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Forum for Health Economics & Policy

Volume 12, Issue 2 2009 Article 3

(HEALTH ECONOMICS)

Health Insurance Demand and the Generosity

of Benefits: Fixed Effects Estimates of the

Price Elasticity

Paul D. Jacobs

Congressional Budget Office, [email protected]

Copyright c2009 The Berkeley Electronic Press. All rights reserved.


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Health Insurance Demand and the Generosity

of Benefits: Fixed Effects Estimates of the

Price Elasticity

Paul D. Jacobs

Abstract

This paper explores a central question in health economics: How sensitive is worker demandfor health insurance? After controlling for variables omitted in other analyses, such as the gen-

erosity of plan coverage and aspects of worker demand that are constant within firms over time, I

estimate a price elasticity (between -0.014 and -0.017) which is smaller than previous estimates.

The analysis also finds that employees are more likely to take-up policies with greater insurance

protection from hospital expenses, but not for increased coverage for prescription drug or provider

office visit expenses. Taken together, increases in worker-paid premiums explain about 60 percent

of the fall in take-up of employer policies over time, whereas increases in insurance cost-sharing

explain about 10 percent of that change. Changes in employer contributions for health insurance

had a limited effect on take-up compared with the amounts employees paid out-of-pocket for pre-

miums. An implication of these findings is that policies which attempt to subsidize employee-paid

portions of the premium would be an expensive and potentially ineffective strategy for achieving

greater coverage, particularly if the quality of that coverage is not perceived as worthwhile.

KEYWORDS: insurance demand, coverage, take-up, out-of-pocket premiums, cost-sharing, mea-

surement error, fixed effects, actuarial value

As my dissertation committee chair, Thomas Hertz generously provided support and econometric

expertise throughout the development of this paper. Jonathan Gruber, also a member of my com-

mittee, contributed valuable insights for which I am very grateful. This paper was based on data

from the Kaiser Family Foundation, which I thank for allowing access to several years of their Em-ployer Health Benefits Survey. Gary Claxton and Bianca DiJulio in the Health Care Marketplace

Project of the Foundation were helpful and encouraging colleagues who taught me a great deal

about the survey. Finally, I owe an incredible debt to Martha Heberlein for reviewing numerous

earlier drafts of this paper. The analysis and views expressed in this paper are those of the author

alone and should not be interpreted as those of the Congressional Budget Office.


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1. IntroductionEmployer-sponsored health insurance is the predominant source of healthinsurance coverage in the United States. In 2001, 81 percent of workers werecovered by an employer or union plan, but by 2005 this figure had fallen to 77percent. Increasingly restrictive employee eligibility requirements and a rollbackin the number of employers who offered health insurance precipitated most of thisdecline. However, a quarter of the fall a decrease in coverage of about onepercent of all employees in the United States can be attributed to an increasingnumber of employees who refused employer offers of insurance (Clemans-Copeand Garrett, 2006). One explanation of this trend may be the increasing cost ofemployer health insurance: a recent study of Californians showed that 62 percentof all uninsured workers who were offered insurance by their employersperceived the cost of their employers offers to be unaffordable (Brown et al.,2007).

This paper measures the sensitivity of workers to changes in their out-of-pocket (OOP) and employer-paid premiums by calculating the effect of thesechanges on employee take-up of health insurance.

One innovation of this paper is the extent to which some of the decline incoverage can be attributed to simultaneous changes in the actuarial value (referredto below as plan benefit generosity) of health insurance offers by employers.Insurance products are designed to protect the insured from the risk of uncertainlosses. When the costs for accessing health services increase (e.g. increasingdeductibles or copayments for services), the plans coverage for a given set ofhealth services is less valuable, and therefore individuals may be less willing to

take up coverage. Since employers may change the required OOP contribution toparticipate in insurance coverage at the same time that the generosity of thatcoverage changes, price elasticity estimates that ignore generosity may be biased.

Another innovation of this paper is methodological: I estimate a priceelasticity using two econometric techniques that are uncommon in the previoushealth insurance demand literature: 1) by using firm-level fixed effects I addressthe issue of omitted variables bias; and 2) by adding a measurement errorcorrection, I reduce the effect of such errors, which are exacerbated when usingfixed effects. Thus, this paper addresses the attenuation bias due to measurementerror that is likely prevalent in previous estimates, while additionally controllingfor aspects of worker demand that are often unobserved in firm-level data such as

socio-economic characteristics (e.g., their gender, age, or educational attainment),and availability of non-firm sources of coverage (i.e. coverage through a spouseor through public insurance programs).

Economists and policymakers are interested in the extent to which workersrefuse offers of employer health insurance because of costs. After deriving new

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Jacobs: Health Insurance Demand and the Generosity of Benefits

Published by The Berkeley Electronic Press, 2009


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estimates of this price elasticity, I relate them to health policies for increasingcoverage. Accurate estimates of sensitivities to price and benefit generosity areuseful for designing subsidy schedules and benefits packages for plans proposed

in federal or state health insurance expansions.Section 2 reviews some of the previous research on the price elasticity of

health insurance. Sections 3 and 4 discuss the dataset and the empirical model.Section 5 presents results and discusses their sensitivity to measurement error.Section 6 concludes.

2. Previous EstimatesDemand elasticity estimates are a popular topic in empirical health economicsresearch. Elasticity coefficients are commonly estimated as the response ofworker take-up to changes in premiums. Take-up is typically defined as a binaryvariable at the individual level indicating whether the employee accepts an offerof employer insurance, or at the firm level as a continuous variable denoting theproportion of workers who enroll in an employers health plan among thoseeligible for such coverage.

Prior estimates of the price elasticity of employer-sponsored coveragemostly find significant, albeit small, responses of take-up to OOP premium costs,but may be subject to omitted variables bias.1 Because most surveys collect eitherfirm-level or household-level data, but not both, the possibility of bias often existswhen factors relevant to a workers decision to accept firm-based coverage are notincluded as controls. Examples of such omitted variables in firm-level surveysinclude the composition and characteristics of the workforce and the insurance

coverage options available to workers from non-employer sources. If thesefactors are correlated with total premiums or the portion of the premiumemployers decide to charge for coverage (the direct price workers face to take upcoverage), but omitted in the specification, then elasticity estimates arenecessarily biased.

