Differences Across States, 1966: An Econometric Analysis - National

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

Volume Title: Determinants of Expenditures for Physicians' Services in the United States 1948–68

Volume Author/Editor: Victor R. Fuchs and Marcia J. Kramer

Volume Publisher: NBER

Volume ISBN: 0-87014-247-X

Volume URL: http://www.nber.org/books/fuch73-1

Publication Date: 1973

Chapter Title: Differences Across States, 1966: An Econometric Analysis

Chapter Author: Victor R. Fuchs, Marcia J. Kramer

Chapter URL: http://www.nber.org/chapters/c3529

Chapter pages in book: (p. 21 - 42)

2Differences Across States, 1966:

An Econometric Analysis2.1 Introduction

Part 1 has suggested the importance of advances inmedical technology in explaining postwar trends inexpenditures, utilization, and physician productivity. Inorder to gain an understanding of physician and patientbehavior net of technological change, we now turn to across-sectional model. By examining differences acrossstates at a single point in time we are in effect holdingmedical technology fairly constant. There may be somelag in the spread of new knowledge from one state toanother, but the difference between the frontier ofknowledge in the most and least advanced states in anygiven year is far less than the change that occurredbetween 1948 and 1968 in the United States as awhole.1

Another advantage of the cross-sectional approach isthat it provides an opportunity to learn something aboutthe factors influencing the supply of physicians. It iswidely recognized that there are substantial barriers toentry into medicine. These are partly financial andpartly caused by the reluctance of organized medicine toexpand the volume of training facilities to the pointwhere all applicants with an ability to pay would beaccepted. Moreover, it takes a long time to establish anew medical school, and there is a lag of five or moreyears between the time a student enters medical schooland the time he begins to practice. It follows that thetotal number of practicing physicians in the countrycannot be responsive to any important degree to annualchanges in price or other market conditions. By contrast,the potential elasticity of physician supply going to anyone state is very great. Previous investigators havealready demonstrated that licensing procedures pose nosignificant impediment to interstate migration of physi-

'Differences in actual medical practice across states areundoubtedly larger than differences in the frontier of medicalknowledge. Our interpretation of the technological factor indemand, however, is predicated upon the assumption that thedemand for physicians' services increases with an expansion inthe range of services physicians are technically able to offer.Variations in actual medical practice across states are viewedprimarily as the consequence of variations in demand rather thanas their cause.

cians. (See [7], [24] .) With entry into the total marketeffectively limited, the geographical distribution ofphysicians has become a matter of particular concern.

2.2 A Framework for Analysis

Per capita expenditures for physicians' services varyconsiderably across states. In 1966, such expenditureswere $68.68 in California compared with $26.42 inSouth Carolina.2 l'his is a greater variation than thechange that occurred in the national average between1948 and 1965.

How are we to explain such large variations inexpenditures? By definition, expenditures are equal toquantity multiplied by price. More fundamentally, then,our task is to explain interstate variations in price andquantity. To do this economists employ a general modelof demand and supply. In such a model the quantitydemanded by consumers depends upon price and manyother variables, some of which are applicable to anycommodity, e.g., per capita income, and others that maybe relevant only to one or a few commodities, e.g.,health insurance. The quantity provided by suppliers isalso treated as a function of price and other variables. Inequilibrium, the quantity demanded is exactly equal tothe quantity supplied; hence, actual quantity and actual'price are simultaneously determined through the inter-action of the demand and supply functions.

Specification of a model for physicians' servicesestablishes a general framework within which a broadrange of hypotheses regarding the behavior of patientsand physicians can be investigated. Each structuralequation of the model offers an explanation for thedeterminants of a particular aspect of the market for

2The range of variation in per capita disposable income wasless in that year for the thirty-three states in our

having a high value of $3,185 in Connecticut and a low$1,586 in Mississippi. The coefficients of variation for per

physician expenditures and per capita income were 24.0cent and 16.0 per cent, respectively. State data for 1965 and

show about the same degree of variation as in 1966.

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Differences Across States, 1966 Expenditures for Physicians' Services

physicians' services. Our model has one equation dealingwith variations in demand, one for the number ofphysicians, one for physician productivity, and one forthe amount of insurance coverage.

Because the variables we wish to explain are notdetermined independently of one another, it is notpossible to test our behavioral hypotheses accuratelywith ordinary least-squares regression equations. Forexample, one clear implication of the interdependencyamong these variables is that we cannot discover the trueinfluence of price on physicians' locational choice bysimply relating the total number of physicians practicingin a state to the observed price of physicians' servicesthere. Possibly a demand-induced rise in price does tendto attract many physicians to a state; but this increase insupply will serve to depress price back towards itsoriginal level if the population can only be induced topurchase the additional services at a somewhat reducedprice.

To cope with this problem we estimate each of thestructural equations of our model by means of two-stageleast squares. This procedure allows one to statisticallydisentangle the web of mutual causality in order toisolate the specific effect of one variable on another. Themethod consists of obtaining predicted values for eachendogenous variable by regressing it on all of theexogenous variables in the model.3 This is the first stage.The structural equation for each endogenous variable isthen estimated by regressing the actual value of thatvariable on the predicted values of appropriate endoge-nous variables and on relevant exogenous variables. Thisis the second stage. With endogenous variables repre-sented by their predicted values, the estimated regressioncoefficients are not biased by any effect that thedependent variables may have on them.

When employing this two-stage procedure for esti-mating relationships involving simultaneously deter-mined variables, only those exogenous variables thatappear in the model should be used in estimation of thefirst stage. Use of any other exogenous variables mayimprove the fit in a given sample, but this improvementis spurious because the additional variables play noindependent role in the system. A priori considerationscan suggest which vanables, endogenous and exogenous,are potentially important in explaining the variation we

3Endogenous variables are determined within the system("jomtly determined"), while exogenous variables are deter-mined outside the system ("predetermined").

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observe, but the final determination of which variablesto include in the model is itself an empirical question.Once experimentation with a preliminary, large-scalemodel determines that certain exogenous variables areactually of no value in the second-stage equations, a newset of first-stage endogenous variable estimates should beformed, based only on the more restricted set ofexogenous variables that have been shown to bear asignificant relation to the supply-demand mechanism.4The rejected hypotheses of the initial model are, ofcourse, an integral part of the conclusions of such ananalysis.

The model we present in the following sectionexcludes many variables that one might reasonablyexpect to affect the demand for, or supply of, physi-cians' services. The reason for their omission is that testsbased upon a preliminary model employing seventeenexogenous variables revealed that only five of these did,in fact, appear in the system.5 On these grounds weexcluded the other twelve exogenous variables from thecondensed version of the model presented below, whichalone can be considered to possess an unbiased set offirst-stage (predicted) endogenous variables. Discussionsof the excluded variables and their role in the originalmodel are incorporated into section 2.3, under theappropriate subheadings. A complete list of the variablesappearing in each model is presented in Table 16.

2.3 Specification of the Model

The interrelationships among the six endogenousand five exogenous variables of our final model can besummarized by four structural equations and twoidentities :6

A A A A(1) Q*D = Q*D (AP or NP, BEN*, MD*, INC*,

BEDS*).

I' 4(2) MD* = MD* (AP, Q/MD, MED SCLS,

BEDS*, INC*).

4We are indebted to Christopher Sims of the National Bureaufor bringing this to our attention.

Some of the excluded exogenous variables were significantin equations in which they appeared, e.g., race as a determinantof health status, but because the endogenous variable health wasfound to be insignificant in the demand equation, both healthand race factored out of the system.

circumflex (A) over a variable indicates that its predictedvalue is used in estimating the equation. An asterisk (*) indicatesthat the variable is phrased in per capita terms.

Expenditures for Physicians' Services Differences Across States, 1966

TABLE 16A A

(3) Q/MD = Q/MD (AP, MD, BEDS*).

FinalModel

Preliminary Full Title of Variable (Units)Model

Endogenous

Quantity per capita (visits)8.Private physicians per 100,000

populationQuantity per private physician

(vjsjts)aAverage price (dollars)Insurance benefits per capita

(dollars)

NP NP Net price (dollars)INF MRT Infant mortality rate per 1,000

live birthsDTH RI Crude death rate per 1,000

population

Disposable personal income percapita (dollars)

Short-term hospital beds per1,000 population

Number of medical schoolsRatio of health insurance

premiums to benefitsUnion members per 100 popula-

tion

EDUC Median years of education,persons 25 and over

Per cent blackPer cent 65 and overPer cent urbanBirths per 1,000 populationMean temperature, average of

major cities (degrees F.)S&L GOV* State and local government

expenditures for health percapita (dollars)

HOSP MDC Hospital staff physicians per100,000 population

Change in disposable persona.!income per capita 1960-66(dollars)

%PART Per cent of private physicians inpartnership practice

%SPEC Per cent of private physicianswho are specialists

MD OMG Physicians per 100,000populationu

A

(4) BEN* = BEN*(Q*,AP,UNIONS*,PRM/BEN, INC*).

