Partially Identifying Treatment Effects with an ...faculty.smu.edu/millimet/classes/eco7377/papers/kreider hill.pdf · Partially Identifying Treatment Effects with an Application

Partially Identifying TreatmentEffects with an Application toCovering the Uninsured

Brent KreiderSteven C. Hill

ABSTRACT

We extend the nonparametric literature on partially identified probability

distributions and use our analytical results to provide .sharp hounds on the

impact of universal health insurance on provider visits and medical

expenditures. Our approach accounts for uncertainly about the reliahiUty

of self reported insurance status as well as uncertainty created by

unknown counterfactuals. We construct health in.surance validation data

using detailed information from the Medical Expenditure Panel Sur\-ey.

Imposing relatively weak nonparametric a.ssumptions, we estimate that

under universal coverage monthly per capita provider visits and expenditures

would rise hy le.ss than 8 percent and ¡6 percent, respectively, across the

nonelderly population.

Brent Kreider Is an associate profes.ior of economics at Iowa State University. Steven C. Hill is a senioreconomisi In the Center for Financing. Access and Cost Trends (CFACT) ofthe AgencvJ'or HealthcareResearch and Quality (AHRQl. Dr. Kreider acknowledges genemus financial support hv a grant fromthe Robert Wood Johnson Foundation thmugh the Economic Research Initiative on the UninsuredlERIU), We received many helpful comments on earlier versions of this paper from participants al the2(Ktí ERVl conference al the University of Michigan, the 2004 Southern Economic AsswiationMeeting, the CFACT seminar series. Georgetown University. Iowa State University, the University ofVirginia, the Inaugural Conference ofthe American Society of Health Economist.^, and other readers.Discussant comments from John Bound und Shakeeb Klutn were especially u.seful. as were cumments(rom anonymous referees. Kathleen McMillan provided expert programming to construct key healthin.surance variables, and Dzmitr}- Asinski provided valuable asxistatice with the dala. The viewsexpressed in thi.s paper are those of lhe authors, and no official endorsement hy AIIRQ tir the U.S.Department of Health atid Human Senîces is intended or should be inferred. All errors remtiin our¡iwn. The data used in thi.s article can he used in ihe AHRQ Data Center and the faciiiiies ofthe U.S.Census Research Data Center (RDC) network beginning October 2009 through September 2012.Cimtaci Sti-ven C. Hill. CÍACT. AHRQ. 540 Gaither Rd. RockviUe. MD 20850. [email protected] November 20()7; accepted January 2008]

ISSN 022 166X E ISSN I.'i48 8004 8 2009 by lhe Board of Regents ofthe University of Wisconsin System

THE JOURNAL OF HUMAN RESOURCES • 44 ' 2

410 Tbe Joumal of Human Resources

I. Introduction

Numerous academic studies have investigated relationships betweenhealth in.surance status and a wide variety of outcomes such as healthcare utilization,health status, labor supply, and participation in public assistance programs. In morethan 70 articles surveyed by Gruber and Madrian (2004), Levy and Meltzer (2004),and Buchmueller et al. (2005), nearly all parameters of interest are identified usingparametric approaches.'

We develop the Iirst nonparametric framework for studying the potential impact ofuniversal health insurance on the nation's use of medical services. Within this frame-work, we study relationships between insurance status and use of services (expendi-tures and number of provider visits) in an environment of uncertainty about bothcounterfactual utilization outcomes and status quo insurance status. Uncertaintyabout counterfactuals arises because insurance status is not randomly assigned.For example, families that expect to use more health services have more incentiveto acquire heallh insurance. More generally, insurance status depends on individualand family characteristics that may also influence healthcare use. Utilization patternsamong households who become insured though expanded programs would not nec-essarily resemble observed utilization patterns among households that had alreadyself-selected into insured status on their own.

Beyond the uncertainty created by unknown counterfactuals. validation studieshave recently called into question the reliability of households' responses to ques-tions about their current insurance status. Significant misreporiing has been docu-mented in several popular surveys including the Current Population Survey (CPS).the Survey of Income and Program Participation (SIPP), the Behavioral Risk FactorSurveillance System (BRFSS) survey, the Medical Expenditure Panel Survey(MEPS), and others (Davern et al. 2007; Card, Hildreth. and Shore-Sheppard2004; Hill 2007/2008; Nelson et al. 2000). Estimated error rates, which vary acrosssurveys, have been linked in part to difficulties in recalling past coverage and diffi-culties reporting the status of other family members (Nelson et al. 2000; Pascale2007). The Census Bureau now issues caveats aboui tbe accuracy of insurance esti-mates from the CPS (DeNaves-Watt. Proctor, and Hill Lee 2005).

Using matched .surveys of employers and their employees, Berger, Black, andScott ( 1998) find that 21 percent of the workers and their employers disagree aboutwhether the worker was eligible for insurance. Their study appears to represent theonly prior analysis of potentially mismeasured insurance status in an econometricframework. Assuming exogenous measurement error in a classical errors-in variablessetting (after accounting for the binary nature of the mismeasured variable), they findthai even nonsystematic reporting error seriously biases their estimated effect ofinsurance eligibility on wage growth.

The presence of reporting errors compromises a researcher's ability to make reli-able inferences about the status quo. and it further confounds identification of

1. A.1 an exception. Olson (1998) uses semipantmetric techniques to estimate the relationship betweenwomen's labor hours and the availahility of heallh insurance through a spouse. More recently. Gerfinand Schellhom (2CM36) use nonparamefric techniques and Swiss dala lo bound the effects of dedutiibleson the probability of visiting a physician.

Kreider and Hill 41

counterfactual outcomes associated with policies that would alter the di.stributioti ofitisurance coverage within the population, such as national health insurance." Consis-tent with .such concerns, some advocates have argued that uncertainty about the ntini-hers and characteristics of the uninsured constitutes an important barrier toidentifying optimal policy solutions (for example. Hunter 2()()4; Woolhandler andHininielstein 2ÜÜ7). Highlighting surprising degrees of insurance classification errorin many popular national surveys, along with dratnatic incon.sistencies in responseswhen experimental followup insurance questions have been posed, Czajka and Lewis( 1999) write: "Until we can make progress in separating the measurement error fromthe reality of uninsurance, our policy solutions will continue to be inefficient, and ourability to measure our successes will continue to be limited."

Our analysis extends the nonparameiric literature on partially identified probabil-ily distributions in several dimensions. First, we provide sharp bounds on the condi-lional mean of a random variable (in our ease healthcare visits or expenditures) forthe case that a binary conditioning variable (insurance status) is subject to arbitraryendogenous classification error. In this environment, insurance reporting errors areallowed to be arbitrarily related to true insurance status and healthcare use. The.seresults extend parts oí the analyses of Horowitz and Manski (1998) and Kreiderand Pepper (2(K)7). Second, we formally assess how statistical identification of atreatment effect decays with the degree of uncertainty about the status quo. Our ap-proach extends the nonparametric treatment effect literature for the case that someireatments are unobserved (especially Molinari, Forthcoming).^ Third, we relax theiiondifferential errors independence assumption evaluated, for example, by Bollinger11996) and Bound, Brown, and Mathiowetz (2001) embedded in the classical errors-in-variables model. As an alternative, we evaluate the identifying power of a weaker•'nonincreasing errors" monotonicity assumption that presumes that misreporting ofinsurance status does not rise with the level of utilization. This assumption allows forthe possibiliiy, for example, that using health services informs a patient of her trueinsurance status.*

We exploit detailed data in the 1996 MEPS to construct health insurance valida-lion dala for a nonrandom portion of the sample based on insurance cards, policybooklets, and followback interviews with employers and insurance companies. Thenext section describes these data and our health insurance verification strategy. Sec-tion III fonnalizes the identification problem associated with estimating a particulardescriptive statistic, the gap in health service use between the status quo insured anduninsured under existing policies, when insurance status is subject to arbitrary

2. The extent to which universal coverage would increase use of services and expenditures has been esti-mated in a variety of parametric siudies ¡Insiitute of Medicine 2(X)3: Blumberg et ai 2006). Estimates ofincremental spending range from $34 to $69 billion per year depending on the stalislical assumptions andihoice of comparison groups.

} . To isolate idcniiticuiion problems associated with partially unobserved insurance statu.s as a conditioningvariable or Ireatmeni. we assume that olher variables in the analysis are measured without error.4. Using methods in Lewbel (2007), the treatment eft'ecls could be point-identilled in certain cases if wehad instruments thai affeci insurance status but not classification error or the average treatment effect. Forrelated work on potentially endogenous classification errors in a linear regression framework, see Fra/is andU>ewenstein (2003). Given the difficulty in identifying plausible instruments in our application, we con-sider what can be identified in the absence of instruments.

412 The Journal of Human Resources

patterns of classification error. We derive bounds on the unknown utilization gap un-der alternative assumptions about the nature and degree of reporting errors. Extend-ing these results. Section IV investigates what can be learned about the impact ofnational health insurance on the use of health services. Combining our "nonincreas-ing errors" a.ssumption with common monotonicity assumptions iti the treatmenteffects literature, .such as monotone treatment response (related to moral hazard)and monotone treatment selection (related to adverse selection), we can provide rea-sonably tigbt bound.s on the impact of universal coverage without relying on some ofthe more controversial assumptions involving functional forms and independence.

Our primary set of estimates focuses on policies that would extend coverage to theuninsured using the same mixture of private and public insurance that exi.sts underthe status quo. Another set of estimates focuses on policies ihat would extend exist-ing public programs to cover the uninsured. Both types of expansions have beenimplemented by states. Hawaii, Illinois, Pennsylvania, and Washington created pub-lic programs open to all uninsured children but with premiums for higher incomefamilies (Kaiser Commission on Medicaid and the Uninsured 2007). Maine, Massa-chusetts, and Vermont expanded public programs and developed new programs withsubsidized premiums and other features ( Kaye and Snyder 2001). Massachusetts alsomandates that individuals purchase insurance, facilitated with subsidies for low-income adults and fees for employers that do not provide coverage (Holahan andBlumberg 20<}6). California and other states are considering proposals with featuressimilar to those of Massachusetts, and prominent presidential candidates also advo-cate covering the uninsured with a mixture of private and public insurance. Section Vcompares our nonparametric estimates with those from parametric studies, and Sec-tion VI concludes.

n. The Medical Expenditure Panel Survey

The data come from the 1996 Medical Expenditure Panel Survey(MEPS), a nationally representative household survey conducted by the U.S. Agencyfor Health care Research and Quality. In the MEPS Household Component (MEPSHC), each family (reporting unit) was interviewed five times over two and a halfyears to obtain annual data reflecting a two-year reference period (Cohen 1997). Thispaper focuses on the nonelderly population because almost all adults become eligiblefor Medicare at age 65. The sample contains 18,851 individuals.

We study insurance and service use in July 1996. We focus on July because the1996 MEPS has a followback survey of employers, unions, and insurance companieswhich reported insurance information as of July 1, 1996. We use 1996 data becausethat is the only year for which respttndents to the followback survey reported on theemployees' and policyholders' insurance status rather than whether the establish-ment offered insurance."^ Studying insurance and service use in one month alsoreduces the likelihood of confounding the dynamics of insurance status with

5. These dau are available al ihe AHRQ Data Center.

Kreider and Hill 413

misreported insurance stattis because employment-related insurance typically coversan entire month.

A. Insurance Status Reported in the Household Component

The MEPS HC asks about insurance from a comprehensive list of all possible sour-ces of insurance. In the firs! interview, conducted between March and August 1996,MEPS HC asked the family respondent about insurance held at any time since Jan-uary 1st. Because employment-related insurance is the most prevalent source of in-surance, the family respondent was asked about ail jobs held by coresiding familymembers since January 1st. jobs family members had retired frotii, and the lastjob held. The family respondent was asked whether the employee had insurance fromeach job. Then the family respondent was asked whether anyone had:

• Medicare

• Medicaid

• Champus/Champva

• For those who did not report Medicaid, any other type of health insurancethrough any state or local government agency which provided hospital and phy-sician benefits

• Health benefits from other state programs or other public programs providingcoverage for healthcare services^

• Other sources of private insurance, such as from a group or association, insur-ance company, previous employer, or union.