The most relevant study of the price elasticity of employer-sponsoredhealth insurance was an analysis of firm-level take-up data by Cutler (2003),which also used the Kaiser Family Foundation/Health Research and EducationalTrusts (KFF/HRET) Annual Survey of Employer Health Benefits (EHBS).Cutlers results suggested employees mostly respond to out-of-pocket premiumcosts, but he also found a significant effect for the full value of the policys

premium (the employer plus employee shares). The elasticities of take-up with

1. Such a small price response can still help to explain a large proportion of the reductionin take-up, since health premium growth consistently exceeds inflation and other price indicators.Health insurance premiums have increased a cumulative of 78 percent from 2001 to 2007 (KaiserFamily Foundation/Health Research and Education Trust, 2007).

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respect to premiums implied by his results range from -0.03 using ordinarily leastsquares (OLS) to a preferred estimate of -0.09 using an instrumental variablesapproach. To assuage the concern that omitted variables associated with worker

characteristics may bias the OOP premium coefficient, Cutler argued that thiscoefficient was stable after adding several firm-level controls. This argumentdoes not fully address the bias because there may be additional factors whichinfluence take-up that are related to both worker preferences for insurance andhow employers set OOP premium rates, and which do not appear in Cutlersestimates. To address this potential endogeneity, Cutler also used state variationin marginal tax rates as an instrument for health insurance premiums. However,this approach has been criticized because higher state income tax rates mayencourage firms to offer health benefits and thus would be related to workerdemand for insurance.

Other estimates of take-up elasticities have also found a weak sensitivity

to premiums among workers. An implication of such studies is that subsidies tothe costs of employer health insurance may not substantially increase the numberof persons covered. One set of estimates by Chernew et al. (1997) ranged from-0.033 to -0.095 depending on the portion of the demand curve along which theelasticity was estimated. Similarly, using a household survey linked withinformation on premium costs and plan offerings by employers, Blumberg et al.(2001) found that out-of-pocket premiums were more significant than totalpremiums, but overall the elasticity was also small (-0.04). Gruber andWashington (2005) used a unique natural experimental where OOP premiumschanged several times for federal employees over the course of several years, andfound a small price elasticity (-0.02), and a high degree of substitution between

plans offered by the same employer when plan prices increased.

3. DataSix years of the EHBS surveys from 2001 to 2006 were pooled to form the datafor this analysis. These surveys focus on employer and employee characteristics,plan eligibility and participation, premiums and premium sharing betweenemployees and employers, and the cost-sharing and benefits of employersponsored plans. Each year the sample is randomly drawn from Dun & BradstreetCorporations list of private and public employers which have three or moreworkers. The survey is stratified to produce sufficient samples for specificindustry and firm size categories. Survey weights are constructed to matchindustry and firm size totals reported by the U.S. Census Bureaus Statistics ofU.S. Businesses. Because the Dun & Bradstreet list is extensive and regularlyupdated and the EHBS sample is randomly selected, the survey is effectively

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representative of the distribution of U.S. businesses in the United States in aparticular year.

Depending on the year, the response rate for the EHBS surveys used for

this paper ranged between 48 and 50 percent. A firm was included in the paneldataset constructed for this paper if the firm was interviewed in more than oneyear of the six EHBS cross-sections, forming a final sample of 8,752 firm-yearobservations from 2,426 firms (an average of 3.6 observations per firm). Firmsare eligible for the panel portion of each years EHBS if they have 10 or moreemployees and if they completed one of the last two prior years EHBS surveys.

Survey weights were not used in the regressions below. If a coefficient isrelatively stable across population units, and a single coefficient is of interest,researchers are usually advised to ignore sampling weights, which is the case inthis analysis.

2However, while the EHBS is designed to be nationally

representative, there are reasons to believe that the panel of firms used in this

analysis is not truly representative. Only firms with 10 or more employees formthe panel portion of the survey. In addition, a firms decision about whether toparticipate in the survey may be related to characteristics associated with theiremployees demand for health insurance. To address this concern, a re-weightingmethod was performed to adjust regression coefficients for possible attrition bias.This correction yielded nearly identical estimates to those derived withoutcorrecting for this possible source of bias, indicating that the results below are notsignificantly different from those that would be obtained using the nationallyrepresentative sample.3

To further gauge the representativeness of the dataset used in this paper, Ialso compared the distribution of workers by industry and firm size with Bureau

of Labor Statistics data from the Current Population Survey (2007). For mostindustry categories (transportation/utilities, manufacturing, wholesale/retail,financial, and services) the differences were small and not usually greater than afew percentage points. The distribution of firm size was also very similar; theonly difference being the percentage of firms with more than 1000 workers (theEHBS sample used in this paper shows 54 percent versus about 48 percent in theCurrent Population Survey).

2. In the fixed effects results, interaction terms between premium levels and firmcharacteristics were insignificant, partially justifying the assumption of a homogenous elasticityacross observations. (Deaton, 1997) Further, the elasticities implied by regressions with and

without survey weights were not statistically different.3. The correction factor is the ratio of the predicted probability of attrition constructed

from the independent covariate of interest (in this case the OOP premium variable discussedbelow) to the predicted probability of attrition given that covariate as well as one or moreregressors thought to predict attrition but excluded from the original equation. The choice ofexclusion may result from choice of specification, or for example, if variables would beendogenous if included (Fitzgerald et al., 1998; Hertz, 2007).

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For most of the survey years used, the EHBS collects information on up tofour plans, one for each type in each firm: conventional, preferred providerorganization (PPO), health maintenance organization (HMO), and point-of-

service (POS) plans.4 This unique structure enables analyses of the characteristicsof and enrollment in each plan type. However, to derive unique estimates forcertain key variables, EHBS statisticians have devised firm-level worker-weighted averages of the plan types offered in each firm. To test the effect ontake-up of OOP and total premiums, two of these variables are used below: 1) theweighted-average of the monthly OOP premium (WAOOP) for single personcoverage; and 2) the weighted-average of the total monthly premium for singlecoverage (WAPR), where the weight for both is the percentage of workersenrolled in each plan type (HMO, PPO, POS, etc.).

