Physician Productivity and Returns to Scale By Larry J. Kimbell and John H. Lorant Cobb-Douglas production functions are used to estimate returns to scale in a sample of solo and group medical practices stratified by size and type of practice. Solo practices and small single-specialty groups are stratified by specialty, and large multispecialty groups are stratified as general practicegeneral surgery or comprehensive-care groups. Output measures used are gross revenue, total patient visits, and office visits; input measures reflecting practice scale are number of physicians, number of rooms, and number of nonphysician office personnel. Results indicate increasing returns to scale for solo and small group practices but decreasing returns to scale for very large groups. Possible reasons for inefficiency in large practices and the implications of the findings for public policy on health maintenance organizations are discussed.
Rising prices of medical service give impetus to the search for increased productivity in medical practice. Two questions are central to this search: whether physicians are likely to be more productive in medical groups than in solo practices and whether large group practices are more productive than small ones. Fein [1] speculated that economies of scale do indeed exist in medical practices, but research on the question has been inconclusive. Frech and Ginsburg [2] and Egan [3] suggested that multiphysician firms are more efficient than solo practices; nevertheless, solo firms remain the dominant form of medical practice: only about 20 percent of all physicians engaged in patient care in 1969 were in group practices [4]. Bailey [5] and Newhouse [6] expressed doubt about the existence and nature of scale economies. Bailey argued that any scale economies associated with internal medicine are traceable to laboratory operation rather than to delivery of medical services, and Newhouse stressed the diseconomies of scale associated with dilution of cost control incentives. Solo physicians bear the full effect of higher costs, whereas income sharing, in some groups, dilutes the effect of higher costs on individual physicians' incomes. The purpose of the present study is to examine whether there are returns to scale in a sample of medical practices stratified by size and This research was performed under contract no. HSM 110-70-35 between the National Center for Health Services Research and the University of Southern
California.
Address communications and requests for reprints to Larry J. Kimbell, Associate Professor, Graduate School of Management, University of California, Los Angeles, CA 90024. John H. Lorant is director of the Division of Personnel Management of the American Medical Association.
WNE
W977NTER 1
367
KIMBELL type of practice and, if so, whether they are increasing or decreasing & LORANT returns.
Methodology
Estimates of production depend on the form of production function chosen, the measures of output and definitions of input selected, whether standardizing variables are used to adjust for composition of output, and the scheme of sample stratification. Pilot studies 7--.of data other than those used here suggested that the most appropriate procedure for studying returns to scale is direct estimation of threefactor Cobb-Douglas production functions [8] with a sample stratified by specialty mix [9]. We used three basic measures of output: annual gross revenue, total patient visits per year (at all sites: office, hospital, and a trivial residual category), and office visits per year. We prefer and emphasize the revenue measure because gross revenue is very close to being a valueadded measure of physicians' output: purchased materials and services represent only a small fraction of total practice cost. Also, because accounting procedures, as opposed to the more informal methods used to estimate patient visits, are used to record revenue, gross revenue is a relatively more accurate measure-than patient visits. We assumed in this analysis that three basic inputs determine medical practice output: capital, the labor of physicians, and the labor of aides. We partitioned labor into two types to explore nonphysician sources of medical practice prcductivity and because of strong empirical evidence that output elasticities are substantially higher for physicians than for aides. There is considerable heterogeneity in both case mix and procedure mix. To minimize the effect of this heterogeneity in the analysis, we stratified the available data into relatively homogeneous classes of practices, as described later; -three standardizing variables were used as indicators of case mix and procedure mix. One such standardizing variable is a fee index. If two superficially similar products are sold in the same market at substantially #ifferent prices, one is led to conjecture that there may be real or perceived quality differences. The considerable variation in fees in gieven specialties and in given locations suggests that the fee index may reflect perceived quality or procedure differences as well as pure price differentials. The other standardizing variables are the fraction of patient visits in the hospital and the fraction of gross revenue derived from laboratory and x-ray servces. The specific production function and the variables used were as follows:
Q = aoHRP MDP RMP3 AIDP FEEPl6 exp(yi HOS + y2 LXR) HEALTH
RSERVICAC
368
where
Q = practice output: gross revenue from medical practice, annual total visits (induding office, hospital, and other visits), or annual office visits
HR = average number of hours worked annually by FTE physidan(s) in the practice, estimated as hours worked during a complete week in 1971 or 1972 times average weeks worked per year MD = number of FTE physicians in the practice: full-time physicians plus 0.3 times the number of part-time physicians RM = capital input: total number of waiting, examining, and other rooms used in the practice AID = number of FTE nonphysician office personnel employed by the practice FEE= weighted average of relative prices for 11 common medical procedures, each relative price being the ratio of the physician's fee to the mean fee in his specialty; relative fees are weighted by specialty-specific mean frequencies with which these procedures are performed HOS = fraction of all visits made to patients in the hospital LXR = fraction of gross revenue generated by laboratory and x-ray
PRODUCTIVITY AND RETURNS TO SCALE
services The coefficients of these variables were estimated for each output measure by regressing the logarithm of output on the logarithm of HR., MD, RM, AID, and FEE; HOS and LXR were entered directly as fractions. Proportionate expansion of the firm is represented by proportionate increases in the stocks of physicians, aides, and rooms, so that the return-to-scale estimate is given by ,82 ,83 + ,84.
Sample Stratification Our earlier pilot work [7] indicated that specialty mix should be the basis for sample stratification. Two basic types of practices were identified: single-specialty (induding solo) practices and multispecialty practices; the latter category contains two subtypes, general and comprehensive. Single-specialty practices had at least 90 percent of their physicians in one specialty; the remaining physicians were almost always general practitioners (who might specalize in the type of care rendered by the dominant type of specialists). Nine single-specialty categories were analyzed: general practice, internal medicine, pediatrics, other medical specialties, general surgery, obstetrics/gynecology, ophthalmology, orthopedic surgery, and other surgery. The first type of multispecialty group had both medical and surgical specialists, but such groups were not as diversified as the term "multispecialty" might suggest. The typical practice in this stratum, labeled GP-GS, had five general practitioners and one general surgeon; a few had one other type of specialist. On a continuum from singlespecialty general practices to large practices with all major specialties, the GP-GS groups clearly fall dose to the single-specialty end. Multispecialty groups of the second type are characterized by broad specialty representation; we call them comprehensive care (CC) practices. All these practices had medical specialists (usually internists), general surgeons, and at least one obstetrician or pediatrician. Practices
WINTER 1977
369
KIMBELL that did not include all four of these specialties were concentrated in the smaller size classes. These four core specialties were the ones around which others were added; that is, as practice size and diversity increased, CC firms tended to obtain specialists of these types before adding other
& LORANT
specialties.
Data Sources Cross-sectional data provided by the American Medical Association's Seventh Periodic Survey of Physicians and the Survey of Medical Groups, both conducted in 1971, are specifically tailored for estimation of production functions. These surveys provide information, over a wide range of firm sizes, on measures of output as well as data on labor and capital inputs for the practices surveyed. They also provide information on such variables as number of physicians and their specialties, procedures performed, and fees charged. The survey of groups was mailed to a census of all practices with more than seven physicians, and it therefore produced more responses from large groups than are commonly obtained from mailings to randomly selected physicians. Moreover, the group data do not suffer from the "allocation problem" that mars responses of individual group physicians (for example, an individual group physician, if asked about the aides he personally uses, may report all aides in the group instead of the subset he uses). Thus the group survey data, together with data on solo practices, afford a much stronger basis than previously available for studying the continuum from small to large practices.