For each source of insurance, MEPS HC asked which family members were coveredand when.^

In the second interview, conducted between August and December 1996, MEPSHC asked questions based on jobs and insurance reported to be held at the time ofthe first interview to determine whether previously reported insurance was still heldor when it ended. MEPS also asked about new jobs and insurance from those jobs,public insurance acquired since the first interview, and insurance acquired from othersources since the first interview. The recall period is not especially long, typicallyfour to seven months. Responses to the questions from the first and second interviewwere used to construct indicators of insurance coverage at any time during July 1996and uninsurance, the residual category. Family respondents reported 80.7 percent ofthe nonelderly population was insured in July 1996 and 19.3 percent were uninsured(Table I).

6, A very small number oí individuals arc reportedly covered through Aid lo Fatnilies with DependentChildren (AFDC) or Supplemental Security Income (SSI), and these are counted as Medicaid. Other sour-ces, such as the Veterans Administration and the Indian Health Services, are not included in measures ofhdspiial/physician Insumnce,

7, State-specific program names arc used in the questions. Insurance status is noi imputed to families withmissing data, which are rare.


s

a

Î J

s:

M. '

• O

0a.ai•J:

«

s3

•i

3i ês ^

O

O

o o Ov

d (N ^ —

o oOO

ound

• ^ o— OO

(M

d* *— , inri r- rin O 00 0 0

So

Uu

In su

r

'S

s

E4J

1/1 5 Cl

o ra•> 1 &•

CL

S -a t/i2 c T3

"î J5 ™ in4-* — - . ca

> E U Si _ cU (/•, cU . O !JÎ

> _ V- :«p ra ,P c

£ 3 T3. « 4J

OaT3 iCC C -c•s ^ ÏJ^ X •*C ^ C<U C Uo (d pu. Oj u.

Cu 2 CU

ampl

e

o«.ri

uu

lato

ry

Srara

(n O

z

"5 ' i ^ —

"û Q..Sts

CL. o _

"3 2 s.


B. Service Use and Expenditures

In each interview, the MEPS asks about healthcare services used by all coresidingfamily members since the last interview. The MEPS also obtains permission to inter-view a sample of the medical providers identified in the Household Component sur-veys to supplement household-reported healthcare expenditure and source ofpayment information. We create measures of service use and expenditures in July1996; number of provider visits for ambulatory medical care (a medical providervisit, hospital outpatient visit, or emergency room visit), an indicator for whetherthe sample person had a hospital stay or ambulatory services, and expenditttres forhospital stays and ambulatory services. Twenty-one percent ofthe (weighted) sampleused medical care in that month."* Persons who the family respondent said were in-sured in July were nearly 80 percent more likely to have used medical care (22.5 per-cent of the insured versus 12.7 percent of the uninsured. Table I ). The mean numberof provider visits is also much greater for the reportedly insured, as are mean expen-ditures,

C. Verification Data

We use detailed data to identify sample members for whom there is evidence cor-roborating their insurance status. The 1996 MEPS includes three sources that can beused to confirm health insurance reported by families: (1) the HC interviewers askrespondents to show insurance cards, (2) the HC interviewers ask respondents to pro-vide policy booklets, and (3) separate interviews were conducted with family mem-bers' employers and insurance companies. Respondents for the family, employers, orinsurance companies could err in reporting a person's insurance status; none providesa gold standard of information. Nonetheless, we use confirmations of insurance statusto formally verify the insurance status of some sample members. This approach rep-resents a compromise between taking reported insurance status at face value for allsample members and discarding valuable family respondents' reports about insur-ance status.

We label sample members as verified insured if an insurance card was shown at thetime ofthe interview, a policy booklet was given to the interviewer, or if an employeror insurance company confirmed that the person was covered by insurance. We as-sume that a report that a sample member is uninsured is accurate as long as thereis no contradictory information from any family member's employers and allemployers provided data. The person's insurance status was not verified (but not as-sumed to be incorrect) if there were insufficient verification data or if employers orinsurance companies contradicted the family respondent. See Hill (2007/2008) fordetails.

As shown in Table I, we find that 80.2 percent of the reportedly insured were con-firmed as insured by a card, policy booklet, or an establishment. For the few cases inwhich a respondent produced an insurance card but the establishment reported thatthe person was uninsured, we treat these cases as verified insured based on the phys-ical evidence of insurance. Among the reportedly uninsured. 11.7 percent are verified

8. In the MEPS. outpatient prescripiion medications, medical supplies, and durable medical equipment arcnot linked to specific months: these expenditures are excluded.


(Table I ). This relatively low number reliccts the lack of an employed family mem-ber in some uninsured families and the lack of response by some employers. Recallthat uninsurance is verified under this strategy only if all of the family's employersresponded and confirmed that they did not provide insurance to the sample member.Overall. 67 pereent of the sample was verified.

III. Identifying Utilization Differences Between theInsured and Uninsured

We now study what can be learned about differences in healthcareutilization between the insured and uninsured when we cannot perlectly distinguishbetween the truly insured and uninsured. In Section IV, we extend the analysis be-yond descriptive statistics to assess what can be learned about the potential impactsof universal coverage. We ignore heterogeneity of insurance plans and treat coverageas a binary event. Let / = 1 indicate that a person is truly insured, with / — 0 other-wise. Instead of observing / , we observe the self-reported counterpart /. A latent var-iable Z indicates whether a report is accurate. If / and / coincide, then Z — 1;otherwise, Z* = 0. Let K = I indicate that / is verified to be accurate (that is. Z 'is known to equal 1). If >' = 0. then Z" may be either I or O."* In no case is the vaiueof Z' assumed to be ().'"

Let U denote the amount of healthcare services consumed during the reference pe-riod. Typically, the amount of care is measured as health expenditures or number ofprovider visits. Policymakers are al.so interested in the proportion of the populationthat u.ses any medical care, in which ease V ean be treated as a binary variable. In thissection, we investigate what ean be learned about the status quo utilization gap be-tween the insured and uninsured.

(1) A = E{u\r = \)-E{u\r = 0),

when trtie insurance status, /*. is unobserved for part ofthe sample."The utilization gap A is not identified since we observe E(U\I) but not E{U\r).

Our objective is to provide worst-case bounds on A. To partially identify E(U\r),we will first derive bounds on the fraction of Ihe population that consumes no morethan a particular amount of care / conditional on unobserved insurance status,P{U -^tlr). We can then provide bounds on E(U\I^) by integrating over theseworst-case probabilities.

We begin by writing

9. In their analysis of testing for environmental poHutants, tïominitz and Sherman (2004) were the lirst toformalize the idea of distinguishing between "verified" and "unverified" observations in the datii.to. That is. we eonservatively allow for the possibility that the MEPS insurance classification is accurateeven if the classification is not formally verified.11. Our noiaiion leaves implicit any other covariates of ititeresl. We focus on bounditig the utilizatioti gapfor the nonelderly population as a whole, but it is straightforward to condition on subpopulations of interest.Note tbat we are not estimating a regression, and tbere are no regression orthogooality conditions to be sat-isñed.


^ t r =

Neilher the numerator nor the denominator is identified, but assumptions on ihe pat-tern of classification errors can place restrictions on relationships between the unob-served quantities. Let Q^=P{U^tJ ^ 1,Z' = 0 ) and e , " = / ' ( t / < i , / = 0 ,Z ' = 0)denote the fraction of false positive and false negative insurance classifications,respectively, for those whose medical consumption did not exceed t. Lettí-*=P(U>,j = \Z' =O)ar\dB;'=P{U>îJ = 0 ,Z ' - 0) denote the analogousfractions for those whose use of care exceeded r. We can then decompose the numer-ator and denominator in Equation 2 into identified and unidentified quantities:

P(U < / / = n -I- fl"-«-"

where P{U^t.l= 1) and P{I = 1} are identified by the data. In the numerator,8," —6^ reflects the unob.served excess of false negative versus false positive insur-ance classifications among those whose use of services did not exceed /. In the de-nominator (e~ + 0,' " ) - (Ö^ + Ö,'"*") reflects the unobserved excess of false negativeversus false positive insurance classifications within the entire population. Utilizationamong the uninsured, P(C/is /] / ' = 0), can be decomposed in a similar fashion.

We now assess what can be learned about A. First, we present "arbitrary errors"bounds that impose no structure on the distribution of false positives and false neg-atives. This environment that allows for arbitrary error patterns is termed "corruptsampling" (Horowitz and Manski 1995). We then consider the identifying powerof assumptions that restrict the patterns of errors. Results in this section also informour treatment effect bounds in Section IV.

A. Arbitrary error hounds

Our analytic framework allows us to trace out bounds on our unknown parameters ofinterest as function of a researcher's confidence in reported insurance status. Follow-ing Horowitz and Manski (1995), we consider a lower bound, i; on the accuracy rateamong unverified cases. Setting v = I corresponds to an assumption that reported in-surance status is always accurate, the implicit assumption in previous analyses. Set-ting 1' = 0 corresponds to an assumption that nothing is known about the accuracy ofunverified reports. We will evaluate patterns of identification decay for our parame-ters of interest as v departs from I.

Since we do not observe true insurance status for unverified re.sponses. the accu-racy of such responses cannot logically be known. Nevertheless, our empirical anal-ysis considers four candidates for v: 0.50, 0.84, 0.92, and 1. For the mostconservative value, v = 0.50. the researcher need only make the common classifica-tion error assumption that accurate responses are more prevalent than reporting errors(see, for example. Bollinger 1996; Frazis and Loewenstein 2003).

The otber candidate thresholds, v = 0.84 and v = 0.92. are derived from studiesthat have investigated the reliability of self-reported insurance status in the MEPSand other surveys. Among the reportedly insured (/ ^ 1), let Ä = 1 and M = Í


denote reported private and public coverage, respectively, and let R' and M* denotetrue coverage. If both private and public coverage are reported in the month, which israre, private coverage is assumed to take precedence; in such cases, we label reportedcoverage as R — I and M = Q (and analogously for true coverage). Suppressing theconditioning on K - 0, the probability of misclassification is given by

p(z' ==. 0) = p{r = o\R = i)p{R= 1) + p(r = o\M = \)P{M= i)

= \\I = O)P(I = 0) + P{M' = \\l = O)P{I = 0).

For the first term, we conservatively allow the proportion that is truly uninsuredamong those reporting private coverage, P{/ ' — 0\R — 1 ), to be as high as the pro-portion simply lacking private coverage, P{R' = 0\R = I). Similarly, we allow thetrue rate of being uninsured among those reporting public coverage,P{r = OjAf = 1). to be as high as the rate of simply lacking public coverage,P{M' = 0\M = 1). Imposing these inequalities, we can write

P{Z* = 1} > v = ]-P{R* =0\R= l)P{R= ])-P{M' =0\M ^

-P{R* =l\i = O)P{I = 0)-P{M' - 11/ - O)P{I = 0).

The observed probabilities among the unverified cases are P{R = l ) = 0 . 3 5 ,f (M — 1) =0 .13 , and P(I = 0) = 0,51. Estimates of the unobserved contradictionrates are inferred from other studies. Hill (2007/2008) estimates that the probabilityof truly lacking private insurance when it was reported, PiR' = 0\R = I), is about0.02, with the possibility that it could be as large as 0.12. Our two estimated thresh-olds, I" = 0.84 and v = 0.92, incorporate the larger and smaller values, respectively.The probability of truly having private insurance when no insurance was reported,P{R* = 1|/ = 0), is e.stimated to be no higher than O.iO.

For both values of y, we assutne that the rate of false positives among those report-ing public coverage, PiM' = 0|M = 1}, does not exceed 0.03. Card, Hildreth, andShore-Sheppard (2004) estimate that the rate of false positives for Medicaid in the SIPPranges from 0.01 to 0.03. Like the MEPS. the SIPP is a longitudinal, household survey.The MEPS and the SIPP also have similar recall periods and yield fairly similar esti-mates of enrollment in Medicaid and the State Children's Health Insurance Program(SCHIP) (Peterson and Grady 2005). Estimates oíP(M' = I]/ = 0) range from 0.02(for V = 0.92) to 0.12 (for v = 0.84). The.se values are derived from benchmarkingstudies of the MEPS (Banthin and Sing 2006: Nelson 2003; Peterson and Grady2005). with the lower value refiecting an estimate that most (83 percent) of thosewho failed to report their public insurance instead reported private insurance (Callet al. 2007). Further motivation is provided in an appendix available from the authors.