(5) Q*D (MD*) (Q/MD)

(6)Expenditures — Benefits

Expenditures

AP.Q* — BEN*(AP).

These relationships are presented diagrammatically inFigures 1 and 2.

A

a G.P. outpatient visit equivalents.blotal of six sample years.

Figure 2.—Effects of Exogenous Variables onEndogenous Variables

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List of Variables

QeMDC

Q/MD

APBEN*

Q*MD

Q/MD

APBEN*

Exogenous

INC* INC*

BEDS* BEDS*

MED SCLS MED SCLSPRM/BEN PRM/BEN

UNION UNION*

B

oJ

%BLK%AGED%URBBRTH RTTEMP

Figure 1.—Relationships Among Endogenous Variables,Alternate Specifications


In this equilibrium model of the market for physi-cians' services, the quantity of service demanded percapita (Q*D) is identically equal to the product of thetwo supply variables, number of physicians per capita(MD*) and quantity of service per physician (Q/MD).7Because it seems unreasonable to suppose that purchasesof medical insurance are unrelated to the price andquantity of the physicians' services covered, medicalinsurance benefits appear endogenously in the model.Price is represented by two variables: the average pricereceived by physicians for their services (AP) and the netprice paid by consumers (NP), which AP exceedsaccording to the degree to which insurance benefits payfor the cost of the average visit. AP and NP are thuscomparable to the time series variables of the same namediscussed in Part 1. The exogenous variables in thissystem are per capita income (INC*), number of medicalschools (MED SCLS), hospital beds per capita (BEDS*),labor union members per capita (UNION*), and theratio of health insurance premiums to health insurancebenefits (PRM/BEN).

Both the demand for and the supply of physicians'services are thought to be subject to special forces.Whenever possible, we have attempted to incorporatethe unique features often attributed to this market intoour model. The following equation-by-equation discus-sion of the four structural equations listed aboveconsiders these issues and indicates the range of ques-tions that can be illuminated by a cross-sectionalanalysis.

Demand (Q*D)

Prices and income are the customary economicdeterminants of market demand. How important arethese financial considerations to consumers in deter-mining their demand for physicians' services? Is thequantity of service demanded at all sensitive to its ownprice, and if so, to what extent? Does the quantitydemanded vary with income? What is the incomeelasticity?

What is the role of medical insurance in demand?Some investigators believe that it is a major influence onthe quantity of care purchased, yet our analysis of the

'It would, of course, be possible to combine the twodimensions of supply into one overall supply equation, but to doso would be to discard much valuable information regarding thebehavior of physicians.

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time series data yields no evidence indicative of asystematic relationship between changes in benefit levelsand changes in Q*

A related question concerns the mechanism by whichinsurance operates on demand (if, indeed, it does). Inone specification of the model, NP replaces AP as therelevant demand price variable. The argument for sodoing is that the impact of insurance can be entirelyattributed to the reduction it effects in the net price ofcare.' The substitution of NP for AP also implies thatpatients are indifferent to variations in the averageamount collected by physicians so long as they are notpersonally responsible for financing the differentials. Aless restrictive test of the role of insurance in demandretains AP as the price variable and adds to the equationthe benefits variable, BEN*. This specification leavesopen the manner in which insurance affects demand. Italso allows for the possibility that consumers areinfluenced even by those variations in AP which do nottranslate into variations in NP. If price-consciousness is afirmly ingrained consumer trait, changes in the institu-tional arrangements governing a particular market maynot be strong enough to suppress altogether the usualbehavior mechanism whereby low cost goods and serv-ices are sought out, regardless of who gets the bill.

Certain services provided by private practice physi-cians can only be consumed in hospitals: intensivediagnostic work-ups and most surgical procedures arecommon examples. To a limited extent, then, theservices offered by hospitals and by private practicephysicians constitute a joint consumption product,hospitalized medical care. If for any reason the supply ofhospital beds influences the quantity of hospital carepeople purchase, an increase in BEDS* may affect thedemand for physicians' services as well.

The market for physicians' services is characterizedby a high degree of consumer ignorance concerning theneed for services and the central role of the physician asan authoritative advisor regarding their use. Given thesecircumstances, we hypothesize that physicians are ableto generate a demand for their services without loweringprice; we therefore include MD* in the demand equa-tion. When physicians are abundant in a state, they mayorder care which is not medically indicated (e.g.,unnecessary surgery) or of only marginal importance(e.g., cosmetic procedures, numerous postoperativevisits, overzealous well-baby care). Alternatively, whenphysicians are very scarce, patients may lower their


expectations and handle minor complaints with a mini-mum of physician intervention. There is also anotherreason why the supply of physicians might exercise adirect influence on the demand for physicians' services.A significant part of the cost incurred by the patient isin the form of time spent in travel and in waiting rooms.A reduction in the relative scarcity of physicians isusually associated with both an improvement in theirlocational distribution and a decrease in waiting roomtime. To the extent that the ease or difficulty of seeing aphysician is a determinant of demand, we have a secondjustification for including MD* in the demand equation.

The independent variables in our demand equationthus fall into two categories: economic variables com-mon to any demand analysis (price, income) andinstitutional factors peculiar to this market (insurance,hospital bed supply, physician supply). Ten additionalvariables—most of which fall under the heading of"taste" factors—were tested in the preliminary version ofthe model (see section 2.2). Because none proved to bestatistically significant or measurably improved the fit ofthe equations, these were omitted from the final versionof the model presented here, inasmuch as their inclusionwould have injected a bias into the first-stage endoge-nous variable estimates. The rejected demand variablesare: education (median years of school of persons 25and over), urbanization, two measures of health status(the infant mortality rate and the crude death rate), percent black, per cent aged, the birth rate, mean annualtemperature, per capita state and local governmentexpenditures for physicians' services, and number ofhospital staff physicians per capita. The last twovariables attempted to measure the availability of alter-native sources of supply of physicians' services (servicesby physicians other than private practitioners, who aloneenter our study).

Supply of Physicians (MD*)

It is hypothesized that one variable influencingphysician location is price. AP is clearly the relevantsupply price variable, since it is of little import to thephysician whether payment originates with his patientsor with insurance companies.8 To what extent is the

8Physician behavior might conceivably be affected if thesource of payment were governmental, because of the conse-quent red tape and the physician's personal political philosophy.However, only private insurance is considered in this analysis;data on governmental expenditures for physicians' services areunavailable on a state basis.

present level of inequality in the distribution ofphysicians—the number of private practitioners per100,000 ranges from sixty in Mississippi to 134 in NewYork—attributable to differences in price?

With price held constant, per capita income serves asa taste factor in this equation. Specifically, INC* is herea proxy for the level of cultural, educational, social, andrecreational opportunities which a state has to offer.Because physicians as a group are very high earners,nonpecuniary factors of this sort may be a majorconsideration in their location decision.

Another possible influence on physician distributionis the quality and availability of complementary medicalfacilities. As a test of this hypothesis we include MEDSCLS and BEDS* in the MD* supply equation.

Finally, we investigate the possibility that physiciansare disinclined to open a practice in states where theaverage workload of their would-be colleagues is high.We should observe a negative sign on the endogenousvariable Q/MD if it is true that physicians shun areaswhere they might feel under pressure to work long hoursand/or spend less time per patient than they deemoptimal.

Originally, we hypothesized that physicians wouldshow some partiality toward their state of origin prior toentry into medical school, but tests with this variable inthe preliminary model led to its rejection. Also, nosupport was found for the view that physicians aredrawn to practice in the medically neediest states, withmedical need being measured by infant mortality (anendogenous variable), and therefore health, too, wasexcluded from this equation in the final model.

Quantity of Service per Physician (Q/MD)

The real quantity of services provided by individ-ual physicians varies considerably across states, thecoefficient of variation being 15.4 per cent. Theseproductivity differences are an important factor in theinterstate variations in physician gross income, which arequite large in view of the fairly high uniformity of skillamong physicians.

Three factors are considered as possible influences onphysician productivity. As with the supply variable, therelationship with price is an important matter toinvestigate. Do physicians respond to higher prices by

25


working more hours and by seeing more patients perhour, or do they display a backward-bending supplycurve, cutting back on their workload and maintainingtheir income while gaining the benefits of additionalleisure and a less hectic pace of activity?

An increase in the supply of hospital beds shouldraise Q/MD if physicians have a tendency to hospitalizemore readily whenever the necessary facilities are avail-able.9 This behavior might arise if there is a technologi-cal imperative on the part of physicians to practice themost up-to-date medicine within their grasp.