5Most of the results discussed

below use the OOP premium values for single person coverage rather than forfamily coverage. In practice, both may affect a workers decision to take up

coverage, and thus the results for family premiums are also discussed below.Table 1 shows summary statistics for the variables used for both the

pooled cross-sectional OLS and fixed effects regressions. The summary statisticsfor the cross-sectional data are weighted by the number of employees. For thecross-sectional regressions, categorical variables are used to capture the effect ofregion (West, Midwest, and South compared with the Northeast), industry(compared with Government (not shown)), firm size (Medium: 51-300 workers,Large: 301-1000 workers, Very Large: 1001-5000 workers, and Jumbo: 5001+workers compared with Small firms with between 10 and 50 workers) and ability-to-pay (firms that have less than 10 percent low-earnings workers or 10-25percent low-earnings workers compared with firms that have more than 25

percent low-earnings workers).6 Firm size is included because it is negativelyrelated to the size of the loading factor employers face, i.e., the costs of coveragein excess of the cost of benefits. (The significance of unionization on take-up wasalso tested, but only for the years 2002 through 2006 since union status was notincluded in the 2001 survey.) In the fixed effects regressions, I use continuoustime-varying variables (number of employees and its value squared andpercentage of low-earnings workers and its value squared) to capture the within-firm variation for these controls (lower panel of table 1).

4. The EHBS also collects information on high-deductible health plans, but theiremergence in recent years means that a six-year comparison of such information could not be

made.5. An alternative approach, using the plan type with the lowest monthly OOP premium

for single coverage (MINOOP), is also discussed below although resulting estimates were nearlyidentical. The minimum premium among plans offered is a potentially good predictor of take-up

because, for workers deciding whether to take up employer insurance, an alternative source ofcoverage, or go uninsured, the lowest-priced plan is likely to be an important alternative.

6. The low-earnings category is defined as a workers making less than $20,000 a year.

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Table 1. Summary Statistics for Cross-sectional OLS and Fixed Effects

Equations, KFF/HRET, EHBS, 2001-2006

Summary statistics for OLS equations (worker weighted)

Variable Obs. Mean Std. dev. Min Max

Take-up (dependent variable) 8749 0.88 0.13 0 1

MINOOP (per month) 8749 37.74 39.53 0 c

WAOOP single (per month) 8749 43.37 40.97 0c

WAOOP family (per month) 8728 203.06 151.86 0 c

WAPR (per month) 8749 291.63 89.21 50 c


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To approximate benefit generosity, the cost-sharing features used in thispaper include many of the plan characteristics that determine how much enrolleeswould pay for medical goods and services, including: deductibles, co-insurance

payments and percentages, and out-of-pocket maximum limits (which serve as anupper limit to an individual or familys exposure to medical spending). Toapproximate generosity using a single measurement, I calculated the percentageof a typical medical bill that the insurer would pay for various categories ofmedical expenses. Table 1 shows these variables: the percent (%) of the averagedoctor, hospital, or prescription drug (Rx) bill that the insurer would pay. Theseproxies for plan generosity were designed to measure the degree of financialprotection the plans would provide for a typical medical bill.7 The cost-sharingquestions used to construct generosity proxies were consistently available for the2004 through 2006 surveys. Thus, the analytical results which include insurancegenerosity as a covariate are reported separately from the 2001 through 2006

results. Because the EHBS collects information on each of several plan types, agenerosity measure was constructed for each of the three major plan types (HMO,PPO, and POS). The maximum generosity value among a firms plan types wasused to approximate the generosity of coverage for prescription drugs, hospitalpayments, and office visits for the firm.

4. Empirical MethodsThe analysis below measures health insurance demand elasticity as the percentagechange in health plan take-up with respect to a percentage change in the averagehealth insurance premium within a firm. Unlike conventional goods, the price ofhealth insurance coverage can be measured in several ways. The followingsections discuss, in order, which price variables are used, the empirical strategy toestimate their effect on take-up of coverage, and adjustments that are made formeasurement error in the collection of premium data.

4.1 Which Price?When measuring the demand elasticity for health insurance, there are severalchoices for the appropriate measurement of price for an employee purchasing

7. Typical medical expenses were defined as the mean medical expenditures incurred byall individuals with a given type of expenditure in 2004. These values were $779 for physicianoffice visits, $1,037 for prescription drug expenses, and $13,687 for in-patient hospital expenses.These values serve as baselines to compare the cost-sharing features of plans, and they arearbitrary to the extent that one could have chosen any value in excess of most individuals cost-sharing limits to derive relative variation in the percentages paid by insurance plans (Agency forHealthcare Research and Quality, 2004).

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coverage through his/her employer. Employees may view either the totalpremium (employee plus employer shares) or rather their own contribution, orsome combination of the two, as the relevant price.

The primary reasons workers demand health insurance benefits are toreduce their exposure to potential medical costs and to gain access to health careproviders. Most firms charge OOP payments for health coverage partly todiscourage workers who do not value the benefit from enrolling. (They may alsocharge different premiums among their plan choices to encourage enrollment incertain plans or to encourage their workers to take up non-employer healthbenefits, etc.) This paper will test how sensitive workers are to changes in theOOP premiums they must pay to enroll into a health plan.

Even when employee OOP premium levels do not change, increases intotal premiums could cause lower take-up if workers no longer find coverageworthwhile at that price, and are influenced by the amount their employers pay for

premiums. When fringe benefit costs increase, wages typically fall whenproductivity is held constant, and employees may prefer increases in earnings toincreases in benefits. However, increases in total health insurance costs couldalso cause higher take-up, other factors remaining constant. Higher totalpremiums often imply the aggregate cost of medical care treatments areincreasing, and thus the worker is exposed to greater potential health care costs ifthey choose not to insure (Cutler, 2003). If workers are risk averse, increasinghealth care costs (and subsequently higher premiums) may be associated with ahigher likelihood to insure.

Empirically, nearly all of the studies reviewed above find that the OOPportion of the premium negatively affects the decision to take up, and that the

effect of the total or employer portions of the premium is insignificant or weaklypositive (e.g., Chernew et al.). The analysis below tests the effect of both prices the OOP portion of the premium paid by workers and the employer portion of thepremium. While the sign of the OOP coefficient is expected to be negative orzero, the predicted sign for the total premium, as outlined above, is ambiguous.

4.2 Empirical ModelTo accurately measure the effect of price on take-up, this paper accounts fordeterminants of take-up which have not been addressed in prior studies. Usingfirm-level fixed effects, this paper controls for the influence of time-invariant

demographic characteristics which are often unavailable in firm surveys andwithout which elasticity estimates would be biased. These factors include theoccupation, race/ethnicity, educational level, and gender mix of a firmsworkforce, which are assumed to be constant over the shorter time periods studiedin this paper. Other time-invariant factors controlled for using this technique

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include: managerial policies which might influence worker take-up, as well asfactors relating to competition for a firms labor force. To the extent that otherfactors are relatively constant within a firm over time, this approach also

addresses differential worker access to coverage from outside the firm. Thesemay include employer offers of coverage for spouses, or through eligibility forpublic programs, such as Medicaid, the State Childrens Health InsuranceProgram (SCHIP), or Medicare, which may bias coefficients, particularly ifemployers change OOP premiums in response to changes in the availability ofthese options.

