This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research

Volume Title: The Role of Health Insurance in the Health Services Sector

Volume Author/Editor: Richard N. Rosett

Volume Publisher: NBER

Volume ISBN: 0-87014-272-0

Volume URL: http://www.nber.org/books/rose76-1

Publication Date: 1976

Chapter Title: Demand for Health Care among the Urban Poor, with Special Emphasis on the Role of Time

Chapter Author: Jan Paul Acton

Chapter URL: http://www.nber.org/chapters/c3819

Chapter pages in book: (p. 163 - 214)

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163

JAN PAU

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165

5JAN PAUL Demand for Health

Care among theUrban Poor, withSpecial Emphasis onthe Role of Time

1. INTRODUCTIONThis study examines the demand for medical services by type ofprovider with particular emphasis on the role of time as a determin-ing factor. The demand for health and medical services has at-tracted considerable interest in recent years because of the drama-tic increase in health expenditures and because of substantial costinflation in that sector. Although the causes of this rise in demandand cost inflation are complex to analyze, there is reason to believethat the substantial spread of reimbursement insurance in the lasttwenty years has played a major role by reducing the out-of-pocketmoney price the consumer faces in buying medical care.' Healthresearch is focusing more and more on the economic determinants

This report was sponsored by the New York City Health Services Administration and the U.S.Office of Economic Opportunity as R-1151-OEOINYC. I would like to thank Y. Ben-Porath, D.DeTray, A. Ginsberg, M. Grossman, H. Luff, C. Morris, J. Newhouse, L. Orr, C. Phelps, IiZeckhauser, and the two discussants for useful comments and suggestions at various stages ofthis work. The views expressed here are those of the author and not necessarily those of TheRand Corporation or its sponsors.

165

of this demand, explicitly including third-party expenses.2 Surpris-ingly, there has been almost no discussion of alternative rationingmechanisms that might become effective if money prices continueto decrease in importance as a result of spreading third-partyreimbursement. Since there is every reason to believe that moneyprices will continue to decline in relative importance because of(1)the secular trend in third-party coverage, (2) the rising opportunitycost of time, (3) increases in time required to receive care, and,perhaps most important, (4) the prospect of national health insur-ance, it is necessary to examine other factors that may controldemand.

This paper suggests that travel time and waiting time may replacemoney prices as the chief determinant of demand.3 First, a model ofthe demand for medical services is developed with time explicitlyincluded as part of the price of the goods purchased. From themodel we predict that the time-price elasticity of demand formedical services will exceed the money-price elasticity as out-of-pocket money prices decrease, and also that changes in time priceswill have a greater effect on demand for free medical services thanon the demand for non-free services. We can further predict adifferential effect of earned and non-earned income on the demandfor medical services. A rise in non-earned income increases thedemand for medical services; the effect of a rise in earned incomecannot be predicted because it produces both an income and a priceeffect (by raising the opportunity cost of time).

The data used to test the predictions of this model were takenfrom two household surveys conducted in New York City. The cityis a particularly good laboratory to estimate the importance of timeprices and possible behavior under national health insurancebecause of the long-standing availability of free ambulatory andinpatient care through municipal hospitals and clinics. Thus, weget some notion of the steady-state behavior of a population withfree, governmentally sponsored care available. Demand equationsare estimated for four types of medical care: public ambulatory,private ambulatory, public inpatient, and private inpatient. Inaddition to a number of controlling variables for health andsociodemographic status, the important explanatory variables in-clude travel and waiting times for alternative sources of care, andearned and non-earned income. The results indicate that in low-income neighborhoods of New York City, time-price elasticitiesalready exceed the money-price elasticity of demand for care.

The paper concludes with a number of implications for policy

I

with regarbulatory fasidies for s

2. CONSUl'MEDICAL

Details of I3;4 the majtrates on tnon-earneiThe empirandity, the forservices, Idrawn.

Assumemedical sservices.sume m airepresente

Maximiz

(la) U=U(m,

subject to(ib) (p

whereU = utilm = meX = allp = outt = owq = moS = OW

w = earY =y = norT =

goc

161 Di1661

Acton

nses.2 Surpris-ative rationingrices continueng third-partyye that moneybecause of(1)ig opportunityive care, and,1 health insur-may control

may replaceirst, a model oftime explicitlysed. From thef demand foricity as out-of-in time prices

1 services thanther predict aon the demandincreases the

incomeme and a price

Lel were takenCity. The city

of timeith insurancenbulatory andlies. Thus, we where)pulation with u =and equations mic ambulatory, x =

inpatient. In p =health and t =

variables in- q =of care, and

te that in low-ice elasticities =d for care. =ions for policy

167 Demand for Health Care among the Urban Poor

with regard to locating health facilities, queuing practices at am-bulatory facilities, and the possibility of substituting income sub-sidies for subsidies for medical services.

2. CONSUMPTION MODEL OF THE DEMAND FORMEDICAL SERVICESDetails of the model and its implications are described in Appendix3;4 the major predictions are summarized here. The model concen-trates on the role of money prices, time prices, and earned andnon-earned income in determining the demand for medical care.The empirical section concentrates on demand for care from publicand private providers of ambulatory and inpatient care. For simplic-ity, the formal model is developed in terms of only one provider ofservices, but the implications for several providers can easily bedrawn.

Assume that two goods enter the individual's utility function:medical services, m, and a composite, X, for all other goods andservices. Assuming fixed proportions of money and time to con-sume m and X and the full income assumption, the model can berepresented as follows:

Maximize(la) U=U(m,X)

subject to

(Ib) (p +wt)m +(q +ws)X =y +wT

utilitymedical servicesall other goods and servicesout-of-pocket money price per unit of medical servicesown-time input per unit of medical services consumedmoney price per unit of Xown-time input per unit of Xearnings per hourtotal (full) incomenon-earned incometotal amount of time available for market and own production ofgoods and services

First, notice that the consumption of medical services, m, does That is! t]not affect the amount of time available for production, T.5 Second, equalsis the out-of-pocket expenditure for a unit of medical services, siiare t

incorporating any deductible and coinsurance rate the individual two elastifaces from insurance. It would be appealing to make these insur- namely, tance parameters endogenous, but data limitations do not permit the c

estimation of demand for insurance along with the demand for as wt p.services.6 Third, the manner in which the goods produce utility is elasticitynot specified. Some researchers have included "health" in the the out-outility function and allowed health to be produced by combining becausemedical services with other inputs.7 Health enters because of a of subsiddemand for the "healthy days" it will cause. The interested reader changes imay consult Phelps (1972) or Grossman (1972a) for these alternative for free nmotivations of the demand for medical services. For present pus- time pncposes, an understanding of this mechanism is not necessary. The greater psimpler formulation used here yields most of the same predictionsas the other specifications. Furthermore, the data do not allow us toestimate the manner in which medical services are translated intohealth. Effects

of a Change in Price effects arAssumptions sufficient to make money function as a price in cient to rdetermining the demand for medical services are also sufficient to that an iimake time function as a price.8 Therefore, the first prediction the demderived from this model is that if medical services are a normal income i:good, time will function as a price, producing negative own-time/ of demarprice elasticities of demand and positive cross-time/price elas- The efticities. priori be

One of my chief interests in this study is the relative importance hour proof money and time prices in determining the demand for medical also raisservices. If we let IT equal the total price per unit of medical time-inteservices (that is, iT = p + wt), then the elasticity of demand for servicesmedical services withrespect to money price is services

and servinto a

(2a) Thnp —17•

and the elasticity with respect to time price is9 (9W

where [i

(2b) = 0 maximiz

168 Acton 0

169I

That is, the elasticity with respect to one component of the priceequals the elasticity with respect to the total price weighted by theshare of the total price owing to that component. Comparing thesetwo elasticities yields the second prediction from the formal model;namely, that

lmt < imp

as wt p. Clearly, as p falls to zero and wt does not, the time-priceelasticity will exceed the money-price elasticity. In other words, asthe out-of-pocket payment for a unit of medical services falls,because of either increasing insurance coverage or the availabilityof subsidized care, demand becomes relatively more sensitive tochanges in time prices. Furthennore, this implies that the demandfor free medical services should be more responsive to changes intime prices than demand for non-free services, because time is agreater proportion of total price at free than at non-free providers.

Effects of a Change in Income

Exogenous changes in income can arise either from a change inearnings per hour or from a change in non-earned income. The twoeffects are not, in general, equal. The assumptions that are suffi-cient to make money function as a price are also sufficient to meanthat an increase in non-earned income will produce an increase inthe demand for medical services. So the first prediction aboutincome is that there will be a positive non-earned income elasticityof demand for normal goods.

The effects of a change in the wage rate cannot be determined apriori because of offsetting influences. An increase in earnings perhour produces an income effect, which acts to increase demand. Italso raises the opportunity cost of time, which reduces demand fortime-intensive activities. The net effect on the demand for medicalservices depends on the time intensity of the price of medicalservices relative to the time intensity of the price of all other goodsand services. We can break the effects of a change in the wage rate,w, into an income effect and a substitution effect:

(3) = (T —mt Xs(q +ws) (p +wt) — Xt(q +ws)2c9w

where IDI

is a determinant of the matrix of coefficients from themaximization equations. The first term is an income effect and is,

169 Demand for Health Care among the Urban Poor

¼

rvices, m, doesn, Second, pdical services,the individual

ke these insur-not permit the

demand foroduce utility is'health" in the

by combinings because of aterested readeriese alternativeor present pur-necessary. Theme predictionsnot allow us totranslated into

as a price iniso sufficient tofirst prediction

are a normalative own-time!ime/price elas-

tive importancemd for medicalmit of medicalof demand for

I

j

DI

by assumption, positive. The second term is the substitution of m Acton, 19for X because of a change in w. We can establish that the substitu- ciation intion term is positive if and only if

(4) > wt(q+ws) (p+wt)

3. THEDAthat is, if the time price is a larger proportion of the total price forthe composite good, X, than it is for medical services, m. The In this sesubstitution effect is necessarily negative for free sources of medi- the defincal care since the condition in Equation (4) will not be met as long effect ofas there is a non-zero monetary price for X; that is, an increase in surveysthe wage rate will always cause a substitution effect away from the Center (1free good. Of course, the net effect of a change in wages may still be The surv

• to increase the demand for medical services if the income effect baseline• exceeds the substitution effect. Intuitively, however, the effect of a Charles

wage change on the demand for free medical services is primarily a hood Heprice effect (and therefore is likely to be negative) and the effect of ducted oa wage change on the demand for non-free sources is primarily an will refeincome effect (and therefore is likely to be positive), complete

almost 5,completirespectivPredictions from Other Formal Models

The simplified consumption model is adequate to generate empiri- Ancally verifiable hypotheses for the variables of primary interest in detail abthis study. The Grossman (1972a, 1972b) investment model pro- Consequvides additional predictions regarding the effects of education and A weaknage. Grossman enters health into the utility function and lets health by the iibe produced by combining medical and other inputs. He argues cially m€that if education raises health productivity (e.g., more highly usually ieducated persons are more skillful in combining medical inputs to the undiproduce health) and if the price elasticity of demand for health is ticitiesless than 1, then when all other things are accounted for, he expects concentrto find a negative relation between education and the amount of.medical services demanded)°

The second implication of the Grossman formulation involvesr SelectedCinvestment in neaitn over tne iiie cycle. II tne price elasticity ot

demand for health is less than 1, then the effect of age on the The Redemand for medical care is positive if the depreciation rate on racial brhealth rises with age and is negative if it falls with age. In general, white,"we may suspect that the depreciation rate increases over the life (77 percycle, causing a positive effect of age on the consumption of years); amedical care. However, the evidence presented below (and in $5,030 p

170 IActon 171

)stitution of mit the substitu-

Acton, 1973) suggests that in poor populations, substantial depre-ciation in the health stock may be occurring early in life.

total price forvices, m. Theurces of medi-be met as longan increase inaway from the:es may still beincome effectthe effect of a

s is primarily ad the effect ofs primarily an

nerate empiri-ary interest innt model pro-education andand lets healthtts. He arguesmore highly

dical inputs tod for health isfor, he expectsthe amount of

3. THE DATA BASE

In this section I discuss the source of the data used for estimation,the definition of the variables used for analysis, and the expectedeffect of these variables. The data used came from two householdsurveys conducted in 1968 by the National Opinion ResearchCenter (NORC) for the Office of Economic Opportunity (OEO).The surveys were conducted in Brooklyn, New York, to establishbaseline characteristics on the population before the Red Hook andCharles Drew (in Bedford-Stuyvesant/Crown Heights) Neighbor-hood Health centers were established. Both surveys were con-ducted on straight probability samples of the target population. (Iwill refer to them as Red Hook and Bedford-Crown.) In thecompleted survey, approximately 1,500 households, containingalmost 5,000 individuals, had been interviewed in each study. Thecompletion rates were 82 and 81 per cent for the two samples,respectively, and there is no evidence of bias in the incompleteinterviews." -