One of the most critical matters to be investigated iswhether areas with a relative scarcity of physicians arepartly relieved by enjoying higher physician produc-tivity. It is our hypothesis that the average physician,because of the nature of his professional training, feelsunder some ethical and social compulsion to supplyadditional services, even at the same rate of remunera-tion, when he is in an area poorly endowed withphysicians. Thus, we anticipate a negative sign on theMD* variable in the Q/MD equation.

Two other variables were initially tested in thisregression: the degree of physician specialization and theextent of partnership (as opposed to solo proprietorship)practice. As neither proved to be significant, the twowere omitted from the final model now under considera-tion.

Insurance (BEN*)

The argument for treating insurance as an endoge-nous phenomenon can be made on two grounds. Thefirst is that the amount of insurance purchased dependsupon the expected level of outlays people are insuringagainst. Assuming a generally risk-averse population, anincrease in expected outlays should call forth thepurchase of additional insurance protection. Expectedoutlays will be highly dependent upon expenditures inthe recent past, and the best proxy for this in our modelis expenditures in the present. The predicted values ofboth expenditure components, price and quantity, ap-pear as explanatory variables in the insurance equationas a test of this hypothesis. If it is correct, the estimatedcoefficients of both variables should be (approximately)

9Our measure of physician output weights hospital inpatientvisits higher than outpatient visits because of differences in theirrelative prices.

26

equal when the regressions are estimated in double-logarithmic form. If risk aversion itself rises (is constant,or falls) with the level of expected loss, the coefficientswill exceed (equal, or fall short of) 1 .0.

The other rationale for regarding insurance as endoge-nous lays stress on the cost of insurance itself ratherthan on the perceived need for the financial protection itoffers. The cost of insurance is defined by the relationP1V = (PRM/BEN) (AP) — AP. PRM/BEN is the ratio ofhealth insurance premiums to benefits, i.e., the averageprice of purchasing one dollar of health insurancebenefits (a figure greater than one). PlY thus representsthe average price of insuring one G.P. visit equivalentover and above the price of purchasing it directly. Thereason for carrying insurance is that, in the event ofextraordinary medical expenses, the return to an individ-ual who expends PRM/BEN will be many times greaterthan one. Of course, there is also the inherent chancethat the return will be as low as zero, but that is thegamble an insured person takes. On the average, aninsurance payment of PW is the nonrecoverable priceone pays to be reimbursed for one G.P. visit equivalent.The cost of insuring a given number of visits is thus seento depend on two factors, the "fairness" of insurancepolicies and the price of physicians' services.

PRM/BEN is exogenous in our model, being depen-dent upon such factors as the extent of group coveragecompared with individual coverage, and the relativeimportance of policies issued by nonprofit insuringorganizations such as Blue Shield. AP, by contrast, isendogenous. If Ply is found to influence the consumer'swillingness to insure, insurance itself is endogenous as aresult of this dependence. Because PIV is the price ofinsuring one visit equivalent and not the price of adollar's worth of insurance benefits, the dependentvariable in this specification should really be the numberof insured visit equivalents, or BEN*/AP. For consist-ency with the financial protection theory of insurance,which demands a dollar measure of benefits, we main-tain the BEN* form throughout. When we wish tointerpret the price coefficient as the price elasticity ofdemand for insured visits, however, we must firstsubtract 1.0 from its estimated value.

In addition to PRM/BEN, two other exogenousvariables enter the insurance function: per capita incomeand the degree of unionization. The potential effective-ness of unions derives from their role in winning fringebenefits in the form of health insurance policies (particu-


larly desirable because of their untaxed status). Union-ization should raise the percentage of the populationcovered by insurance, since the decision to insure is nolonger left to the discretion of the individual, and mayalso increase the mean level of benefits per insured.

In the preliminary version of our model we tested thehypothesis that people are differentially inclined toinsure a newly acquired.standard of living as comparedto one which has been long held. The change in percapita income over the previous six years provedinsignificant in the benefits equation, however, and sowas dropped from the final list of exogenous variables.Also rejected on the basis of these early tests was thelevel of education as a determinant of BEN*.

2.4 The Data

The data used in this analysis come from a varietyof sources and are of varying reliability. The criticalexpenditures and visit series regrettably are not of a kindin which we can place a high degree of confidence.Because interstate variations in these quantities aresubstantial and move in directions that remain fairlyconsistent from one year to the next, empirical analysisof the available data does seem justifiable. Nonetheless,until such time as a better data base has been estab-lished, conclusions derived from this study can only besuggestive of the true underlying relationships.

Expenditures

Our study population consists of the thirty-threestates for which expenditures data are available for1966.' ° Most of the omitted states have small popula-tions; their absence does not have much effect on theresults because each observation in our model isweighted by the square root of the state population. Thethirty-three states accounted for 90 per cent of the totalU.S. population. The expenditures data come from theInternal Revenue Service and represent the reportedgross receipts from medical practice of all self-employedphysicians. Thus, this series is comparable to theexpenditures data examined in the section on timetrends (Part I).

Availability of expenditures data was one of the keyfactors in our selection of a year for the cross-sectional

'°All series refer to 1966 unless otherwise indicated.

analysis. As of this writing, state data on the grossbusiness receipts of "offices of physicians and surgeons"have been published for only five other postwar years.With the exception of 1949 (for which these figures areobtainable for forty-eight states), the size of the samplehas been limited (twenty-seven states for fiscal 1960-61,twenty-two for 1963, twenty-eight for 1965, andtwenty-six for 1967). The other controlling factor in ourdecision was the availability of data on physician visitsfrom the National Health Survey. The choice here wasbetween 1957-59, 1963-64, and 1966-67. 1966 waschosen because the requisite expenditures data wereavailable for a relatively large number of states and visitdata were also specific to that year.

The accuracy of the expenditures series is not easy tocheck. The possibility of some underreporting of incomeis suggested by the fact that the IRS data imply averagegross receipts per physician of $46,600, compared with amedian of $49,000 reported in Medical Economics forthe same year. On the other hand, at least some of thisdisparity is explainable by the fact that Medical Eco-nomics only surveys full-time, self-employed physiciansunder the age of sixty-five, while the IRS total includesthe smaller average receipts of older physicians and ofhospital staff and faculty physicians who devote just afraction of their working time to private practice.Furthermore, only if the degree of underreporting variedsignificantly across states would this factor impair thevalidity of an analysis of variations in expenditures.

Far more serious is the distinct possibility that errorsin this señes are not uniform across states but have asizable random component. Our suspicions on this countare based upon intertemporal correlations of expendi-tures per capita across the twenty-six states for whichthese data are available for 1965, 1966, and 1967. Thecorrelation coefficient for the 1965-66 comparison is0.863, and for 1966-67, 0.9 12.1 1 While these figures arehigh enough to show that there is something systematicworth investigating in the pattern of variation in 1966expenditures, they compare unfavorably with the(weighted) correlation coefficients for per capita dis-posable income in these states from one year to thenext: 0.998 for 1965-66 and 0.997 for 1966-67. Closerexamination of the official expenditures data revealsthat states with the most extreme jumps in expenditureshad parallel shifts in the number of physicians said to be

''These correlations are weighted by 1966 state population.The unweighted correlations are 0.760 and 0.824, respectively.

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tiling business income tax returns. These reported shiftsin the number of physicians filing returns show virtuallyno correspondence to changes in the number of physi-cians practicing in each state, a statistical series kept bythe American Medical Association.'2 To cite two of themost extreme examples, the IRS figures show a gain of45.1 per cent from 1966 to 1967 in the number ofphysicians filing returns in Wisconsin, and a fall of 25.8per cent in the number filing in Louisiana. According tothe AMA, however, the number of practicing physiciansin these two states rose by 1.2 per cent and 2.0 per cent,respectively, over this period.13 It is apparent thatofficial statistics on health care expenditures are in muchneed of improvement. Changes in nationwide expendi-tures totals over long periods no doubt provide a fairlyaccurate indication of changes actually taking place. Forspecific years or specific states, however, deficiencies inthe statistical data now constitute a major impedimentto serious research.

Physicians

The scope of the market for physicians' servicesrelevant to our study does not extend beyond the

I 2 Simple regressions across states of the annual change inEXPt+i

total expenditures on the annual change in physi-EXPt

be highly significant and the explanatory power of the equation

IRS however, bears almost no relation to theMDt+,percentage change in private practitioners as recordedMDt'

by the AMA, even though the correlation between IRS and

bounds of private practice. As the official expendituresseries is limited to physicians' gross receipts fromself-employment practice, so the MD series we havechosen (our source is the American Medical Association)is restricted to private practitioners.