Evidence from the Sample Strata
With the sample stratified jointly by practice size (number of FTE physicians) and specialty mix, a strategic partition appeared between the set containing solo practices and single-specialty groups and the set of multispecialty practices. Few in the former set had more than 4.5 FTE physicians, whereas most in the latter set had more than this number of physicians. Therefore comparisons of data on solo practice with data on small group practice are confined to the category of single-specialty practices, whereas comparisons of size within the group practice mode are limited to the category of multispecialty groups. This size division suggests that the simple but common distinction between group and solo practice is rather crude for precise statistical analysis. Although stratification of the sample does not control for such variables as fees and aides per physician, the resulting partitions of the data provide some descriptive evidence pertaining to returns to scale that is worth examining before we consider the results from regression analysis of the production functions. Table 1 shows sample means, by specialty type among solo and HEALTH single-specialty group practices, of gross revenue, net income, and RESEARCH patient visits per physician and of average revenue per patient visit. Gross revenue per FTE physician was higher in small single-specialty 370 group practice than in solo practice for eight of the nine relevant
specialty strata. These differences in gross revenue were accompanied by PRODUCTIVITY net income differences that exceeded $10,000 per physician per year in AND RETURNS TO SCALE several strata. The higher gross revenues for group physicians were not due to more patient visits: in six of nine single-specialty strata, group physicians provided fewer visits than did solo practitioners. Moreover, visit was higher for groups, even for the three specialties in which the average group physician provided more visits than the average solo practitioner. Table 2 shows the same types of data for multispecialty groups as are shown for single-specialty practices in Table 1. The evidence on large-scale groups is contained almost entirely in the CC stratum of multispecialty groups; no group in the GP-GS stratum had more than 13.5 physicians. Thus the comprehensive care groups provide most of the insights into scale effects pertinent to health maintenance organizations, for example, which are often conceived as very large
average revenue per
groups.
Among the CC groups, gross revenue per FTE physician falls substantially with the first size increment and then follows a shallow U-shaped pattern, rising slightly for the largest groups. Net income per physician, however, tends to decline monotonically with size. Annual patient visits per physician drop sharply with the first size increment
Table 1. Sample Means of Revenue, Income, and Patient Visits for Solo Practices and Single-specialty Groups, by Specialty (Number of physicians per practice= MD; number of practices in each cell shown in
parentheses) Gross revenue*
($103)
Specialty
MD=l
General practice ....... Internal medicine
Pediatrics .............
Net income*
($10I)
Rising prices of medical service give impetus to the search for increased productivity in medical practice. Two questions are central to this search: whether physicians are likely to be more productive in medical groups than in solo practices and whether large group practices are more productive than small ones. Fein [1] speculated that economies of scale do indeed exist in medical practices, but research on the question has been inconclusive. Frech and Ginsburg [2] and Egan [3] suggested that multiphysician firms are more efficient than solo practices; nevertheless, solo firms remain the dominant form of medical practice: only about 20 percent of all physicians engaged in patient care in 1969 were in group practices [4]. Bailey [5] and Newhouse [6] expressed doubt about the existence and nature of scale economies. Bailey argued that any scale economies associated with internal medicine are traceable to laboratory operation rather than to delivery of medical services, and Newhouse stressed the diseconomies of scale associated with dilution of cost control incentives. Solo physicians bear the full effect of higher costs, whereas income sharing, in some groups, dilutes the effect of higher costs on individual physicians' incomes. The purpose of the present study is to examine whether there are returns to scale in a sample of medical practices stratified by size and This research was performed under contract no. HSM 110-70-35 between the National Center for Health Services Research and the University of Southern
California.
Address communications and requests for reprints to Larry J. Kimbell, Associate Professor, Graduate School of Management, University of California, Los Angeles, CA 90024. John H. Lorant is director of the Division of Personnel Management of the American Medical Association.
WNE
W977NTER 1
367
KIMBELL type of practice and, if so, whether they are increasing or decreasing & LORANT returns.