While we have attempted to be conservative in our derivations of v. these deriva-tions necessarily involve extrapolating information from respondents for whom val-idation data are available. Misreporting rates in our sample of unverified respondentsmay not reflect estimated misreporting rates in other samples. While the descriptiveutilization gap results presented later in this section are sensitive to values of v. ourmain conclusions in Section IV about the impact of universal health insurance on uti-lization (which impose additional monotonicity assumptions) are fairly robust to thechoice of V across a wide range of values.

Kreiderand Hill 419

In Proposition 1, we formalize what can be known about the utilization gap be-tween the truly insured and truly uninsured given only a lower bound,, v. on the frac-tion of accurate insurance classifications among unverified cases:

Proposition I: Let P{Z' = 1|K — 0)>:i'. and suppose that nothing is known aboutthe pattern of repotting errors. Then the mean utilization rate among the truly in-sured is hounded sharply as follows:

< E{U\r = 1) < / UdFLJ J

usitig the distrihution functions

P{l= l ) - a /

and values

min{(f)(v),/»(¿/ < / , / = L y = 0)} if 6| < 0

P(U > tj = 0, y = 0)}} othetîse

/,/ = 0,K = 0)} if of > 0a, = ^ max{O,min{P(i/< i , / = 0, y Ô), t t )(v)-

P ( t / > / , / = I , r - O ) } } otherwise,

where i\>{v) = (1 -v)P{Y = 0). Analogtms bounds for the utilization rate among theuninsured, £ ( [ / | / ' = 0), are obtained by replacing ¡ — 1 with / = 0 and vice versa.

Proof. See Appendix 1.

Notice that increasing v narrows the bound.s over some ranges of v but not others, andthe rate of identification decay can be highly nonlinear as v declines. When ;• = 0,these bounds can be derived from Horowitz and Manski's (1998) censored rcgressorbounds (their Section 4.1 ). In that context, some observations of a conditioning vari-able are missing in the data. Kreider and Pepper's (2007) Proposition 2 bounds applywhen V = 0 and the outcome U is binary.'"

12, Krcidor and Pepper |2O()7) siu(Jy how labur fi>rce parlicipalion varies with disability siatus given a kickof knowledge of any particular respondent's true disability status. Our Proposition I extends their Propo-sition 2 by considering conlinuou,'; outcomes and by assessing identification for values uf v greater than 0within unverified classificalions. Their proposiiion. however, is more genera! in the dimension ihal they donot impose our identifying assumption thai all verified cases are accurate; they allow for the possibility oferrors within verified cases.


We next bound the difference in use between the insured and uninsured. We couldcompute a valid lower (upper) bound on the utilization gap. A, by subtracting the Prop-osition I upper (lower) bound on E(U\r = 0) from the Proposition 1 lower (upper)bound on E{U\I' = I ). While these bounds on A would be valid, they would not nec-essarily be as tight as possible. In particular, they would not impose the constraints thatthe parameters a^ (a~) in the Proposition I bounds on £(i/ | /* = I) are identical to theparameters a " (a*) in the bounds on E{U\r = 0). Therefore, we compute sharpbounds on á using numerical methods that impose these constraints.'"'

B. Arbitrary error results

Table 2 presents estimated bounds on the utilization gap. A, for any use of services,number of provider visits, and expenditures. The arbitrary error bounds are providedin Column i. When v = I. A is fx>int-identified as the self-reported gap obtainedfrom taking the data at face value. For example, the gap in the proportion of insuredand uninsured that used services in July 1996 is point-identified as P{U = \\I ~\) — P(U = 1|/ = 0) = 0.098. The gaps in the number of provider visits and expen-ditures are point identified as 0.186 and $77. respectively. Ninety-five percent confi-dence intervals for the gap in any use. number of visits, and expenditures arecalculated as [0.083, O.I 12], [0.136, 0.237], and [$47, $107], respectively.'"^

Under arbitrary errors, identification of these utilization gaps deteriorates rapidlyas V departs from 1. For the reference case v = 0.92. for example, the difference inthe number of provider visits per month may lie anywhere between -0.135 and 0.472,while the difference in expenditures may lie anywhere between -$40 and $117 (Table2). In neither case is the sign of A identified, even ignoring the additional uncertaintyassociated with sampling variability. In fact, without imposing assumptions on thepatterns of errors, we cannot identify whether the insured were more likely to useservices than the uninsured unless v exceeds 0.95 (not shown). Similarly, we cannotidentify whether the insured had more provider visits unless v exceeds 0.98, nor canwe identify whether the insured had greater expenditures unless v exceeds 0.99. Thisrepresents an important negative result: being almost fully confident in the accuracyof the data is nol enough, by itself, to be informative about even the sign of the uti-lization gap between the insured and uninsured.

C. Restrictions on reporting error patterns

The parameter bounds thus far have allowed for arbitrary patterns of insurance clas-sification errors, including the possibility that reporting errors are endogenously re-lated to true insurance status or the healthcare utilization outcome. In contrast, mosteconomic research presumes that mea.surement error is exogenous to the extent thatit exists at all. In this section, we make transparent the identifying power of twocommon (nonnested) independenee assumptions tbat tighten the Proposition 1bounds. Then we introduce a weaker alternative assumption that is more plausiblein our context.

13. Gau.ss programs are available from the authors upon request.14. Throughout [his analysis, we compute confidence intervals around the estimated identification regionsusing methods recently developed by Chemo/hukov, Hong, and Tamer (2007). We use balanced repealedreplication methods lo account for the complex survey design (Wnlier 1985).

Kreiderand Hill 421

I

Ú s

o2

o

o

ft•5 tú_ ^

So'"'

CQ 5 2¿

Ö Ö Ö Ö Ö Ö Ö Ö00 m —' u-i r- ' — OG r s

ooooooooI I

DO ro ̂ — "^ o ^ rî^^ r s ^^ í^ f̂ •̂ " ^f r̂ ^d d d d d d d d

öödddöd-Î I

s 00

o o o o o o o00 ro OO ~ 00 — 00Os OO Os 00 Os 00 Os

O O O O O O

o

00

o

137

o

186,

o

137

o

186,

o

137

o

00

o

137

o o o o

oX

' O O O O C O O O

oo' ro OÍ w-j rN' rJ Tt —

S oo lo r̂ j — O 00 —O O O O O ro W~i

' ^ ö d ö ö ö ö ö ö

O C o o oI I

^ -oo r ^ i r - J ro r - - r j - r - r - -—; — q q q — ^£;r--<óci<dcicic¿cic¿

I I I I 1

iS — (N 'í- ro u-i 00 ' ^

— (N CN OÍ rN (N rodödiöciSööOO ro 'í-' sD d ro oí —g oo r'-j 5 00 a\ — m

o o o o o »n n-io o o o o

I I 1o o

'—'o

186.

o

136

MO

135,

192

vi

238,

o

304

o

761,

í js

o601

o o o o oI I I

(N od

OJ

dOO

dod


uc5

Q-.OÙc

'sD£- C• ^

MÇ

3V)

<

OtWcO

ao

( C

las

U

uC

c

re

c •-'c p

¿.s

OoZ

II

tLU

cOD.O S.

-o

t : tu

O (J

C

5J o <

00

00

-^ f^ O " ^ r

r- *i- Y ^ "̂~ OO !-•• m

•̂ — \O 001 1

00Ö

• N

g. "SE e

1 ^¿S ë . "—. o --t3 ' 6 oTu ¿s ^

5 ^ I

i= I

3 :i

Ü S

II <u .> — •a —

5 =: ^ ^- VI .2 «II -^ S ^

II u u

•rv -s ^

.s û- il- E g

•5 n i ^

& . UJ T3 ••- -M-


First, a researcher might consider an orthogonality assumption that insurance clas-sification errors arise independently of true insurance status:

(4) p(r = \\z*) = p{r = 1).

This assumption may be relatively innocuous compared with the set of homogeneityand exogeneity assumptions imposed in standard parametric frameworks. Still, sto-ries can be told in which this assumption may be violated. Reporting errors maynot be orthogonal to true insurance status if, for example, better educated respond-ents are both more likely to be insured and more likely to accurately answer surveyquestions. Similarly. Card, Hildreth, and Shore-Sheppard (2004) provide evidencethat errors in reporting Medicaid coverage vary with family income, which is alsoa key aspect of Medicaid eligibility.

Alternatively, or in combination with Equation 4, a researcher might place restric-tions on the relationship between insurance classification errors and the use of healthservices. In the popular classical measurement error framework, reported insurancestatus does not depend on the level of healthcare utilization conditiotial on true in-surance status:

(5) P{l = \\I\U) =P{I = l|r)forr - 0 , 1 .

Aigner (1973) and Bollinger (1996) study this type of "nondifferential" classifica-lion error for the case of a binary conditioning variable. When the independence As-sumption 5 holds, Bollinger's Theorem 1 can be used to show that A is boundedbelow by the reported utilization gap £'(t/|/ = l ) - £ ( t / | / = O) (>0) as long as v ex-ceeds 0.50. Reflecting well-known attenuation bias a.ssociated with random measure-ment etTor, the magnitude of the reported utilization gap represents a downward-biased estimate of the magnitude of the true utilization gap. Berger. Black, and Scott( 1998) impose the nondifferentiai errors assumption in the only previous economet-ric analysis that allows for misreported insurance status.

Bound. Brown, and Mathiowetz (2001, p. 3725) note, however, that in general thenondifferential measurement error assumption is strong and often implausible. In ourcontext, the nondifferential assumption is most likely to be violated if using health-care infonns respondents about their true insurance status. For example, a healthcareprovider may enroll a patient in Medicaid. More generally, a regular user of healthservices (or a user with high expenditures) presumably is more likely to know herinsurance status than an infrequent user of services.

We propose a weaker alternative assumption on tbe pattern of reporting errors.Relaxing the nondifferential assumption in Equation 5, we suppose that the probabilityof misreporting insurance status does not rise with the level of healthcare utihzation:

(6) p{i =\\r = 0 , i / i ) < / > ( / = 1 / ' = 0.i /o)

lor U] ^ Ufí. The nondifferential assumption represents a special case. In the nextsection, we illustrate how the identifying power of this monotone "nonincreasing er-ror rate" assumption compares with the standard nondifferential errors assumption.

424 The Joumai of Human Resources

D. Restricted error pattern results

Columns 2-4 in Table 2 illustrate the identifying power of these stronger assump-tions. In each column, restricting the patterns of reporting errors translates into con-siderably narrower bounds compared with the arbitrary errors ca.se. We focusprimarily on the relatively weak "nonincreasing errors" bounds in Column 4 thatdo not require any independence assumptions.'"

Recall that we cannot identify the sign of A for provider visits under arbitraryerrors unless at least 98 percent of the unverified responses are known to be accurate;for expenditures, the corresponding critical value is 99 percent. Under the nonin-creasing errors assumption, however, the critical values fall dramatically to 78 per-cent and 64 percent, respectively (not shown). For the reference case v = 0.92under nonincreasing errors, A is estimated to lie within [0.133, 0.264] for the meannumber of visits per month and within [$68. $85] for expenditures (Table 2). Thesebounds for visits are 0.066 vi.sits wider than the corresponding nondifferential errorsbounds in Column 3. but they are 0.476 visits narrower than the arbitrary errorsbounds in Column 1. Similarly, the nonincreasing errors bounds for expendituresare $14 wider than the nondifferential errors bounds, but they are $140 narrowerthan the arbitrary errors bounds. The comparisons are similar after accounting forsampling variability. i

IV. Utilization under Universal Health Insurance

We now turn to inferences about healthcare utilization under a hypo-thetical policy of universal health insurance. Let U{¡* = 1) denote the amount ofhealth services an individual would have used in July 1996 if insured. This outcomeis observed in the data only for sample members who are verified to be currently in-sured; it is unobserved for those verified to be uninsured and for those whose insur-ance status is not verified. We wish to leam the population's expected utilization ifeveryone were insured. E[U{r — 1)]. If current insurance status were randomlyassigned, then the utilization among the currently insured, E{U\I* = 1). would rep-resent the besi prediction ofthe utilization rate under universal coverage. Since / ' isnot observed for all individuals, we could instead bound E(U\¡' = 1 ) using the meth-ods derived in the previous sections. As discussed earlier, however, the observed dis-tribution of health insurance coverage in the population is not randomly assigned.Instead, insurance status is affected by characteristics potentially related to the u.seof medical resources.

ln the absence of random assignment or other a.ssumptions, the quantityE[U{r = I)] is not identified even if reported insurance status is always accurate.Unlike identification of the conditional utilization rate E{U\r — I), identificationof the "treatment" outcome E[V{1* = I}] requires knowledge about the counterfac-tual utilization rate of the uninsured had they instead been insured. Uncertainty about

15. We numerically computed bounds under the various assutnptions by searching over logically allowedcombinations of false positives and false negatives {6~.Ö',~.6J' ,6'*}-


the accuracy of reported insurance status, the focus of the current paper, further com-plicates identification of counterfactuals.