An advantage in using survey data is that it provides much moredetail about the variables of interest than the use of aggregate data.Consequently, it allows more precise estimates of the relationships.A weakness of survey data is that it relies chiefly on self-reportingby the individual for some of the most important variables (espe-cially medical utilization and income). Since the actual amounts areusually under-reported, the coefficients may be biased. As long asthe under-reporting (or over-reporting) is proportional, the elas-ticities will be unaffected.'2 Consequently, the empirical sectionconcentrates on the elasticities of the important variables.

ation involvese elasticity ofof age on theiation rate on

In general,over the life

nsumption of'elow (and in

J

Selected Characteristics of the Red Hook PopulationThe Red Hook population contains about 25,000 persons. Theracial breakdown is 26 per cent Puerto Rican, 43 per cent "otherwhite," and 30 per cent black. It is a relatively stable neighborhood(77 per cent had lived in the Red Hook area for more than fiveyears); average family size is 4.7 persons. The average income is$5,030 per year. In twenty per cent of the households at least one

171I

Demand for Health Care among the Urban Poor

j

member was receiving welfare, and 23 per cent fell below the OEO Definition ofpoverty line. The mean age is 27.3 years and the mean educationallevel is 6.8 years in the full sample. This subs(

Approximately 33 per cent of the Red Hook population saw a empiricalphysician in the outpatient department (OPD) of a municipal medicalhospital or a free-standing clinic during the year, and 48 per cent alphabeticsaw a physician in his private office. The average number of visits values. Thfor users of these physicians is 5.2 and 3.8 per year. In the and inpatipreceding year, over 9 per cent of the survey population was clinic is (hospitalized at least once, and, on the average, hospitalized persons Days of hspent 14.6 days in the hospital during the year. Almost 14 per cent or propne.of the population reported having at least one chronic health sion herecondition limiting activity. There is a strong negative correlation income, sbetween number of chronic conditions and family income, with the that may 1under $3,000 individuals reporting five times as many chronicconditions as the over $7,000. Price

Althoughtravel timqueried a

Selected Characteristics of the Bedford-Crown consider I

Population theis not sev

The general characteristics of the Bedford-Crown survey are simi- zerolar to the Red Hook population and can be summarized quickly. The quBedford-Stuyvesant/Crown Heights is a predominantly black form. Afbneighborhood. Blacks constitute 84 per cent of all residents, Puerto practitionRicans, 7 per cent, and "other white," 9 per cent. The mean income usually tais $5,599. In Bedford-Crown, almost 20 per cent of the families fall times usebelow the OEO poverty line and in 24 per cent at least one member Survey Nwas receiving welfare. Average household size is 4.3 persons. NORC thFemales head 41 per cent of the Bedford-Crown households; only care, and32 per cent of households were so headed in Red Hook. The mean waiting tiage is 25.2 and educational level is 7.3 years in the full sample. necessar)

Although almost 15 per cent of respondents reported at least one with thechronic health condition that limited activity, medical utilization complish

• appears generally lower in Bedford-Crown than in Red Hook. and twoBroken down by type of physician visit, 29 per cent saw a physician waiting tat the OPD of a municipal hospital or a clinic (5.0 visits per year), TOPDCand 40 per cent saw a physician in his private office (3.9 visits). The not, andhospitalization rate was similar to what it was in Red Hook. Less time to athan 8 per cent of the population was hospitalized for an average of a private15.3 days per TPRIV a

172I

Acton 173I

C

elow the OEO Definition of Variables Used and Expected Effectan educational This subsection discusses the nature of the variables used for thepulation saw a empirical analysis and their expected effect on the demand for

a municipal medical services. For reference, Appendix 1 lists the variables in48 per cent alphabetical order and provides a brief definition and the mean

umber of visits values. The four dependent variables cover the volume of ambulatoryr year. In the and inpatient care. The number of physician visits in an OPD oropulation was clinic is OPDC and the number of private office visits is PRIV.talized persons Days of hospitalization in public (municipal) and private (voluntaryost 14 per cent or proprietary) hospitals are DAZPUB and DAZPRIV. The discus-chronic health sion here will focus on explanatory variables by type—time price,ive correlation income, sociodemographic, and so forth—and the interpretationcome, with the that may be given to them.many chronic

Price VariablesAlthough the surveys conducted by NORC provide us with bothtravel time and waiting time information, the respondents were notqueried about the money prices paid for medical services. I willconsider the bias the omitted money-price variables may cause inthe estimation after discussing the time variables, but the problemis not severe since the appropriate monetary price for free care is

irvey are simi- zero anyway.Lrized quickly. The questions about travel time and waiting time were similar ininantly black form. After determining the usual source of medical care (general;idents, Puerto practitioner, specialist, clinic, etc.) NORC asked: "How long does itmean income usually take you to get there (the way you usually go)?" (The travel

families fall times used for this analysis are for a round trip.) In the Red Hookst one member Survey NORC asked a similar question about usual waiting time.s 4.3 persons. NORC then asked if there were a most trusted source of medicaluseholds; only care, and if so, what it was (same options as usual source). Again, a)ok. The mean waiting time question was posed in Red Hook. For analysis, it wasfull sample. necessary to associate these times for usual and trusted sourcesed at least one with the dependent variables OPDC and PRIV. This was ac-ical utilization complished by creating travel time variables, TOPDC and TPRIV,in Red Hook. and two waiting time variables, ATOPDC and ATPRIV. Theaw a physician waiting time to usual source of care was used for creating theis its per year), TOPDC variables if the usual source was an OPD or clinic; if it was3.9 visits). The not, and the trusted source was an OPD or clinic, then the travel

Hook. Less time to a trusted source was used. Similarly, if the usual source wasr an average of a private practitioner, then that time information was used to create

TPRIV and ATPRIV. If the usual source was not a private prac-

173 Demand for Health Care among the Urban Poor

j

titioner, but the trusted source was, the trusted source information time pricewas used. When trusted and usual providers were of the same type, bias thethe time information for the usual source was used. When the above (toward Z€algorithm failed to assign a value to one or more of the time bias downvariables (typically because usual and trusted sources of care were For a niboth private and TOPDC and ATOPDC were therefore not availa- more resible), the mean value for those who reported a time was used.'4 waiting ti

Depending on the particular application of the results, the chief varies witinterest may be in the effect of the time variables themselves, or unobservthere may be more interest in the effect of the time variables implicit nmultiplied by the opportunity cost of the unit of time. Each of the may be rnfour time-price variables is multiplied by the earned income per traveling.minute for working persons to create four alternative time-price demand fvariables: CTOPDC, CATOPDC, CTPRIV, and CATPRIV. If theperson is not working or there is no earned income reported for thefamily, 1 cent per minute is used as the value of time.'5 Income

The travel and waiting time data were reported in intervals. For Earned (}ipurposes of estimation, I used interval midpoints. The highest the survevalue (recorded as an open interval) was calculated by smoothing a reported icumulative distribution function through the interval midpoints per year.and estimating an intercept. The mean value for travel time to the were $4,sources of care generally requiring no out-of-pocket money expendi- showedture, TOPDC, was 72.9 minutes in Red Hook and 64.0 minutes in demandBedford-Crown. The corresponding mean travel time for private medical sphysician visits, TPRIV, which generally required a money pay- for publicment, was 44.6 minutes for Red Hook and 48.8 for Bedford-Crown. as inferioThe greater mean value for travel time to "free" sources of care elasticityprovides preliminary evidence to support the theoretical model respect todeveloped above; people seem to be substituting time payments for earned inmoney payments in their demand for care. The mean waiting times Relativfrom Red Hook are 59.1 minutes for ATOPDC and 73.7 minutes for sures inATPRIV. Although waiting time appears to be longer at private incomeproviders, the total time required to receive free care still exceeds procedurthat for non-free care. CTPRIV,

The expected effect of the time variables should be clear from the only to wtheoretical development. TOPDC and ATOPDC are the own-timeprices for OPDC and the cross-time prices for PRIV. They shouldhave a negative effect on utilization at OPDC and a positive effect Ageon PRIV. Similarly, TPRIV and ATPRIV are the own-time prices The age tfor PRIV and cross-time prices for OPDC and should act accord- in the deiingly. The absence of money-price information acts to bias the tion suggestimated effect of time prices associated with non-free sources of ciation racare. If there is a negative correlation between money prices and of variati

174 Acton 175 D

I

Ttime prices, then the absence of money prices in the regression willbias the coefficient on TPRIV upward. This will bias upward(toward zero) the effect of own-time price in the PRIV equation andbias downward the effect of cross-time prices in OPDC.

For a number of reasons, the demand for medical services may bemore responsive to changes in travel time than to changes inwaiting time. Travel frequently requires a monetary expense thatvaries with distance or time; distant facilities require a higher (andunobserved) financial payment. Waiting time does not entail thisimplicit monetary charge. Furthermore, all other things equal, itmay be more pleasant to spend a given amount of time waiting thantraveling. Both effects lead us to expect a greater elasticity ofdemand for travel time than for waiting time.

IncomeEarned (EARN) and non-earned (NEARN) income were asked inthe survey instrument by household. The mean earned incomereported in Red Hook was $4,110 and non-earned income was $920per year. The earned and non-earned incomes for Bedford-Crownwere $4,532 and $1,067, respectively. The theoretical modelshowed an unambiguously positive non-earned income elasticity ofdemand for medical services. The model was developed withmedical services as only one good. When there are four componentsfor public and private ambulatory and inpatient care, some may actas inferior goods. In particular, there may be a negative incomeelasticity of demand for OPDC and DAZPUB. The elasticity withrespect to earned income was indeterminate because an increase inearned income also increased the opportunity cost of time.

Relatively few problems were encountered in the income mea-sures in this data file. The figures for earned and non-earnedincome apply to each member of the family. This differs from theprocedure used to create the variables CTOPDC, CATOPDC,CTPRIV, and CATPRIV, wherein earned income was attributedonly to working members of the family. 16

Age

The age term is entered as AGE and AGE2 to allow for nonlinearityin the demand for medical services. The Grossman (1972) formula-tion suggested a positive correlation between age and the depre-ciation rate on health. The nonlinear specification allows detectionof variations in the depreciation rate through the life cycle. In

175 Demand for Health Care among the Urban Poor

]

I

ce informationthe same type,Ihen the abovee of the times of care wereore not availa-was used.'4suits, the chiefthemselves, ortime variablesLe. Each of the

income perive time-priceTPRIV. If the

for the

intervals. ForThe highest

y smoothing aval midpointsel time to theoney expendi-4.0 minutes inne for private

money pay-edford-Crown.ources of care,retical model

e payments forwaiting times1.7 minutes forger at privatee still exceeds

clear from thethe own-timeThey should

positive effecten-time pricesld act accord-ts to bias theree sources ofey prices and

particular, Acton (1973) suggested that the city's poor populationmay be experiencing significant depreciation early in life.

InsuranceThe insurance information is coded in categories that are notmutually exclusive. For ambulatory care, I was forced to create avariable, NOAMB, taking the value .1 if the person unambiguouslyhad no ambulatory coverage. In Red Hook, this meant he either hadno insurance at all or Medicare without the doctor coverage andwithout private insurance. In Bedford-Crown, this meant only thatthere was no coverage at all. For inpatient care, two dummyvariables, CAID and CARE, could be created to indicate if theperson had Medicaid or Medicare. Ideally, I would have liked tohave the specific deductible and coinsurance rates, of the personfaced at the margin, but this was totally beyond the available data.

NOAMB should have a positive sign in the equation for OPDCand a negative sign in the PRIV equation, if their effects aresignificant. If we assume that, all other things the same (such asout-of-pocket payment), people would prefer to be in a non-governmental hospital, then CAID and CARE should have anegative sign in the equation for DAZPUB and a positive sign inthe DAZPRIV equation. Indeed, it is the popular impression inNew York City that the availability of Medicare and Medicaidcaused an exodus of patients from city municipal hospitals to theprivate and voluntary hospitals.

Several measures of health status are available that seem to beequally effective in explaining use.'7 I chose CHRON, the numberof chronic health conditions that limit activity, because it wasavailable in both surveys. Other variables that could have beenused in one data file or the other include number of days in bed lastyear; number of days in bed or indoors last year; and self-perceivedhealth status (excellent, good, fair, poor). When I ran regressionswith these alternative measures, they all appeared with the antici-pated sign and were highly significant (t ratios on the coefficient inexcess of 4) and the remaining coefficients were quite stable.