Of course, a fixed effects specification is not a panacea for omittedvariables bias. While the influence of time invariant factors is removed, otherfactors may change over time which could be correlated with worker demand foremployer health benefits. One such factor is changes in worker or dependenteligibility for Medicaid or SCHIP. Indeed, in response to economic or budgetary

pressures, states have adjusted eligibility levels and enrollment procedures duringthe same years which were used in the analysis for this paper. An employer mightalso change OOP premiums over time because premiums rose as the health ofsome workers worsened or as workers aged. Since such trends are also likely tobe correlated with worker demand for benefits, price coefficients which use intra-firm heterogeneity would also be biased.

While these factors are undoubtedly important, many of them are arguablystable over relatively short time periods, and specifically the short time framesover which most firms are observed in the EHBS. Also, while firms certainly canand probably do react to such changes, they may not be able to do soimmediately. Firms usually set their benefit policies once a year, reducing the

speed with which they can react to changes in the competitive or policyenvironments. Further, the average number of years that a firm is followed in thesample used in this paper is 3.6 years which implies that, on average, firms wouldhave had 2 or 3 chances to change benefits in response to changes in the policy orcompetitive environments. Anecdotal evidence suggests that firms are lesswilling to make extreme changes to benefits packages over short time periods.This, in combination with the short length of time over which the EHBS paneltracks firms, suggests there is a limited degree to which public coverage eligibilitychanges or employee turnover could affect a firms decision to change benefits.Furthermore, since most of the variation in the demographic mix and thecompetitive and state policy environments is likely to be between firms rather

than within firms over time, a fixed effects model will improve the elasticityestimate over one from an ordinary least squares model.

Recognizing that past research finds the OOP portion of premiums to bethe relevant margin, the empirical model begins with this test. Following Cutler, I

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first present a model of take-up for firm-year observations in the panel samplewithout fixed effects:

(1) TUit= 0 + 1WAOOPit+ Xit+ itHere TUit is the take-up rate (the percentage of eligible employees in the firm whoenroll in any plan offered by the firm) of firm i in time period t, and WAOOPit isthe weighted average over the firms plan types of the workers portion of themonthly premium for single coverage, which corresponds most closely to a singlefirm-level measurement of OOP costs for workers. Included inXit are controls forthe size of the firm, the ability-to-pay of the workforce (measured as thepercentage of workers in the firm with earnings below $20,000), indicatorvariables for the industry and region of the firm, the survey year, and, for aseparate estimation on the latter three survey years, the benefit generosity of plans

offered. The error term, it, consists of unexplained variation in take-up in thecross-sectional results discussed below.

The variables inXit control for observable differences between and withinfirms in worker demand for health insurance. However, it will also includedemographic and other characteristics of a firms workforce which are likely to besystematically related to the WAOOP variable and, if so, would influenceemployee demand for insurance. Ordinary least squares estimates of (1) wouldthen be biased. To address this, I first decompose the error term into firm-levelcharacteristics of health insurance demand and a random error term:

(2) it= i+ eitThe inclusion of firm-specific intercepts, i, removes firm-level components ofworker health insurance demand if (1) is estimated using firm-level fixed effects.Variation in take-up is then estimated from variation in firm-level employee oremployer premium costs, and results in an unbiased estimate of the take-upelasticity, where the subscript a variables denote inter-temporal, firm-specificmeans8:

(3) TUit- TUai= 1(WAOOPit- WAOOPai) + (Zit Zai) + (eit eai)Inter-temporal variation in WAOOPshould be exogenous to changes in take-up;

the former is mostly caused by the annual growth in medical costs, holding

8. A natural alternative to (3) the random effects estimator was considered, butrejected on the basis of a Hausman test the more consistent fixed effects coefficients weresignificantly different than the more efficient random effects coefficients. The chi-squaredstatistic was 584.94 with seven degrees of freedom (p


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constant other factors such as the health risk of the covered population and thegenerosity of benefits. (The Z matrix is analogous to the X matrix in (1), butincludes only those variables which vary over time within a firm.)

A negative estimate of1 implies employee take-up is negatively relatedto monthly OOP costs. A negative estimate of2, which is used to denote thecorresponding coefficient for the full premium (WAPR), implies a negativerelationship between take-up and total premiums. A positive estimate of 2implies that increased health costs may be inducing more individuals to insure.So far, this model improves on past estimates by: 1) using the fixed effectsestimator to remove the influence of time-invariant, firm-specific factors; and 2)including benefit generosity differences between firms and over time.

If employee preferences for health insurance are negatively correlatedwith firms chosen levels of out-of-pocket premiums, then prior estimates may benegatively biased. For example, this may occur because employee demand for

health insurance is large and either: 1) labor markets are tight, so employers willtend to attract employees with lower OOP payments; 2) employers believecoverage increases productivity and thus want to encourage take-up; 3) employersmay wish to be seen as benevolent and/or they recognize the value theiremployees place in subsidized coverage; or 4) if a firm does not offer a cafeteriaplan where employee premiums can be paid with pre-tax dollars, so whenmarginal tax rates are high, there is more to be gained when employers pay healthpremiums with pre-tax compensation dollars. (Of course, preferences forinsurance and OOP premiums may also be positively correlated if employers raisemonthly OOP levels when individuals have relatively high demand for insurance,which could be the case if the converse of one or more of the above statements

typically holds and this correlation outweighs the strength of any negativecorrelation.) It is also not clear whether employers will charge their employeesmore or less OOP for insurance if they have other, non-firm, health insurancecoverage options. If there are better or more numerous coverage options foremployees, employers may subsidize more of the premium to encourage greatertake-up, or employers may subsidize less of the premium to reduce their costsand/or because employees have a preference for non-firm options. In sum, theomitted variable bias due to missing employee demand characteristics or non-firmcoverage options cannot be signed a priori.

4.3 Measurement Error AttenuationAlthough OLS regressions may be subject to attenuation bias in parameters due tomeasurement error in right-hand side variables, the problem is generallycompounded in panel settings, when reporting or other errors in measurement arenot highly correlated over time (Griliches and Hausman, 1986). In a panel setting

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without a reliability ratio, one method to produce an unbiased estimate is to solvefor the vector by combining parameters from the fixed effects and anotherdifferenced (e.g., first, second, or third, etc.) estimate (Griliches and Hausman).

