimating models like (4). FollowingDavid Cox (1972, 1975), we estimate a continu-ous-time, semi-parametric, partial-likelihood pro-portional hazard model. This method allows usto estimate the � coefficients without imposingany parametric assumptions about the form ofthe baseline hazard function �0(t), which is par-tialled out of the estimation equation. Themodel therefore produces a globally concaveand well-behaved likelihood function. Right-censoring is easily handled in this framework.To control for the insurance company’s riskclassification, we include indicator variables forissue year, rating category, and issue age.29

Finkelstein and Poterba (2004) show that se-lection can occur along many dimensions of aninsurance contract. We therefore include mea-sures of each of the four main policy character-istics that determine the quantity of insurance inthe contract. These are: (a) the deductible, (b)the total number of days for which benefits maybe received over the lifetime of the policy(“benefit period”), (c) the maximum amount ofincurred nursing home care expenditures thatthe policy will reimburse per day in care (“max-imum daily benefit”), and (d) the degree ofescalation of the nominal maximum daily ben-efit (“benefit escalation”). The positive correla-

tion property predicts that the hazard rate shouldbe increasing in the benefit amount, the benefitperiod, and the amount of benefit escalation, allof which increase the amount of insurance in thecontract, and analogously, decreasing in the sizeof the deductible. We also control for the remain-ing policy features (see notes to Appendix Table B).

The first two columns of Appendix Table Breport results for the entire sample of policies.Some of these policies have been in effect for anextremely short period of time. In principle, thisshould not present an issue for our estimationsince the assumption of the proportional hazardmodel is that the covariates affect the baselinehazard multiplicatively. Nonetheless, to investi-gate whether our results are affected by the lengthof the panel, the next pair of columns shows thatthe results are quite similar if we restrict the sam-ple to the approximately one-third of policies is-sued in 1997 or 1998, all of which have betweenthree and five years of exposure.

The top portion of the table shows the esti-mated coefficients for issue age and rating cat-egory, which reflect the insurance company’srisk-categorization. These variables are all sta-tistically significant. As expected, the hazardrate increases monotonically with both issueage and risk categorization, and pairs of adja-cent issue age categories or rating categories arestatistically significantly different from eachother.30

The remainder of the table reports the coeffi-cients on the covariates used to test the positivecorrelation property; the predicted sign for eachcovariate is summarized in the right-most column.There is little evidence to support the positivecorrelation prediction. The coefficients on the ben-efit escalation and benefit period variablestend to have the opposite sign from what ispredicted. The coefficients on the deductibleand daily benefit variables typically have theexpected sign, but the estimated effects arealmost uniformly insignificantly differentfrom zero and the magnitudes are quantita-

29 For ease of presentation, we include indicator vari-ables for age in five roughly equal-size bins correspondingto less than 60, 60–64, 65–69, 70–74, and 75�. Includingseparate indicator variables for each age rather than five-year intervals does not affect the coefficients of interest. Wedo not directly control for the premium because we havecontrolled for all of the characteristics of the individual andthe policy that determine it.

30 The precision of our estimates, and specifically ourability to detect these statistically significant differences inthe hazard rate across issue age and rating categories, helpsalleviate any concerns that the failure rate may be too low toprovide sufficient power to identify significant differencesin the hazard rate across the covariates of interest, shouldthey exist.


APPENDIX TABLE B—HAZARD OF RECEIVING NURSING HOME CARE FOR HUNDREDTH CONSECUTIVE DAY

Covariates in regression

Policies issued 1997–2001

Policies issued 1997 or1998

Prediction of “positivecorrelation” propertyCoefficient

Standarderror Coefficient

Standarderror

Issue age categoryAge 60 (omitted) — — — —Age 60–64 1.199*** (0.423) 1.039** (0.505)Age 65–69 1.729*** (0.423) 1.798*** (0.475)Age 70–74 2.944*** (0.400) 2.928*** (0.469)Age 75� 4.010*** (0.403) 3.913*** (0.473)

Rating categoryHigh risk (omitted) — — — —Rated standard risk �0.535*** (0.175) �0.562*** (0.200)Rated low risk �1.100*** (0.259) �0.964*** (0.322)

Deductible100-day deductible (omitted) — — — —60-day deductible 0.024 (0.208) �0.030 (0.252) Positive

20-day deductible

0.233 (0.238) 0.312 (0.268) Positive and larger thancoefficient on 60-daydeductible

Daily benefitDaily benefit � $100(omitted)

— — — —

Daily benefit � $100 0.095 (0.127) �0.007 (0.141) Positive

Daily benefit � $100

0.240* (0.134) 0.143 (0.151) Positive and larger thancoefficient on $100daily benefit

Benefit period1–4 years, no extension(omitted)

— — — —

1–4 years, possibleextension

�0.306 (0.207) �0.509** (0.254) Positive

5� years, no extension �0.391** (0.162) �0.543 (0.193) Positive

5� years, possible extension

�0.160 (0.343) �0.257 (0.389) Positive and larger thancoefficient on “5�years, no extension”

Unlimited

0.168 (0.153) 0.075 (0.175) Positive and larger thancoefficient on “5�years, possibleextension”

Escalation of benefits“Index option” (omitted) — — — —5-percent compoundescalation

�0.102 (0.236) �0.254 0.288 Negative

5-percent “simple”escalation

0.111 (0.131) 0.016 (0.154) Negative and less thancoefficient on 5-percent compoundescalation

No escalation0.335 (0.333) — Negative and less than

other coefficients

Failure rate 0.3% 0.6%N 144,798 49,888

Notes: Estimates from a Cox proportional hazard model. Failure defined as at least 100 days of continuous nursing home use.Also included are: indicators of issue year, whether the policy is tax qualified, and frequency of policy premium payments.All covariates shown in table are indicator variables. Daily benefit categories were chosen to divide the sample intoapproximately equal-sized groups. Indicator variables to measure the benefit period distinguish among benefit periods of 1–4years, 5� years (but finite), and unlimited; policies with finite benefit periods are further distinguished by whether benefit canbe extended under certainty circumstances. Indicates for the four possible benefit escalation options are (in order of increasinggenerosity): constant nominal benefits, increases of 5 percent per year of the original benefit (“simple” escalation), 5 percentper year compounded (“compound” escalation), and the greater of 5 percent compounded annually over three years orCPI-growth over the last three years at the option of the policy holder (“indexed”).


tively unimportant. For example, the changein hazard rate associated with a 20-day de-ductible compared to a 100-day deductible(which is the largest right-signed coefficient)is not only statistically insignificant but isalso substantially smaller than the change inhazard associated with any five-year increasein issue age.

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