CHRON is expected to appear with a positive sign in all equa-tions. Persons with chronic conditions are more likely to sufferlosses to their health stock during the year, making (at least partial)

176I

Acton

EducationThe higihypothesefficientticities),equationprefer pinegativecoefficiebiased tceffect an

j

1771(

replacemihealth stahave aforms of ccaptured iwill be enpersists, i'OPDC ar

HospitalizatioiiDays of bcare werements inthey shoLhospitaliztory care.and DAZthose whconsumeprivate h(care, othepositivemanyoutpatienpeoplemcare inlong hosishift to if

Health Status

populationn life.

that are noted to create anambiguouslyt he either hadcoverage and

ieant only thattwo dummy

ndicate if thehave liked toof the person

available data.tion for OPDC

effects aresame (such asbe in a non-hould have aositive sign inimpression inand Medicaidospitals to the

at seem to beN, the numberecause it wasuld have beenlays in bed lastself-perceivedan regressionsvith the antici-è coefficient inite stable.gn in all equa-ikely to sufferat least partial)

J

replacement more likely.'8 This is the gross effect of a decrement inhealth status. It may be that sufficient decrements in health willhave a significant income effect, causing a shift to less expensiveforms of care. The chief influence of this income effect should becaptured in the income coefficients (which is one reason why theywill be entered nonlinearly). If a differential effect on health statuspersists, it will probably be reflected in a greater coefficient in theOPDC and DAZPUB equations than in the other two equations.

HospitalizationDays of both public (DAZPUB) and private (DAZPRIV) hospitalcare were entered in the ambulatory equations to measure decre-ments in the health stock that occurred during the year. As such,they should act like the health status measures; the more days ofhospitalization, the more likely the person is to consume ambula-tory care.'9 This should produce positive coefficients on DAZPUBand DAZPRIV in both the OPDC and PRIV equations. In general,those who received public inpatient care should be more likely toconsume public than private ambulatory care. Those who receivedprivate hospital care are more likely to consume private ambulatorycare, other things being equal. At least two factors could lead to apositive coefflcient on DAZPRIV in the OPDC equation. First,many people have insurance that covers inpatient care but notoutpatient care (Medicare without Part B is an example).2° Thesepeople may seek inpatient care in private hospitals and ambulatorycare in public facilities. Second, there may be an income effect of along hospitalization in a private facility that causes the person toshift to the public sector for his ambulatory care.

EducationThe highest grade completed is coded in years (EDUC). If thehypothesis is correct that more highly educated persons are moreefficient producers of health (along with appropriate price elas-ticities), then there should be a negative coefficient in all fourequations. If, on the other hand, more highly educated personsprefer private rather than public providers, then we should have anegative coefficient in the OPDC and DAZPUB equations. Thecoefficient in the PRIV and DAZPRIV equations would then bebiased toward zero because of the offsetting effects of the efficienteffect and the preference.

177I

Demand for Health Care among the Urban Poor

r

Race isthatOTwo dummy variables, BLACK and PR (Puerto Rican), were with thecreated. Since many of the factors expected to affect demand are indepenalready entered (particularly, income and health status), the coeffi- strainedcients on these two variables should reflect differences owing to variancepreferences for a particular type of provider or to discrimination never cofaced by members of particular races. Such i

negativeproporticex particula

A dummy variable, MALE, was created, taking the value 1 if male Tobin (1and zero otherwise. The expectation, based on the aggregate such datconsumption by sex (and ignoring childbearing as the explanation), index ftcis that males will be less intensive users of the system. This may, expectedhowever, reflect a higher opportunity cost of time that is not explanatcontrolled, for in aggregate data; the current test should shed some lying 01light on the partial effect of sex, given value of time. An interesting In theadditional hypothesis to test with this data base is that once they functionbecome ill, men will tend to remain under care longer (in a public not specsystem that does not require a significant monetary payment at the restrictiomargin) because they have let their health stock deteriorate more importaithan women have. Thus, we may find a positive coefficient on system cMALE in DAZPUB. around

TherereferencHousehold Size For reas

The final variable is household size (HSIZE). All other things attentioibeing the same, larger households will have a lower income per are verycapita, reducing the demand for care at non-free sources. On the nitudesother hand, taking a lifetime view of family decision making, the Sectionnumber of children is an object of choice, making total family effect ofincome the relevant variable and causing HSIZE to be relatively elasticitiinsignificant, variable

variable

4. ESTIMATION TECHNIQUES AND RESULTS The Time \Before discussing the results of the estimation, let me comment on The effeestimation techniques. Whenever a non-negligible proportion of travel athe observations of the dependent variable takes on an extreme opportufvalue (either high or low), the assumptions underlying ordinary in naturleast squares (OLS) regression break down. Intuitively, the reason demand

178 Acton 179

Rican), werect demand areus), the coeffi-nces owing todiscrimination

ralue 1 if malethe aggregate

explanation),em. This may,ie that is notüld shed someAn interestingthat once theyer (in a publicayment at the

'teriorate morecoefficient on

1 other thingser income per)urCes. On the)fl making, the

total familybe relatively

.TSe comment onproportion offl an extreme

lying ordinaryely, the reason

TT is that OLS requires equal variance in the error terms associatedwith the dependent variable, regardless of the values of theindependent variables. When the dependent variable is con-strained (say, it must be greater than or equal to zero), then thevariance is reduced near zero. Indeed, in this example, we cannever consider negative values.

Such is the case in the estimation here; we never considernegative consumption of medical services. Furthermore, a largeproportion of the population reports a zero consumption of any oneparticular type of service. This general problem was addressed byTobin (1958), who developed a maximum likelihood estimator forsuch data (called the tobit estimator). The technique estimates anindex from which the probability of a non-zero purchase and theexpected value of that purchase can be determined, given theexplanatory variables. As the data approach the assumptions under-lying OLS estimation, the tobit results approach OLS results.

In the theoretical model developed in Section 2, a general utilityfunction was used. For purposes of estimation, I have deliberatelynot specified a particular utility function in order to put as fewrestrictions as possible on the results. Instead, I have enteredimportant explanatory variables in linear and quadratic form. Thesystem can be viewed as the first two terms of a Taylor expansionaround whatever is the true model.

The results of the tobit estimation are given in tables 1 and 2. Forreference, the OLS estimation results are presented in Appendix 2.For reasons just discussed, the tobit estimations receive all ourattention. In general, the coefficients presented in tables 1 and 2are very significant.2' Furthermore, their signs and relative mag-nitudes lend support to the theoretical implication derived inSection 2. Since it is difficult to make a quick judgment of the neteffect of variables entered in quadratic form, table 3 gives theelasticities of the expected value locus of the four dependentvariables with respect to all quadratically estimated explanatoryvariables, calculated at the mean values.

The Time VariablesThe effects of time can be measured either from table 1, in whichtravel and waiting times are multiplied by a measure of theopportunity cost of time, or from table 2, in which time is enteredin natural units only. As shown in Appendix 3, the elasticity ofdemand with respect to time equals the elasticity with respect to

j179

IDemand for Health Care among the Urban Poor

TA

BLE

1T

OB

IT R

egre

ssio

n R

esul

ts w

ith T

ime

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ghte

d by

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ate

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I I I private cathe much

Hshh183 Di

time weighted by the opportunity cost of time. There are likely tobe biases in each set of coefficients such that the true elasticitieswith respect to time prices are greater in absolute value than thoseestimated. Consider first the specification with time weighted bythe opportunity cost of time (table 1). Since the opportunity cost oftime had to be imputed to nonworking persons and is not entirelyprecise even for working persons, the wage rate is measured witherror. This error will bias the coefficients on the time variables intable 1 toward zero. Thus, the true elasticities will be greater (inabsolute value) than those implied by the first specification. Con-sider the alternative specification employing time in natural units(table 2). In light of the model developed in Appendix 3, w t isthe correct variable, so that regressions employing t alone consti-tute an omitted variable bias. If w and t are negatively correlated (asseems reasonable), the coefficients estimated in Table 2 will alsobe biased toward zero.22 In general, the elasticities implied by thecoefficients in table 2 exceed in absolute value those implied bytable 1, suggesting that the bias resulting from the error inmeasuring the opportunity cost of time is greater than the biascaused by omitting it from the specification. I shall discuss bothspecifications; almost all the remaining coefficients are quite stablebetween tables 1 and 2. The chief exceptions are the incomecoefficients—which are discussed in the next subsection—but evenso, their elasticities are reasonably stable. The other apparentinstabilities (PR and BLACK in the DAZPUB equations) reflectcoefficients that were not significantly different from zero in eitherspecification. Since both sets of estimated elasticities understatethe true elasticity, I will concentrate on the generally larger onesimplied by table 2.

Let us first concentrate on the travel time-price elasticities forambulatory care using time in natural units. The elasticities aregiven in table 4. In this table we find support for many of thehypotheses generated in Section 2. Travel time is indeed function-ing as a normal price, producing negative own-time/price elas-ticities and positive cross-time/price elasticities. Furthermore, themagnitude of the own-time/price elasticities exceeds that of own-money/price elasticities reported by other researchers. Using dis-aggregated data from several sources, Phelps and Newhouse (1973)derive money-price elasticities for private care on the order of—0.15 in the range of 25 per cent to 0 per cent coinsurance—wellbelow (in absolute value) the —0.25 to —0.337 estimated here forprivate care and —0.6 to —1.0 estimated for public care. Even usingthe much higher elasticities for all ambulatory care of between —0.5

183I

Demand for Health Care among the Urban Poor

TABLE 4 Travel Time-Price Elasticities for Ambulatory Care[equations (9), (10), (13), and (14)]

Red Hook

TOPDC TPRIV

—BedfordTOPDC

-Crown———-

TPRIV

OPDC — .958 .332 — .619 .137PRIV .640 — .252 .629 — .337

and —1.0 reported by Rosett and Huang (1971), Feldstein (1971),and Davis and Russell (1972), the travel-time elasticities appear tobe of at least a comparable size.

The hypotheses developed above also suggested that demandshould be more responsive to changes in TOPDC than to changesin TPRIV—which is the case. In both Red Hook, and Bedford-Crown, the own-travel time-price elasticities with respect toTOPDC exceed those for TPRIV by a factor of two or three times.Similarly, the cross elasticities for TOPDC are significantly greaterthan those for TPRIV. The elasticities calculated for the Cvariables support the conclusions drawn for the TIME variablesabove. Found in table 3 are negative own-price elasticities, posi-tive cross-price elasticities, and larger responses to CTOPDC andCTPRIV. The one exception is Equation (6), in which there is anegative cross-time/price elasticity of demand for PRIV with re-spect to CTOPDC:

The effect of waiting time is similar to travel time as a deterrni-nant of demand. But, as predicted, the elasticities with respect towaiting time are smaller (in absolute value) than the elasticitieswith respect to travel time. The own-waiting time-price elasticitiesof demand for OPDC and PRIV are —0.120 for ATOPDC and—0.050 for ATPRIV. The cross elasticities are 0.196 for ATPRIVand —0.202 for ATOPDC. The last figure, giving a negative cross-price elasticity of demand for PRIV with respect to ATOPDC, is theonly violation of the theoretical implications developed above.23Otherwise, waiting time also functions as a normal price, withdemand being more responsive to changes in waiting time atOPD's and clinics than it is to waiting times at private physicians'offices.

We can draw some limited inferences about the effect of timeprices on the demand for inpatient care. We do not have a directmeasure of the time prices associated with hospitalization. Theeffects of travel and waiting times for outpatient care should be

interpretedtime one rnshould be tiwish to cothospitals—tare located(12), inpatietutes. The bone is to UBedford-Crlevel of anaresidents oserious heatient care a

IncomeThe theoreforms of i

should becase the elthe elasticbecause ofI suggeste(sources ofsupport thwith resperespect tofor privatelittle evidinferior goDAZPUBof the inc(and Bedfomust be

A wordInstead o:variables,total incotnativehigh degrwaiting a

L

184 Acton185 D

interpreted primarily as cross prices to inpatient care—the moretime one must spend getting ambulatory care, the more likely oneshould be to demand inpatient care. To a limited degree, we maywish to consider TOPDC as a measure of travel time to publichospitals—the DAZPUB variable—because all municipal OPD'sare located in a hospital. In Red Hook equations (3), (4), (11), and(12), inpatient and outpatient care seem to be operating as substi-tutes. The longer one must wait for ambulatory care, the more likelyone is to use inpatient care. The opposite appears to be. true inBedford-Crown. It is not clear why this difference exists at thislevel of analysis, but it may be compatible with the hypothesis thatresidents of Bedford-Crown are seeking care only for the moreserious health conditions, and in those cases, inpatient and outpa-tient care are complements.24

IncomeThe theoretical model predicted that the elasticity of demand for allforms of medical services with respect to non-earned incomeshould be positive unless public care is an inferior good, in whichcase the elasticity is negative in OPDC and DAZPUB. The sign ofthe elasticity with respect to earned income was indeterminatebecause of offsetting effects of income and the time price, althoughI suggested that it should be lower for free sources than for non-freesources of care. Broadly speaking, the empirical results in table 3support these hypotheses. With few exceptions, a positive elasticitywith respect to non-earned income was found in all equations. Withrespect to earned income, a generally positive elasticity was foundfor private care and a negative elasticity for public care. There islittle evidence to support the hypothesis that public care is aninferior good (that is, that the elasticityof demand for OPDC andDAZPUB with respect to NEARN is negative). Although the signsof the income elasticities are reasonably stable between Red Hookand Bedford-Crown, the size varies and the whole set of findingsmust be regarded as provisional.

