ABSTRACT

THE DEMAND AND SUPPLY OF PROFESSIONAL
HOSPITAL NURSES: INTRAbHOSPITAL
RESOURCE ALLOCATION
By

Jesse Sharp Hixson

The dissertation topic was motivated by the protracted
debate over the "shortage" of professional hospital nurses
of the past two decades, and by the apparent absence of ra-
tional basis for recent health manpower policies instituted
through the public sector. The primary emphasis of the
dissertation is upon conceptualization of the economics of
the hospital industry within the framework of a theoretical
model of the demand and supply of nurses' services.

Derivation of the demand function for nurses' services
is based on the fact that the dominant organizational form
of the industry allows wide latitude for discretion in
allocatory decisions with respect to both the supply vector
of hospital services and the demand vector for factors of
production. A total utility model of the firm is therefore
employed, viewing the hospital as the arbiter of relative
values of output components. A construction based on pref-
erence function maximization, wherein the ranking of the
hospital's preferences was obtained by amalgamating the
utility functions of the individuals involved in its deci-

sion process, yielded solutions for product specification

Jesse Sharp Hixson

and corresponding demand functions for factors of production
under several decision criteria, including maximization of
output valued at factor cost and maximization of utility

as a function of budget allocations to the various hospital
departments.

The supply of nurses was derived from a construction
based on individual utility maximization. In addition to
income and leisure, the individual's utility function con-
tained working conditions as an argument assumed to be
functionally related to a vector of technical magnitudes
utilized by the hospital in producing nursing care. From
this construction, the implications of differential product
specification between hospitals for the supply function of
nurses's services and the cost of producing nursing care
are analyzed.

Statistical analysis of data from official agencies
and individual hospitals shows that, while the short-run
supply of nurses in inelastic with respect to the wage
rate, supply is not unresponsive to other hospital par-
ameters of action. Turnover rates of professional nurses
are sensitive to hospitals' product specifications in terms
of input combinations used to produce nursing care which,
in turn, are sensitive to the degree of influence of the
professional nursing element in the hospital decision
process. Thus, whereas hospitals which relegate nurses'

professional sensibilities to a second order of importance

Jesse Sharp Hixson

in the allocating decision complain that nurses are not
available in the labor market, hospitals which pursue an
explicit strategy to minimize turnover by offering incen—
tives to which nurses respond experience no "shortage"

of nurses.

THE DEMAND AND SUPPLY OF PROFESSIONAL
HOSPITAL NURSES: INTRA-HOSPITAL

RESOURCE ALLOCATION

By

Jesse Sharp Hixson

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

1969

C>COPYright by
JESSE SHARP HIXSON

1969

"A'l‘A

ACKNOWLEDGMENTS

The final form of this dissertation reflects the
specialized inputs of many persons who provided advice
and criticism throughout its development. In addition to
that of Professor John P. Henderson, Chairman, I grate-
fully acknowledge the help of the other members of my dis-
sertation committee: Professor Byron W. Brown, who
pointed out many of the econometric problems encountered
in the development of the empirical analysis; and Profes-
sor Walter M. Burnett whose knowledge of the health ser-
vice industry was indispensable, and who obtained finan—
cial support for the field study from the Michigan State
University School of Hotel, Restaurant, and Institutional
Management.

I also express my gratitude to Professor Thomas R.
Saving, without whose help in the initial development of
the analytic approach to the topic the dissertation would
have not been attempted, and to the hospital administra-
tors (who I am bound not to name) without whose partici-
pation in the field study the dissertation could not have
been completed. All along the way, I benefited from stim-

ulating conversations with Mr. David W. Dunlop, and from

ii

the helpful advice and assistance of Mr. Jeffrey A. Both
in doing battle with the computer and in using Professor
James B. Ramsey's tests for specification error.

Finally, I thank my wife, both for her moral support
and for her inside connection with the Michigan State Uni-
versity Library-~without which my life would have been
incredibly complicated during the writing of this disser-

tation.

iii

|.ll.l|| Illl I J.] I II I I. l.‘l'.l ‘II I I ll. '1 ‘l. IIIF yllllll

TABLE OF CONTENTS

ACKNOWLEDGMENTS . . . . . . . . . . .
LIST OF TABLES. . . . . . . . .
LIST OF FIGURES
Chapter
I. INTRODUCTION.