To bound the impact of universal coverage on utilization, we begin by using thelaw of total probability to decompose the projected utilization rate under universalcoverage into verified and unverified current insurance status;

(7) E[U{r = 1)] = E[U{r = \)\Y = l]PiY - 1)

= O]P{Y = 0).

The data identify P(Y = I) and P(K = 0) but neither utilization term. The first terminvolving verified insurance status can be written as

E[U{r = 1 ) | K = 1] = E{U\r = l.Y= l ) / > n

l ) | r=O.K= \]{\-Pn)

where P\]^P{I' = l j ^ ^ 1) denotes the status quo insurance rate among verifiedcases. All the terms in Equation 8 are observed except for the counterfactual expectedutilization among the uninsured under the status quo. E\U[r = \)\l' =0.Y — I).Without additional assumptions, this quantity may lie anywhere within the supportof U. [0. supt/].

Returning to Equation 7 and decomposing the third term itivolving the unverifiedcases obtains

(9) E[u(r = i)\Y = Oj = E{u\r = 1, y = O)P¡Q

+ E[U{r= l ) | r = 0 . } ' = 0]{!-Pin)

where Pm = P{r = i\Y = Q) is the status quo insurance rate among unverifiedcases. None of the quantities in Equation 9 are identified. We do not know /*io,and we cannot match healthcare use outcomes to insurance status when insurancestatus is unknown, Intrtxlucing this framework under the implicit assumption that\' = 0. Molinari's (Forthcoming) innovative analysis shows that we can learn some-thing about the first term. E{U\/' = I, K — 0), if the researcher has outside informa-tion restricting the range of P\Q (denoted p in her framework).'*" She estimates thetreatment effect of drug use on employment when drug use is unobserved for partof the sample. We extend her analysis in two dimensions when v > 0.

First, an assumption on v translates into internally generated restrictions on P\o asa function of v. We can write the unobserved insurance rate among unverified cases,P\(), as a function of the reported rate and unobserved misclassification rates:

+ p(i - o,z ' = o|y - o) -p( / = i.z* = o\Y = 0).

Allowing the unidentified terms to vary over their feasible ranges obtains/*i(>e [Pio^P\o\ where

Ift. In Molinari's framework, Y = 0 (our notation) denotes survey nonresponse instead of lack of verifica-[ion. Mulinari (2008) presents a genera] trealment of the idenlitication problem for a variety of measure-ment isNues.


= 0) + min{l-v,/>f/ = O|K = O)}.

When V = 0, P]Q is trivially bounded to lie within [0,1]; at the other extreme whenv = I, Pio = /»( /= I i K - 0 ) .

Second, considering a positive value of v allows us to restrict the expected utiliza-tion rate among the unverifiably truly uninsured, E{U\I' = 0, K = 0). which in tumallows us to tighten Molinari's bounds on the expected utilization rate among theunverifiably truly insured, E(U\r = 1,1' = 0). Her framework can be used to pro-vide sharp bounds at v = 0 and v = \. Proposition 2 allows us to fill in identificationpatterns for values of v between 0 and 1. For a particular value of r, we can bound thepopulation's use of health services under universal eoverage as follows:'

Proposition 2. Given P{Z' — \\Y — 0) S: v and a known value P\o e [P]Q{V),îo(v)]. the population's healthcare utilization rate under mandatory universal in-surance coverage is sharply bounded as follows:

E{U\l = 1, K - l)P{I = I, K - I) + PifíP(Y - 0) ii

E{U\¡ = 1, K = l)P{l = I, K = 1) + PiüPiY = 0) i

+ [/»(/ = O, y = 1} + {i-p,o)/ '(i ' = o)]supí/

where

0 / ^min{<í.{v.

-P{U ^ / , / -

17. This analysis does nol accounl for potential increases in gross prices for healthcare resulling from uni-versal coverage. Since such price increases would not increase ulilJzalion. ihese upper bounds onE(U\l = I ) should still apply. For our main analysis, we also assume Ihat insurance coverage to the unin-sured would be representative of llie curren! mix of public and privaie coverage available lo the insured.


If P\Q is unknown, the lower and upper bounds in Equation IJ are replaced by theinßmum and supremum, respectively, of these bounds over values ofP\Q G [Pu,, Fio].

Proof: See Appendix i.

The proof follows the general outline of Molinari s (Forthcoming) Proposition I der-ivation. Her Proposition 1 is .similar except that her counterparts for the probabilitydistributions G ,̂ and GH implicitly assume that i' = 0 such that nothing is knownabout the reliability of unverified classifications. For thai case, the bounds in Equa-tion II collapse to her bounds after setting n i ( i , v ) = O . H T Í M ' ) = 1, and[^10-/^lo] = [0. 1]. She al.so allows for the possibility that the researcher has outsideinformation restricting Pjo to a range narrower than [0. 1], including the possibilityihal P\{] is known. In that case, something can be learned about E[U{r = l ) |y = 0] even though i l | — 0 and Hi = \. Her bounds are as narrow as possible givenher imposed assumptions.

In the special case that current insurance status is known to be accurately mea-sured {v = I ). the Proposition 2 bounds collapse to the following well-known bounds(Manski 1995):

= \)P{I= 1) Ê\V{r = 1)] <

üiven the absence of reporting errors in this case, the width of these bounds dependsonly on the proportion uninsured, P[I = 0), and the uninsured"s upper bound use ofservices in the counterfactual state of being insured, supt/.

For the binary utilization case, supU in Proposition 2 is naturally set equal to 1.Yet there is no natural limit to the number of provider visits or dollars spent on med-ical services. Unless a researcher is nevertheless willing to set an upper bound on U,it must be recognized that an informative upper bound on E[U(r = 1)] cannot belogically identified under the weak conditions specified in Proposition 2. For ourProposition 2 empirical results, we set supiV to 1.82 for number of visits and to$862 for expenditures reflecting mean values among individuals who (1) perceivedthemselves to be in poor health at the time of the first interview and (2) were verifiedtil be privately insured. These values reflect the 92nd percentile for visits and the 98'^percentile for expenditures. We do not require any assumptions on supU for theProposition 3 bounds or monotone instrumental variable (MIV) bounds that follow.We conservatively treat the insurance rate among unverified classifications. Pio, asunknown. Therefore, we allow this value to lie anywhere within its logically consis-tent range [P^Q, P\(t\, conditional on v (see the last part of Proposition 2).

.A, Monotonicity Assumptions

The preceding bounds can be narrowed substantially under common monotonicityassumptions on treatment response and treatment selection. The monotone treatmentresponse assumption (MTR), introduced by Manski (1997), specifies that an individ-ual's utilization is at least as high in the insured state as in the uninsured state:

(12) i / , ( r = 1) > Ui{r = 0).

Given moral hazard, we would expect some individuals to increase their use of healthservices upon becoming insured; presumably, the use of services would not decline.


Under a monotone treatment selection (MTS) assumption introduced in Manski andPepper (20(X)), expected utilization under either "treatment" (insured or uninsured)would be at least as high among the currently insured as among the currently uninsured:

(13) E[U{r=j)\r = i]Ê[U{r=f)\r=O] for y = O.I.

The MTS assumption is related to adverse selection: those who have self-selectedthemselves into the insured state may tend to be more prone to use health servicesthan Iheir uninsured counterparts. "* While the MTS assumption would presumablynot hold for certain subpopulalions, we only require that the tendency holds on av-erage for the nonelderly population as a whole.

In support of the aggregate MTS assumption, public insurance programs alreadycover some of the least healthy populations. For example, people with substantialdisabilities (who typically need considerable healthcare) are often insured by Med-icaid or Medicare. Most states also use the Medicaid medically needy option to pro-vide coverage to families with children whose healthcare expenditures are quitesubstantial relative to their incomes. More generally, those at relatively low risk ofneeding health services are less likely to seek coverage, as are people less predis-posed to seek health services. For example, low demand for insurance may partly re-flect preferences for avoiding medical care (Vistnes and Monheit 2008). Using theCommunity Tracking Household Survey, Hirth et al. (2006) estimate that 86 percentof workers who were not oftered insurance at their job have low demand for insur-ance. Compared with workers who are offered insurance at their job, they find thatworkers who are not offered insurance tend to be younger, have lower familyincomes, and have less education - all factors as.sociated with lower healthcare use. Incontrast, however, some of the uninsured may have found it difficult to obtain insuranceat affordable prices due to preexisting conditions. Yet while medical underwriting can bea barrier to obtaining private insurance, data from the 1996 MEPS indicate that less than 3petx^nt of uninsured adults were "ever denied health insurance because of poor health."

Some evidence of aggregate adverse selection has been reported in parametric stud-ies of the effects of insurance. Using data from the MEPS to estimate a model of privateinsurance coverage and office-based doctor visits. Deb, Munkin. and Trivedi (2006) findthat half of the observed lower healthcare use among uninsured adults compared withprivately insured adults can be attributed to self-selection rather than the lack of insur-ance. Dor, Sudano, and Baker (2006) find similar evidence of selection into private in-surance.'^ If aggregate MTS does not hold in the population, however, then theProposition 3 upper bound (see below) reverts to tbe Proposition 2 upper bound.

When both MTR and MTS hold, a result in Manski and Pepper (2000, Corollary2.2) implies

(14) E{U) ̂ E[U{r = l)\ ^ E i U \ r = I).

18. The MTS assumption relaxes the commonly imposed "exogenous treatment seteclion" (ETS) assump-tion. E{U{r =y)|/ ' = I] = E[U{r =j)\r =0]forj = {O, l}. thai assumes away the possibility of self-selection (see Manski and Pepper 2000. p. 1(H)1).19, However, the findings by Deb. Munkin. and Trivedi (2006) and Dor, Sudano, and Baker (2006) reiy inpart on the types of parametric a.ssumpüotis we are trjing to avoid.


The lower bound on the population's use of services under universal coverage isE(U), the status quo national utilization rate in the absence of universal coverage.The upper bound is the status quo utilization rate among those currently insured. Thisresult combined with lhe upper bound on £(i/ | /* = 1 ) derived in Proposition I leadslo Ihc following proposition:

Proposition 3. Suppose that the MTR and MTS assumptions hold across the pop-ulation and P{Z* — 1 ¡K — 0)^w. Then the expected use of services under insurance( overage is bounded above by JUdEi where

r ,,, P{U^tJ=i)-a;>{v)-at,P{U>t,IÔ,Y = O)y

tj= l , r = O)} if 8f<0

- { max{O,mm{P{U ^ t,I = 1. K = 0),<t)(v)

-P{U>tJ = 0,Y = 0)}} otherwise

^tJ = \)-P{Ü>tJ = \)-^{v).In the empirical work that follows, we also consider the additional identifying powerOÏ lhe independence and nonincreasing errors assumptions considered in Section

inc.

B. Universal Coverage Results

The fraction of the nonelderly population that used health services in July 1996 was0.206. and lhe mean number of provider visits and exr)enditures were 0.412 and $99,respectively. We are interested in placing worsi-case bounds on average utilizationoutcomes under a policy of mandated health insurance coverage. Our main analysispresumes that new coverage extended to the uninsured would be representative ofthecurrent mix of public and private coverage available to the insured. Later, we con-sider policies that would cover the uninsured by expanding public programs.

In the absence of monotonicity or independence assumptions, the Proposition 2bounds apply. Point estimates of these bounds, along with 95 percent confidenceintervals, are presented in Table 3. Column I. Under the standard implicit assumptionIhal insurance status is reported accurately, v = 1. we estimate that the fraction of thenonelderly population using health services in July if everyone became insuredwould lie in the range ¡Ü.I82. 0.374], with 95 percent confidence interval [0.173,0.383]. In percentage terms, the impact would lie within the range [-12 percent,-1-82 percent), with 95 percent confidence interval [-16 percent, +86 percent]. The es-timated upper bounds on mean provider visits and expenditures per month are 0,712(+73 percent) and $258 (+161 percent), respectively, which rise to 0.735 (+78 per-cent) and $281 (+184 percent) after accounting for sampling variability. In each case,the identification uncertainty associated with unknown counterfactual outcomes ismuch greater than the uncertainty associated with sampling variability. Clearly, wecannot learn much about the impact of universal coverage without imposing strongerassumptions, even if there is no uncertainty about the accuracy of status quo classi-fications. Figures 1 -3 trace out the 95 percent confidence intervals for any use. visits,

430 TTie Joumal of Human Resources

03

•S

"a

c;

USc

1.