A word on alternative specification of the equations is in order.Instead of using earned and non-earned income as explanatoryvariables, I also estimated the entire set of equations using onlytotal income—entered as income and income squared.25 This alter-native specification was used because I thought there might be ahigh degree of collinearity between EARN and NEARN and thewaiting and travel time variables, especially when they were

185 Demand for Health Care among the Urban Poor

ulatory Care

dford-Crown—---—

TPRIV

.137— .337

eldstein (1971),icities appear to

ed that demandthan to changesk and Bedford-rith respect toor three times.

ificantly greateror therIME variableslasticities, posi-

CTOPDC andrhich there is aPRIV with re-

as a determi-with respect tothe elasticitiesrice elasticities

• ATOPDC and96 for ATPRIVnegative cros s-kTOPDC, is the

above.23nal price, withvaiting time at'ate physicians'

effect of timet have a direct

Thecare should be

—I

V

weighted by earned income. This alternative specification left the wealth attribremaining coefficients virtually unchanged (to the third decimal (wT) be theplace) and the significance of INC and INC2 was roughly the same all employe(as either EARN and EARN2 or NEARN and NEARN2. The other wealthpoint worth mentioning about alternative specifications is the effect care in Redof the C TIME versus the TIME variables on the income elas- Inticities. Although the EARN elasticities vary somewhat, the elas- specificatiorticities with respect to NEARN are identical in the two specifica- (9k16).tions.

In Red Hook, there is substantial support for the hypothesis that•medical services are normal goods, producing an elasticity of A edemand with respect to non-earned income of about 0.04 or 0.05 forambulatory care and 0.16 for inpatient care.26 The elasticities with The humanrespect'to earned income are positive for private sources of care and demand fornegative for public sources, supporting the suggestion that they price elastishould be smaller for the free sources of care because a change in where in ththe wage rate has a greater price effect in demand for free care. In age coefficinet, the price effect of a wage change dominates in the demand for (equationspublic care and the income effect dominates in the demand for (11), (12), Cprivate care. years). Both

The Bedford-Crown results produce elasticities somewhat less in tial decremconformity with the predictions of the model and there are two sign only curvereversals of corresponding elasticities between the C TIME and physician cTIME specifications. I will discuss only aberrations from the cients arepicture just described for Red Hook. In equations (6) and (14), thereis a negative non-earned income elasticity of demand for privatephysician care that appears robust, suggesting that public care is a Insurancenormal good and private ambulatory care is an inferior good. WhenI discuss the effects of race on demand for care, there is some Thesuggestion of discrimination, and part of the effect may appear here. care. In allThe two sign reversals occur for earned income in equations (5) and the coeffici(13) and for non-earned income in equations (7) and (15). The latter and (15)) amay be explained by the critical point lying near the mean of the general. TIdata, but the former is not so easily accounted for. Medicare

Otherwise, the general pattern of effects of income on demand for privatecare that was reported in Red Hook holds in Bedford-Crown. The lowers deroniy support in either set of regressions for the hypothesis that duced signpublic care is an inferior good is in Equation (15), in which the The picturnon-earned income elasticity of demand for DAZPUB is _0.019.27 certain,

From the estimated elasticities with respect to non-earned in- explanatorcome we can calculate the approximate magnitude of the full results (atwealth elasticity. The full wealth elasticity equals the non-earned with aiincome elasticity multiplied by the increase of the share of full physicians

186I

Acton 187 De

Age

wealth attributable to non-earned income.28 Let full earned income(wT) be the earning of a person employed full time and assume thatall employed persons are working full time.29 Then the implied fullwealth elasticity of demand is 0.202 for OPDC and 0.251 for privatecare in Red Hook.3°

In discussing the remaining effects, I will concentrate on thespecification with the time variables in natural units, equations(9)—(16).

The human capital formulation predicts a positive correlation of thedemand for care and rate of depreciation on the health stock (if theprice elasticity of demand for health is less than 1). We can inferwhere in the life cycle depreciation is greatest by examining theage coefficients. The age curve is either monotonically decreasing(equations (9) and (13)) or is an inverted U shape (equations (10),(11), (12), (15), and (16) all peak between thirty-two and thirty-sixyears). Both patterns support the conclusion that there are substan-tial decrements in health early in life for these populations. Theonly curve that is monotonically rising is the demand for privatephysician care in Bedford-Crown (equation (14)), and its coeffi-cients are not significantly different from zero.

InsuranceThe greatest effect of insurance is seen in the demand for hospitalcare. In all cases, the estimated coefficients are positive, althoughthe coefficients in the DAZPUB equations (equations (3), (7), (11),and (15)) are not statistically significantly different from zero ingeneral. The significant effects support the popular image thatMedicare and Medicaid caused an increase in the demand forprivate hospitalization. We cannot conclude, however, that thislowers demand for public hospital care (which should have pro-duced significant negative coefficients in the DAZPUB equations).The picture with respect to insurance for ambulatory care is lesscertain, no doubt because of the imprecise definition of theexplanatory variable NOAMB. The only statistically significantresults (at 5 per cent or lower, equations (2) and (10)) showpeoplewith no ambulatory insurance demanding less care from privatephysicians.

187I

Demand for Health Care among the Urban Poor

ification left thee third decimal

oughly the sameRN2. The otherions is the effect

income elas-ewhat, the elas-e two specifica-

hypothesis thattan elasticity oft 0.04 or 0.05 forelasticities withtrees of care and

that theyuse a change infor free care. Inthe demand for

the demand for

omewhat less inere are two signe andtions from the) and (14), thereand for privatepublic care is aior good. When

there is someray appear here.quations (5) and(15). The latter

he mean of the

e on demand for)rd-Crown. Thehypothesis that), in which theUB is _0.019.27non-earned in-ide of the fullthe non-earnedre share of full

I

HospitalizationBy and large, people who reported being hospitalized were likelyto be users of ambulatory facilities. As suggested, people whoreported public hospitalization were more likely to use publicambulatory care than private ambulatory care (the coefficients forDAZPUB in the PRIV equations (2), (6), (10), and (14) were eithernegative or not significantly different from zero). Those whoreported private hospitalization were significantly more likely touse both public and private ambulatory care.

Health StatusThe health status variables are the most consistently significantpredictors of demand for care. Greater numbers of chronic healthconditions produce higher utilization of all forms of medical ser-vices (with t ratios ranging from 4 to over 16). We suggested thatpoorer health stock might produce an income effect, causing greaterdemand for free than for non-free care from those with chronicconditions. The evidence is consistent with this hypothesis.3'

EducationIt was postulated that if educated persons were more efficientproducers of health and the price elasticity of health is less than 1,then the coefficient on education would be negative. On the otherhand, those with higher education might have developed a taste formore health services, particularly non-free services. The two effectstogether should yield a negative coefficient on EDUC in the OPDCand DAZPUB equations and coefficients biased upward in PRIVand DAZPRIV. This pattern is found in the estimated demand forambulatory care. There is a significant negative coefficient oneducation in the demand for OPDC and clinic services. The mixedeffect of efficiency and taste is shown by coefficients biased upwardin equations (2), (6), (10), and (14). In the demand for inpatient care,education has.a positive effect in all but one case, when its t value is0.84.

Generally, the coefficients on the race variables are very significantfor ambulatory care but not significant for inpatient care. The

relations arPuerto Ricaface discriricant negatiiequations a:definite subconstant. Tnificant, buconclusion

sexGross consion the dunpossible excient in thdeterioratelonger.relations, ations is not

Household SFinally, allnegative C(entirelyHSIZEintsize is mcicially that

5. CONCLLIMPLICA

Conclusion

Race The objeinfluencinlooking f

188 Acton 189 De

ized were likelyed, people whoy to use public

e coefficients for(14) were eitherro). Those whoy more likely to

7,

Sex

relations are compatible with an interpretation that blacks andPuerto Ricans either have an aversion to private care or that theyface discrimination in private ambulatory care. There are signifi-cant negative coefficients on both BLACK and PR in the PRIVequations and significant positive coefficients in OPDC. There is adefinite substitution of public for private care, all other things heldconstant. The coefficients in the hospital equations are less sig-nificant, but when their t value exceeds 1.96 they support theconclusion of substituting public for private care.

ently significantchronic health

of medical ser-e suggested thatt, causing greaterse with chronicypothesis.31

more efficientth is less than 1,ye. On the othereloped a taste for

The two effectsLJC in the OPDCupward in PRIVated demand fore coefficient onrices. The mixedts biased upwardor inpatient care,hen its t value is

very significantLtient care. The

Gross consumption figures lead us to expect a negative coefficienton the dummy variable for MALE in all demand equations. Thepossible exception would be a positive (or at least greater) coeffi-cient in the DAZPUB equation if men had let their health stockdeteriorate more and thus, once hospitalized, would be confinedlonger. These two expectations are supported in all the estimatedrelations, although the positive coefficient in the DAZPUB equa-tions is not significantly different from zero.

Household SizeFinally, all other things held the same, HSIZE should produce anegative coefficient in paid sources of care. For reasons that are notentirely clear, there is also frequently a negative coefficient onHSIZE in the public sources of care. It may be that the larger familysize is increasing the opportunity cost of everyone's time (espe-cially that of the parents) and thus reducing all use of services.

5. CONCLUSION AND SELECTED POLICYIMPLICATIONS

Conclusion

The objective of this study was to measure the major factorsinfluencing demand for medical services. In particular, we werelooking for a mechanism that might replace money prices in

189 Demand for Health Care among the Urban Poor

r

determining demand as money price out of pocket diminished. I because ofThere was considerable theoretical and empirical support for the enactment csuggestion that time prices would fill that role. Travel and waiting lower oppotime appear to be operating as normal prices, producing a negative reduction oown-price elasticity and a positive cross-price elasticity of demand opportunityfor medical services. As predicted, elasticities were greater with Conclusionrespect to times associated with free care than with times associated costs andwith non-free care. The magnitude of the own-elasticity with there is ukrespect to travel time is —0.6 to —1.0 for public outpatient care and increases tibetween —0.25 and —0.34 for private outpatient care. These elas- waiting tinticities are significantly greater than the money-price elasticities of referrals).32about —0.15 over the range 0 to 25 per cent coinsurance reported by those with IPhelps and Newhouse (1972) for a Palo Alto group and equal or the vector oexceed the higher values reported by Feldstein (1971), Davis and would beRussell (1972), and Rosett and Huang (1973). The estimated elas- of a reduciticities with respect to travel time weighted by earnings are in the . distributiororder of —0.15 to —0.2 for OPDC care and nearly zero for private Among tcare, but, as discussed, these estimates are biased significantly wishes to i:toward zero. Furthermore, as predicted, demand is more sensitive travel timeto changes in travel time than to changes in waiting time, producingelasticities several times as large for travel as for waiting time. The tuted for suconclusion is clear that time is already functioning as a rationingdevice for demand in this New York population, and its importanceseems to exceed that of money prièes. Clinic Location

From the theoretical model, we derived a prediction of positiveelasticity of demand with respect to non-earned income. A picture A significaof mixed statistical significance was found, but when significant, outpatientelasticities were around 0.04 to 0.05 for ambulatory care and 0.15 to time. A flu]0.20 for inpatient care. The sign of the earned income elasticity of for

a priori because of the offsetting facilities toincome and price effects of a wage change, but a change in the wage travel timerate was expected to act more like income effect on the demand for will increanon-free care. In fact, negative elasticities were found for free care when the cand positive elasticities for non-free care, roughly of the same new clinicabsolute magnitude as the non-earned income elasticities. building a I

the averag€to serve thdistant facSelected Policy Implications should, not

A number of policy considerations are suggested by the significant clinics or tielasticities found for time prices and earned and non-earned number ofincome. The most important involves the distribution of medical sizes, the bservices, as out-of-pocket monetary expenses are reduced, either means of

190 Acton .

. 191

cket diminished.,l support for theaye! and waitingLucing a negativeticity of demandere greater withtimes associated

ri-elasticity withtpatient care and

These elas-ice elasticities ofance reported byup and equal or1971), Davis and

estimated elas-rnings are in thezero for private

sed significantlys more sensitivetime, producingaiting time. Theig as a rationingid its importance

ction of positivecome. A picturerhen significant,care and 0.15 to

ome elasticity ofof the offsetting

ange in the wagethe demand for

und for free carebly of the same.sticities.

the significantand non-earnedution of medicalreduced, either

because of continued spread of health insurance or because of theenactment of some federal health insurance scheme. Persons with alower opportunity cost of time will take more advantage of areduction of out-of-pocket monetary costs than those with higheropportunity cost of time because their time prices are lower. Thisconclusion holds even with no differential subsidy of monetarycosts and no supply response to an increase in demand. Moreover,there is likely to be a supply response to a shift in demand thatincreases the time needed to receive medical services (increasedwaiting time or perhaps increased travel time owing to morereferrals).32 This will increase further the relative shift in favor ofthose with lower opportunity cost of time (although the increase inthe vector of time prices will reduce aggregate demand over what itwould be with no supply response). In any case, the generhi effectof a reduction in personal monetary prices will be to shift thedistribution of medical services.