II. ECONOMIC INDICATIONS OF A SHORTAGE OF
HOSPITAL NURSES. . . . . .

A Profile of the Nurse Force
The Economic Status of Hospital Nurses
Is There a Shortage of Nurses?.
Trends in Wages. .
Imperfections in the Market for
Nurses' Services . .
The Elasticity of Supply of Nurses'
Services . . . . . .

III. ECONOMIC STRUCTURE OF THE HOSPITAL
INDUSTRY . . . . .

Profile of the Hospital Industry

The Voluntary Hospital: Organizational

Structure. . . . . .
The Voluntary Hospital. Demand for
Factors of Production. .

IV. THE ANALYTICAL FRAMEWORK.

The Demand for Hospital Nurses.
The Role of the Physician . .
The Supply of Hospital Services
The Supply of Nurses and Optimality
of Production .
The Supply of Nurses' Services.
Optimality of Production.

iv

Page
ii
vi

vii

10
10
l2
l5
16
25

29

35
35
38
U6
51

53

53
61

76
82

Chapter Page

V. EMPIRICAL PROCEDURE AND RESULTS. . . . . 87
Statement of Hypotheses . . . . . . 87

Testing the Hypotheses. . . . . . . 91
Collecting the Data. . . . . . . 92

The Supply of Nurses . . . . . . 96

The Demand for Nurses . . . . . . 121

VI. CONCLUSION. . . . . . . . . . . . 149
BIBLIOGRAPHY . . . . . . . . . . . . . 155

[I II‘ I'll ll." l I I‘ll'l'alvll ‘I II." I II

Table

10.

11.

LIST OF TABLES

Page
Registered nurses by marital and activity
status, 1962 . . . . . . . . . . 11
Registered nurses employed in nursing, by
field of employment, 1962. . . . . . . 12
Average weekly earnings of females for
standard work week in selected cities, 1963. 14
Per cent increase of average earnings in
selected occupations, 1960-1966. . . . . 18
Average weekly earnings of female nursing
staff employees in non-governmentgshort-
term general hospitals, by region and city,
1957, 1960, 1963, and 1966 . . . . . . 20
Statistical profile of the hospital indus-
try, 1966 . . . . . . . . 36
Regression‘results for ratios of personnel
to patients . . . . . . . . . . . 109
Regression results for ratios of general
duty registered nurses to auxiliary nursing
personnel . . . . . . . . . . . . 112
Results of specification error tests . . . 117
Matrix of simple correlations . . . . . 139
Signs of the significant relationships'
between explanatory variables and staffing
ratios . . . . . . . . . . . . . 145

vi

LIST OF FIGURES

Figure

1. Voluntary hospital administrative organiza-
tion chart . . . . . . . . . . .

2. Determination of the Optimal combination of
inputs, outputs, income and leisure.

3. Work-leisure choice . . . . . .

A. The supply of labor . . . . . .

vii

Page

40

58
81
81

CHAPTER I

INTRODUCTION

The past two decades have witnessed much discussion
of a "shortage" of registered nurses in the nation's hos-
pitals.l The protracted discourse on the causes and con-
sequences of the alleged shortage, both within the hos-
pital industry and among the general public, has served
to transform the perceived problem into a matter of

2

national concern and a target for public policy. The

impetus for the federal government's inclusion of

 

lBibliographies of Journal articles dealing with
the nurse "shortage" may be found in the Cumulative
Index of Hospital Literature (Chicago: American Hospi-
tal Association) under the heading Nurses, Shortage, and
in the Cumulative Index to Nursing Literature (Glendale,
California: Seventh-Day Adventist Hospital Association)
under the heading NursinggResources.

2Examples of Federal involvement with the nurse
"shortage" include: the Health Professions Education
Assistance and Vocational Education Acts of 1963; the
Nurse Training Act of 196A; provisions under the Man-
power Development and Training Act for training practi-
cal nurses and nurses aides and for refresher training
programs for professional nurses; the Allied Health Pro—
fessions Personnel Training Act of 1966; and the estab-
lishment of the President's Committee on Health Manpower
in 1966. (U. S. Department of Labor: Professional and
Supporting Personnel, Washington, D.C., 1967; Technology
gnd Manpower in the Health Service Industry 1965-75.
(Manpower Research Bulletin number in), Washington, D.C.,

1967.)

professional and auxiliary nursing personnel in its frame-
work of manpower policy was provided by the Surgeon Gen-
eral's Consultant Group on Nursing, which reported in
1963:

A severe shortage of nurses exists in the United
States today. It is both quantitative and quali-
tative. Quantitatively, the shortage makes it
impossible to supply hospitals and other health
facilities and organizations with sufficient num-
bers of adequately prepared nurses. Qualitatively,
it impairs the effectiveness of nursing care.