Another commonly used technique is to find an instrument for the variable that ismeasured with error (Griliches, 1977).

However, if a second measurement of the variable is available, thereliability ratio (denoted ) can be directly estimated (Angrist and Krueger, 1998).This method is employed below to adjust cross-sectional and fixed effectscoefficients, using a second, also mismeasured, estimate of the total premiumreported by firms. The additional measurement used below is derived from aquestion in each years EHBS asking respondents to estimate the percentagechange in their premiums from the previous year. Using the prior years reportedlevel for the premium, WAPRit-1, and one plus the reported percent change in thepremium between periods, gWAPRit, a second estimate of the current years

premium (denoted WAPR2it) can be constructed as follows:

(4) WAPR2it= (gWAPRit) * WAPRit-1This additional estimate, in conjunction with the actual reported level of thepremium in the current year, can be used to approximate the signal-to-noise ratioof variation in premiums.9 This is done by first assuming all premium levels,WAPRit and WAPRit-1, aremeasured with mean zero, white noise errors, denoted:t and t-1. Then, after making a few additional assumptions, the correlationbetween WAPR2itand WAPRitwill result in the reliability ratio:

(5) = corr(WAPRit+ t, gWAPRit*(WAPRit-1 + t-1))Equation (5) reduces to the reliability ratio the ratio of the true variance inWAPRit to its total variance by employing one of the usual measurement errorassumptions (corr(WAPRit, t) is equal to zero), and also by adding the additionalassumptions that: 1) the growth rate, gWAPRit is not measured with error, 2) thecorrelation between growth rates and the error term is zero (corr(gWAPRit* t-1,t)= 0) and; 3) the correlation between premiums and their growth rate is zero (i.e.corr(WAPRit, gWAPRit * t-1) = 0). The first of these additional assumptions is

9. After adjusting the reliability ratio technique for the loss of degrees of freedom in thefixed effects model, this procedure is computationally identical to using the second measurementas an instrument for the first. Practical limitations prevented this latter strategy from beingimplemented. Namely, the second measurement of the premium was only available as aninstrument for particular firm-year observations which had a corresponding lagged premium value.Thus, the instrumental variable results would have only been applicable to a subset of the fullsample.

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justified since this model is primarily designed to capture either the effects ofmeasurement error in premiums or measurement error in the changes in premiumsover time, so it is redundant to simultaneously treat other estimates as also

measured with error. The second is justified on analogous grounds as for thetypical measurement error model where the errors are assumed to be white noiseterms. The third assumption is justified empirically; the intertemporal correlationbetween premiums and their growth rates was only 0.019.

To construct a reliability ratio for fixed effects estimates, percentagechanges in reported premiums (WAPRit-WAPRit-1)/ WAPRit-1 are compared tothe reported percentage change between years, gWAPRit. These two estimates ofthe percentage change in premiums are used to determine the reliability ratio ofdifferenced data in the EHBS, denoted fe. In either the level or difference-from-mean cases, can be estimated as the coefficient in a regression where themeasurement to be used in the ultimate analysis is an explanatory variable for the

measurement which corresponds less-closely (Angrist and Krueger). In this case,the measurements derived from respondent-estimated percentages WAPR2itandgWAPRit are regressed against those derived from reported levels WAPRit and(WAPRit-WAPRit-1)/WAPRit-1, respectively while including all other covariateswhich belong in the final estimation equation.

Estimates of the reliability ratio for WAPR are shown below in Table 2.One assurance of the validity of this approach is that the values in levels anddifferences are comparable to reliability ratios estimated for data in other surveys(Angrist and Krueger). Since there is no second measurement of WAOOP orMINOOP, the estimates of reliability in Table 2 are used as a proxy for thereliability of OOP premium values.

Table 2. Estimates of the Reliability Ratio for Premiums

Type of estimate Reliability ratio for WAPR

Levels (c) 0.716

Differences (fe) 0.404

Source: KFF/HRET, EHBS, 2001-2006

With the reliability ratios in Table 2 for the OLS and fixed effects models,respectively, the measurement error-corrected estimates were calculated bysolving for:

(6) = (XX n )-1 (XTU)

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Where the variance-covariance matrix of the measurement error, , times thesample size, n, is subtracted from the error-ladenXXmatrix, which now includesall covariates for ease of interpretation (Deaton). TUis the take-up vector.

5. ResultsThis section presents the results of both the cross-sectional OLS and fixed effectsestimates of the health insurance take-up price elasticity. The first part of thissection focuses on the results from analyzing the sensitivity of worker take-up toOOP premiums and other covariates. The results are corrected for measurementerror, but mention is also made of non-corrected results, which are comparable toresults from elsewhere in the literature. The second section focuses on resultsrelating to plan generosity. The third section discusses results for the totalpremium as well as several regressions which attempt to separate the causaleffects of OOP and total premiums.

5.1 OOP Premium ResultsTable 3 shows OLS results from estimating the take-up elasticity using six pooledcross-sections (2001 to 2006) of the EHBS without firm-level effects. The OLSmodel using cross-sectional data allows one to see the effect of a wider range ofcovariates since firm-specific characteristics that do not change over time can beincluded. Further, this approach is more efficient than a fixed effects estimatesince the EHBS panel is relatively short and unbalanced there are 2,426 firmsand 8,752 firm-year observations, implying that between one-third and one-fourth

of the degrees of freedom are lost during fixed effects estimation. However,regardless of the greater efficiency of these estimates, they are biased. Thus,fixed effects estimates, presented following the OLS results, are preferred.

As Table 3 shows, in the pooled cross-sectional regression, the firm-leveltake-up of health benefits is negatively related to OOP premiums, as washypothesized at the start. The cross-sectional estimate of the OOP coefficient issimilar (-0.00165 and -0.00172), regardless of whether the weighted-average orminimum OOP plan premium was used as the price measure. These measurementerror-corrected values imply that a single dollar increase in monthly OOPpremiums may decrease the percentage of workers taking up insurance within afirm by about 0.17 percentage points. Using the population means for take-up

and OOP premiums, this coefficient implies an elasticity between -0.08 and -0.09,which is at the higher end of the range of estimates reviewed in the literature.Again, this estimate is subject to potentially large omitted variables bias, andshould be treated with appropriate skepticism.