Among the important additional policy considerations, if onewishes to increase aggregate demand for services, are shorteningtravel time to medical facilities, shortening waiting time, andconsidering the degree to which income subsidies might be substi-tuted for subsidized purchase of medical services.

Clinic Location

A significant own-time/price elasticity of demand was found foroutpatient department and clinic services with respect to traveltime. A number of policy options are available to the governmentfor altering travel time, ranging from improved transportationfacilities to the building of new clinics and health centers. Thetravel time elasticities show that moving centers "closer" in timewill increase the demand for care at those centers. For instance,when the city, OEO, or another agency is thinking about opening anew clinic to serve a target population, it may want to considerbuilding a number of smaller clinics that are substantially closer, onthe average, to the individuals, rather than building one large clinicto serve the population.33 Faster means of transportation to moredistant facilities may achieve the same goal. This observationshould not be interpreted as a recommendation to create moreclinics or to create smaller clinics. Obviously the decision rests on anumber of factors, such as the cost of building centers of varioussizes, the benefit of serving additional persons, and the alternativemeans of achieving the same goals. One alternative means of

I191

IDemand for Health Care among the Urban Poor

I

achieving the goal of increased service is to reduce waiting time in health instexisting and new facilities, health insusimilar inc

Shorter Queues tradeoff wit3 indicate tThere are two points to consider about waiting time and the with a cuidemand for care. First, it is a popular impression that patients have income ofto wait considerably longer in outpatient departments of hospitals demand foithan in private physicians' offices. The reported waiting times for probably a1968 show that, for this population, mean waiting time was less at income elaOPD's and clinics than in private physicians' offices. The second nent. If tipoint, however, is that longer waiting times do discourage use, and medical semechanisms that reduce waiting time should increase use. For tion,36 andinstance, appointments rather than unscheduled visits in OPD's cent of mcmight prove successful in reducing waiting time. This implication coinsurancis not limited to the city. Many hospitals across the nation use a 5,000), theisystem of giving all the patients a morning appointment (say 9:00) Clearly, oror an afternoon appointment (say 1:30). If this algorithm results in a gate medicwait, on the average, of ninety minutes and an alternative schedul- and theing (say appointments on the hour for 9, 10, or 11) reduces the range of siaverage wait to thirty minutes, the elasticities reported in table 3

suggest that this will increase demand approximately 12 per cent.34

Tradeoffs of Subsidized Care and Income Supplements APPENDIXMany people have expressed concern over the level of medicalservices consumed by the poor and conclude that a variety ofmeasures are needed to improve access. In one form or another, Definitions C

most boil down to a subsidized provision of services, whether AGEthrough social insurance schemes such as Medicaid or variousnational health insurance proposals, or through direct provision of AGE2care as in neighborhood health centers or the requirement that ATOPDCHill-Burton hospitals provide charity care. Seldom considered isthe extent to which changing the income distribution will meet thedesire to subsidize the medical purchase (Davis, 1972). ATOPDC2The equations reported in tables 1 and 2 put us in a position toaddress this question of substituting income maintenance for sub- ATPRIVsidized medical care to achieve a given increase in health consump-tion. Although it will not meet the objective of risk spreading,income maintenance will increase aggregate medical care demand ATPRIV2for the poor. Since income maintenance is a non-earned source of

BLACKincome, the elasticity of demand for medical care with respect tochanges in non-earned income is used.33 Two of the prominent

192I

Acton193

health insurance proposals,, the administration's comprehensivehealth insurance proposal (CHIP) and the Kennedy-Mills bill, havesimilar income-related coinsurance features and demonstrate thetradeoff with income maintenance. The Red Hook results in table3 indicate that a $1,000 increase in non-earned income for a familywith a current (1968) non-earned income of $450 and earnedincome of about $4,100 will produce a 6.3 per cent increase in the

• demand for private practitioners' care per member. This change isprobably a lower bound on the increase, since the non-earnedincome elasticity may be biased downward by a transitory compo-nent. If the money-price elasticity of demand for ambulatorymedical services is around —0.15 over the range under considera-tion,36 and the out-of-pocket expenditure is reduced from 25 percent of money price to 15 per cent (the upper limit on CHIP'scoinsurance rate and the rate for a family with income of $2,500—5,000), then the demand for private care will increase by 8 per cent.Clearly, one means of achieving the objective of increased aggre-gate medical consumption by the poor is income supplementation,and the magnitude of the change may be very comparable over therange of subsidy and income guarantee under consideration.

Definitions of Variables Used and Their Mean Values37

AGE = Age in years. Means = (27.3, 25.2).

AGE2 = AGE2. Means = (1,200, 1,006).

ATOPDC = Waiting time, on the average, at municipal outpatient de-partments (MDOPD) or free-standing clinics (CLIN), inminutes. Available for Red Hook only. Mean = (59.1).

ATOPDC2 = ATOPDC2. Mean = (3,717).

ATPRIV = Waiting time, on the average, in a private physician's of-fice, in minutes. Available for Red Hook only. Mean =(73.7).

ATPRIV2 = ATPRIV2. Mean = (6,530).

BLACK = Dummy variable equaling 1 if Negro or indeterminate, or• other than Puerto Rican, Mexican-American, American

Indian, or other white. Means = (0.30, 0.84).

193 Demand for Health Care among the Urban PoorI

I

waiting time in

g time and theiat patients haveents of hospitalsvaiting times fortime was less atces. The secondcourage use, andcrease use. Forvisits in OPD's

This implicationthe nation use aLtment (say 9:00)rithm results in arnative schedul-11) reduces theorted in table 3ly 12 per cent.34

evel of medicalhat a variety ofform or another,rvices, whethericaid or variousrect provision ofequirement thatm considered ison will meet the972).in a position to

tenance for sub-consump-

risk spreading,cal care demand

source ofwith respect to

f the prominent

APPENDIX 1

4

CAID = One if the person has Medicaid coverage and is under 65 NOAMByears of age; zero otherwise. Means = (0.32, 0.36).

CARE = One if person has Medicare coverage; zero otherwise.Means = (0.07, 0.04). OPDC

C TIME = For all time variables prefixed by C it is the correspondingvariable without the prefix C multiplied by the oppor-tunity cost of time. The opportunity cost of time is PRmeasured by the earnings per minute of family workers PRIVif the individual is working and is set to 1 cent per min-ute if the individual is not working or if there is no re-ported earned income for the family. TOPDC

CATOPDC Mean = ($1.17).

CATOPDC2 Mean = ( 3.61). TOPDC2CATPRIV Mean = ($1.39). TPRIVCATPRIVZ Mean = ( 5.32).

CTOPDC Means = ($1.42, $1.57). TPRIV2

CTOPDC2 Means = ( 5.46, 6.66).

CTPRIV Means = ($0.88, $1.24).

CTPRIV2 Means = ( 2.98, 6.76).

CHRON Number of reported chronic health conditions that limitactivity. Means = (0.20, 0.21).

DAZPRIV = Number of days hospitalized in last year in a nongovern-mental hospital. Means = (1.07, 0.69).

DAZPUB = Number of days hospitalized in last year in a city or othergovernmental hospital. Mean = (0.30, 0.50).

EARN = Earned family income in last year. Means = ($4,110,$4,532).

EARN2 = Means = (35388091, 45129544).

EDUC = Highest grade completed, in years. Means = (6.8, 7.3).

HSIZE = Number of persons in individual's household. Means =(4.7, 4.3).

MALE = One if male, zero if female. Means (0.46, 0.44).

NEARN = Non-earned family income in last year. Means = ($920,$1,067).

NEARN2 = NEARN2. Means = (3326386, 3996932).

194I

Acton 195 Der

= One if the person unambiguously has no insurance cov-erage for ambulatory care; zero otherwise. Means = (0.21,0.23).

= Number of visits in last year to a physician in outpatientdepartment of a municipal hospital or to a clinic not con-nected to a hospital. Means = (1.68, 1.46).

= One if Puerto Rican; zero otherwise. Means = (0.26, 0.07).

= Number of visits in last year to a physician in his privateoffice. Means = (1.83, 1.56).

= Travel time, on the average, to and from municipal out-patient department or free-standing clinic, in minutes.Means = (72.9, 64.0).

= TOPDC2. Means = (6,085, 4,424).

= Travel time, on the average, to and from private physi-cian's office (PRIV), in minutes. Means = (44.6, 48.8).

= Means = (3,096, 3,521).

195I

Demand for Health Care among the Urban Poor

NOAMB

OPDC

PR

PRIV

TOPDC

TOPDC2TPRIV

TPRIV2

e and is under 650.32, 0.36).

zero otherwise.

he correspondinged by the oppor-

cost of time isof family workerso 1 cent per mm-if there is no re-

ditions that limit

r in a nongovern-

in a city or other.50).

leans = ($4,110,

ns = (6.8, 7.3).

• ehold. Means =

.46, 0.44).

Means = ($920,

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3

APPENDIX 3(A-4a) Umm

op

Detail of the Formal Model of Demand for MedicalServices (A4b)

The formal model is developed in terms of a two-good utility andfunction, medical services, m, and a composite good, X, and haspeople pay in both money and time for each good. If the proportion (A-4c) €o + wt) -of money and the price per unit of the good remains fixed and thefull wealth assumption is used, the objective is to maximize If we desigi

(A-la) U = U(m,X) then

subject toDl

(A-lb) (p +wt)nz +(q +ws)X =.y +wT

where the variables are defined as on p. 167. 1 assume that allequations are twice differentiable and that the first derivatives of (A4d)the utility function are positive, the second derivatives, negative, = uand the cross derivatives are positive.38 The conditions for maximiz-ing utility are found by forming the Lagrangian expression —

(A-2) L = U(m ,X) + X [m (p + wt) + X(q + ws) — y — wT] Assuming tiis unambigDifferentiating with respect to the three unknowns, m, X, and

and setting these equal to zero yields the first-order conditions for a ru e.maximization:

(A-3a) +wt) =0

(A-4e) —=(A-3b) = + X(q + ws) =0

—11and

(A-3c) +wt) +X(q +ws) —y —wT 0Since A isunambiguotwhere by definition good; with

— OCT A — Similarly,U,,, = -i---— anu

= of m on the

Effects of a Change in Pnce (A-5a) UmmTo calculate the effect of a change in the out-of-pocket money priceof in on the demand for ni, we must differentiate the system ofequations (A-3) with respect to p, yielding: (A5b) Uxm

198 .Acton 199 Dem

Om OX OK(A-4a) Umm + Um¼' + (p + = K

op op op

dical OX OX(A-4b) Uvm + + (q + ws) = 0

äp Op Op

wo-good utility andod, X, and has OX

f the proportion (A.4c) (p + wt) + (q + ws) = — m

s fixed and themaximize If we designate the determinant of the matrix of coefficients D ,

then

Umm Umx (p +wt) I

ID (q + ws) I

(p+wt) (q+ws) 0assume that allt derivatives of (AAd)

lives, negative, = Umx (q + ws)(p + wt) + (q + ws)(p + wt)ns for maximiz-

— (p + wt)2 — Umm (q + ws)2pressiOnAssuming that and Umm <0 and that and Umx >0, then ID

I

is unambiguously positive. We can solve for ôm/t9p by Cramer'sIS, in, X, and K,

conditions for a—X (p+wt)1

—m (q +ws) 0

o (q +ws)

DI

— +ws) (p +wt) + X(q +ws)2

Since A is necessarily negative by (A-3a) and (A-3b), Om/Op isunambiguously negative. Medical services, m, is acting as a normalgood; with a higher money price, people demand less.