Although the number of nurses in practice has
increased substantially, demands for nursing ser-
vice have increased even faster. Rising rates of
hospitalization, growth of medical science, and
increased employment of nurses in doctors' offices
have so expanded the demand for nursing services
that the shortage has become a critical national
problem. Practical nurses and auxiliary nursing
personnel have been used increasingly to supple-
ment or take the place of professional nurses.3

There are several definitions or concepts of short:
age being used in discussions of the current quantity of
health manpower employed in the United States.” Several
of these concepts will be discussed with respect to the
"shortage" of professional nurses.

First, a widely used measure of "shortage" is the
difference between the ratio of nurses to total popula-

tion in a given area and the ratio deemed necessary to

 

3The Surgeon General's Consultant Group on Nursing,
Towards Quality in Nursing: Needs and Goals (Washington,

D.C., 1963): p. 3.

“For examples, see: Rashi Fein, The Doctor Short-
age (New York: The Brookings Institution, 1967), pp. 5-
13; U. S. Department of Labor, Technology and Manpower in
the Health Service Industry 1965-75, p. 18.

 

provide a certain desired standard of nursing care. This
was the approach used by the Surgeon General's Consultant
Group on Nursing. On the basis of projected population
growth and potential output of nursing school graduates,
the Consultant Group predicted that there would be 680,000
nurses employed in 1970 when the number needed for "safe,
therapeutically effective, and efficient" care would be
850,000.5

Second, the needs expressed by hospitals for addi-
tional nursing personnel are often used as a measure of
the nurse "shortage." A survey conducted by the American
Hospital Association and the United States Public Health
Service in 1966 showed that hospitals needed at that time
an additional 79,470 professional nurses, Al,AOA practi-
cal nurses, and 69,7A9 nursing aides.6 These figures
were derived from each hospital's estimate of additional
personnel believed necessary to provide "optimal" care
for its current patient load. The expressed need for
additional registered nurses was classified as the most
urgent personnel requirement in hospitals, and represented
a 22 per cent increase over current employment.

A third widely used measure of the "shortage" of

hospital nurses is the number of vacant budgeted positions

 

5Surgeon General's Consultant Group, Towards Quality
in Nursing, p. 23.

 

 

6American Hospital Association, Manpower Resources
in Hospitals - 1966 (Chicago: American Hospital Associa-
tion, 19673, p. 3.

 

for nurses. The per cent of budgeted nursing positions
unfilled in hospitals has been increasing for the past
20 years. In 1962, 23 per cent of the budgeted full-
time hospital positions for general duty nurses were

7 A survey of 103 large non-federal short-term

vacant.
general hospitals conducted by the American Nurses
Association in 1967 showed that the median number of
vacant budgeted positions for registered nurses was 1A.2
per cent, while one-third of the hospitals in the sample
had over 20 per cent of their budgeted positions for
nurses vacant.

The estimates of the magnitude of the nurse "short-
age" cited above are based on discrepancies between
actual employment levels and employment levels consistent
with someone's minimum, desired, or optimal standard.
Typically, the existence of a "shortage" is predicated on
the proposition that the nation's "need" for nurses is
out—stripping the "supply," or that the present "demand"
exceeds the present "supply." When vacant budgeted posi-
tions are used to quantify the "shortage," nothing is said
about the duration of vacancies, nor is vacancy adequately

defined; it is not known whether funds are available to

 

7American Nurses Association, Facts About Nursing
(New York: American Nurses Association, 1966), p. 19.

 

8American Nurses Association, Facts About Nursing
(New York: American Nurses Association, 1967), p. 21.

 

fill those positions or if they represent a divergence
from the number that would be filled in the absence of
economic restrictions.