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Table 3. Results from Cross-sectional OLS Regressions, EHBS, 2001-2006

Variable Weighted avg. OOP Minimum OOP

Coefficient p-value Coefficient p-value

WAOOP -0.00165 0.000 -- --

MINOOP -- -- -0.00172 0.000

=5001 workers) 0.05437 0.000 0.04159 0.000

Mining/construction -0.04235 0.000 -0.03934 0.000

Manufacturing -0.01608 0.008 -0.01549 0.011

Transportation/utilities -0.00571 0.468 -0.00484 0.538

Wholesale -0.02720 0.001 -0.02642 0.001

Retail -0.09405 0.000 -0.09115 0.000

Financial -0.03495 0.000 -0.03631 0.000

Service -0.06076 0.000 -0.06286 0.000Healthcare -0.06450 0.000 -0.06434 0.000

Midwest -0.00620 0.174 -0.00288 0.527

South 0.02727 0.000 0.02878 0.000

West -0.00582 0.263 -0.00593 0.255

Constant 0.86499 0.000 0.86781 0.000

R2 0.23 0.23

Observations 8752 8752


Notes: Excluded variables are 2001 for year, government for industry,northeast for region, and less than 50 workers (small) for firm size.

Coefficients corrected for measurement error in premiums with reliabilityequal to 0.716.

Without correcting for measurement error, the cross-sectional coefficientsfor OOP, which are comparable to other studies, are -0.00113 and -0.00118

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respectively (not shown in Table 3). These measures imply a correspondinglower elasticity of approximately -0.06, which is equal to the median of theestimates from the literature reviewed for this paper, suggesting measurement

error may have attenuated previous estimates.Ability-to-pay is also related to take-up in the cross-sectional estimates

reported in Table 3. Compared to firms with more than 25 percent of theirworkforce making less than $20,000 (relatively less well-paid workers), thosewith 10 to 25 percent low-earnings workers have greater take-up (about 3 to 4percentage points) and those with less than 10 percent lower-earnings workershave take-up rates that are, on average, about 5 points higher. Workers withgreater earnings are more likely to take up health coverage, perhaps because theycan better afford the OOP payments that firms charge, or because higher earningsare correlated with greater wealth or other factors which increase the value ofinsurance. The interaction term between the percentage of low-earnings workers

and the OOP premium was significant (coefficient of -0.000013, p=0.000, notshown). This implies that whereas a $16 per month increase in workercontributions for premiums would cause a 1.4 percentage point decrease in take-up in the average firm, in a firm with 10 percentage points more low-earningsworkers, this same increase in cost would cause a 2.3 percentage point decrease.

Firm size is also correlated with take-up. Compared with smaller firms(those with less than 50 workers) who may have higher administrative costs, offerless generous benefits or a narrower range of plan choices, large firms have take-up rates that are between 4 and 6 percentage points higher. Take-up rates variedby industry, ranging from approximately equal to those in the government sector(transportation/utilities) to 9 percentage points lower (retail), with other

meaningful differences for the healthcare, service, and mining/constructionindustries. Compared to firms in the Northeast, firms in the South had 3percentage points higher take-up. Finally, workers in unionized firms took-upcoverage 1.6 percentage points more frequently than workers in non-unionizedfirms (p


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WAOOPorMINOOPpremium coefficient. Without correcting for measurementerror, the fixed effects coefficient is about a third as large (-0.0001) implying anelasticity between -0.005 and -0.006. Compared with cross-sectional estimates,

fixed effects estimates are about five times smaller in absolute value afteradjusting for measurement error and controlling for potential omitted aspects ofworker demand for insurance. These results suggest that omitted variable bias isindeed a substantial problem in previous cross-sectional OLS estimates of healthinsurance demand.10

Ability-to-pay, as measured by intra-firm deviations in the percentage ofthe workforce who earn less than $20,000 and its square, were both significant(Table 4). The combined effect of these variables implies that for firms with 10percentage points more workers making less than $20,000, they will have take-uprates that are about 0.6 percentage points less. As one would expect, a higherproportion of lower-earnings workers leads to lower take-up of health insurance.11

Table 4 also shows that there is a very small effect on take-up for firmsthat increased in size over time (the coefficients are too small to be visible giventhe significant digits shown in Table 4). Every increase of 5,000 employees in afirm leads to a 1 percentage point lower take-up rate. This result may seemcounterintuitive for the reason that increasing firm size reduces the per capita costof insurance, and because of a potential correlation between firm size and demandfor health insurance benefits. However, firms whose workforces quickly expandmay make some or all of these new employees eligible for insurance, but workersmay take weeks or months to enroll in new plans. Further, new employees mayhave systematically lower demand for coverage than workers already at a job,may have alternative sources of coverage which they prefer to their new firms

offer, or newly-hired temporary workers may have less stable relationships withemployers and/or lower earnings, all of which would lower take-up rates whenfirms expand.

10. Because OLS estimates appear negatively biased, it can be inferred that the omittedvariable (worker demand for health insurance) is negatively correlated with the OOP premiumvariable of interest: firms tend to lower OOP premiums when worker demand for health insuranceis high. This negative correlation indicates that, in this sample of firms, most lowered OOP costswhen demand for health insurance was high.

11. Unlike in the OLS estimates, the interaction between premiums and the percentage oflow-earnings workers in a firm was not significant and thus not shown.

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Table 4. Results from Fixed Effects Regressions, EHBS, 2001-2006

The results of this analysis also suggest workers who support families maybe very insensitive to the prices they pay to cover their spouses and children, and

that changes in take-up of health insurance may be primarily driven by singleworkers. The OOP family premium was a significant predictor of take-up in theOLS but not the fixed effects regressions (not shown). The measurement error-corrected OLS and fixed effects coefficients for the family premium were-0.00026 (p=0.000) and -0.00006 (p=0.119), respectively. The fixed effect resultfor single coverage, which was significant, was more than five times larger thanthat for family premiums (-0.0003 versus -0.00006). This result is not aconsequence of greater noise in the family premium variable; the standard errorfor the single coverage premium was almost three times that of that for familycoverage (0.00011 versus 0.00004).