Similarly, we can calculate the effect of a change in the time priceof m on the demand form. Differentiating with respect tot yields

Om OX OX(A-5a) Umm + U mX + (p + wt)— = — KID

:et money pricethe system of OX OX —

(A-5b) + +(q +ws) — 0at at at

199I

Demand for Health Care among the Urban Poor

r

and The three

ölfl(A-5c) (p + wt) + (q + ws) = — mw (A-7a) 71mun =

Using Cramer's rule again, and

Umx (p+wt) f (A-7b)

0 (q +ws)Consequen

fl2W (q+ws) 0(A-5d) =& DI

as— —mw +ws) +wt) + Aw(q +ws)2— IDI p<Wt

which is also unambiguously negative. That is, time is also func-tioning as a price in determining the consumption of m. Effects of a

For reference, it is interesting to calculate the total price elastic- The effectsity of demand form. Differentiating equations (A-3) with respect to systernatica(p + wt), we find effect of a

calculate. tt9m oX+U(A-6a) Umm O(p + wy) mX

O(p + wt)+ (p + wt)

O(p + wt)=

(A-8a) U,!,fl'3tJ

OX ox+U(A6b) U.vm O(p + wt) XO(p + wt) + (q + ws)

O(p + wt)= 0

(A-8b)and

andOm OX

(A-6c) (p+wt) +ô(p + wt) q + ws) O(p + wt) = — m(A-8c) (p + wt)

So,Thus,

—X Umx (p +wt) I

0 (q +ws) I

Om = — m (q + ws) 0 I

O(p +wt) IDI (A-8d) =+ws) +wt) +X(q +ws)2

IDIThus, we find that

(A-6e) Om = which is unis normal;+wt) Op

201 IDec

200 Acton

The three price elasticities are related in the following manner:tot

(A-7a) = Tlmt = + ri)

(A-7b) Tlmp (p +wt)Consequently, it follows that

as

Thnp Thni

p tot

ime is also func-n of m.otal price elastic-3) with respect to

= —x

ox+wt) —

Effects of a Change in IncomeThe effects of a change in earned and non-earned income aresystematically related, but they are not, in general, the same. Theeffect of a change in non-earned income is straighiforward tocalculate. Differentiating equations (A-3) with respect to y yields:

OX OX(A-8a) U,,,,, + + (p + tot)— = 0

Oy Otj c3y

(A-8b) UVm + +(q = 0oy oy oy

andOX

(A-Sc) (p +wt)—+(q +ws)—=1oh O1J

I

Thus,

0(A-8d) =oU

which is unambiguously positive. The demand for medical servicesis normal; with more non-earned income, people demand more.

201 Demand for Health Care among the Urban Poor

and

(q +ws)2

Umv (p +wt)

(q + ws)

(q +ws) 0

DI= (q + ws) — U.vx (p + wt)

DI

We can see the effect of a change in the earnings per hour by NOTESdifferentiating with respect to w:

1. See Netim OX OX(A-9a) Umm + + (p +wt)— = — xt 2 Seeesp

Ow Ow Ow and3. If denr

tim OX OX(A9b) Uvm + + (q + ws)— = — As increaseOw Ow Ow increase

treatingand

Intim(A-9c) (p + wt) + (q + ws) = — mt — Xs + T time, TI

Ow (1965);Holtmai

Cramer's rule yields: correcti:include

—At (p +wt) I timeiniinformai

— As (q + ws) If such

(A-9d) tim T —mt —Xs (q + ws) 0 correlatitime in

Ow D increasesupplyrits absei

(T —mt —Xs)Umx(q +ws) —(T —mt +wt) — As(q +ws)(p +wt)+ At(q +ws)2 one canpatternsresults rthese ot

The effects of a change in the wage rate can be broken down into an 4. Similar

income effect and substitution effect: (1973).5. See Gro

tim Am As (q + ws) (p + wt) — At(q + ws)2 I

6. See Ph(A-9e) = (T— mt — Xs) — endoger

Ow DI I 7. See LaiattributeThe first term, the income effect, is by assumption positive. The 8. Althoug

sign of the substitution effect depends on the relative time intensity that the/ of the goods m and X. If the time component of total price is larger positive,

for X than it is for m, there will be a positive substitution from x to derivatii

m. That is, the substitution term is positive if and only if 9. As showthe longutilizati(ws wt

(A-lOa) > 10. lnthec(q +ws) (p +wt)It is easy to show that the substitution effect is negative if medical negativecare is "free." Substituting p = 0 into (A-lOa), canceling common 11, NORC cterms, and multiplying through by (q + ws) yields was the

improve(A-lob) ws <(q +ws) Hook sa

Bedford-Therefore, the substitution effect is negative. is availa

202 Acton 203 Der

A

1. See Newhouse and Acton (1974) for a discussion of this point.2. See especially Davis and Russell(1972), Feldstein (1971), Phelps (1973), Phelps

and Newhouse (1973), and Rosett and Huang (1973).3. If demand increases in response to spreading insurance, in addition to

increases in waiting and travel time, the supply responses may be to (1)increase the number of referrals to other providers, (2) cause a postponement intreating some conditions, or (3) change the quality of services being provided.Increased referrals and postponement are alternative forms of greater timecosts. In this study, I am concentrating directly on the role of waiting and traveltime. The importance of time in determining demand was explored by Becker(1965); its importance in medical care, by, among others, Leveson (1970),Holtman (1972), and Auster and Ro (1972). In her comments, Mrs. Campbellcorrectly points out that "waiting time" in this survey probably does notinclude the amount of time spent in an examination room unattended or thetime in transit between different tests or parts of the facility. This more detailedinformation would be interesting to explore but was unavailable in this survey.If such additional "hidden" time charges are independent of or proportional totime in the waiting room, the elasticities are unaffected; if they are negativelycorrelated, then the empirical results are misleading. She also comments thatincreased referrals or postponement of appointments may be an importantsupply response to spreading coverage—with which I agree. I do not agree thatits absence in these equations limits their value for policy assessment. Unlessone can demonstrate that suppliers will discriminate systematically in theirpatterns of postponement and referrals, then the waiting time and travel timeresults reported below are partial effects that should be observed regardless ofthese other effects.

4. Similar models can be found in Grossman (1970), Becker (1965), and Acton(1973).

5. See Grossman (1972) for a formulation accommodating this feature.6. See Phelps (1973) for a theoretical and empirical treatment with insurance

endogenou s.7. See Lancaster (1966) for a similar formulation of demand in terms of the

attributes of a good.8. Although they are more restrictive than necessary, sufficient assumptions are

that the first derivatives of the utility function with respect to a good arepositive, that the second derivatives are negative, and that the cross-partialderivatives are positive.

9. As shown in Appendix 3, 7?mufl = 7imt These elasticities are approximate only inthe long run if insurance premiums are adjusted to reflect the changes inutilization.

10. In the consumption model, given a neutral effect of education on all householdactivities, the elasticity with respect to wealth must also be less than ito have anegative effect on education; Grossman (1972a, pp. 36—37).

11. NORC conducted ten baseline surveys for OEO. The Bedford-Crown surveywas the second survey and Red Hook the third. The survey instrumentimproved somewhat, so occasionally we have useful information on the RedHook sample that is not available for Bedford-Crown. A description of theBedford-Crown study, along with the survey instrument and selected findings,is available in Richardson (1969a). A similar report on the Red Hook study is

203I

Demand for Health Care among the Urban Poor

NOTESngs per hour by

s)(p +wt)+ At(q+ws)2

cen down into an

At(q +ws)2

on positive. Theye time intensitytal price is larger:itution from X toonly if

gative if medicalnceling common

Richardson (1969b). Selected findings for the first three NORC studies (Atlantaand the two Brooklyn surveys) are presented in Richardson (1970).

12. Let k proportion of the variable x be reported, then the estimated (price)elasticity = = (ôx/âp) the same elasticity that wouldhave been estimated with correct reporting.

13. Conversations with OEO officials have indicated that the acceptance of theneighborhood health centers has been different from the two populations. TheRed Hook population is changing its behavior by coming to the center for earlycare and preventive medicine. In Bedford-Crown, the population comes inchiefly for treatment of advanced and chronic conditions. There may be somepersistent differences in the two populations that will be reflected in theanalysis below. It could simply be a different acceptance of the neighborhoodhealth centers. The Bedford-Crown center is located in a very rough neighbor-hood and, purportedly, taxi drivers refuse to travel there. This does not appearto be true for the Red Hook neighborhood.

14. The use of a mean value rather than zero for these nonresponses was necessaryto avoid the implausible situation that higher own-time prices are associatedwith lower utilization except for zero utilization when own-time prices arezero. A predicted value of own-time price might have been used, but thatoption is deferred for further analysis. It was necessary to use the mean valuefor about three-fourths of the times associated with free care and aboutone-fourth of the times associated with non-free care in both samples.

Using the mean to replace missing values reduced the efficiency in estimat-ing that coefficient, but Charles Phelps demonstrated that use of the mean forsome observations does not bias the remaining coefficients if the mean isuncorrelated with the remaining variables. Consider the bivariate case inwhich m observations on; are known and the next p are replaced with themean (their true value is +u,). The OLS estimator of/I is b = +

+ Ep(x +u)2] = {Lj(xxfI) +xe} + +u)(x/3++ + u)2]. The measurement error for the subset, p, of

observation is = — x1) so that = and + = 0, where the sub-scripts on variances indicate the subsample to which they relate. The probabil-ity limit of b can be shown to be plim b + + + +

Since, in subsample of size p, 4 + + = 0 and = it followsthat = oI,, and plim b = (4m + 0)13/((4m + 0) = /3.

15. It is necessary to use a non-zero value for the opportunity cost of a unit of time iftravel and waiting time are to play a role in determining demand for a specificprovider by nonworking persons. Otherwise, we are assuming that, in effect,the person is indifferent whether he travels a short distance for care or travels agreat distance. Furthermore, physician visits by children frequently cause anadult to spend time accompanying them. The value of 60 cents per hour for thisgroup is arbitrary, but it can be motivated to some degree as a plausible valuefor the cost of hiring a babysitter. The value of 60 cents is lower than anyobserved value of eai-nings per hour in either sample (which was over $1 perhour). A number of researchers have taken a much more detailed look atvaluing the time of persons out of the labor force (see, for instance, Gronau,1973a and b, and references cited). I did not feel a more complicated approachwas justified in the current application because of limited information abouttime allocation of individual family members.

16. I took the total reported income and subtracted the elements that werenon-earned to create the earned income variable. In a few cases, the sum of

205 Dt

non-earnrecordedcases, th

17. Ideally,but its alcorrelate

18. In additistock of]given restock.health h

19. To someother, bsensitivihospital

20. If everyproblem

21. Thetsta

they pro

test the

significa

The n

hospitali

22. Figure 1

People

on the Iiof the

low timproportiprices ii

greater

FIGURE laRelationown-time pricand quantity

q

204 Acton

.1

Tstudies (Atlanta

n (1970).e estimated (price)lasticity that would

e acceptance of thevo populations. Thethe center for early

opulation comes inThere may be somebe reflected in theDf the neighborhoodery rough neighbor-his does not appear

onses was necessaryrices are associated

pwn-time prices arebeen used, but thatuse the mean valueee care and aboutoth samples.ificiency in estimat-use of the mean for

ents if the mean ise bivariate case ine replaced with thef3 b = +

.+ +u)(xf3+r the subset, p, of0, where the sub-

relate. The probabil-+ +

a- = at, it follows

)stOfa unit of time ifemand for a specific•ming that, in effect,e for care or travels afrequently cause an

ents per hour for thisas a plausible values is lower than anyich was over $1 perre detailed look at

or instance, Gronau,Dmplicated approachd information about

elements that werew cases, the sum of

205I

Demand for Health Care among the Urban Poor

non-earned incomes exceeded the stated total income (typically, zero wasrecorded for total, but a monthly social security income was reported). In thesecases, the amount created by summing up the components was used.

17. Ideally, health status lagged one period would be used. It was not available,but its absence is not too serious since the underlying stock of health is highlycorrelated from one year to the next.

18. In addition, people with more chronic health conditions probably have a lowerstock of health to begin with, so that it takes more medical inputs to achieve agiven replacement of health than it would if they had started with a greaterstock. This argument assumes that the function transforming medical inputs tohealth has decreasing returns to scale.

19. To some degree, inpatient and outpatient care may be substitutes for eachother, but I expect their complementary nature to dominate. I checked thesensitivity of the remaining coefficients to the inclusion and exclusion of thesehospital variables and found the coefficients practically unchanged.

20. If everyone's insurance coverage were known in detail, this would not be aproblem; but NOAMB is an imperfect measure, as indicated above.

21. The t statistics are asymptotic tests in the tobit framework. With samples of 5,000,they probably are good guides to significance. Furthermore, the chi2 statisticstest the hypothesis that the vector of coefficients is zero; they, too, are highlysignificant.

The reader should not attach too much importance to the equations for publichospitalization since the number of non-zero observations is very small.

22. Figure 1A shows the quantity of care demanded as a function of either t or wt.People who appear to have high time inputs to the purchase of care (indicatedon the line marked t) tend to have proportionately lower values of wt becauseof the negative correlation of w and t. Conversely, those who appear to havelow time inputs tend to have higher opportunity costs of time and thereforeproportionately higher values of wt. The sanie result holds for the cross-timeprices indicated in Fig. lB. Thus, the true elasticity with respect to wt will begreater than that implied by the regression on t alone.

FIGURE 1 a FIGURE 1 bRelation between Relation betweenown-time prices cross-time pricesand quantity and quantity

q q

t, wt t, wt

I.