The common denominator of these widely used defi-
nitions of shortage is a concept of 2229 which neglects
economic considerations. In the sense that the "short-
age" of nurses represents unsatisfied needs in an
environment of limited resources, it is a reflection of
the fundamental and universal problem which has given
rise to the science of economics. In this sense, the
"shortage" of nurses is a tautology. Because all eco-
nomic resources'are scarce, discussions of "need" are
trivial unless placed in objective contexts which recog-
nize the mechanisms by which resources are allocated to
satisfy competing wants. The analytical framework of
economics, being designed to answer questions about how
the most output can be obtained from a limited quantity
of resources, places problems of resource allocation in
objective contexts whereby non-trivial meanings and opera-
tional theorems can be derived about the nature of "short-
ages." The economic approach recognizes the necessity of
defining the feasable set of alternatives and of estab-
lishing priorities in the face of constraints. Although
the hospital industry is founded on traditions of charity
and public service and may stress need subjectively

determined as opposed to demand in the distribution of

its products, it cannot abstract from the economic environ-
ment within which it competes for resources in formulating
goals and objectives for its role in the economy. Irre-
spective of the ideals that may motivate the production
and distribution of hospital services, the industry is not
independent of the price system since it must compete for
manpower in an economy where resources are allocated
through market mechanisms. Thus the "need" for nurses is
economically relevant only if expressed by effective de-
mand in the labor market, and objective statements about

a shortage can be made only with reference to the condi-
tion of the market and the forces determining the demand
and supply of nurses' services.

It is the purpose of this dissertation to bring the
tools of economic analysis to bear on the problem of the
"shortage" of hospital nurses in order to establish a
framework from which objective statements can be made
about the various issues involved. By approaching the
problem from the viewpoint of the supply and demand for a
factor of production employed by an industry producing a
consumption good subject to specific technological and
budget constraints, the analysis will attempt to ration-
alize the production of hospital services and isolate the
factors underlying the alleged "shortage." Although
empirical tests of hypotheses will be conducted with data

obtained in a field study of hospitals, primary emphasis

will be placed on conceptualization of the economic frame-
work of the hospital industry and derivation of an ana-
lytical model of the demand and supply of nurses' ser-
vices.

Even though medical economics is an expanding field,
economists have not yet begun to apply their tools of
analysis intensively to rationalization of production in
the health care industry. Economists' historical lack of
attention to this field can be traced to the peculiar
characteristics of the market for medical services: the
traditional analytic framework which subsumes consumer
sovereignty, profit motivation, and price-rationing mech-
anisms is not applicable to a situation where adminis-
trative discretion and the interplay of professional
opinions dominate allocatory decisions.9 Economic analy-
sis of the hospital demand for factors of production re-
quires the integration of these institutional factors
into a theoretical framework; because the hospital does
not determine employment and production magnitudes simul-
taneously to maximize a single-valued objective function,
a theory of managerial behavior is required to identify
the arguments in the hospital utility function which con-
trol hospital choice with respect to demand for inputs

and supply of output. Consequently, a primary objective

 

gselma J. Mushkin, "Toward a Definition of Health
Economics," Public Health Reports 79, no. 9 (September,
1958). pp. 785-93.

 

 

of this dissertation will be the development of a formal
conception of the hospital decision process and its inte-
gration into the theory of the firm in order to develop
the implications of discretionary behavior for the demand
for nurses' services.

The theoretical approach to the problem is not with-
out methodological precedent. The development of behav-
ioral, satisficing, and managerial-discretion models
within the broad class of "alternative" theories of the
firm has provided a general framework suited to analysis
of the impact of discretionary behavior on the choices of
the firm.10 But because the theoretical development of
managerial-discretion models is conducted at a higher
level of generality than the conventional theory of the
firm wherein competitive forces are assumed to prevail to
restrict the opportunity set of the decision-makers, the
operational significance of models incorporating latitude
for managerial discretion depends on ability to identify
the relevant objectives of the firm in each particular

case.11 To lend empirical significance to the general

 

loSee C. E. Ferguson, "The Theory of Multidimen-
sional Utility Analysis in Relation to Multiple-Goal
Business Behavior: A Synthesis," Southern Economic Jour—
eel, 32 (October, 1965), pp. 169-175; Oliver E. William—
son, The Economics of Discretionary Behavior: Managerial;
Objectives in a Theory of the Firm (Englewood Cliffs:
Prentice Hall, Inc., 196A).

llFritz Machlup, "Theories of the Firm: Marginal—
ist, Behavioral, Managerial," American Economic Review,
LVII (March, 1967), pp. 15-16.

 

theoretical construct, the analysis will incorporate the
hypotheses of organization theorists, medical care soci-
ologists, and other researchers in the field of hospital
organization with data obtained in a field study of hos-
pitals in an attempt to measure the effects of discre-
tionary behavior on the demand and supply of nurses'
services.