5.2 Plan GenerosityTable 5 shows OLS and fixed effects estimates of take-up which include benefitgenerosity variables as controls. Due to the smaller sample size, and the shorterpanel (three years as opposed to six), there is a substantial loss in efficiency for

Variable

Weighted average OOP Minimum OOP


WAOOP -0.00031 0.017 -- --

MINOOP -- -- -0.00029 0.026

% low-earnings -0.00059 0.020 -0.00058 0.020

% low-earnings sq. 0.00001 0.018 0.00001 0.019

Employees (#) 0.00000 0.000 0.00000 0.000

Employees sq. (#) 0.00000 0.001 0.00000 0.001

2002 0.00255 0.542 0.00233 0.576

2003 0.00180 0.690 0.00130 0.771

2004 -0.00576 0.237 -0.00660 0.167

2005 -0.00466 0.375 -0.00562 0.2742006 -0.00053 0.927 -0.00187 0.735

Constant 0.87453 0.000 0.87317 0.000

R2 0.01 0.01

Observations 8752 8752


Note: Coefficients corrected for measurement error in premiums withreliability equal to 0.404.

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the fixed effects estimates. Nevertheless, the OLS results in Table 5 show that thegenerosity of hospital coverage was a significant predictor of higher take-up. The0.163 coefficient implies that a 10 percentage point increase in the minimum

amount that a firms insurance plans would pay for a hospital bill results in a 1.6percentage point increase in take-up of health insurance. Although insignificant(p=0.102), a 10 percentage point increase in the share of the prescription drug billthe firms plans would pay also is associated with an increase in take-up (0.64percentage points, derived from a coefficient of 0.064).

Table 5. Cross-sectional OLS and Fixed Effects Results, Including and

Excluding the Generosity of Doctor, Prescription Drug, and Hospital

Coverage, EHBS, 2004-2006

OLS Fixed effects

w/ generosity w/ generosity w/o generosity

Variables Coeff.

p-

value Coeff.

p-

value Coeff.

p-

value

WAOOP -0.00105 0.000 -0.00009 0.276 -0.00009 0.275

% Low-earningsa

a-0.00038 0.049 -0.00037 0.057

Employees (#)a

a0.00000 0.010 0.00000 0.015

% Doctor billinsurer Pays -0.01295 0.601 -0.03341 0.263 -- --

% Hospital billinsurer Pays 0.16298 0.004 0.13576 0.031 -- --

% Rx bill insurerpays 0.06416 0.102 0.05326 0.235 -- --

2005 0.00727 0.112 -0.00298 0.485 -0.00286 0.501

2006 0.01294 0.006 0.00221 0.635 0.00091 0.842

Constant 0.63687 0.000 0.70787 0.000 0.85580 0.000

R2 0.20 0.02 0.02

Observations 4192 4192 4192


Notes: Squared terms for number and percent low-earnings employeesexcluded because they were insignificant. Results not corrected formeasurement error.

aVariable only used in fixed effects regressions.

The middle columns of Table 5 show that worker take-up is sensitive tothe generosity of coverage that employers offer, and specifically to the percent ofhospital expenses covered by a plan. As the fixed effects results show, firms withinsurance plans which paid 10 percent more of the cost of hospital expenses had atake-up rate that was 1.4 percentage points higher. (This coefficient is essentially

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identical to the OLS result for the generosity of hospital coverage.) The findingof greater sensitivity to hospital coverage suggests that more generous coveragefor larger expenses increases the likelihood of insurance purchase. Although

hospital expenses typically occur less frequently than those for prescription drugsor health provider office visits, the evidence in Table 5 suggests worker take up issensitive to the generosity of hospital coverage, rather than to coverage for lessexpensive, but more frequent treatments, such as prescriptions or provider visits.

Another important question is whether the benefit generosity resultschange the interpretation of the elasticity coefficients reported in Section 5.1. Asthe set of fixed effects results in Table 5 show, the coefficient on WAOOP isessentially identical with or without generosity variables. This providescompelling evidence that the absence of plan generosity data does not bias thefull-sample elasticity estimate shown above, unless take-up was differentiallyaffected by plan generosity in particular years.

5.3 Employer PremiumUnlike the results for OOP premiums, which confirm the predicted negativerelationship between the costs employees pay and their likelihood of taking uphealth insurance, those derived using the full premium are less consistent. Table6 shows cross-sectional and fixed effects estimates of coefficients for twocombinations of health insurance premium variables: 1) the weighted averagetotal premium, WAPR (employee plus employer portions); and 2) the weighted-average OOP (WAOOP) and the employer portion of the premium (the differencebetween WAPR and WAOOP).

As found elsewhere in the literature on take-up, the effect of the totalpremium is statistically insignificant from zero, yet weakly positive (the top leftcolumn of Table 6).

12However, as the left column in the bottom panel of Table 6

shows, in the fixed effects equation, WAPRs coefficient is small, only -0.00007,yet negative and statistically significant. The negative sign implies that increasesin the total value of the premium may encourage workers to obtain alternativesources of health coverage or to go uninsured. And perhaps as theory asserts,these workers may decline coverage in order to increase their cash earningsbecause there is a tradeoff between benefits and cash earnings and some mayprefer the latter. An alternative explanation, which conforms with the cross-sectional result where the effect of total premiums was insignificant, is that

increases in the total premium are correlated with increases in the OOP costs

12. Since the reliability ratio for each of these variables was assumed to beapproximately equal (0.716 for cross-sectional estimates and 0.404 for changes over time), theestimates are not corrected for measurement error because these adjustments would be identicalwithin each specification.

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workers pay, which subsequently lowers take-up. Indeed, the correlationcoefficient between annual changes in both OOP and total premiums is 0.33.Since changes in WAOOPand WAPR are highly correlated, and WAOOP is an

omitted variable in the left-hand panels of Table 6, changes in premiums (WAPR)may be affecting take-up primarily through its effect on changes in OOP costs.

Table 6. Comparison of OLS and Fixed Effects Estimates Including Total,

and Employer and Employee Premiums, EHBS, 2001-2006

Variable Total premium

Employee and

employer premiums


OLS (cross-section)

WAPR 0.00002 0.651 -- --

WAOOP -- -- -0.00165 0.000

WAPR-WAOOP -- -- 0.00000 0.926

Fixed Effects

WAPR -0.00007 0.015 -- --

WAOOP -- -- -0.00015 0.007

WAPR-WAOOP -- -- -0.00006 0.042


Note: Results are not corrected for measurement error.

To provide an accurate interpretation of the effects of OOP and totalpremiums independently, I subtracted the worker portion of the premium(WAOOP) from the total premium (WAPR) and used this as a separate predictorof take-up. If the total cost of health insurance premiums truly affects take-up that is, workers perceive and react to both the employee share and the full cost ofthe premium then the employer-only portion of the premium should also be arelevant cost to workers and a significant predictor of take-up. This effect can becaptured by changes in the employer portion of premiums separately fromchanges in the amount workers pay out-of-pocket. As the right column of Table 6shows, the employer portion of insurance premiums does seem to negativelyaffect take-up, demonstrating the possibility that workers are reacting toincreasing employer costs by declining health insurance. Nevertheless, theinfluence of OOP premiums still seems much larger than that for the employerpremium.