Unlike the IRS count of physicians filing businessincome tax returns, the AMA data have the conceptual;advantage of including salaried physicians in privatepractice, whose services go to meet the same demand asthose of the self-employed and whose contribution togross receipts may be considerable. The fact that theAMA bases its count on the results of routine question.naires sent annually to all physicians while the IRSestimate derives from a sample of physicians filing arather unpopular tax report makes the AMA seriessuperior from a statistical viewpoint. Also, as notedabove, the extreme instability of the IRS figures callsinto question that data-gathering process itself. Unfortu-nately, neither the AMA nor the IRS series permits us tocalculate precisely the number of full-time equivalentphysicians in private practice; the former covers physi-cians whose principal mode of employment is privatepractice, while the latter covers all physicians with someself-employment income, no matter how small a fractionof their professional time is involved. On balance,however, the AMA series probably more closely approx-imates the desired figure of full-time equivalent physi-cians, since it includes some but not all part-timers andsince it is not restricted to the self-employed.

Quantity and Average Price

Two of the most important series, quantity ofservice and average price, are not directly available andmust be estimated. The quantity series we estimate is ameasure of "general practitioner (G. P.) outpatient visit

R2 equivalents," a fairly homogeneous unit across states..40 'Dividing expenditures by quantity then gives us an

implicit price series, which represents the average priceof a G. P. outpatient visit equivalent.

The quantity series is derived in the following way.The National Center for Health Statistics has published

.03 data on home and office visits per capita for the fourcensus regions in 1966-67 and for the nine censusdivisions in 1957-59. We assume an intraregion per

.01 capita visit distribution of the 1966-67 data based on thedistribution that prevailed in the earlier period. Theresulting home and office visit figure for each division isthen attributed to each state within that division.

cians filing returns show the independent variable toIRSt

MD for any given year is on the order of .99.

Dependent IndependentVariable Variable

Coefficient(Standard Error)

.50(.13)

EXP67EXP66

EXP66EXP65

IRS67IRS66

IRS66IRS65

.66 .63

IRS67IRS66

IRS66IRS65

MD67MD66

MD66MD65

(.10)

1.82(1.99)

1.09(2.69)

'3The AMA figures refer to private practice physicians only.

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Next, the number of hospital visits is estimated foreach state from the number of patient days spent innonfederal short-term hospitals. Our assumption of onevisit for each day of stay is supported by MedicalEconomics, which reports that the median number ofhospital visits made by private practitioners in 1966 wastwenty-two per week and that the median number ofweeks worked per year was forty-eight. If privatepractitioners in the thirty-three states of our studyconformed to the Medical Economics medians, theywould have made 177 million hospital visits. In fact, thetotal number of patient days in these states was veryclose to this, 185 million. Combining these disparatevisit series, hospital inpatient visits are given a weight of1.71 relative to home and office visits, this being thenational ratio of average charges for the two categoriesof visits, according to Department of Health, Education,and Welfare statistics.14

A final adjustment takes account of the fact that thedistribution of total visits between G. P.'s and specialistsvaries across states. A visit to a specialist is accorded aweight of 1 .93 relative to a G. P. visit, based on the ratioof average gross receipts per visit. In estimating thepercentage of total visits made by specialists in eachstate, we, of course, make an allowance for the smallervisit load of specialists (.63 as many visits as G. P.'s).'

There undoubtedly are some errors in the resultingquantity series and the price series derived from it, butwe are not aware of any systematic biases. Someconfirmation of the validity of the overall approach maybe found in the fact that the resulting average price for aG. P. visit in our series is $5.75, which is very close tothe $5.48 implicit in Medical Economics data for thesame year.

Other Variables

All series pertaining to insurance are based upondata in the Source Book of Health Insurance, an annualpublication of the Health Insurance Institute. The twoendogenous insurance variables, BEN* and NP, referonly to insurance coverage for physicians' services, i.e.,surgical, regular medical, and a share of major medical.

of Research and Statistics, Social Security Adminis-tration, U.S. Department of Health, Education, and Welfare,

Medicare Survey Report," Health Insurance Statistics,CMS-12, January 27, 1970.

figures are derived from survey data published inMedical Economics (see Appendix C).

The exogenous PRM/BEN variable pertains to all formsof health insurance (physician, hospital, and disability).

Information regarding the number of medical schoolsin each state (MED SCLS) is taken from the annualeducation issue of the Journal of the American MedicalAssociation. BEDS* represents the bed capacity ofshort-term, general, and other special hospitals, a seriesmade available by the American Hospital Association.Figures on per capita disposable personal income in eachstate (INC*) are published in the Sur&'ey of CurrentBusiness. The Statistical Abstract of the United Statesprovides data on labor union membership (UNION*).

Summary statistics for all variables are presented inTable 17. A complete description of the methoddeveloped to estimate Q* and the details of all othercalculations may be found in Appendix C, which alsoincludes specific source references, data tables listing themost important series, and a correlation matrix.

2.5 Regression Results

Table 18 presents the results of the second-stageregressions. All of the equations are estimated indouble-logarithmic form, the estimated coefficients thusrepresenting elasticities.' 6 To avoid problems of hetero-scedasticity, each observation is weighted by the squareroot of the state's population.' In computing the tstatistics for each variable, we have made those adjust-ments appropriate for two-stage eStimatiOfl.' 8

'6The one exception applies to MED SCLS, which is phrasedas a linear variable because it sometimes takes on the value zero.

''Plots of the residuals from unweighted regressions demon-strate an inverse relationship between population and the size ofthe unexplained residual.

'8t statistics are ordinarily obtained by dividing eachcoefficient by its standard error, but this procedure is not validwhen the predicted values of endogenous variables appear on theright-hand side of an equation. In such cases the followingadjustment is necessary: (1) Recompute the residuals for eachobservation by applying the estimated second-stage regressioncoefficients to the actual values of the included endogenousvariables. (2) Obtain the ratio of the sum of squared residualsfrom the recomputed equation to the sum of squared residualsfrom the estimated regression. (3) Multiply each of the original tstatistics for a particular regression equation by this factor(which may be equal to, greater than, or less than, 1.0) in orderto arrive at a set of adjusted t statistics applicable to thesecond-stage regression. We are most grateful to ChristopherSims for bringing this to our attention.

29

0

TAB

LE 1

7

Sum

mar

y St

atis

tics,

Thirt

y-th

ree

Stat

es, 1

966

Coe

ffic

ient

Sym

bol

Full

Title

of V

aria

ble

(Uni

ts)

Mea

naD

evia

tion

of V

aria

tion

(Per

Cen

t)

EXP*

Q*

Expe

nditu

res p

er c

apita

(dol

lars

)Q

uant

ity p

er c

apita

(vis

its)b

44.4

97.

7110

.66

.72

24.0 9.4

AP

Ave

rage

pric

e (d

olla

rs)

5.75

1.16

20.1

NP

Net

pric

e (d

olla

rs)

3.70

1.16

31.4

BEN

*In

sura

nce

bene

fits p

er c

apita

(dol

lars

)16

.00

4.29

26.8

MD

*Pr

ivat

e ph

ysic

ians

per

100

,000

pop

ulat

ion

95.4

22.6

23.6

EXP/

MD

QIM

DEx

pend

iture

s (gr

oss i

ncom

e) p

er p

rivat

e ph

ysic

ian

(dol

lars

)Q

uant

ity p

er p

rivat

e ph

ysic

ian

(vis

its)b

47,0

038,

354

5 $0

01,

290

12.6

15.4

DTH

RT

deat

h ra

te p

er 1

,000

pop

ulat

ion

9.42

.93

9.9

INF

MR

TIn

fant

mor

talit

y ra

te p

er 1

,000

live

birt

hs23

.73.

213

.6IN

C*

Dis

posa

ble

pers

onal

inco

me

per c

apita

(dol

lars

)2,

605

418

16.0

MED

SC

LSN

umbe

r of m

edic

al sc

hool

s3.

622.

8277

.9U

NIO

N*

Uni

on m

embe

rs p

er 1

00 p

opul

atio

n9.

54.

042

.4B

EDS*

Shor

t-ter

m h

ospi

tal b

eds p

er 1

,000

pop

ulat

ion

3.78

.53

14.1

PRM

IBEN

Rat

io o

f hea

lth in

sura

nce

prem

ium

s to

bene

fits

1.27

.08

6.6

%SP

ECPe

r cen

t of p

rivat

e ph

ysic

ians

who

are

spec

ialis

ts64

.95.

99.

0C

hang

e in

dis

posa

ble

pers

onal

inco

me

per c

apita

, 196

0-66

(dol

lars

)66

389

13.4

EDU

CM

edia

n ye

ars o

f edu

catio

n, p

erso

ns 2

5 &

ove

r10

.5.9

89.

3%

AG

EDPe

r cen

t 65

and

over

931.

414

.7%

BLK

Per c

ent b

lack

11.2

8.7

78.3

%PA

RT

Per c

ent o

f priv

ate

phys

icia

ns in

par

tner

ship

pra

ctic

e24

.18.