The analysis will begin in Chapter II with an exam-
ination of wage movements and the competitive structure
of the market for nurses' services to determine if indi-
cations of an economic shortage can be found. In Chapter
III, the organization of the hospital industry will be
examined and its peculiar institutional characteristics
highlighted to form a base for the development in Chapter
IV of a theoretical model of the demand and supply of
hospital nurses' services. In Chapter V, behavioral
assumptions will be imposed on the theoretical structure
to yield empirically testable hypotheses which will be
tested with data collected from short-term general hos-
pitals. Concluding remarks based on the results of the

analysis will be made in Chapter VI.

CHAPTER II

ECONOMIC INDICATIONS OF A SHORTAGE

OF HOSPITAL NURSES

A Profile of the Nurse Force

Data on nurses compiled from various sources are
published by the American Nurses Association in its annual
issues of Facts About Nursing.l These data are used to
provide the following profile of the nurse force.

Nursing is a female—dominated profession; of the
total number of professional nurses in the United States,
99 per cent are women. Since the mid-1950's, one-third
of all professional nurses under 60 years of age who are
licensed to practice have not been employed in nursing.
The major proportion of those nurses who do choose to
practice are married. Table 1 shows the marital and ac-
tivity status of the nurse force in 1962.

Nurses who are willing to work part-time provide a
large and growing source of manpower for hospitals. From
a survey of American Hospital Association registered hos-

pitals in 1966, the Public Health Service estimated that

 

1American Nurses Association, Facts About Nursing
(New York: American Nurses Association, Annually).

lO

ll

29 per cent of the total practicing hospital nurses were

employed on a part-time basis.2

TABLE l.-—Registered nurses by marital and activity
status, 1962.

 

 

Actively Not Activity
gizifigl employed in employed status not
nursing in nursing reported
Total number 532,118 282,819 32,59“
percentage 100.0 100.0 100.0
Single 25.6 5.3 6.9
Married 61.0 8“. 12.8
Widowed, divorced
or separated 11.0 “.8 2.7
Marital status not
reported 2.“ 5.2 77.6

 

Source: Facts About Nursing, 1967, p. 16.

Nurses find employment in a variety of fields.
Table 2 shows the total number of nurses that were prac-
ticing in each major field in 1962.

About two-thirds of the practicing nurses are

3 In addition, a large number of

employed by hospitals.
the self-employed private duty nurses work in hospitals,
although the exact proportion is not known. Of the total
number of hospital nurses, about 60 per cent are general

duty nurses, i.e., are not in administrative positions.

Thus over “0 per cent of the active nurses are employed

 

2Ibid., 1967, p. 17.

31bid.

12

as general duty nurses in hospitals. Because they pre-
dominate in the hospital employment of nurses, their wage
levels will be used as the base of comparison in the next

section.

TABLE 2.-—Registered nurses employed in nursing, by field
of employment, 1962.

 

 

Field of Employment Number Employed % of Total
All Fields 532,118 100.0
Hospital or other Institution 335,“0“ _63.0
School of Nursing 16,29“ 321
Private Duty 6“,155 12.1
Public Health 23,983 “.5
School Nurse 16,70“ 3.1
Industrial Nurse 17,569 3.3
Office Nurse “3,558 8.2
Other 2,“96 .5
Field not Reported 11,955 2.2

 

Source: Facts About Nursing, 1967, p. 15.

 

The Economic Status of
Hospital Nurses

 

 

The Bureau of Labor Statistics has gathered wage and
employment data in a tri-annual Hospital Wage Survey since
1957.“ These data are the main source of information
about the economic status of hospital nurses. They can be

compared with occupational wage data from BLS and other

sources to show the economic status of hospital nursing

 

LlU. S. Department of Labor, Industry Wage Survey:
Hospitals (Bureau of Labor Statistics Bulletins 1210,
129“, 1“09, and 1553) (Washington, D.C., 1958, 1961, 196“,
1967).

 

 

13

relative to other comparable (female-dominated) occupa-
tions.