Methodology
Estimates of production depend on the form of production function chosen, the measures of output and definitions of input selected, whether standardizing variables are used to adjust for composition of output, and the scheme of sample stratification. Pilot studies 7--.of data other than those used here suggested that the most appropriate procedure for studying returns to scale is direct estimation of threefactor Cobb-Douglas production functions [8] with a sample stratified by specialty mix [9]. We used three basic measures of output: annual gross revenue, total patient visits per year (at all sites: office, hospital, and a trivial residual category), and office visits per year. We prefer and emphasize the revenue measure because gross revenue is very close to being a valueadded measure of physicians' output: purchased materials and services represent only a small fraction of total practice cost. Also, because accounting procedures, as opposed to the more informal methods used to estimate patient visits, are used to record revenue, gross revenue is a relatively more accurate measure-than patient visits. We assumed in this analysis that three basic inputs determine medical practice output: capital, the labor of physicians, and the labor of aides. We partitioned labor into two types to explore nonphysician sources of medical practice prcductivity and because of strong empirical evidence that output elasticities are substantially higher for physicians than for aides. There is considerable heterogeneity in both case mix and procedure mix. To minimize the effect of this heterogeneity in the analysis, we stratified the available data into relatively homogeneous classes of practices, as described later; -three standardizing variables were used as indicators of case mix and procedure mix. One such standardizing variable is a fee index. If two superficially similar products are sold in the same market at substantially #ifferent prices, one is led to conjecture that there may be real or perceived quality differences. The considerable variation in fees in gieven specialties and in given locations suggests that the fee index may reflect perceived quality or procedure differences as well as pure price differentials. The other standardizing variables are the fraction of patient visits in the hospital and the fraction of gross revenue derived from laboratory and x-ray servces. The specific production function and the variables used were as follows:
Q = aoHRP MDP RMP3 AIDP FEEPl6 exp(yi HOS + y2 LXR) HEALTH
RSERVICAC
368
where
Q = practice output: gross revenue from medical practice, annual total visits (induding office, hospital, and other visits), or annual office visits
HR = average number of hours worked annually by FTE physidan(s) in the practice, estimated as hours worked during a complete week in 1971 or 1972 times average weeks worked per year MD = number of FTE physicians in the practice: full-time physicians plus 0.3 times the number of part-time physicians RM = capital input: total number of waiting, examining, and other rooms used in the practice AID = number of FTE nonphysician office personnel employed by the practice FEE= weighted average of relative prices for 11 common medical procedures, each relative price being the ratio of the physician's fee to the mean fee in his specialty; relative fees are weighted by specialty-specific mean frequencies with which these procedures are performed HOS = fraction of all visits made to patients in the hospital LXR = fraction of gross revenue generated by laboratory and x-ray
PRODUCTIVITY AND RETURNS TO SCALE
services The coefficients of these variables were estimated for each output measure by regressing the logarithm of output on the logarithm of HR., MD, RM, AID, and FEE; HOS and LXR were entered directly as fractions. Proportionate expansion of the firm is represented by proportionate increases in the stocks of physicians, aides, and rooms, so that the return-to-scale estimate is given by ,82 ,83 + ,84.
Sample Stratification Our earlier pilot work [7] indicated that specialty mix should be the basis for sample stratification. Two basic types of practices were identified: single-specialty (induding solo) practices and multispecialty practices; the latter category contains two subtypes, general and comprehensive. Single-specialty practices had at least 90 percent of their physicians in one specialty; the remaining physicians were almost always general practitioners (who might specalize in the type of care rendered by the dominant type of specialists). Nine single-specialty categories were analyzed: general practice, internal medicine, pediatrics, other medical specialties, general surgery, obstetrics/gynecology, ophthalmology, orthopedic surgery, and other surgery. The first type of multispecialty group had both medical and surgical specialists, but such groups were not as diversified as the term "multispecialty" might suggest. The typical practice in this stratum, labeled GP-GS, had five general practitioners and one general surgeon; a few had one other type of specialist. On a continuum from singlespecialty general practices to large practices with all major specialties, the GP-GS groups clearly fall dose to the single-specialty end. Multispecialty groups of the second type are characterized by broad specialty representation; we call them comprehensive care (CC) practices. All these practices had medical specialists (usually internists), general surgeons, and at least one obstetrician or pediatrician. Practices
WINTER 1977
369
KIMBELL that did not include all four of these specialties were concentrated in the smaller size classes. These four core specialties were the ones around which others were added; that is, as practice size and diversity increased, CC firms tended to obtain specialists of these types before adding other
& LORANT
specialties.