635

.5B

RTH

RT

Birt

h ra

te p

er 1

,000

pop

ulat

ion

183

1.17

6.3

MD

OR

IG*

Phys

icia

ns o

rigin

atin

g pe

r 1,0

00 p

opul

atio

nc2.

08.6

129

.4S&

L G

OV

*St

ate

and

loca

l gov

ernm

ent e

xpen

ditu

res f

or h

ealth

, per

cap

ita (d

olla

rs)

34.2

611

.41

33.3

HO

SP M

D*

Hos

pita

l sta

ff p

hysi

cian

s per

100

,000

pop

ulat

ion

28.4

13.9

49.1

TEM

PM

ean

tem

pera

ture

, ave

rage

of m

ajor

citi

es (d

egre

es F

.)56

.37.

112

3%

UR

BPe

r cen

t urb

an70

.613

.819

3

a Ea

ch o

bser

vatio

nw

eigh

ted

by sq

uare

root

of p

opul

atio

n of

stat

e.b

G. P

.ou

tpat

ient

vis

its e

quiv

alen

ts.

CT

otal

of si

x sa

mpl

e ye

ars.


TABLE 18

Results of Weighted, Logarithmic Regressions, Second Stage, Interstate Model, 1966 (N33)

Part A: Q (Quantity per Capita)

(5,92)0571b

(9.25)

0.269(1.64)

-0.29&'(-3.58)

0205a(-2.25)

-0.104(-1.65)

A.1

A.2

A.3

A.4

A.5

A.6

A.7

A.8

A.9

A.10.

A.11....

0.177(1.99)

0.31 3b

(9.97)

.515

.578

.588

.585

.566

.732

.727

.735

.715

.746

.752

0449b(9.94)

0.1 99a(2.54)

0.042(0.61)

0153b(-3.24)

(-5.28)

(-5.55)

(-5.63)

(-4.16)

0,388b(6.28)

0397b(6.90)

0.42&'(15.10)

0507b(11.22)

0.35 9b(7.34)

0335b(12.01)

-0.059(-0.69)

0.193(1.95)0•252b

(6.06)

B.1

B.2

B.3

B.4

B3

B.6

.521

.754

.731

.509

.775

.784

Part B: MD (Physicians per 100,000 Population)0059b

(5.99)

0•036b 0750b(4.37) (5.51)

0050b(8.46)

0.061 b(5.63)

(4.16)

0,036b(8.54)

(6.40)

-0.107(-0.48)

0.4908(2.21)

0.07 1(0.40)

0.419(1.64)1052b

(4.26)0492b

(2.86)

(Continued)31

• Differences Across States, 1966 Expenditures for Physicians' Services

TABLE 18—Concluded

Equation MED SCLSC INC* BEDS*QJMD

B.7

B.8

B.9

B.10

Part B: MD (Physicians per 100,000 Population)—Continued

.791 0037b 1144b 0550b

(10.34) (14.64) (7.04)

.755 0039b 0759b -0.161(4.47) (5.57) (-1.02)

.783 0.032 0.994 -0.199(0.69) (0.71) (2.35) (-0.11)

.776 0.027 0.080 0.752 0.443 -0.382(0.36) (0.27) (0.31) (0.92) (-0.13)

Equation BEDS*

Part C: QJMD (Quantity per Physician).420 -0.828k'

(-3.84)

.603 0622b(-3.25)

.622 -0.297 -0.494(-0.57) (-1.50)

.622 0.012 0.259 -0.672(0.01) (0.39) (-1.21)

.635 0.25 2(0.71) (-2.80)

C.1

C.2

C.3 -.

C.4

C.5

Equation UNION* PRM/BEN

D.1

D.2

D.3

D.4

D.5

D.6

D.7

Part D: BEN* (Physician Insurance Benefits per Capita).735

(9.47)

.812 0•761b 0254b(3.39) (3.70)

.819 1•465b 1576b 0739b(10.89) (-5.04) (-4.26)

.754 1270b -0.259 0.761(3.62) (-0.93) (1.43)

.814 1•605b 1691b -0.277(6.66) (-5.04) (-3.87) (-0.68)

.823 0.130 1116a -0.430(3.28) (1.48) (-2.22) (-1.42)

.820 0.513 0.201 -0.596 -0.030 0.634(0.77) (1.82) (-0.82) (-0.06) (0.91)

Note: Adjusted t itatistics appear in parentheses.a Significant at .05 level. at .01 level. CLinear variable.

32


Part A: Demand (Q*)

Income. Estimates of the income elasticity of de-mand vary over a wide range (0.04 to 0.57), but,taken together, the equations support the findings ofprevious investigators that physicians' services are con-sidered to be very much of a necessity, with an incomeelasticity substantially below 1 .0. Our results correspondparticularly closely with those of Andersen and Benham[4], even though the units of observation are quitedifferent (1966 state averages in one instance, 1964family units in the other).'9 Simple regressions withincome as the sole independent variable produce elastici-ties of 0.41 and 0.31, respectively, both coefficientssignificant at the 0.01 level. The results for multipleregressions are also similar. In our more successfuldemand equations (A.6-A.1 1) we observe considerablylower and much less significant income coefficients(0.20 in A.6, 0.04 in A.7), when indeed income appearsat all. Andersen and Benham report a statisticallyinsignificant income elasticity of 0.01 in multiple regres-sion.20

It should, of course, be stressed that all of thesevalues refer to the responsiveness of quantity—not ofexpenditures—to changes in income. The differencebetween the two is not trivial, given the tendency of APto rise with income. A simple regression with per capitaexpenditures as the dependent variable yields an incomecoefficient of 0.96.

One factor that might possibly contribute to the verylow income elasticity of demand is the high correlationof income with earnings, which, in turn, is a goodindication of the price of time. Physicians' services areusually time-intensive, and this means that they are morecostly to those with high earnings. Had we estimated theeffect of income with earnings held constant, it is likely

'9Andersen and Benham, in their calculations for physicianuse, employ an estimate of "permanent income" as theindependent variable rather than measured income, but this doesnot imply incomparability with our results since the transitorycomponent of income is largely eliminated by using groupeddata.

30Other demand elasticities reported in the literature are0.62 and 0.21, respectively, in Feldstein [17] and Fein (15].The elasticity implicit in Fein's book was computed by HerbertKlaxman [271.

that a higher elasticity would result.2 Unfortunately,the requisite state data are not available.

Chart 4

Ratio of Number of Physician Visits by Persons with FamilyIncome Greater than $10,000 to Visits by Persons withFamily Income Less than $3,000, by Age and Sex, 1966-67

-

_________________________

Source: U.S. Department of Health, Education, and Welfare,"Volume of Physician Visits, United States, July 1966-June1967," Vital and Health Statistics, Series 10, No. 49, November1968, p. 19.

The importance of the earnings factor can be appreci-ated from Chart 4, which shows, for various age and sexclasses, the 1966 ratio of per capita physician visits madeby persons with family incomes over $10,000 to thosemade by persons with family incomes under $3,000.

2 Morris Silver postulates a positive relationship betweenearnings and expenditures for physicians' services, and his resultsbear this out (40J. But such a finding can be readily explainedby the close association between earnings and price. It does notnecessarily contradict our view that high earnings have a negativeimpact on the quantity component of expenditures.

2.4 -

2.2 -

2.0 -

1.8 -

I.e -

1.4 -

1.2 -

,IlI'I'

I %

IIII

'I

I

\ I—

"-S.-

.8 - —

.6- —

.4 - —

.2 - —

o 1 I I

Under 5 15- 25- 35- 45- 55- 65- 755 14 24 34 44 54 64 74 Bover

Age groups

33


Both sexes under the age of fourteen display very highvisit-relatives; the same holds true for males agedsixty-five and over. In essence, earnings are held nearlyconstant (at approximately zero) as family income risesfor these groups, allowing us to observe the effect ondemand of income alone. The implicit income elasticitiesof demand are still less than 1.0, but hardly negligible.By contrast, income exerts no systematic influence uponvisits of persons aged fifteen to sixty-four; the positiveeffect of income on demand, we believe, is nullified bythe negative effect of earnings (i.e., the price of time).Also in accord with our expectations is the fact thatamong the twenty-five to sixty-four age group, wheremale labor-force participation rates are roughly twice aslarge as those for females, income exerts somewhat moreof an influence on visits by females than visits by males.Indeed, only two of the eighteen age-sex categoriesbehave in a contrary fashion to what we would expectunder our hypothesis if it were the sole means ofexplaining age-sex differences in the effect of income ondemand.22

Omission of quality differences from our quantitymeasure may also be exerting a downward bias on theestimated income elasticity, but the nature of medicaleducation in this country (all recognized schools musthave AMA accreditation, and National Board Examina-tions are increasingly employed as a state licensurerequirement) makes it unlikely that state-to-state qualitydifferences among physicians are an important factor.On balance, we believe that variations in earnings, on theone hand, and patients' belief in the essential nature ofphysicians' services, on the other, are responsible for thelow income elasticity of demand.23

We should emphasize that problems of multicollin-earity prevent any firm conclusions regarding the exactmagnitude of the income coefficient. Thus, our incomeelasticities are consistently larger and generally moresignificant in the equations that do not consider MD*a variable than in those that do. The great improvementin explanatory power which results with the introduc-tion of MD* (A.6 versus A.2, A.7 versus A.5) and the

• 22Visit-relatives for women sixty-five to seventy-five andseventy-five and over rise rapidly, as predicted, over low incomeclasses, but then fall even more steeply, for some unknownreason, over high income classes.