"2

o

i g

Sis

(/l c ^

g ïi §ta Û: gai. =o. Ë

îi

LUn .ä

^ il-c ey 3

ö ö ö d d d ö o d d d d d d d d

o c o o o o o o o o o o o o o o

•^ ri

Hjd

00 00 r-l — rl- - , -. , - - , Ï T t l Ô ' . O O O v O O O ' O

Ö Ö Ö Ö Ö Ö Ö ^ÖÖÖÖÖÖÖ

O O O O O O O O

O O O C r ^ M - O — Q C l3 <O O rJ n Tf Q (^

^ u^ "/^ ^ v^ ^ ^

d d d d d d d d

374]

182.

0

o

383

173

0

o

422]

155.

0

o

432

145

0

o

448

153.

0

o

459

o

506]

153.

0

o

142

0

o

712]

362.

0

o

735

339

0

o

779

305.

0

o

801

283

0

o

827

305.

0

o

3 0

O

30

O

985

305.

0

o

006]

283

i

o

o- r- fn o~ ^ rs


Iii.

O)

3 01) O.

u '~

^ ë

!£.§

•a ë


Fraction Using Any Services

95% LÍB under MTR + MTSwhen error rales do nolincrease with ulilizalion

95% UB under MTR + MTSwith nondifferenlial errors

95% UB under arbitrary errorsand no MTR, MTS

95% UB under MTR + MTSwilh orthogonal errors

95% UB uniier MTR+MTS

LB under MTR+MTS

5% LB under artntraryand no MTR. .MTS

0.50 0.55

tup [« half of the

imy be inaccuralc er bound on the proportionof unverified eases thai werereported atcurotely (v)

Figure 1Bounds on the Eraction of the Nonelderly Population that Would Have Used AnyHospital or Ambulatory Services If the Uninsured Had a Mix of Private and PublicInsurance, July 1996

Notes: MTR = monotone ireatment response: an uninsured individual's use would not decline if shebecame insured. MTS = monotone trealment selection: under universal coverage, the currently in-sured would use at least as much services as the currently uninsured. Orthogonal errors imposesP(/'ÎIZ'=Ü) ^P(/'=1|Z*^1). nondifferential errors imposes P(/ =1|/*) = P(/=l|/*.i/). and nonin-creasing error rates imposes P(/ =l|/*=O,i;,) s P(/ =||/"=0,i/o) and P(/ =| | / '=0.f / | ) ^P(/ —1| / ~().í/ü) for Uj ^ i/o where U — use. visits, or expenditures; / = true insurance status;/ — reported insurance status; Z* - I if / ' = /. Vertical dotted lines reflect proposed values of v mo-tivaled in the text. Insurance staius is verified for 67% of the sample. Confidence intervals for thebounds were computed using methods provided by Chemozhukov, Hong, and Tamer (2007).Data: Medical Expenditure Panel Survey Household Component and linked Insurance Component,1996. Sample members age 0 lo 64 as of July, 1996.

and expenditures, respectively, across all values of v between 0.5 and I. As v departsfrom I, the Proposition 2 bounds naturally become even wider.

The Proptjsltion 3 bounds apply when MTR and MTS are imposed. As .seen inTable 3, Column 2 and the figures, the bounds narrow dramatically compared with


Mean Visits

45% UB under arbitrary enorsiiiid no MTR. MTS

95% UB under MTR ^ M T T "when error rales <Iij noiincrease with mlliï.itîon

. y5% UB under MTR + MTS \ „ , „ , , ,„ , ^ , ™ _ „ . ,. , _ . , . , \ 95% UB untkr MTR * M TS

with orthouimal error;, \ , . ,.„, . ,\ with nondllrertnlial errors

\ • * • - - • i i i i W i i i i

LB iinJor MTR+MTS • i " ' " ' * H""

5% LB under arhiirary errüísand 110 MTR, MTS

• <!•

<Í5% UB underMTR + MTS

•

0,47

0.41

0.50 0,55 0,60 0,65 0,70 0,75 0,80 0,85V = 0.84

up to half ui Ihe utivcrifiinsuranoE class illcaliunsmay he inucvtirate

0,90 0.95 1.00v = ü,')2 f

no reponitigerrom

Lower bound on the pn>pi)rtioiiof unverified ca.ses that werereported u^curutcly (vj

Figure 2Bounds on the Nonelderly Population's Mean Number of Provider Vi.sits If theUninsured Had a Mix of Private and Public Insurance. July !996Notes: MTR — motiotone Ireattnem response: an uninsured individual's use would not decline if shebecame insured, MTS — monotone ireatmenl selection: under universa] coverage, the cunently in-jured would use al least as much services as the currently uninsured, Orthogotial errors imposesP(/*^||Z*==Ü) =P{/*:=1|Z'=1). nondiflereniial errors imposes P(/ =Í|/") = P(/ - l | / ' . i / l . itntt notiin-

error rates imposes P(/ ^ | | /*^0. i / | ) < P(/ =l\l'=O.Uo) and P(/ =1|/'=(},Í/,) ^!'(/ - I |/'=O,i/(j) for U, > U[) where U = use, visits, or expenditures; /* = true insurance status;/ ^ reported insurance status; Z" - 1 if / ' — /. Vertical dotted lines reflect proposed values of v mo-livated in the text. Insurance status is verified for 67% of ihe sample. Confidence intervals tor thehounds were computed using methods provided by Chemozhukov. Hong, and Tamer (2007).Data: Medical Expenditure Panel Survey Household Component and linked Insurance Component,l')9ft. Sample members age 0 to 64 as of Juíy, 1996.

Column 1. The lower bounds rise to the status quo utilization rates of 0.412 visits and$99 per month. Similarly, the upper bounds decline, but they continue to depetid onthe value of v. When v = 0.92, for example, the mean number of visits under univer-sal coverage would rise to no more than 0.503 (a 22 percent increase), while per cap-ita expenditures would rise to no more than $124 (a 25 percent increase).


Mean Expenditures ($)

95% UB under urbiirary errorsand 110 MTR, MTS

_

'. '*5% UB undei MTR + MTS iwhen error rales do noiincrt^se with utili/adon

: • • • 95% UB under MTR + MTS\ wjih orthogonol errors

" 'J5% UB under MTR+MTS \ \

I • •; '»5% UB under MTR + MTS /

wiih rinndifrerenliul error>

LB under MTR+MTS

5% ¡.B under arbitraryerrors and no MTR, MTS

SlulUH quo

0.50 0.55 0,60t

up to half of rhe unveriiiedinsumncc (,iui-siri<jHÜi>Tutmay he inatcurule

0,65 0,70 0,75 0,80 0,85 0.90 0.95V = 0,92

1.00

tnil repaning

tower bound on öie proportionof unverltled cases that werereported accurately (i)

Figure 3Bounds on the Nonelderly Population's Mean Hospital and Ambulatory E.xpenditures

If the Uninsured Had a Mix of Private atid Public Insurance. July ¡996

Notes: MTR ~- monoione troaiment response: an uninsured individiiiii's use would noi decline if shebecame insured. MTS — monolone Ireatmeni selection: under universal coverage, lhe currently in-sured would use at lea.st as much services as the currently uninsured. Onhogonal errors imposes

P(/^ t ), and nonin-' = 1). nondifferential errors imposes P(/:= 11creasing error rates imposes P(/ - l | / '=O,i / i ) ^ P(/ =l|/*=O,i/o) and P(/ - l | /*-O,í/ ,) ^P(/ -l|/ '=O,[/o) for i/| 2: i/(j where U = use, visits, or expenditures; /* = true insurance status;/ = reported insurance status; Z* = t if / ' = /. Vertical dotted lines refleci proposed values of v mo-tivated in the text. Insurance status is verified for 67% of the sample. Confidence ititervals for thebounds were computed using methods provided by Chemozhukov, Hong, atid Tatiier (2007),Data: Medical Expenditure Panel Survey Household Componetit and linked Insurance Component,1996. Sample members age 0 to 64 as of July, 1996.

These bounds can be narrowed further under stronger assumptions about the pat-terns of reporting etTors. Columns 3 and 4 in Table 3 present bounds on ElUif = I )]under the orthogonality and nondifferential errors assumptions, respeetively. dis-cussed in Section II!C. We focus especially on the more plausible "nonincreasingerrors" assumption in which the prevalence of insurance status misreporting falls


weakly with the level of utilization. These results are presented in Column 5. Whenr = 0.92, the mean number of visits per month among the nonelderly populationwould rise to no more than 0.463 (a 12 percent increase) under universal coverage,while per capita monthly expenditures would rise to no more than $117 (an 18 per-cent increase).

C. Monotone Instrumental Variables

We next use monotone instrumental variables (MIV) techniques developed by Manskiand Pepper (2(M)0) and extended by Kreider and Pepper (2O()7) to assess how theProposiiion 3 bounds can be narrowed when combined with monotoniciiy assump-uons linking utilization outcomes and observed covariates such as age or health sta-1 us. Consider age and use of health services. The incidence of many health conditionsrises with age, and many health conditions are persistent onee developed. These ten-dencies suggest that, on average, utilization among adults under universal coveragewould be nondecreasing in age. It this assumption holds, then we can improve uponIhe previously derived bounds by enforcing the restriction that upper bounds identi-iied for younger groups cannot exceed upper bounds identified tor older groups.

We treat age and general health status as MI Vs. We divide the population into 18age groups: 0-30, 31-32. 33-34, ..., 63-64." Within each age group, we assume thatuse of services under universal coverage would be nondecreasing in reported worsegeneral health across the following categories: poor/fair, good, very good, and excel-lent. Formally, consider the utilization rate within some age group, age' (the exten-sion to multiple MIV dimensions is straightforward). The age MIV assumption impliesthe following inequality restriction:

(15) agey ^ age' £ age2=>E[U{r = \)\age])]

= \)\age')] <

This mean monotonicity condition for an instrument relaxes the more typical (and^tronger) mean independence assumption. Under mean independence, the inequal-ities across the expectations in Equation 15 would be replaced with equalities (Manskiand Pepper 2000). In our application, however, it is not obvious where to find instru-ments that would satisfy mean independence.

The conditional expectations in Equation 15 are not identified, but they can bebounded using the methods described above. Let LB(uge) and UB(age} be the knowntower and upper bounds, respectively, given the available information on E(U\r.age): in computing these bounds, we assume that MTR and MTS continue tohold. (Under the MTS assumption, note that the treatment / ' is itself an MIV.J Thenusing Manski and Pepper (2(XX). Proposition I ), we have

21). For ihe youngest group, we conservatively choose an age range that extends well inlo adulihood. New-boms tend to use .substantial care, but then the use of services lends to decline with a child's age as theIrcqucniy of rccomnicnded preventive care visits decreases. Use of services tends to rise again inadulthtxxliîlh the onset of chronic conditions.