Table 3 tabulates data from several BLS wage sur-
veys conducted in 1963. The table presents a cross-
sectional comparison of average weekly earnings of females
for several hospital and non-hospital employments in
selected metropolitan areas. The table shows that average
earnings of general duty nurses in non-government hos-
pitals were consistently below those of secretaries, whose
jobs do not necessarily require post high-school educa—
tion. The wages of nurses employed in industry were con-
sistently higher than the wages of hospital nurses. Al-
though hospital and non-hospital nursing wages were
significantly different, the wages of stenographers em-
ployed by hospitals appear to be competitive with wages
of those employed outside of hospitals. This situation
is no doubt a reflection of the fact that hospitals domi-
nate the market for nurses' services while facing com-
petitively determined wage rates for secretarial personnel.

The average weekly earnings of all the general duty
nurses included in the 1963 BLS hospital wage survey was
$86.50, or $“,“98 per year. This was $1,“6“ per year less

than the average salary of classroom teachers in 1963-6“

1“

TABLE 3.--Average weekly earnings of females for standard
work week in selected cities, 1963.

 

Non-Government Non—Hospital Industry

 

 

Hospitals
City General -

Duty Steno+ Secre- Steno- Industrial

Nurse graphers.taries graphers Nurses
Atlanta $75.00 $70.00 $ 93.50 $75.00 $102.50
Baltimore 82.00 70.00 95.50 75.50 10“.50
Boston 86.00 72.50 92.00 7“.50 98.00
Buffalo 91.00 --- 99.50 79.50 107.00
Chicago 9“.00 83.00 101.50 83.50 103.“0
Cincinnati 85.00 72.00 98.00 72.00 10“.00
Cleveland 93.00 83.50 103.50 82.00 108.00
Dallas 83.50 --- 92.50 7“.00 98.50
Los Angeles 95.00 92.50 105.00 89.50 113.00
Memphis 75.00 --- 79.50 68.00 92.50
Minneapolis 89.00 79.00 89.50 7“.00 98.00
New York 96.00 9“.00 101.00 80.50 108.00
Philadelphia 80.00 69.50 96.50 76.50 103.00
Portland 86.50 --- 90.50 76.50 103.50

San Francisco 95.50 79.50 102.50 8“.50 111.00

 

Source: Bureau of Labor Statistics Bulletins
l3“5, 1385, and 1“09.

15

reported by the National Education Association Research
Division.5

Relative to other female-dominated occupations and
professions, nursing is not a pecuniarily attractive
career. The internal rate of return to a baccalaureate
degree in nursing is clearly below that to the equiva-
lent degree in education. The internal rate of return to
a nursing diploma (i.e., a nursing degree earned from a
hospital school of nursing), while slightly higher than
that to a baccalaureate degree in education, is well
below the return to an investment in a secretarial
course.6 The structure of wage rates in the female-
intensive occupations, and the implied rates of return to
the educational investments required to enter them, sug-
gest that the decision to enter nursing is weighted

heavily by non-pecuniary factors.

Is There a Shortage of Nurses?

 

It was shown in the previous section that the eco-
nomic status of hospital nurses is low relative to other
fields of nursing and to occupations which are viewed as
alternatives for women in general. However, this fact

provides no clue as to whether an economic shortage of

 

5National Education Association, Economic Status of
Teachers in 1963-6“ (Washington, D.C.: National Educa—
tion Association, 196“).

6Donald Yett, "The Nursing Shortage and the Nurse
Training Act," Hospital Topics, June, 1966, p. 30.

 

 

 

16

nurses exists, for an economic shortage is defined as a
divergence between demand and supply at prevailing wage

7 In the absence of market imperfections that pre-

rates.
vent wages from rising in response to excess demand, an
economic shortage will be eliminated by market forces
causing an increase in wages. The higher wage will serve
to ration the available supply of nurses between demanders
in the short-run, and to attract new nurses into the mar-
ket in the long run. If market imperfections prevented
wages from rising in the short-run, the shortage would
persist into the long-run since additional personnel would
not be attracted into the market. Thus the existence of

a shortage can be ascertained only by examining the dy-

namics of wages and the competitive structure of the

industry.

Trends in Wages
If the hospital demand for nurses were increasing
more rapidly than the supply and market forces were operat-
ing freely, several trends would be observed. First, hos-
pital nursing wages would rise relative to the general

trend of wage increases in the economy, i.e., nursing

 

7This is the basic definition of an economic short-
age from which both the static and dynamic implications
of the concept are derived. For a thorough discussion of
alternative concepts of economic shortage, see A. A.
Alchian, K. J. Arrow, and W. M. Caprone, "An Economic
Analysis of the Market for Scientists and Engineers,"
The RAND Corporation, RM-2190-RC, June 6, 1958.

l7

wages would increase relatively more than wages in occupa-
tions that are not experiencing growth in demand relative
to supply. Second, within the nurse market, hospital
nursing wages would increase relative to wages in other
fields of nursing as hospitals attempted to bid nurses
away from alternative employments. Finally, more nursing
activities in hospitals would be performed by less ex-
pensive substitutes for nurses (practical nurses and
nursing aides) as nurses' services became more expensive.
Data from several sources will be examined below to see
if the expected trends can be observed in the face of the.
"shortage" of nurses.