23This is not to say that all, or even most, physicians'services are technically essential for health. To believe in theirefficacy is.sufficient to make the average individual treat them asa necessity in his budget.

34

consistently high t statistic attaching to the physicianvariable lend credence to the latter specification. It isclear that, of the two variables, MD* is dominant, withincome playing a comparatively minor role. Thesequalifications notwithstanding, there is nothing in theseequations—regardless of what combination of variableswe consider—to suggest an income elasticity even ap-proaching 1.0. All of the evidence indicates that thedemand for physicians' services is quite income-inelastic,though precisely to what degree we cannot accuratelysay.

Price and Insurance. The price elasticity of de-mand for physicians' services appears to be unusuallylow. None of the equations reported in Table 18.Ashow AP or NP coefficients exceeding (in absolute value)—0.36. The t statistics on the price variables indicate thata high degree of confidence can be placed in this finding.Our result parallels Paul Feldstein's finding [17] of alow demand price elasticity of —0.19, also significantlydifferent from zero.24

There are three principal explanations for the relativeinsensitivity of demand to changes in price. First, itshould be remembered that the demand for physicians'services is derived from the consumer's demand forhealth. Michael Grossman has estimated the price elastic-ity of demand for health at —0.5 [22], which seemsreasonable, given the absence of any close substitutes forhealth. The price elasticity of demand for a derivedinput must be lower than for the final commodity unlessthere are important possibilities of substitution withother inputs. This leads to the second explanation,namely, that there are many legal and psychologicalbarriers against the substitution of persons without theM.D. degree in the physicians's role, even though suchpersons might be good substitutes in a technical sense.Similarly, there are many factors other than medicalmanpower that contribute to the individual's productionof health, inciuding diet, housing, recreation, and educa-tion. These may, in fact, be excellent alternatives tophysicians' services in the long run, but may not be soregarded by the patient.25

Finally, it should be noted that the price paid is onlypart of the total cost of physicians' services to the

24Feldstein's study pertained to physician visits by familiesin 1953.

25The same argument can be made with regard to "negativeinputs" in the production of health, including such consumptionitems as tobacco, alcohol, narcotics, and (occasionally) motorvehicles.


patient. In addition to possible inconvenience, thepatient must reckon with costs of transportation and,more important, time spent in travel, waiting, and duringthe visit itself. These indirect costs (IC) vary greatlyfrom individual to individual, though in general wewould expect a positive association between them andthe direct cost of a visit (AP) because IC is closelydependent upon the price of time, AP varies withincome, and both income and the price of time arehighly correlated with earnings. In the event that IC andAP are perfectly correlated, variations in AP are exactlyproportional to variations in the total price of a visit andthe AP coefficients we estimate are not biased, despitethe omission of an IC variable. If, however, IC tends torise faster than AP, we are underestimating the trueinterstate variation in price and thereby overestimatingthe price elasticity of demand, and vice versa. Thedirection of possible bias from this source is notascertainable.

The relevance of insurance to demand is tested in twoways. We first investigate the role of insurance using theBEN* variable. Unfortunately, strong multicollinearitybetween income and benefits prevents any conclusionson this score. The is essentially unchanged, whetherwe employ income, benefits, or both in the demandregression (A.2-A.4); while either variable alone is highlysignificant, both show much lower t values when theyappear jointly. It is impossible to infer how much of theobserved variation in Q* is attributable to each of thesevariables, or what the true coefficients of each are.

NP is superior to BEN* as a measure of insurancebecause of its much smaller correlation with INC* (0.14versus 0.86). Using NP we may consider all economicinfluences on demand simultaneously (he., income,average price, and insurance, the latter two embodied inthe NP variable). With insurance thus accounted for, weobserve a somewhat smaller but still very significantincome elasticity as compared to the case of income andaverage price considered alone (A.5 versus A.2). Thehigh correlation between AP and NP nonetheless compli-cates the critical judgment as to whether insurance per seis important to demand. In some instances AP is thestronger variable (A.6 versus A.5), while in others thesituation is reversed and NP is stronger (A.8 versus A.9).But in any case, the price elasticity of demand is notmuch affected by the choice between these two pricevariables.

What we can say with assurance concerning the roleof insurance in demand is that the elasticity of Q* with

respect to BEN* is, at most, fairly low. That is, evenunder the extreme assumption that INC* is of no realimportance in this relation, the elasticity with respect toBEN* is only 0.31. The very large t statistic on BEN* inA.4 indicates not only that this coefficient is signifi-cantly greater than 0, but also that it is significantly lessthan 0.4. Such a finding is not in line with our priornotions concerning the effect of insurance, despite thefact that in at least one instance comparable findingshave been reported in the literature.26 Some discussionof possible explanations is, therefore, in order.

First, the prevailing impression about insurance isthat it induces higher utilization by lowering the pricefaced by the consumer. Yet if this is the mechanismthrough which insurance operates on demand, and ifdemand is price-inelastic, as we have found the caseto be, it is to be expected that demand will also beinsurance-inelastic. For example, if benefits initiallyreimburse 40 per cent of average price, a 1 per cent risein BEN* will produce a 0.67 per cent fall in NP (from0.60 AP to 0.596 AP). With a (net) price elasticity of—0.20, this will result in only a 0.13 per cent rise in Q*(close to the 0.18 rise shown by A.3). On the otherhand, if demand were highly responsive to price changes,say with an elasticity of—i .5, the same 1 per cent rise inBEN* would call forth a 1.00 per cent rise in Q*. Itshould be noted that we would expect the effect ofinsurance on demand to be greater among persons with avery low or negligible price of time (the young, theelderly, the unemployed), because incremental insurancebenefits for them result in a much larger percentagechange in the full price of a visit.

A second factor is that private insurance for physi-cians' services is usually heavily biased toward coverageof relatively nondiscretionary care. Surgical proceduresand in-hospital care are far more likely to be reimbursedthan routine office visits or preventive services [34] ; Thisrestriction in coverage may greatly reduce the impact ofinsurance relative to what it might have been.

Physicians. The highly significant role of MD* inthe demand equation requires some discussion. Itcannot be attributed to a supply-induced fall in the

26Paul Feldstein [17J uses an insurance variable (the ratio ofbenefits to expenditures) in his demand analysis. Contrary to hisexpectations, the elasticity is negative, though insignificant.Regrettably, no discussion of this finding appears in the text.

35


physician's fee because price (AP or NP) is already heldconstant. Rather, it seems to be the result of thefollowing forces.

First, an increase in MD* is likely to reduce theaverage distance separating patient and physician, as wellas the average waiting time. The consequent saving intime and transportation expense lowers the total cost ofa visit to the patient even if fees are held constant. Givena low price elasticity of demand, however, this factoralone is insufficient to account for the magnitude of theMD* coefficient.

A second possibility is that physicians themselvesinflate demand whenever the supply of medical man-power is relatively slack. This thesis is put forthpersuasively by Eli Ginzberg: ".. . the supply of medicalresources has thus far effectively generated its owndemand.... Much unnécessary surgery continues to beperformed.... There is substantial overdoctoring for ahost of diseases, including, in particular, infections ofthe upper respiratory tract.. . . [physicians] usuallyhave wide margins of discretion about whether torecommend that a patient return to the office for one ormore follow-up visits [21] ."

A supply-induced demand change is fully sufficient asan explanation for the role of MD* in the Q* equationsof Table 1 8.A; if verified, its implications for policy areprofound. Evidence that the additional physicians' serv-ices provided under loose supply conditions are, in fact,of a marginal nature is presented in the discussion of theeffect of physicians' services on health in section 2.6.This much is to be expected if, as Ginzberg also suggests,physicians gravitate towards the more serious cases astheir supply becomes taut.