(16) sup LB{agei) < E{U{r = l)\age')] ^ mf UB{age2).upe, ^ aae' "Í'^J - "S«'

The MIV bound on expected utilization under universal eoverage is obtained usingthe law of total probability;

(17) I P{ageâge-){ sup LB{age:)} < E[U{r = I)]age- agei ^ age'

< I Piage = age'){ inf UB{age2)}.age'

Thus, to find the MIV bounds on the utilization rate, one takes the appropriateweighted average of the lower and upper bounds across the different values of theinstrument. This MlVe.stimator is consistent bul biased in finite samples. To accountfor this bias, we employ Kreider and Pepper's (2007) modified MIV estimator thatestimates and adjusts for finite-sample bias.^'

While there is substantial debate in the literature about the appropriateness of self-reported health variables in regression models of employment (see, for example.Bound 1991). the MIV assumption does not require reported health status lo be anunbiased indicator of true health status or to be exogenously reported. What is re-quired is that utilization under universal eoverage would be nondecreasing in ageand reported health status.^^

The MIV assumptions cannot be verified by the data because the expectations inEquation 15 involve unobserved counterfactual utilization outcomes; moreover, wedo not observe status quo insurance status in the presence of reporting errors. Thejoint assumption that i' = I and MIV-MTS hold, however, potentially ean be rejectedby the data using a test similar to one suggested by Manski and Pepper {2000. foot-note 9). For each age group, agej, and health category, H¿, the following inequalitiesmust hold: 1

E{U\I=l,agej,Hk)Ê[U{f= i)\f = l,

^ E[U{I = \)\I = \,agej-,Hk-]^ E{U\I = \,

Thus, in the absence of measurement error. E{U\/ — I, agej, H/,) should be mono-tonic in age and reported health. For each pair of adjacent age and health statusgroups among the reportedly insured, we conducted a one-sided test of whether uti-lization is decreasing in age and/or in worse health. We conducted identical tests for

21. See Kreider and Pepper (2007) for estitnation details.22. Health status is routinely included as an explanatory variable in paratuciric siudies ol' the effects of in-surance on service use and expenditures, along with an implicit as.sumption of homogeneity ol' effecisacross individuals. While reported health status is difticuli to quantify in surveys and tnay be mi s measured,reported general heallh has external validity in that it predicts mortality and changes in functioning (Idlerand Benyamini 1997; Idler and Kasl 1995). We do no! use reports of chronic condition.s, which lend to bemisreported; ihe uninsured are especially likely lo underrepori conditions because ihey are less likely toseek care and acquire diagnoses (Baker. Stabile, and Deri 2004; Miller, Banihin, and Moellcr 2004).


Ihe probability of service use, number of visits, and expenditures. One test for visitswas rejected ai the 5 percent significance level, but this is not statistically significantLitter accounting for the multiplicity of tests. As seen in Table 4, the nonelderly pop-ulation's use of hospital or ambulatory services among the reportedly insured isI'oughly monotonie in age and perceived health staius. After accounting for samplingvariability, we cannot reject the hypothesis that utilization is monotonie in theseattributes. This is consistent with the many studies that have found that reportedhealth status strongly predicts service use and expenditures (Balkrishnan, Anderson,and Bowton 2()(X); Bicrman et al 1999; DeSalvo et al. 2005: Miilupalo et al. 1997).

1). MIV Results

MIV results are presented in the last two columns of Table 3, assuming MTR andMTS continue to hold. The identifying power of the MTV assumption can be assessedby comparing Columns 2 and 6 for the case of arbitrary error patterns and by com-paring Columns 5 and 7 for the case of "nonincreasing errors." We focus on tbe lat-ter comparison for i' = 0.92. In Column 5. we estimate that the fraction of thenonclderly population using health services in a month would rise no more than13 percent above the status quo to 0.232. Under the additional MIV assumption inColumn 7, we estimate that this fraction would rise no more than 9 percent to0.224. Improvements in the upper bounds for mean number of visits and expendi-tures are similar. Under the MIV assumption, the upper bound on the number of visitsper month improves from 0.463 to 0.444, and the upper bound on expendituresimproves from $117 to $115. Thus, in this setting, visits would increase no more than8 percent under universal coverage and expenditures per capita would increase no

Table 4Percent of Reportedly Insured. Nonelderly Population Using Hospital or Physician

ex by Af;e and Perceived Health Stalu.\. July 1996

Age

Oto 2930 to 3435 to 4040 to 4445 to 5050 to 5455 to 6060 to 64

Excellent

16.115.216.918.318.420.230.424.2

Perceived

Very Good

17.421.120.422.827.228.029.335.8

Health Status

Good

23.621.629.427.4MS26Sn.138.4

Poor or Fair

29.740.541.442.149.851.246.052.6

Dala: Medical Kxpenditure Panel Survey Household Component (19%). Sample members age 0 lo 64 as ofJuly. 1996 reportedly covered by insurance.


more than 16 percent. In what follows, we refer to these estimates as our preferredbounds. I

E. Expanding Public Coverage

To this point, our analysis presumes that the package of health benefits made avail-able to the uninsured under universal coverage would reflect the mixture of benefitsavailable to the privately and publicly insured under the .status quo. Many recent pro-posals for extending health insurance to the uninsured, however, involve expansionsof existing public programs like Medicaid. As part of our sensitivity analysis, we in-vestigate how the estimated bounds in Table 3 would change if we focus attention onpolicies that would cover the uninsured through expansions of public insurance. Todo so, we repeat the preceding nonparametric bounds analysis over the subsample ofindividuals classified as uninsured or publicly insured. Within this subsample, we es-timate upper bounds on utilization under a policy that extends public insurance to theuninsured. Upper-bound utilization rates (for any use, visits, and expenditures) forthe entire nonelderly population are then computed as a weighted average of the.seupper bounds for the non-privately insured and the status quo utilization rates ofthe privately insured.

This approach requires two simplifying assumptions. First, we assume that reportsof private coverage are accurate; any insurance classification errors are confined toerrors among the reportedly uninsured and publicly insured. For cases in which val-idation data are available in the MFPS. Hill (2007/2008) finds that private insuranceis very accurately reported—most respondents are aware of whether they have pri-vate coverage. In contrast, there is evidence of more extensive tnisreporting of publiccoverage in surveys (Call el al. 2(X}7; Card. Hildreth, Shore-Sheppard 2004; Davernet al. 2007). In our restricted sample that excludes the privately insured, the propor-tion of inaccurate insurance classifications is likely to be higher. To account for thisgreater uncertainty, we replace the thresholds v = 0.92 and v = 0.84 considered inthe tnain analysis with the lower thresholds r — 0.89 and v = 0.77.

Second, our approach presumes that service use by the currently privately insuredwould not rise due to the expansion of public insurance. Like the studies by Hadleyand Holahan (2003) and Miller, Banthin, and Moelier (2004), we do not attempt toestimate the potential con.sequences of "crowd oui" in which some people with pri-vate coverage might switch to the newly available public coverage. Based on the lit-erature reviewed by Duchovny and Nelson (2007), .switchers from private policieswould likely comprise between a quarter to a half of new enrollees under an ex-panded public insurance program. Our derived upper bounds in this section are validif the switchers would u.se no more care, on average, under their new public policies.While public programs that require small or no premium payments are potentiallyattractive to many private policyholders, a priori it is not clear whether on balancedifferences in benefits and providers would differentially attract less healthy, pri-vately insured people to public coverage or repel them. Medicaid and SCHIP pro-grams tend to have generous cost sharing and cover more services than privateinsurance, which would disproportionately attract the less healthy. On the other hand,Medicaid typically pays providers lower fees than private insurance, and lower feesreduce provider willingness to participate in the Medicaid program and reduce


enroUees" access to care (Cohen 1993; Mitchell 1991).^^ Econometric studies findsimilar access to care in public and private programs (Long, Coughlin, and Kling2OQ5: Seiden and Hudson 2006), which suggests that any incentive or disincentivefor less healthy individuals to switch from private to public coverage is likelysmall. "̂ If. on balance, healthier privately insured people (or people otherwise lessprone to use care) would be attracted to public coverage, then our estimates remainvalid upper bounds. If the opposite is true, then the bounds depend on supi/ andhence would be wide.

Table 5 presents our estimated upper bounds on the impacts of expanding publiccoverage. The estimates are broadly similar to those presented in Table 3. but the up-per bounds that Incorporate MTR and MTS are uniformly higher for a given degreeof confidence in the data. These higher values do not imply that healthcare expenseswould necessitrily be higher under public expansions than under a mixture of publicund private expansions. Instead, the higher upper bounds reflect more uncertainty abt)utthe impacts of public expansions. Recall from Table 1 that the status quo use of healthservices is greater among the publicly insured than among the privately insured. Thesedifferences are reflected in the upper bounds. Moreover, the confidence intervals arewider for expanding public coverage than for covering the uninsured with a mix of pri-vate and public insurance. These wider intervals reflect smaller samples of peoplereporting public coverage than people reporting any insurance.

When V = 1 and the MIV assumption is not imposed, the upper bound on the meannumber of tnonthly provider visits per month by the nonelderly population under uni-versal coverage rises from 0.448 with a mix of private and public coverage {Table 3)to 0.473 with expanded public coverage (Table 5). The upper bound on meanmonthly expenditures rises from $114 to $121. When the MIV assumption is addi-tionally imposed, the upper bound on visits ri.ses from 0.440 to 0.457, and the upperbound on expenditures rises from $114 to $120. Our preferred results presented inColumn 7 impo.sc MIV with nonincreasing errors. When v - 0.89. the fraction ofthe nonelderiy population using services during a month under expanded public in-surance would rise no more than 14 percent to 0.235, the mean number of monthlyvisits would rise no more than 22 percent to 0.503, and mean monthly expenditureswould rise no more than 26 percent to $125.

V. Comparisons with Parametric Studies

Parametric point estimates of increased healthcare utilization underuniversal coverage lie within our preferred estimated bounds. These estimates, whichimpose MTR, MTS, MIV, and "nonincreasing errors." are reported in Table 3, Col-umn 7 with V = 0.92 when expanded coverage involves a mixture of public and

23, Hadley and Holahan (2003/21)04) provide evidence lhat public coverage reduces health expendituresrelalive lo private coverage, consisiem with lower fees paid [o providers by Medicaid than by private in-surance,14. Several ecnnometric studies of service use find no differenlial impact of private relative to public cov-erage for a variety of populations and mca,sures of service use (Glied et al. 1998; Hadley and Holahan 2003;Kaesmer 1999; Long, Coughlin. and Kling 2005; Seiden and Hudson 2006).

440 The Joumal of Human Resources

f

I3es

< -S

.fl2 ta

"S E«

ö d d ö d d d o d d d ö ö d d d

o o o o o o o o

00 o oo 00 t-- 00 00

i

Ö Ö Ö Ö

O n ij-iO [ 1r- >o r-

O O O O O O O - T O O O O O O

d

ErP

f^ oo ^^ CO 00 [^ ^D o^ f^ r—• ^1 t—• ^ *o i n ^?r ^ f i f ^ - ^ ^ i n ï n i n . [ í ^ ^ a ^ o ^ ^ - ^ ^ v % f N l nc s r - t f s r i r ^ r i n f N • 5 ; ' ^ ^ . ' ^ ' ' ' ; ' ' ^ ' O ' ' ^ ' ' l

.s o o o o o o o o

O¿ d d d d d d d d

o o o o o o o o

r - o \ o o — o o r t c f > n

öööööööö

374]

0

383]

173

0

0

405]

0

415]

0

405]

0

415]

0

405]

0

415]

0

708]

358.

0

0

732]

335

0

0

770]

791

-Ton

335.

031

4 0

lie

f\

0 —1 00 - -

= 0 o_ 0

^ m P ;^2, £, 0 0

Kreiderand Hilt 441

ST ' ^ i l

— u ç II

= £ 17 VI I

. " I

2 2« II — o

r. E

5 ,ç u —S II

'^è.

T3U

ç

c

• a

5• 3no/

=

3Vl

c'5

t:

• . . .

£

o

• ~

Í3

s: -3 "îJ

2 O bcma.Si

a i

S.

sÍ J

53

¡5 S '3 "3" ~ ?) Q. "J

a.ss .=

l ' a

tlil

3

.s íi


private insurance and in Table 5; they are reported in Column 7 with v = 0.89 whenpublic coverage is extended to the uninsured.

In parametric studies., Miller. Banthin. and Moeller (2004) and Hadley and Holahan(2003) estimate that expanding public programs to cover all the uninsured would in-crease annual total expenditures between 9 percent and 10 percent. Our correspond-ing nonparametric upper bound when v — 0.89 is 26 percent. Their estimates, likeour own, do not account for any crowding out of private coverage. Their models as-sume no measurement error, and self-seleclion into insured status is allowed onlythrough a set of observed characteristics. One likely reason our worst-case upperbounds are substantially higher than their point estimates is that we do not imposethe homogeneity assumption that the impact of insurance coverage on utilizationis identical across individuals with the same observed characteristics. Miller. Banlhin.and Moeller and Hadley and Holahan also estimate that covering the uninsured witbprivate insurance would increase annual total expenditures between 11 percent and17 percent, depending on their specific a.ssumptions. For Massachusetts. Blumberget al. (2006) estimate the impact of potential expansions that would resemble themixture of private and public coverage expansions enacted in that state. They esti-mate that expenditures would increase by about 12 percent.^^ Our corresponding up-per bound when v = 0.92 is 16 percent.