23. This apparent contradiction may be because the estimated maximum occurs 1 they do nwhere ATOPDC = 45 minutes. The mean, used for calculating the elasticity, is monetary59 minutes, which is one standard deviation above the critical point, physician

24. Using a 1965 survey of users of the municipal hospitals' OPDs (specifying a (1970), Fsimultaneous equation system with public and private ambulatory care and discussioipublic hospitalization all endogenous), I found complementarity in public attempt tambulatory and inpatient care. See Acton (1973).

Iopportuni

25. This comparison was carried out using OLS—whose results approach tobitasymptotically—because patterns of significance and collinearity were found to 33. One formcarry over well to tobit results. centrally

26. These estimated elasticities may be biased downward by a transitory compo- 34. This is arnent in non-earned income. The negative elasticity for private hospital days, 35. This calciequations (4) and (12), is caused by the elasticity's being calculated at the mean nal tax raof the data ($920), which was just to the left of the minimum of our estimated 36. The actwrelationship ($939 in Equation (4) and $1,183 in Equation (12), which is within and Phel1one-seventh of a standard deviation of the mean). For approximately half the reports.sample, the non-earned income elasticity has the expected positive sign. For 37. The meamost other equations, the critical point is not within one standard deviation of Crown.the mean of the data. 38. These ass

27. Michael Grossman pointed out that, in general, we can expect to find lower rise in thelasticities with respect to earned income in equations (9)—(16) than inequations (1)—(8). Consider the simplified form of a demand equation,(4a) m =a +bp +cY

where p = wt and Y = y + wT. We expect b <0 and c >0. Substituting into(4a) yields

I

REFERENCE(4b) m =a +cwT +cy

1. Acton,Jasimilar to equations (1)—(8). With wt held constant, the coefficient, c, on full Moearnings should be positive. When we estimate 2. Auster, 1

(4c) m=a-l-b't+c'wT+dy HoEc

the coefficient c' could be negative. The elasticities reported in table 3 3. Becker,generally support this prediction that the earning elasticities in equations I (Se(9)—(16) are lower than those in equations (1k8). —— 4. Davis, K

28. Since (&m/ÔY) = it follows that = (Om/ÔY) (Y/m) = (&m/ôy) Na(YIm) . (YIy) = (Yly). Ins

29. If the reader wishes to make other assumptions about the definition of full 5.wealth, then the elasticities can be adjusted accordingly. For instance, if T is Cataken as referring to a twenty-four-hour day instead of a forty-hour work 6. Feldsteiiweek, the full wealth elasticities reported here should be scaled up by 4.2. Qu

30. The corresponding elasticities for the Bedford-Crown sample, 1.317 and 7. Frech, I—0.7 14, reflect the estimated coefficients on N EARN, and the comments made Coabove apply. . 57

31. It is probably not worth conducting a rigorous test of this hypothesis, which 8. Gronau,requires calculation of the covariance among equations, but it seems valid. H

32. This supply response is likely for a number of reasons. First, it may be optimal 9.from the point of view of the provider to have a queue to even out the variation Polin demand that he experiences, without having to invest in significant excess 10. Grossmacapacity. A shift in demand will generally cause the optimal queue length tochange (for instance, the opportunity cost of an idle moment of the supplier's 11. ,"facility is higher). Second, the suppliers may not be profit maximizers, so that of

206 Acton 207 Del

d maximum occursting the elasticity, is•tical point.OPDs (specifying anbulatory care andnentarity in public

ults approach tobitearity were found to

a transitory compo-ivate hospital days,culated at the meanrn of our estimated

12), which is withinroximately half the

d positive sign. For'indard deviation of

xpect to find loweris (9)—(16) than ind equation,

0. Substituting into

they do not respond to a shift in demand by charging the highest possiblemonetary prices but instead allow time prices to increase. In particular,physicians may be income satisfiers rather than maximizers. See Newhouse(1970),. Frech and Ginsburg (1972), and Newhouse and Sloan (1972) for adiscussion of physician pricing behavior. Third, there may be a consciousattempt to redistribute services by discriminating in favor of those with a loweropportunity cost of time. See Nichols, Smolensky, and Tideman (1971) for adiscussion of the first and third points.

33. One form might be for several satellite clinics to be associated with a morecentrally located referral clinic.

34. This is an arc elasticity based on the elasticity calculated at the mean.35. This calculation ignores substitution effects induced by changes in the margi-

nal tax rate implicit in the income maintenance proposals.36. The actual money-price elasticity may be even lower than this. See Newhouse

and Phelps (1973) for a discussion of the price elasticities in several publishedreports.

37. The mean values are reported first for Red Hook and second for Bedford-Crown.

38. These assumptions are sufficient to imply that both goods are normal and that arise in their price will reduce demand.

REFERENCES

efficient, c, on full

in table 3'cities in equations

) = (e9m/c3y)

'e definition of full'or instance, if T isa forty-hour work

scaled up by 4.2.sample, 1.317 andhe comments made

hypothesis, whichit it seems valid.t, it may be optimalen out the variationii significant excessal queue length tont of the supplier'smaximizers, so that

j

1. Acton, Jan Paul, "Demand for Health Care When Time Prices Vary More ThanMoney Prices," R-1189-OEO/NYC, The Rand Corporation, May 1973b.

2. Auster, Richard, and Kong-Kyan Ro, "The Demand for Hospital Care byHospitalized Individuals," Mimeographed paper presented at the WinterEconometrics Society Meetings, Toronto, 1972.

3. Becker, Gary, "A Theory of the Allocation of Time," Economic Journal, 75(September 1965), pp. 493—517.

4. Davis, Karen, "Health Insurance," in Charles Schultze et al. (eds.), SettingNational Priorities: The 1973 Budget (Washington, D.C.: The BrookingsInstitution, 1972), pp. 213—251.

5. , and Louise Russell, "The Substitution of Hospital Care for InpatientCare," Review of Economics and Statistics, 54 (May 1972), pp. 109—120.

6. Feldstein, Martin S., "An Econometric Model of the Medicare System,"Quarterly Journal of Economics, 85 (1971), pp. 1—20.

7. Frech, H.E., and Paul B. Ginsburg, "Physician Pricing: Monopolistic orCompetitive: Comment," Southern Economic Journal, 38 (1972), pp.573—577.

8. Gronau, Reuben, "The Intrafamily Allocation of Time: The Value of theHousewife's Time," The American Economic Review, forthcoming.

9. ,"The Effects of Children on the Housewife's Value of Time,"Journal ofPolitical Economy, 81 (March—April 1973b), pp. 168—199.

10. Grossman, Michael, The Demand for Health: A Theoretical and EmpiricalInvestigation (New York: National Bureau of Economic Research, 1972a).

11. ,"On the Concept of Health Capital and the Demand for Health,"Journalof Political Economy, 80 (March—April 1972), pp. 223—255.

207 Demand for Health Care among the Urban Poor

econometrici12. Holtman, AG., "Prices, Time, and Technology in the Medical Care Market," as represente

Journal of Human Resources, 7 (Spring 1972), PP. 179—190. determine th13. Lancaster, Kevin, "A New Approach to Consumer Theory ,"Journal of Political Acton's ecEconomy, 74 (April 1966), pp. 132—157.14. Newhouse, Joseph P., "A Model of Physician Pricing," Southern Economic part of the ne

Journal, 37 (October 1970), pp. 174—183. overdue in d15. , and Jan Paul Acton, "Compulsory Health Planning Laws and National medical care

Health Insurance," in Clark Havighurst (ed), Regulating Health medical careFacilities Construction (Washington, D.C.: The American Enterprise been more oInstitute, 1974), University of

16. , and Charles E. Phelps, "On Having Your Cake and Eating It Too: A Sweden thatReview of Estimated Effects of Insurance on Demand for HealthServices," R-1149-NC, The Rand Corporation, April 1974. Demand (ac

17. , and Frank A. Sloan, "Physician Pricing, Monopolistic or Competitive: representedReply," Southern Economic Journal, 38 (April 1972), pp. 577-580. with a desin

18. Nichols, D.E., and TN. Tideman, "Discrimination by Waiting Time in Merit be providedGoods," American Economic Review, 61 (June 1971), pp. 312—323. consumptio

19. Phelps, Charles E., "The Effects of Coinsurance on Demand for PhysicianServices," R-976-OEO, The Rand Corporation, June 1972. This is a defi

20. ,"Demand for Health Insurance: A Theoretical and Empirical Investiga- When thirdtion," R-1054-OEO, The Rand Corporation, July 1973. $

care bill, moi21. ,and Joseph P. Newhouse, "Coinsurance and the Demand for Medical especially m

Services," R-964-OEO/NYC, The Rand Corporation, July 1973.22. Richardson, William C., Charles Drew Neighborhood Health Center Survey party paymei

Bedford-Stuyvesant—Crown Heights, Brooklyn, New York (Chicago: earlier pubhs

NORC, University of Chicago, 1969a). care, I asked23. ,Red Hook Neighborhood Health Center Survey Brooklyn, New York optimal if all

(Chicago: NORC, University of Chicago, 1969b). categories,w$24. , "Measuring the Urban Poor's Use of Physicians' Services in Response to high correlati

Illness Episodes," Medical Care, 8 (1970), pp. 132—142. income distri25. Rosett, Richard N., and Lien-Fu Huang, "The Effects of Health Insurance on the a low opportu

Demand for Medical Care," Journal of Political Economy, 81 (March— policy approApril 1971). consumption

26. Tobin, James, "Estimation of Relationships for Limited Dependent Variables," to test his mEconometrica, 26 (1958), pp. 24—36. earned andu

To discussall different kimodel incluconsumptionbetween wee

In additionconsiderable

I COMMENTS This "waitinlunavailable—"hidden" forrRita Ricardo Campbell There is a

Hoover Institution on War, Revolution and Peace health care,like. This con

As some of you may know, I have been involved in the public policy area in consumer toregard to the financing and delivery of medical care and am not an

209I

Derr208 Acton

'dical Care Market,"179—190"Journal of Political

Southern Economic

g Laws and NationalRegulating Health.merican Enterprise

nd Eating It Too: A)ernand for Health1 1974.istic or Competitive:

pp. 577—580.Liting Time in Merit1), pp. 312—323.mand for Physiciane 1972.Empirical Investiga-73.)eniand for Medical

July 1973.aith Center Surveyew York (Chicago:

Brooklyn, New York

rvices in Response to-142.aith Insurance on theconomy, 81 (March—

'pendent Variables,"

iblic policy area ine and am not an

econometrician. I greatly appreciate, therefore, the efforts of econometricians,as represented by the paper of Jan Acton, and by others at this conference, todetermine the effect of net price on the demand for health care.

Acton's econometric analysis and empirical data about the role of time aspart of the net price paid by the consumer or potential patient, I feel, is longoverdue in discussions about the allocation and quality of the delivery ofmedical care in the U.S. In other countries, where the financing and system ofmedical care are more nationalized, the role of "waiting" in allocation hasbeen more obvious and is recognized. For example, . Professor Spek of theUniversity of Gothenburg defines "demand" for that portion of health care inSweden that is completely free, as follows:

Demand (active, effective) for public care is that part of the need for care which isrepresented by those individuals who come in touch with the system of public carewith a desire for consultation and treatment, and who are willing to wait if this cannotbe provided at once. In each period, demand takes the form of queueing or results inconsumption. .

This is a definition of demand wholly in terms of time.When third-party payments cover two-thirds of the U.S. total personal health

care bill, money price cannot be considered the primary allocation factor andespecially not in those areas of care—hospital and surgical—wherein third-party payments are 92 per cent and about 70—75 per cent, respectively. In anearlier published discussion of methods other than a price to allocate medicalcare, I asked, "Would the distribution of scarce medical resources be moreoptimal if all financial barriers to securing care were removed and no specialcategories were set up?" and stated that "there is as much logic to implying ahigh correlation between income and need for medical care throughout theincome distribution ranges as there is to implying a high correlation betweena low opportunity cost of time and need for medical care."2 It is with this publicpolicy approach that I have read Dr. Acton's paper, which develops aconsumption model and analyzes two sets of specific data re the urban poorto test his model, which includes as variables time prices, money prices,earned and unearned income, and as the outcome measure, physician visits.

To discuss the role of opportunity costs of time, it is necessary to considerall different kinds of time involved in consuming health care. Although Acton'smodel includes "waiting" and travel time,3 it does not cover all forms ofconsumption of time involved in getting medical care nor does it distinguishbetween week days and weekends or after usual work hours.

In addition to the waiting time in a physician's outer office, there may beconsiderable waiting in the actual examination room before seeing an M.D.This "waiting" does not appear to be included—probably the data areunavailable—yet in some clinics and group practices it may be a sizable"hidden" form of waiting.