A third possible explanation for the importance ofis the existence of permanent excess demand for

physicians' services. This is the thesis advanced byMartin Feldstein [16], whose time series analysis of thismarket yielded positive demand price elasticities (as highas 1.67), inconsistent with an equilibrium hypothesis.Feldstein's negative and significant insurance elasticitiesand his occasionally negative income elasticities arelikewise inexplicable under normal market conditions. Inour view, a much simpler interpretation of Feldstein'sresults is the failure to take account of technologicalchange, which shifted the demand curve to the right overtime, and not at a constant rate. Since the cross-sectionregressions, which essentially hold technology constant,

36

are readily interpretable under the assumption of marketequilibrium, we see no reason to substitute either here orin the time series the less defensible explanation ofpermanent excess demand.

Hospital Bed Supply. Introducing BEDS* into anyof the demand equations discussed above seriouslyaffects the conclusions to be drawn regarding price(either AP or NP). A.1O is illustrative: The pricecoefficient approaches zero (in some equations it actu-ally becomes positive) and the variable loses all statisticalsignificance. Indeed, the "best" demand equations, interms of sheer explanatory power is one in whichprice, income, and insurance have all been dropped andonly MD* and BEDS* appear (A.l 1).

Accepting the results of A.l 1 on face value maynonetheless be seriously misleading. To be sure, arationale is advanced here in support of a causalrelationship running from bed supply to demand for•physicians' services. That is, the services of hospitals andof physicians are in many ways a joint consumptionitem, and thus an increase in the former serving to meeta backlog in its demand will permit an expandedconsumption of physicians' services, desired but tech-nically unfeasible previously due to the unavailability ofthe requisite hospital facilities. Beyond this, if thefrequent allegation is true that the supply of hospitalbeds tends to create its own demand, it follows that anyincrease in BEDS*, even if wholly unrelated to theprevailing demand for hospitalization, will (indirectly)raise Q* as well.

The trouble with this explanation for the role ofBEDS* in the Q* equation is that it takes no account ofthe fact that the relationship between these two vari-ables is inherently biased by the very method used toconstruct Q*• Hospital days per capita comprise one ofthe three components of the quantity series, and becausethere is so little interstate variation in occupancy rates,days are almost entirely proportional to bed capacity. Inour judgment, BEDS* is probably significant in the Q*

equation not so much because it bears a causal relation-ship to the dependent variable but rather because of thestatistical dependence of Q* upon BEDS*. Equations insection A that do not include BEDS* are probably moreaccurate indications of the true determinants of demandfor this reason.


Part B: Supply of Physicians (MD*)

Medical schools, price, hospital bed supply, andper capita income are the principal factors influencingphysicians' locational decisions (Table 18.B). Collin-earity among the last three of these variables makes itdifficult to determine precisely the specific effect ofeach, but the four together account for about 78 percent of the variation in MD*.

The role of the medical school in physician location istwofold. As a center of education it draws doctors-to-beto the state, and its affiliated hospitals attract internsand residents. Professional contacts are established, andyoung families take root. As a major medical center, itgenerally promises superior staff and facilities in itsteaching hospitals. Regardless of where they trained,physicians may find it advantageous to have such acomplex within close proximity of their practice, for itallows them to arrange referrals and consultations whilemaintaining contact with the patient. Our estimatedcoefficient, highly significant in all but two cases,indicates that on the average one additional medicalschool in a state raises the number of physicianspracticing there by about 4 per cent.

A glance at equations B.2-B.8 makes apparent thepresence of collinearity among the three other importantlocation variables. Price is highly significant, with coef-ficients ranging from 0.83 to 1 .14, in those equationswhere it appears alone with MED SCLS or where BEDS*is also present (B.3, B.6, B.7), but with BEDS* droppedand INC* retained, the price coefficient falls consider-ably and loses its significance (B.S). In like fashion,INC* is a significant variable, with an elasticity of 0.49to 0.76, when it appears alone with MED SCLS or inconjunction with either AP or BEDS* (B.2, B.S, B.8),but both its coefficient and its adjusted t statisticplummet when all four variables enter the equation(B.6). Similarly, BEDS* is significant if, and only if, APalso appears in the equation (B.6 and B.7, but not B.4 orB.8). It is with caution, therefore, that we proceed to adiscussion of these results.

Our average price measure is clearly superior as asupply variable in this context to physician grossincome, the monetary incentive variable employed byBenham, Maurizi, and Reder [7]. In their analysis thetwo-stage least squares method was utilized to estimatedemand and supply equations for the number of

physicians in each state in 1950, but, while physicianincome had a positive sign in the supply equation, it wasnot statistically significant. This is as expected: businessreceipts are positively related to workload as well as toprice, and it is surely unreasonable to expect doctors tobe attracted to states where they can anticipate littleleisure time. If anything, the opposite hypothesis meritsconsideration, and we investigate this possibility. Unlikethe demand equations, where there was some questionregarding the specification of the relevent price variableitself (AP or NP), AP is obviously the correct choice inthis case, since it matters little, if at all, to the supplierof services who is paying the bills he sends out.

INC* serves in the physician supply equation as ageneral taste variable rather than as an indication offinancial inducements to settlement, since price is alsoheld constant. As predicted, the life style available inhigh-income states does appear to exercise some influ-ence over the location of physicians.27 Hospital bedsupply—which is probably a proxy in a more generalsense for the whole range of medical facilities andauxiliary personnel—also appears to be an importantnonpecuniary consideration in physicians' location deci-sions.

No support is found for the view that physiciansactually shun states where the physician work-load is high. The endogenous Q/MD variable bears theanticipated negative sign but never approaches signifi-cance, and its inclusion, in fact, only serves to reduce theadjusted R2 of the regression (B.9 versus B.7, B.10versus B.6). That certain areas, both rural and urban

2 7 the total number of practicing physicians in thecountry (MDi) is constant in cross-section, an analysis such asthis can only throw light on the reasons for geographic variationin this total. Given the presence of substantial barriers to entryinto medicine, it is wholly unwarranted to conclude that thesame behavioral patterns observed for physicians in cross-sectionwill also apply over time in the determination of MDI. In allprobability, a proportional change in INC* across all stateswould have no effect on or on the partIcular state levels ofMD*,t. It follows that only variations in relative income arepotentially influential in determining the geographic distributionof a given number of physicians. The relative attractiveness of a

state is best represented by , where the denominatorrepresents mean per capita income for the sample. Replacing ourINC* variables with this relative income measure would have noeffect on the estimated elasticities because the correspondingvalues of both variables are proportional in any one year. But itis best kept in mind that the INC* variable of Table 18.B shouldonly be interpreted in a reLative sense.

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ghetto, are unpopular with physicians is indisputable,but fear of overwork does not appear to be a factor intheir judgment.

Part C: Quantity per Physician (0/MD)

The number of physicians per capita is the onlyvariable tested that clearly has a significant impact onphysician productivity. It alone accounts for 60 per centof the variation in Q/MD. The coefficient of thevariable indicates that about two-thirds of the incre-mental supply of physicians' services that might beexpected to ensue with an increase in the number ofphysicians practicing in a state will be effectivelynullified by a reduction in output of the averagepractitioner. These results suggest that increases in thenumber of physicians in a state, whether resulting fromshifts in distribution or expansion of the total stock,may actually result in higher prices for physicians'services. According to the regressions, a 10 per cent risein MD* will lead to a 4 per cent rise in demand as thenew physicians create a market for their services, butthe supply of services may rise by as little as 3 1/3 percent once resident doctors have adjusted to the de-creased urgency of unattended cases and opted for areduction in their activity.

The price elasticity of supply per physician isprobably low. Only a very small degree of confidencecan attach to the initial finding of a negative priceelasticity. Some collinearity between AP and MD* ispresent, as demonstrated by the reduced t statistic ofeach when they appear jointly (C.! and C.2 versusalthough C.3, with price included, is superior to C.2,C.4 is inferior to C.5. These results are not unlike thosereported by Martin Feldstein [16]: price coefficients inhis supply-per-physician equations range from —0.28 to—l .91, with only the higher (absolute) values achievingsignificance at the 5 per cent level. In any case, we findno support for the hypothesis that higher prices induceadditional services from physicians already located in astate.

Adding BEDS* to the productivity equation withonly MD* in it increases the explanatory power by a fairamount (C.5 versus C.2), but the BEDS* coefficient isstatistically insignificant and of a low magnitude.

Part D: Insurance (BEN*)

The purchase of physician insurance by consumers,as distinct from physician care itself, appears to be

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very sensitive to variations in personal income. Wefind elasticities ranging from 0.76 to 1.61, and in allcases but one they are significant at the 1 per cent level(the exception is D.7, where the simultaneous presenceof so many independent variables cancels the signifi-cance of each arid also lowers the INC* elasticity).

Three other hypotheses are investigated relating tothe determinants of BEN*. Again, because of highcorrelations among the independent variables, we testthese theories one at a time before assessing their effectsin combination.

The degree of unionization has a small but importanteffect on BEN*, raising the from 0.74 in D.1 to 0.81in D.2. This conclusion is weakened when PRM/BENand AP also appear in the equation, but even then the

2 is improved by inclusion of UNION* (D.6 versusD.3).