13

13. This method of accounting for employer and employee costs simultaneously shownin the last column of Table 6 produces an estimate for OOP premiums (-0.00015) which is very

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6. ConclusionThis paper explores the sensitivity of workers to the payments their employerscharge to enroll in employer-based health plans. Other researchers have found asmall, but statistically significant and negative relationship between the employeeshare of the premium and the choice to obtain health coverage. This paperconfirms this negative relationship but also finds evidence for an even smallerestimate between -0.014 and -0.017. Using a fixed effects approach with ameasurement error correction, this estimate is robust to characteristics relating tothe generosity of plan coverage and time invariant worker characteristicsassociated with insurance demand, such as worker demographics and the degreeto which workers have health insurance coverage options that are available fromsources other than their workplace.

Even with the low price elasticity estimated in this paper, OOP premiumsstill explain a large proportion of the variation in take-up because these paymentshave increased rapidly in recent years.14 Increases in OOP premiums can explainabout 60 percent of the 1.4 percentage point secular fall in take-up from 2001 to2006.

A novel finding in this paper is that employees do seem sensitive to thelevel of hospital coverage they are offered about 10 percent of the reduction intake-up can be explained by the decreasing generosity of hospital coverage although little or no sensitivity was found to the generosity of physician orprescription drug coverage. Also, while there was a price response in reaction tothe premiums for single coverage, workers appeared insensitive to changes in thecost of family plans, which may demonstrate that families are less willing to go

without health insurance, regardless of cost.The premium estimates here contrast with larger cross-sectional estimates

from elsewhere in the literature, including the range derived by Cutler using thesame survey from 1999, which found an estimate between -0.03 and -0.09.Although this paper uses a measurement error correction which makescomparability with previous estimates less straightforward, without correctingresults for measurement error, the cross-sectional estimate of the price elasticitywas -0.06 in the center of the range from the literature, but almost four times

similar to the non-measurement error adjusted value in the OOP section above (-0.00011). Thisresult is reassuring because it confirms worker take-up is negatively-related to OOP premiums and

this effect does not seem to be corrupted by the exclusion or inclusion of employer premiums.Additionally, the evidence that employees react to increases in the employer paid portion of the

premium seems relatively weak since the coefficients sign reverses from positive in cross-sectional estimates to negative in fixed effects estimates.

14. Exhibit 6.8 in the KFF/HRET survey (2007) shows that between 2000 and 2007, theaverage monthly OOP premium for single coverage increased 107 percent ($28 to $58) and theaverage monthly OOP premium for family coverage increased 102 percent ($135 to $273).

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that obtained using firm-level fixed effects. These sizable differences indicateomitted variables bias may be a pernicious problem in previous estimates. A finalseries of estimates also casts some doubt on the strength of the influence of

employer-paid premiums on workers decisions to take up.By developing a more accurate estimate of health insurance demand

elasticity, one implication of this paper is for estimates of the level of subsidiesneeded to increase insurance coverage among the uninsured who work in firmswith an offer of health insurance. Since the mean take-up rate is approximately0.84 across this six-year sample, an estimate of the monthly insurance subsidy perperson required to increase coverage can be estimated. With a take-up elasticityof -0.016 and a goal of 100 percent coverage among workers with offers ofcoverage, monthly out-of-pocket premiums would have to be reduced almost ten-fold (about 970 percent) from their current level calculated by taking theincreased take-up of 16 percent and then dividing this by the elasticity estimate of

-0.016, with some error due to rounding. This would effectively require reducingthe monthly OOP premium in the 2001 to 2006 EHBS sample from $41.14 to$4.23. Such a reduction is not only potentially unfeasible, it may still result in anuncertain gain in coverage because some workers who have access to public orspousal coverage would not take-up their own employers coverage at any price.

This paper accounts for several of the important determinants of employeetake-up and derives an arguably more accurate estimate of the price elasticity forhealth insurance. However, it is important to remember that decomposing thecauses of take-up will not fully explain changes in employer-provided insurancecoverage. Changes in the rate at which firms offer health insurance and changesin employee eligibility for firm coverage will also influence coverage rates, and

both have been shown to be even more critical to explaining recent coveragechanges than changes in take up. Although relevant to trends in health carecoverage, these factors are necessarily outside of the scope of this paper.

Another implication of this study is the extent to which employees findemployer sponsored insurance (ESI) affordable. Large negative responses toprice increases, or largely positive income elasticities would seem to implycoverage is perceived as unaffordable. To this regard, the results of this study aremixed. At least within the range of premium values to which workers areexposed, most workers are relatively insensitive to price. This could lead one toconclude that employer coverage is generally perceived as being affordable.However, evidence in this paper also suggests that workers are sensitive to the

quality of their health benefits, and that workers with lower earnings may be moresensitive to the prices that firms set to enroll in a plan. Of course, inferencesabout the ostensible affordability of employer plans are difficult to generalize,since those who do not take up insurance may be systematically different fromworkers covered by their employer across unobservable characteristics.

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The findings in this paper also have implications for health economistswho may not have fully investigated the pervasiveness of measurement error intheir research. Measurement error corrections can substantially change the

magnitude of econometric estimates and may be applicable to a broad array ofhealth-related topics. As the estimates in this paper suggest, measurement-errorcorrected estimates can greatly alter findings derived without such corrections,and may equally affect the implications for public policy drawn from suchresearch.

References

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Angrist, Joshua D., and Alan B. Krueger. Empirical Strategies in LaborEconomics. Volume 3 ofHandbook of Labor Economics (1998), edited byOrley Ashenfelter and David Card. Amsterdam: Elsevier.

Blumberg, Linda J., Len M. Nichols, and Jessica S. Banthin. Worker Decisionsto Purchase Health Insurance.International Journal of Health Care Financeand Economics 1, nos. 3-4 (September 2001): 305-325.

Brown, E. Richard, Shana Alex Lavarreda, Ninez Ponce, Jean Yoon, Janet

Cummings, and Thomas Rice. The State of Health Insurance in California:Findings from the 2005 California Health Interview Survey. UCLA Centerfor Health Policy (July 2007),http://www.healthpolicy.ucla.edu/pubs/publication.asp?pubID=226 (accessedOctober 8, 2007).

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