Buchmueller el al. (2005) review studies of the impacts of insurance on theamount of service use. Relying on a variety of comparison methods, parametric stud-ies find that having insurance increases vi.sits among the uninsured between 16 per-cent and 106 percent. More recent studies, however, find a narrower range of effects.Seiden and Hudson (2(X)6) estimate that expanding public insurance to cover unin-sured children would increase their annual probability of having an ambulatory visithy 54 percent, corresponding to an increase of about 7 percent across the nonelderlypopulation as a whole. They find that private coverage would increase the annualprobability by 61 percent, corresponding to an increase of about 8 percent acrossthe population as a whole. Estimates in Deb. Munkin, and Trivedi (2006) suggest thatexpanding private insurance to uninsured adults would increase their number of of-lice-based visits by about 46 percent, corresponding to an increase for tbe adult pop-ulation of about 5 percent. Hadiey and Holahan (2003), who do not account forunobserved factors, estimate that public coverage would increase the annual numberof office-based visits among the uninsured by 41 percent, while private insurancewould increase visits by 30 percent. Their estimates correspond to increases of 5 per-cent and 4 percent, respectively, among all nonelderly. For expansions involving amixture of private and public insurance, our esiimated upper bound on the increasein monthly office-based and hospital outpatient visits is 8 percent.

VI. Conclusion

Policymakers have long been interested in identifying the conse-quences of uninsurance for access to healthcare and the potential impacts of

25. They model premiums, rather than heallhcare expenditures, so their estimates implicitly include insur-ance loading as welt as expenditures for healthcare services.


universal coverage (for example. Institute of Medicine 2003). Identification of pol-icy outcomes, however, is confounded by both the unobservability of counterfac-luals and the potential unreliability of self-reported insurance status. To accountlor these two dislincl types of uncertainty, we developed a nonparametric frame-work that extends the literature on partially identified probability distributionsand treatment effects. Using the new analytical results, we provided tight boundson the impact of universal health insurance on provider visits and medical expen-ditures. As part of the paper's contribution, we showed how to partially identify theconditionai mean of a random variable for the case that a binary conditioning var-iable—in our case health insurance—is subject to arbitrary endogenous measure-ment error.

Our conservative statistical approach provides informative bounds on parametersof interest without imposing parametric assumptions. We began by corroboratingself-reported insurance status for a nonrandom portion of ihe MEPS sample usingoutside information from insurance cards and followback interviews with employersand insurance companies. We allowed for the possibility of insurance reportingerrors within the remainder of the sample and illustrated the sensitivity of our empir-ical results to alternative verification, monotonicity, and independence assumptions.For our preferred estimates, we introduced a "nonincreasing errors" assumption thatrelaxes the strict nondifferential independence assumption embodied in the classicalerrors-in-variables framework. In our application, the weaker monotonicity assump-tion retains much of the identifying power of the independence assumption whileallowing for the possibility that using health services may inform a patient of her trueinsurance status.

Our primary analysis considers the impact of extending insurance to the uninsuredusing the mix of public and private coverage prevalent under the status quo. Pro-grams intended to cover the uninsured in Massachusetts, Maine, and Vermont, andproposals by some presidential candidates, would cover the uninsured with both pri-vate and public insurance. We estimate that the fraction of the nonelderly populationusing ambulatory or hospital services would rise no more than 9 percent under uni-versal coverage. We further estimate that per capita monthly provider visits wouldrise by no more than 8 percent, and mean expenditures per month would rise no moreihan 16 percent. These estimated upper bounds rely on an assumption that no morethan 8 percent of unverified insurance classifications are misreptirted. While the ac-curacy of unverified insurance responses cannot logically be known, we have relaxedthe standard implicit assumption that all classifications are known to be accurate. Un-der our preferred monotonicity assumptions, we find that our estimates are not par-ticularly sensitive to the degree of reporting error within plausible ranges. Thissuggests that, contrary to some assertions, uncertainty about the number of uninsuredmay not be a major impediment to developing programs to cover the uninsured. Ourestimaled upper bounds on the effects of expanding public coverage, however, arenot as tight.

Our analysis has several limitations. First, the cost of covering the uninsured willdepend in part on the generosity of benefits, but our treatment effect approachignores heterogeneity across plan types in treating insurance as binary. Second,our most informative bounds rely on an unverifiable assumption that, on average,households who tend to use more health services have already self-selected

444 The Joumai of Human Resources

themselves into the insured state. While we impose this assumption only across thenonelderly population as a whole (allowing for the possibility that this tendency isreversed within some subpopulations), the validity of the assumption cannot be di-rectly verified. Third, our methods are less useful for estimating the cost of coveringan additional person. Marginal analyses require stronger assumptions about the char-acteristics of the newly insured. Finally, the healthcare system continues to evolve,and our 1996 data (which contain the best available validation information) weregathered before SCHIP was implemented.

The methods developed in this paper can be applied to a wide range of topics thatinvolve identification of conditional expectations or treatment effects given uncer-tainty about the accuracy of a conditioning variable. Our framework, for example,offers an alternative approach to Blau and Gilleskie's (2(K)I) parametric analysisofthe impact of employer-provided retiree health insurance on retirement outcomes.In lhe Health and Retirement Study data used in their study, about 13 percent of therespondents nearing retirement age .said they were unsure about whether they had re-tiree insurance—ihus forming a natural subpopulation of respondents to be charac-terized as providing unreliable treatment information. The methods in this papercould be used to bound lhe effects of retiree insurance on employment, informingpolicymakers about the potential consequences of allowing retirees younger ihan65 to purchase Medicare coverage. More generally, we expect this developing lineof research to improve researchers" understanding of the consequences of nonclassi-cal measurement error for inferences, which should in tum yield more informed pol-icy analyses. i

APPENDIX 1

Proofs

Proof of Proposition 1. To place bounds on A, we begin by logically determining thelowest feasible value of F(Í7 ^t\¡' = I). Differentiating the right hand side of Equa-tion 3, we find that this quantity is increasing in fl|^, the unobserved fraction of indi-viduals with U > t misclas.sified as being insured, and in 6", the unobserved fractionof individuals with U ^ t misctassified as being uninsured. As a worst-case possibil-ity for the lower bound, we must therefore set 6^* = 6," = 0 to obtain;

(18) f(t/^,ir = i )^^y/ , | -_;= •)-;•_.

While 6;̂ and B'~ are unobserved, their ranges are restricted. The unobserved frac-tion that was falsely classified as insured, Ö* = P{U•^tj = \,Z' = 0), cannot ex-ceed the observed fraction that was classified as insured with unknown insuredstatus. Nor can this fraction exceed the total allowed fraction of misclassified cases,^{v) = ( l-v ')P(J ' = 0). Similarly, the unobserved fraction of individuals that wasfalsely classified as being uninsured, 9) ~ = P{U > tJ = 0,Z* — 0), cannot exceedthe observed fraction that was classified as being uninsured with unknown insuredstatus; nor can it exceed the total fraction of misclassified cases:


O ̂ e r < min{(|)(v

To find the lower bound of P(U^t\r = I), we must find the minimum feasiblevalue for the right-hand side of Equation 18. Therefore, for any candidate value of0*, we need 9̂ ~ to attain its maximum allowed value conditional on fi¡^:

tJ = 0,Y = 0)}.

The objective then becomes one oí" minimizing

p{l= l ) -e;- +min{<|)(v)-9

over feasible values of 0^.

Define 0,*" = 4>{v)-P{U >t,I = O,Y = 0), the critical value of 6^ that makes thetwo arguments in the min function equal. First consider values of 6^ ̂ Q*". For suchvalues, the derivative of Equation 19 with respect to fl^ is negative; therefore,we can^ exclude as potential candidates any values of 6* less than 9̂ ^̂ ^̂ = max{0,min|B*,6;^" > >. For 9^>6*", the derivative ha.s the same sign as

(20) h^^p{u < / , / = \)-p{u>t,i ^ i)-*!^)-

When this quantity is negative, we must raise 9^ to its maximum feasible value,Q¡; otherwise, we set H* equal to B* |„. Similar logic provides an upper bound onP{U ^ l | r = 1). After defining h';^P{U>t,l= \)~P{V^t,¡= l)-<t)(v), thepreceding results establish Proposition 1.

Proof of Proposition 2. Using Molinari's (Forthcoming, p. 9) decomposition forthe case of missing observations, we begin by writing the distribution of U amongunverified cases as a weighted average ofthe distributions among unverified insuredand uninsured cases:

(21) / ' ( t /<r |K = o ) = / ' ( { / ^ / | r = i , y = o ) p , o + P ( i / s / | r = o ,K=o) ( i -p ,o ) .

First consider a particular value of Pw e (0, t). Solving for the fraction constimingU^t among the unverified currently insured implies

(22)

The quantity / ' ( i / s / ] / ' = 0, K = 0) in the right-hand-side can be rewritten as

The upper bound on this quantity is obtained by setting ^~ = 0 and 0̂ equal to itsmaximum feasible value. From Section lllA, we know 6* s 9¡''. Combined with the


requirement thatflU s / |/* ^ ^ 0 , K = 0) < I, the value of 6/" is restricted to lie in the

range O ^ 6 ^ ^ 0 ¡ ^ (where 0^ is defined in the proposition). The lower bound isobtained by setting H,"̂ - 0 and 8~ equaljo its maximum feasible value, where 6~

is restricted to lie in the range 0^&; ^ 0 / . Thus. P{Ü ^ t\r = 0. K = Ü} in Equa-tion 23 is bounded to lie within [Hi (/, v).n2(/. v}]- Varying P{U-^t\r = 0, K = 0)

in Equation 22 within this feasible range reveals that P{U:^t\r = l , } ' = 0) mustlie within the range [G¿(r, v),G//(r, v)]."̂ * Integrating across values of r, expected

healthcare utilization among the unverifiably truly insured is bounded as follows:

(24) fudGn ^ E{U\r = 1, y = 0) ^ íudG

Continuing with the case Pio G (0,1), applying this result to the first term in Equa-tion 9 and varying E\U{r = | ) | r = 0. y =;'] within ¡O,supi;] for; ^ 0.1 in Equa-

tions 8 and 9 yields the Proposition 2 bounds. These bounds also apply when P[o is

1 or 0. ln the former case, E[U{r = l)|K = O)] in Equation 9 is identified as

E{U\r = ],Y = O)Ê{U\Y = O) since £(t / [y = 0) = £ ( i / | r = 1, Y =O)P,o +

£:(t/ |r = 0 , >' = O)(l- / ' io) . For Pio = O, we only know that E[U{r = \)\Y =

0)] = E[U{r = 1)1/' - 0, K - 0)] 6 [0, supi/].

References

Aigner, Dennis J. 1973. "Regression with a Binary Independent Variable Subject to Errors of

Observation." Journal of Econometrics l(l):49-59.Baker, Michael, Mark Stabile, and Catherine Deri. 2004. 'What Do Self-Reported, Objective,

Measures of Health Measure?" Journal of Human Resources ."^9(4): 1067-93.Banthin, Jessica S.. and Merrile Sing. 2006. "How Medicaid Enrollnienl Estimates from

MEPS Compare with Administrative Totals." Rockviile. Md.: Agency for Healthcare

Research and Quality, internal tnemorandutn.Balkrishnan. Rajesh, Roger T. Anderson, and David Bowton. 2000. "Self-reported Health

Status Predictors of Healthcare Services Utilization and Charges in Elderly Asthmatic

Patients." Journal of Asthma 37{5):4l5-23.Berger, Mark C , Dan A. Black, and Erank A. Scott. 1998. "How Well Do We Measure

Employer-Provided Health Insurance Coverage?" Contemporary Economic Policy

16(3):356-67.Bierman, Arlene S., Thomas A. Bubolz, Elliott S. Fisher, and John H. Wasson. 1999. "How

Well Does a Single Question aboul Health Predict the Financial Health of Medicare

Managed Care Plans?" Effective Clitiical Practice 2(2):56-62.Blau. David M.. and Donna B. Gilieskie. 2001. "Retiree Health Insurance and Labor Force

Behavior of Older Men in the 1990s." Review of Economics and Statistics 83(1 ):64-80.Blumberg, Linda J., John Holahan. Alan Weil, Lisa Clemans-Cope. Matthew Buettgens.

Fredric Blavin, and Stephen Zuckerman. 2006. "Toward Universal Coverage inMassachusetts." Inquiry 43(2):102-2L

26. Note that v > 0 also directly places restrictions on P{U ̂ ¡\I' = 1, K = 0). However, we ean show thatthe direct restrictions on this quantity represent a subset of the restrictions imposed on it indirectly via cherestrictions on P{U^(\I' = 0, K = 0).