The purchase of insurance seems to be very respon-sive to its price, PIV. This composite variable isdependent both upon the average price of physicians'services and upon the cost of one dollar of insurancebenefits. As predicted by this hypothesis, the coeffi-dents of AP and PRM/BEN are each negative and highlysignificant in D.3. Deducting 1.0 from the estimated APcoefficient allows us to interpret the equation as arepresentation of the demand for insured visit equiva-lents (i.e., BEN*/AP). We see that the price elasticity ofdemand, as indicated by both PlY components, appearsto be quite high, on the order of —1.58 to _1.74.25Apparently, the decision to purchase medical insuranceis influenced much more by income and price than is thedecision to purchase physicians' services.

We find rio support for the financial-protectiontheory of insurance, which holds that the amount ofinsurance people wish to carry varies directly with thelevel of anticipated expenditures they are insuringagainst. This theory predicts equal, positive coefficientsof approximately 1.0 for both AP and Q*,29 yet we find

of some collinearity between these variables andUNION*, the significance level of each of the three is diminishedin D.6, and the coefficients somewhat lower as well.

291t may be argued that insurance purchases are sensitiveboth to their price and to anticipated expenditures levels, andthat AP therefore serves in a dual capacity in the BEN*regression. If this is correct, the AP coefficient we observeshould be on the order of -O.6(+1.O for the expenditures theoryand -1.6 for the price theory). This possibility is tested andrejected in D.5, for the PRM/BEN and AP coefficients areessentially unchanged from their values in D.3, while Q* is nownegative.


in D.4 that the coefficient of AP is negative, while thatof Q* is positive but not statistically significant.Dropping Q* from the regression brings about a slightimprovement in the R2 (D.7 versus D.6, D.5 versus D.3)and permits a much less ambiguous interpretation of therole of AP in insurance purchases. It is only because ofits dependence upon AP that insurance is endogenous tothis system.

Because of the many ambiguities complicating theinterpretation of most of these regression equations, wefeel it wisest to refrain from presenting a reduced-formversion of the model We have seen that two of theexogenous variables_.BEDS* and INC*_lend themselvesto more than one interpretation, depending upon theequation in which they appear, but such distinctionswould be lost in a reduced form. More serious is theproblem of multicollinearity. The consequent instabilityof coefficient estimates is troublesome enough in theinterpretation of individual regression equations, butthen at least it is known which variables must beapproached with caution. In a reduced form, because ofthe intricate pattern of substitutions, this instabilitymay be magnified manyfold and its repercussions feltthroughout the entire system. Depending upon thechoice of equations to represent the model, numerousversions of the reduced form are possible, some withsharply contrasting implications. Under the circum-stances, it seems preferable to state the limitations ofour knowledge rather than compound the possibility oferror.

2.6 The Effect on Health

The degree to which variations in the quantity ofphysiojans' services consumed affect health status, i.e.,Health = f(Q*, .

. .), is a matter of prime concern. Apriori considerations suggest that causality might run inthe reverse direction as well, from health to demand(Q* = g(Health,.. .)l. If so, two-stage least squareswould be the recommended method for determining theeffect of quantity on health, with the predicted value ofthe endogenous Q* variable entering the health regres-sions and vice versa. In the preliminary large-scale modeldescribed in 2.2, this procedure was adopted. As notedearlier, however, tests based upon this model lent nosupport to the hypothesis that variations in health

°In a reduced form, individual regression equations aresolved so that Q* and AP can be expressed wholly in terms ofthe exogenous variables.

contribute to interstate variations in the demand forphysicians' services. Hence, coefficients obtained fromordinary least squares regressions of health on Q* shouldnot be biased.3 1

Two dependent variables have been chosen to repre-sent health status in these regressions: the deathrate (DTH RT) and the infant mortality/ rate (INFMRT). The independent variables include/factors of ageneral nature—income, education, per cent black, andper cent aged (this last only in the DTH RTequations)—and factors specifically related to the con-sumption of physicians' services. In addition to Q*, wetest MD* and per capita expenditures for physicians'services (EXP*) in this equation. The first of these is,theoretically, the desired variable, but because of possi-ble measurement errors we do not rely upon it exclu-sively. No two of these physician variables rely upon thesame data base.

The most important conclusion we can draw from theregressions of Table 19 is that, other things being equal,variation in the consumption of physicians' services doesnot seem to have any significant effect on health, asmeasured by either the crude death rate or the infantmortality rate. This finding is consistent with the workof previous investigators concerning the relative unim-portance of medical care (not restricted to physicians'services) as a determinant of interstate variations indeath rates [5].

Higher educational levels are very strongly associatedwith lower crude death rates. Education is also nega-tively related to infant mortality, but not ,statisticallysignificant.32 Contrary to what many would expect, percapita income is positively related to the crude deathrate after controlling for the effect of education. It is,however, negatively related to infant mortality. Theseresults for education and income confirm the findings of

'Two-stage regressions with health as the dependent vari-able are not feasible within the context of the present model.This is because the exogenous determinants of health do notappear in the model. Their exclusion was based upon theinsignificance of health itself in the demand equation. Toreintroduce health would necessitate bringing back into themodel several exogenous variables that bear no demonstrablerelationship to the market for physicians' services, and, asexplained in 2.2, this, in turn, would impart a bias to all of thefirst-stage predicted endogenous variables.

320ur analysis implicitly assumes causality to run only fromeducation to health, but this is not necessarily the case. See theforthcoming paper by Victor Fuchs and Michael Grossman [201.

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TABLE 19

Results of Weighted, Logarithmic Health Regressions, Ordinary Least Squares, Interstate Model, 1966

(t values in parentheses)

Equation INC* %BLKa EDUC Q* MD* EXP*

Part A

DTH RT DR. 1 .560 -0.008(6.41) (-0.12)

DR. 2 .679 0061b 0364b(8.25) (-3.33)

DR. 3 .814 0333b 0823b(10.71) (4.79) (-6.49)

DR. 4 .811 0•062b 0354b 0.001 0780b(9.90) (4.68) (0.73) (-5.54)

DR. 5 .804 0062b 0347b 0.001 0779b 0.016(9.31) (3.67) (0.71) (-5.42) (0.13)

DR. 6 .811 0062b 0404b 0.001 0739b -0.05 7(9.93) (4.44) (0.87) (-5.04) (-0.99)

DR. 7 .815 0059b 0391b 0.001 0658b -0.079(8.95) (4.85) (0.88) (-3.86) (-1.24)

Part B

INF MRT IM. 1 .796 -0.144(-1.68) (6.47)

IM.2 .787 0011b -0.196(6.33) (-1.19)

IM.3 .791 -0.122 0010b -0.083(-1.22) (5.55) (-0.44)

IM. 4 .785 -0.089 -0.090 -0.079(-0.73) (5.43) (-0.47) (-0.50)

IM. 5 .783 -0.132 -0.090 0.011(-1.08) (5.38) (-0.46) (0.14)

IM. 6 .787 -0.152 0•010b -0.172 0.056(-1.38) (5.10) (-0.75) (0.69)

a Linear variable.at .01 level.

Fuchs [19], Grossman [22], and Auster, Leveson, and 2.7 ConclusionSarachek [5]. The per cent black is positively associatedwith both death variables, but the effect is much greater In Part 2 we have presented a formal econometricwith respect to infant mortality. model of the market for physicians' services in 1966,

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using cross-sectional data for our estimates. The findings,which must be regarded as tentative because of thelimited quantity and uneven quality of available data,tend to be consistent with, and give support to, theinferences drawn from the time series examined inPart 1.

The demand for physicians' services appears to besignificantly influenced by the number of physiciansavailable. The effect exerted on demand by supplyappears to be stronger than that of income, price, orinsurance coverage. Physician supply, across states, ispositively related to price, the presence of medicalschools and hospital beds, and the educational, cultural,and recreational milieu. The quantity of service pro-duced physician is negatively related to the numberof physicians in an area. It does not increase in responseto higher fees. The demand for medical insurance, unlikethe demand for physicians' services, does appear to be

quite sensitive to differences in income. It is alsosignificantly related to the price of insurance and tounionization. Finally, interstate differences in infantmortality and overall death rates are not significantlyrelated to the number of physicians, to the quantity oftheir services, or to expenditures.

If subsequent research should confirm these findings,the implications for public policy are substantial. Ac-cording to a widespread view, large increases in thenumber of physicians will drive down the price of, andexpenditures for, physicians' services, will diminish theinequality in their location, provide a proportionateincrease in the quantity of services, and make asubstantial contribution to improved health levels. Themodel and data we have examined do not provide anysupport for this view.

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Differences Across States, 1966: An Econometric Analysis - National