Data Sources Cross-sectional data provided by the American Medical Association's Seventh Periodic Survey of Physicians and the Survey of Medical Groups, both conducted in 1971, are specifically tailored for estimation of production functions. These surveys provide information, over a wide range of firm sizes, on measures of output as well as data on labor and capital inputs for the practices surveyed. They also provide information on such variables as number of physicians and their specialties, procedures performed, and fees charged. The survey of groups was mailed to a census of all practices with more than seven physicians, and it therefore produced more responses from large groups than are commonly obtained from mailings to randomly selected physicians. Moreover, the group data do not suffer from the "allocation problem" that mars responses of individual group physicians (for example, an individual group physician, if asked about the aides he personally uses, may report all aides in the group instead of the subset he uses). Thus the group survey data, together with data on solo practices, afford a much stronger basis than previously available for studying the continuum from small to large practices.
Evidence from the Sample Strata
With the sample stratified jointly by practice size (number of FTE physicians) and specialty mix, a strategic partition appeared between the set containing solo practices and single-specialty groups and the set of multispecialty practices. Few in the former set had more than 4.5 FTE physicians, whereas most in the latter set had more than this number of physicians. Therefore comparisons of data on solo practice with data on small group practice are confined to the category of single-specialty practices, whereas comparisons of size within the group practice mode are limited to the category of multispecialty groups. This size division suggests that the simple but common distinction between group and solo practice is rather crude for precise statistical analysis. Although stratification of the sample does not control for such variables as fees and aides per physician, the resulting partitions of the data provide some descriptive evidence pertaining to returns to scale that is worth examining before we consider the results from regression analysis of the production functions. Table 1 shows sample means, by specialty type among solo and HEALTH single-specialty group practices, of gross revenue, net income, and RESEARCH patient visits per physician and of average revenue per patient visit. Gross revenue per FTE physician was higher in small single-specialty 370 group practice than in solo practice for eight of the nine relevant
specialty strata. These differences in gross revenue were accompanied by PRODUCTIVITY net income differences that exceeded $10,000 per physician per year in AND RETURNS TO SCALE several strata. The higher gross revenues for group physicians were not due to more patient visits: in six of nine single-specialty strata, group physicians provided fewer visits than did solo practitioners. Moreover, visit was higher for groups, even for the three specialties in which the average group physician provided more visits than the average solo practitioner. Table 2 shows the same types of data for multispecialty groups as are shown for single-specialty practices in Table 1. The evidence on large-scale groups is contained almost entirely in the CC stratum of multispecialty groups; no group in the GP-GS stratum had more than 13.5 physicians. Thus the comprehensive care groups provide most of the insights into scale effects pertinent to health maintenance organizations, for example, which are often conceived as very large
average revenue per
groups.
Among the CC groups, gross revenue per FTE physician falls substantially with the first size increment and then follows a shallow U-shaped pattern, rising slightly for the largest groups. Net income per physician, however, tends to decline monotonically with size. Annual patient visits per physician drop sharply with the first size increment
Table 1. Sample Means of Revenue, Income, and Patient Visits for Solo Practices and Single-specialty Groups, by Specialty (Number of physicians per practice= MD; number of practices in each cell shown in
parentheses) Gross revenue*
($103)
Specialty
MD=l
General practice ....... Internal medicine
Pediatrics .............
Net income*
($10I)