There is also the amount of time spent not in waiting but in consuminghealth care, such as is involved in having examinations, X-rays, tests, and thelike. This consumption of time may be less important in initial decisions by theconsumer to seek medical care, because he may be ignorant of the sub-

209I

Demand for Health Care among the Urban Poor

t

sequent amount of time involved, which is largely controlled by the provider. An intere:The more knowledgeable consumer does, however, consider this potential for the Tear'time' in deciding whether or not to have a postponable operation, or even criticizes thmore routine care, such as an eye examination. However, from an even Kaiser's wibroader point of view, and as stated by Michael Grossman in his Demand for "over theHealth (NBER Occasional Paper No. 119), although "a demand curve for the dissatisfactitime spent producing health [by the consumer] could also be developed, data lengthy waipertaining to this input are, in general, not available" (p. 41). sonal physi

A third concept involving waiting is the time one has to wait for an Kaiserappointment. To relegate to a footnote, as does Acton, suppliers' responses of and retainir"increased referrals and postponement" as an alternative form of greater time cian and hcosts to the consumer is insufficient for public policy decision making. The The genequality of medical care and the resource costs of providing it are affected by relied almostructuring the demand for medical care through imposing long waits for time of enrappointments. For example, to the degree that HMO's or prepaid group quality onlypractice use an appointment system, and most do, they can consciously of quality ocurtail demand by delaying appointments six weeks or two months or more for some typecheck-ups and especially for specialists' care wherein explanations of delay as ofmay be more acceptable to the consumer, whose ignorance exceeds in this ment of thmatter the physician's. The quality of care is less with long waits than with anticipatedshort waits To the extent that the "waiting" induces subscribers to seek care and speciaelsewhere, total costs to a prepaid group are lowered. Data on voluntary The Instioutside utilization of physician services by members of a prepaid group are medical mrsparse and scattered and the reasons for the outside utilization are largely anemia orunexplored. To what degree outside use of services occurs, which otherwise trying to dewould not require out-of-pocket expense to the patient because of various ity rates or,forms of waiting, I do not know, used in thi:

Acton's paper does not incorporate into the analysis these various types of qualified b"time," probably because the empirical data are unavailable. Econometric importancemodeling to encompass more kinds of waiting may encourage better data levels as acollection. From the point of view of public policy, the different types of Whetherwaiting time cannot be ignored and some recognition should be given these time appeEvariables even if they are not in the formal model. functioning

Recent empirical studies emphasize the importance of these, possibly its importarnonmeasurable, inputs as follows: "Patient waiting time was longer for toothersecnonwhites, females, poor people, and the elderly, waiting time was not related

, areas is dto practice size but varied proportionately with use of allied health person- percentagenel,..." in the fee-for-service sector, solo and group. of earned

To determine potential utilization, a state planning agency, New York,5 schedules,recommends that a new prepaid group practice or HMO obtain answers to income ansuch questions as: "How many waiting rooms should there be and where Probablyshould they be located? (1) What will be the average length of a patient visit? time limits(2) How many people will there be at one time in each waiting and Income Sufurther, "How many consultation and examination rooms will be needed for increase aeach physician?" Obviously, HMO's, and for that matter any physician, can income, aistructure demand by the way they answer these and other questions. comparabiAdditionally, HMO's decide how many physicians per 1,000 enrollees, ation."number of hospital beds per 1,000 enrollees, and so on, will be provided.

210 Acton

1

211 D

d by the provider.ider this potentialoperation or even'er, from an evenin his Demand for

',and curve for thee developed, data

as to wait for anhers' responses ofrm of greater timeision making. The

Iit are affected by

ing long waits foror prepaid group

can consciouslymonths or more forlanations of delay

ce exceeds in thisng waits than withribers to seek careData on voluntaryprepaid group arelization are largelys, which otherwiseecause of various

Se various types oflable. Econometricourage better data

different types ofuld be given these

of these, possiblye was longer forme was not relatedlied health person-

gency, Newobtain answers toere be and whereh of a patient visit?Ling area?..." andwill be needed forany physician, can

I other questions.1,000 enrollees,

will be provided.

An interesting evaluation of the California Medical Group (CMG) preparedfor the Teamsters and Food Employers Security Trust Fund in LOS Angeles6criticizes that group as having physician and hospital bed ratios far lower thanKaiser's, which are lower than the average in California, and comments,"over the years, Trust Funds have become increasingly aware of subscriberdissatisfaction with Kaiser services. Difficulties making appointments,lengthy waits to see physicians even with appointments, and hurried, imper-sonal physician contacts are common complaints" (p. 9). For those who areKaiser supporters, the evaluation report recommended turning down CMGand retaining Kaiser because obviously CMG's proposed much lower physi-cian and hospital bed enrollee ratios would increase complaints.

The general approach of quality control in prepaid groups has, in the past,relied almost entirely on providing the subscriber with an alternative choice attime of enrollment, and subsequently once a year. This works to controlquality only if at least one of the alternatives provides an acceptable standardof quality of care. This may not always be the case and there is a need forsome type of continuing review of ambulatory delivery of medical care as wellas of in-hospital care. At a minimum is input control through careful assess-ment of the quantity of the medical care inputs in relationship to theanticipated demand and their quality; e.g., numbers of primary physiciansand specialists, initial training and continuing education, and the like.

The Institute of Medicine's7 proposal to use selected tracers, whereinmedical inputs and health outcomes are directly related, as in iron-deficiencyanemia or middle ear infection, is worth exploring by economists who aretrying to develop better health outcome measures than mortality and morbid-ity rates or, as in Acton's study, the number of physician visits. The latter isused in this study without being subdivided into different types of visits norqualified by number of minutes. The omission of any reference to theimportance of the use of the telephone visit by persons in higher incomelevels as a means of avoiding waiting is disappointing.

Whether Acton's conclusions re the "urban poor" that "travel and waitingtime appear to be operating as normal prices and that "time is alreadyfunctioning as a rationing device for demand in this New York population, andits importance seems to exceed that of money prices,..." can be carried overto other sectors of society as defined by income levels in urban and suburbanareas is doubtful, even if one accepts his fairly rigid assumptions. Thepercentage of third-party payments of total health care costs, levels and ratiosof earned and unearned incomes, use of telephone and of appointmentschedules, level of knowledge re medical care, and so on, differ at differentincome and educational levels.

Probably the most important policy inference discussed by Dr. Acton, andtime limits my discussion of it, is under "Tradeoffs of Subsidized Care andIncome Supplements," in which he states that "income maintenance willincrease aggregate medical demand for the poor" because it is non-earnedincome, and concludes that "the magnitude of the change may be verycomparable over the range of subsidy and income guarantee under consider-ation."

j 211 Demand for Health Care among the Urban Poor

NOTES (queuing tipositive co

1. J. E. Spek, "On the Economic Analysis of Health and Medical Care in a Swedish Health District,' medicalin M. M. Hauser (editor), The Economics of Medical Care, university of York Studies inEconomics, 7 (London: George Allen and lJnwin, 1972), p. 265. waIting tim

2. Rita R. Campbell, Economics of Health and Public Policy (Washington, D.C.: American biasedEnterprise Institute, June 1971), P. 69. Acton.

3. Additionally, for a given person living in a city, travel time from home to the physician's office The travtmay vary greatly, depending on whether it is undertaken during rush hours or not and also d t 'whether one has available a private car or must depend on public transportation, with possibly e cie cyinconvenient schedules and transfers. the equatio

4. The AMA and USC joint studies using AMA's data. as reported in Health Services Research, Acton's I(Winter 1973), p. 326. and familie

5. New York State Health Planning Commission, Group Practice . . . by Anne Bush, September,

1971, pp. 39, 40.6. California Council for Heallh Plan Alternatives, December 6, 1972. services 07. National Academy of Sciences, A Strategy for Evaluating Health Services, D.M. Kessner, Project variability i

Director, Washington, D.C., 1973. visits to theand finds anumber ofmedical camy judgmeof medical

Harry J. Gilman. incorrect

University of Rochester . choice ofphysician

I generally agree With Acton's arguments' about the desirability of measuring the lengththe role of time in the demand for medical services. I also admire most of his ciated witheconometric work. I do not, however, like his data, or the use to which he puts must mean

these data. I am therefore extremely uneasy about his findings, particularly his is the total

principal findings of fairly high time-price elasticities of demand and ex- choice, tht

tremely low or nonexistent income elasticity of demand for medical services, be used, bMeasurement problems aside, casual empiricism suggests that the de- Acton's

mand for medical services is a function of costs other than money prices, in over timeaddition to money prices. Even if we ignore the behavior of lower-income , sick leave,groups and concentrate instead on groups having completely free medical This trend

as part of the pay package (families of military personnel are an oppositeexample), we suspect that their demand for medical services are less than relative r

what they would be if they faced only zero money prices. For if the zero money incorrect.prices represented the marginal costs, individuals facing such costs would These S

increase the consumption of medical services until the value of the last unit demand aconsumed, say, the value of their last visit to the doctor, equaled zero. Since low incomwe do riot observe such consumption behavior, it is reasonable to assume that inconsistethe money prices do not represent the total cost of medical services, reflected i

It does not follow, however, that one can expect the time-price elasticities of ' employmedemand to be much higher (by a factor of 4 or 5) than the money-price At fault

elasticities of demand. Moreover, the nonmonetary constraints need not be this variatexclusively or even largely those imposed by the two specific variables used rising inc(

in this study, travel to and waiting time in the office, Other important variables on the quthat have been omitted from this study are waiting time for appointments visits to a

212 Acton ,. 213

tedish Health District,'ity of York Studies in

gton, D.C. American

the physician's officehours or not and alsornrtation, with possibly

Ith Services Research,

,nfle Bush, September

D.M. Kessner, Project

)ility of measuringadmire most of hise to which he putsgs, particularly hisdemand and ex-

medical services.gests that the de-

money prices, inr of lower-incomeetely free medicalpersonnel are an

ices are less thanif the zero money

such costs wouldlue of the last unitpualed zero. Sinceble to assume that

bi services.rice elasticities ofthe money-price

aints need not beif ic variables usedIlportant variablesfor appointments

(queuing time) and quality of medical services. I suspect that there is apositive correlation between the out-of-pocket costs and the quality ofmedical services. Furthermore, if queuing time were positively correlated withwaiting time in the office, the time-price elasticities of demand would bebiased upward, or away from zero, rather than downward, as claimed byActon.

The travel and waiting time variables used in this study have the addeddeficiency of being endogenous to the equations. This is particularly true inthe equations for the demand for private medical care.

Acton's data consist of questionnaire responses elicited from individualsand families living in two well-defined neighborhoods in New York City. Theseresponses do not include information on money prices paid for medicalservices or on the quality of medical services received. They do showvariability in travel and waiting time as well as variability in the number ofvisits to the doctor and in the number of days of hospital care. Acton expectsand finds an inverse correlation between travel and waiting time and, say, thenumber of visits to the doctor. He reasons correctly that more time spent formedical care increases the time price of such care. He concludes from that, inmy judgment incorrectly, that this negative correlation between time and useof medical care is a measure of the time-price elasticity of demand. This is anincorrect conclusion because the individuals in these neighborhoods have achoice of private physicians. This choice includes the location of thephysician and therefore the distance and time of travel from home as well asthe length of the waiting period. If an individual chooses a physician asso-ciated with more travel and waiting time over one requiring less travel time, itmust mean that the total cost for this physician is lower, for a given quality, thanis the total cost of the lower time-price physician. In the presence of voluntarychoice, therefore, the negative relationship between time and quantity cannotbe used, by itself, to estimate the time-price elasticities of demand.

Acton's arguments about the changing role of money versus time pricesover time also ignore the secular increase in the amount of time available assick leave, thereby reducing an individual's time costs of medical services.This trend is paralleled by a cross-sectional pattern of sick leave benefitsopposite to that of opportunity costs. Therefore, his conclusions about therelative roles of time prices among income groups are probably alsoincorrect.

These several factors lead me to believe that his time-price elasticities ofdemand are, to say the least, extremely unreliable. His unstable but extremelylow income elasticities of demand are also highly questionable. They areinconsistent with the rising demand for medical services over time asreflected in the behavior of price indexes, doctors' incomes, and the growth ofemployment in the medical services industry.

At fault here may be the poor quality of his dependent variable. In one case,this variable is simply the number of visits to a doctor. However, higher orrising income may have a greater effect on the quality of the doctor visited oron the quality of a visit to a given doctor than it does on the number ofvisits to a given doctor. This would be in line with the findings in a number

213 Demand for Health Care among the Urban Poor

of studies on the demand for durable goods, including the demand for chil-dren. All of these studies found a substantially higher quality incomeelasticity of demand than quantity income elasticity of demand.

To some extent the quality effects could have been reflected in a shift fromfree to non-free physician's services, with rising income. Acton's study findsno such income effect. However, it is my impression that his dependentvariable does not truly differentiate, as claimed, between free and money- ROBERprice services.

INN'University of Pent

1. INTROIThe heaandspendnallocatedirectedstatiStiCshealth 0and enhfamily is

The paper iof HealthInstitute atwerethe surveyRobert Eli(M.D.), Rostages ofSalkever, a

214 Acton 215