Büllinger. Christopher R. 1996, "Bounding Mean Regressions When a Binary Variable isMismeasured." Journal of Econometrics 7.1(2):387-99.

Bound, John. 1991. "Self-Reported Versus Objective Measures of Health in RelirenieniModels." Journal of Human Resources 26( l);106-38.

Bound. John, and Richard V Burkhauser. 1999. "Economic Analysis of Transfer ProgramsTargeted on People with Disabilities." ln Hamihaok of Uibor Economics, vol. 3C, eds.Orley AsKenfelier and David Card. 3417-3528. Amsterdam: Elsevier Science.

Bound, John, Charles Brown, and Nancy Mathiowetz. 2(K)1. "Measurement Error in SurveyData." ln Handbook of Econometrics., vol. 5, eds. James J. Heckinan and Edward Learner,3705-3843. Amsterdam: Elsevier Science.

Buchmueller, Thomas C , Kevin Gmmbach. Richard Kronick. and James G. Kahn. 2005."The Effect of Health Insurance on Medical C;ire Utilization and Implications forInsurance Expansion: A Review of the Literature." Medical Care Research and Review62(1)13-30.

Call. Kathleen Thiede, Michael Davem. Gestur Davidson, and Rebecca Nyman. 2007."Accuracy in Self-Reported Heallh Insurance Coverage and Bia^ to Survey Esiimaies ofUninsurance." Presentalion at the Academy Heallh Annual Research Meeting. Orlando. R.

Card, David, Andrew K. G. Hildrcth. and Lara D. Shore-Sheppard. 2004. "The Measurementof Medicaid Coverage in the SIPP: Evidence from a Comparison of Malched Records."Joumul of Business and Economic Statistics 22{4):410-20.

Chemozhukov, Victor, Han Hong, and Elie Tamer. 2(X)7. "Estimation and ConfidenceRegions for Parameter Sets in Econometric MiMJels." Econometrica 75(5): 1243-84.

Cohen, Joel. 1993. "Medicaid Physician Fees and Use of Physician and Hospital Services."¡n</iiiry 30(3):281-92.

. 1997. "Design and Methods of the Medical Expendiiure Panel SurveyHousehold Component." MEPS Methodology Report no. 1. AHCPR Pub. no. 97-0026.Rockville. Md.: Agency for Health Care Policy Research.

Czajka. John L.. and Kimball Lewis. 1999. "Using Universal Survey Data to AnalyzeChildren's Health Insurance Coverage: An Assessment of Issues." Washington, D.C.:Malhemalica Policy Re.search, Inc.. http://aspe.os.dhhs.gov/health/repons/Surveypercent20Data.hlni.

Davem, Michael. Jacob Klerman. David Botigh. Gary Ciborowski, Kathleen Thiede Call,Gestur Davidson, and Lynn Blewett. 2(.K)7. "Fitting Square Pegs Into Round Holes:Linking Medicaid and Cutrent Population Survey Data to Understand the 'MedicaidUndercount."" Presentation at the Centers for Medicare and Medicaid Services, Baltimore,Md.

Deb. Pariha, Mural K. Munkin. and Pravin K. Trivedi. 2006. "Privaie Insurance, Selection,and Health Care Use: A Bayesian Analysis of a Roy-Type Model." Journal of Business andEconomic Slatislics 24(4):4()3-l5.

DeNaves-Walt, Carmen. Bernadette D. Proctor, and Cheryl Hill Lee. 2005. Income, Poverty,and Heallh Insurance Coverage in the United States, 2004. U.S. Census Bureau, CurrentPopulation Reports P6()-229. Washington, D.C.: GPO.

DeSalvo. Karen B., Vincent S. Fan, Mary B. McDonell, and Stephan D. Fihn. 2005."Predicting Mortality and Healthcare Utilization with a Single Question." HSR: HealthServices Research 40(4): 1234-46.

Doniinitz. Jeff, and Roben P. Sherman. 2004. "Sharp Bounds Under Contaminated orCorrupted Sampling wilh Verification, with an Application lo Environmental PollutantData." Journal of Agricultural. Biological and Environmental Statistics 9(3):3l9-38,

Dor, Avi, Joseph Sudano. and David W. Baker. 2006. "The Effect of Privaie Insurance on theHeatlh of Older, Working Age Adults: Evidence trom the Health and Retirement Study."HSR: Health .Sfmccv Research 41(3, Part I):759-87.


Duchovny, Noelia, and Lyie Nelson. 2O()7. 771? State Children's Health Insurance Program.Washington, D.C.: Congressional Budget Office.

Frazis, Harley. and Mark A. Loewenstein. 2003. "Estimating Linear Regressions withMismeasured. Possibly Endogenous, Binary Explanatory Variables," Journal ofEconometrics 117( 1 ): 151 -78.

Gertin, Michael, and Martin Schellhom. 2006. "Nonparametric Bounds on the Effect ofDéductibles in Health Care Insurance on Doetor Visits—Swiss Evidence." HealthEconomics 15(9):l()II-2().

Glied. Sherry. A. Bt)wen Garrett. Christina Hoven, Maritza Rubio-Stipec, Darrel Regier,Robert E. Moore. Sherryl Goodman, Ping Wu, and Hector Bird. 1998. "Child OulpalientMental Health Service Use: Why Doesn't Insurance Matter?" Journal of Mental HealthPolicy and Economics I (4): 173-87.

Gruber. Jonathan, and Brigitte C. Madrian. 2004. "Health Insurance, Labor Supply, and JobMobiliiy: A Critica! Review of the Literature," In Health Policy and the Uninsured, ed.Catherine G. McLaughlin. 97-177. Washington. D.C: Urban Institute.

Hadley. Jack, and John Holahan, 2003/2004. -Is Health Care Spending Higher underMedicaid or Private !n.surance?" Inquiry' 40(4):323-42.

. 2003. "Covering the Uninsured: How Much Would It Cost?" Health AffairsSupplemental Web Exclusives W3: 250-265.

Hill. Steven C. 2007/2008. "The Accuracy of Reported Insurance Status in the MEPS."Inquiry 44(4):443-68.

Hirth, Richard A.. Reagan A, Baughman, Michael E. Chemew, and Emilie C. Shelton. 2006."Worker Preferences, Sorting and Aggregate Patterns ol" Health Insurance Coverage."International Journal of Health Care Finance and Economics 6(4):259-77.

Holahan, John, and Linda Blumberg. 2006. "Massachusetts Health Care Refotin: A Look atthe Issues." Health Affairs 25: w432-w443.

Horowitz, Joel L., and Charles F. Manski, 1995. "Identification and Robustness withContaminated and Corrupted Data." Econometrica 6.'1(2):281-302.

. 1998. "Censoring of Outcomes and Regressors Due to Survey Nonresponse:Identification and Estimation Using Weights and Imputations." Journal of Econometrics84(0:37-58.

Hudson. Julie L., and Thomas M. Seiden, 2007, "Children'.s Eligibility and Coverage: RecentTrends and a Look Ahead." Health Affairs 26(5): w618-w629.

Hunter. Derek. 2004. "Counting the Uninsured: Why Congress Should Look Beyond theCensus Figures." Web Memo #555. Washington, DC: Heritage Foundation.

Idler. Eilen L., and Yael Benyamini. 1997. "Self-rated Health and Mortality: A Review ofTwenty-seven Community Studies." Journal of Health and Social Behavior 38( I ):21-37.

Idler, Ellen L., and Stanislav V. Kasl. 1995. "Self-ratings of Health: Do They Also PredictChange in Functional Ability?" Journal of Gerontology 5()B(6): S344-S353,

Institute of Medicine. 2003, Hidden Costs, Lost Value: Uninsurance in America. Washington,D.C.: National Academy Press.

Kaestner. Robert. 1999. "Health Insurance, the Quantity and Quality of Prenatal Care, andInfant Health." Inquiry 36(2): 162-75.

Kaiser Commission on Medicaid and the Uninsured. 2007. "State Initiatives to CoverChildren." Washington, D.C: Kaiser Family Foundation,

Kaye, Neva, and Andrew Snyder 2(H)7. "Health Reform in Maine, Massachusetts, andVermont: An examination of State Strategies to Improve Access to Affordable, QualityCare." Augusta, Me.: Maine Health Access Foundation Issue Brief,

Kreider, Brent, and John V. Pepper. 2007. "Disability and Employment: Reevaluating theEvidence in Light of Reporting Errors." Journal of the American Statistical Association,


Levy, Heien, and David Meltzer. 2004. "What Do We Reaiiy Know About Whether HealthInsurance Affects Heallh?" In Health Policy and the Uninsured, ed. Catherine G.McLaughlin. 179-204, Washington, D.C.: Urban Institute.

Lewbel. Arthur. 2007. "'Estimation of Average Treatment Effects with Misclassification."Econometrica 75(2);537-51,

Long, Sharon K., Teresa Coughlin, and Jennifer Kling. 2005. "How Well Does MedicaidWork in Improving Access to Care?" HSR: Heidth Services Re.iearch 40(l):39-58.

Manski, Chartes F. 1995. Identification Problems in the Social Sciences. Cambridge, Mass.:Harvard University Press.

_ . 1997. "Monotone Treatment Response." Econometrica 65(6):13i 1-34.Manski. Charles F., and John V. Pepper. 2000. "Monotone Instrumental Variables: With an

Application to the Retums to Schooling," Econmnetrica 68(4):997-IOI0,Miilupalo. Seppo. llkku VuoH, Pekku Oja. Matti Pasanen, and Heiku Urponen. 1997, "Self-

rated Health Stalus as a Health Measure: The Prediclive Value of Self reported HealthStatus on the Use of Physician Services and on Mortality in lhe Working-age Population."Journal of Clinical Epidemiology 50(51:517-28,

Miller, G, Edward, Jessica Banthin, and John Moelier, 20(M, "Covering the Uninsured:Estimates of (he Impaci on Total Health Expendilures for 2002," .A,HRQ Working Paper04007. Rockviile, Md.: Agency for Healthcare Research and Quality.

Mitchell, Janet. 1991. "Physician Participation in Medicaid Revisited." Medical Care29{7):M5-53.

Molinari, Francesca. Forthcoming, "Missing Treatments." Journal of Business and EconomicStatistics.

. 2008. "Partial Identification of Probability Distributions with MisclassifiedDala." Journal of Econometrics 144(n:81-! 17

Monheit, Alan C , and Jessica Primoff Vistnes. 2008, "Health Insurance EnrollmentDecisions: Preferences for Coverage, Worker Sorting, and Insurance Take Up." Inquiry45(2):153-67.

Nelson, David E., Betsy L. Thompson. Nancy J, Davenporl, and Linda J. Penaloza. 2000,"What People Really Know about Their Health Insurance: A Comparison of InfonnationObtained from Individuals and Their Health Insurers," American Joumai of Puhlic Health90(6): 94-8.

Nelson, Lyle. 2003. How Many People Lack Health Insurance and For How Long?Washington, D.C.: Congressional Budget Office,

Olson. Craig A. 1998. "A Comparison of Parametric and Semiparametric Estimates of theEffecl of Sp(tusal Health Insurance Coverage on Weekly Hours Worked by Wives."Jintrnal of Applied Econometrics 13(5):543—65.

Piiscaie, Joanne. 2(K)7. "Measuring Health Insurance in the U.S." Research Report Series(Survey Methodology #2(M)7-1!). Washington, DC: US Census Bureau. StatisticalResearch Division.

Peterson, Chris L., and April Grady. 2005. Medicaid/SCHIP Enrollees: Comparison of Countsfrom Administrative Daia and Survey Estimates. Washington, DC :̂ Congressional ResearchService.

Seiden, Thomas M., and Julie L. Hudson. 2006. "Access to Care and Utilization AmongChildren: Estimating the Effects of Public and Private Coverage." Medical Care 44(5Supplcmeni): I-I9-I-26,

WoUer. Kirk M. 1985. Introduction to Variance Estimation. New York: Springer-Verlag.Woolhandler, Steflie. and David U. Himmelstein. 2007. "Health Reform Failure." Boston

Glohe. September 17, A15.

Documents

Partially Identifying Treatment Effects with an ...faculty.smu.edu/millimet/classes/eco7377/papers/kreider hill.pdf · Partially Identifying Treatment Effects with an Application