Data on wage trends over time may be examined to
determine whether nursing wages have increased in the
face of the alleged shortage or whether they have remained
static relative to the trend of wages for other occupa-
tions. Table “ shows the percentage increase in national
averages of wages for several occupations during the
period 1960—66. The rates of increase are computed from
various BLS data which are not taken from a common sample.
The data on office clerical workers and industrial nurses
are from the annual BLS Area Wage Surveys of 8“ metro-
politan areas, while the data on production workers are-
1imited to areas of industrial concentration and those for
general duty nurses are limited to 15 of the larger metro-

politan areas; the data on public school teachers' wages

18

are taken from sample areas with populations of 50,000 or
more. Wage data from small samples of larger metrOpoli-
tan areas will be biased upward relative to data from
larger samples including smaller areas insofar as wages
are commonly higher in larger cities; the data may serve,
however, for rough comparisons of earnings trends between

occupations.

TABLE “.--Per cent increase of average earnings in selected
occupations, 1960-1966.

 

 

Occupation Per cent Increase

Office Clerical Workers 19.7a
Industrial Nurses 21.6a
Public School Teachers 23.1b
Production Workers '

Durable Goods 2“.9c

Non-durable Goods 22.6C
General Duty Hospital Nurses 28.3c

 

aComputed from an index of straight-time salaries
for a standard work—week.
bComputed from an index of annual salaries.

CComputed from average weekly earnings for a
standard work-week.

Source: Bureau of Labor Statistics Bulletins 129“,
1553, and 1555.

The average earnings of general duty hospital nurses
have increased faster than the earnings of any other occu-

pation shown; it appears, therefore, that the supply of

l9

nurses has diminished relative to the demand and that
hospitals have yielded to market forces in equaling or
surpassing the national trend of wage increases over the
period. Within the nurse market, hospital nursing wages
have increased relative to wages in industrial nursing,
which could reflect an increase in hospital demand rela-
tive to industrial demand for nurses.

Wage changes within hospitals may be examined to
determine how hospitals have coped with the "shortage" of
nurses. Data from the four BLS hospital wage surveys are
tabulated in Table 5, which shows average weekly earnings,
and their percentage change between survey periods, for
the three types of nursing service personnel employed in
non-government hospitals in the cities included in the
surveys. A comparison of wage changes between employment
categories within three-year periods shows that each occu-
pation made relative gains in average wages over others
with approximately equal frequency; e.g., registered
nurses made relative gains over practical nurses, and
vice-versa, in about one-half of the observations. How-
ever, when only those instances are counted where EEEf
stantial gains were made, lower skilled groups gained on
higher skilled groups in more instances than higher
skilled groups gained on lower skilled groups. For ex—
ample, if we define a'three-year differential increase

of “ per cent as substantial, practical nurses made

2()

TABLE 5.--Average weekly earnings of female nursing staff employees in non-
government short-term general hospitals, by region
and city, 1957, 1900, 1963, and 1960.

 

Average Weekly Earnings

 

General Duty Practical Nursing
Prof. Eurse Nurse Aide

 

 

 

; t H _ s
_ y .,1,., weekly
hnante

Average 1 Average , Average p
e 1
Earnings ’ Earnings

. Weekly
CEIanV-e ,_ .
- Earnings

\
4

>74

._/

ange

 

USFTHEAST

Boston 11'] ? 2L.EU 3 “0.50 3 39.50
b , .33 50.0 09.50 20., “8.00 21.5
I, 0.0J 3.6 06.50 6.1 $“.CO 12.5
M: 705.5J 22.7 55.00 27.3 68.00 25.9
Buffalo 17s: £0.00 £5.00 3 .00
00 70.8“ 55.00 31. “t 0‘ “3.

11.

C; K} 3 ’)

o/u LL;-

C\ L.
C
Q‘- \J (D

r.
H
.1‘).
(i. r31 (j
b—w—Jw
OCH»:
fl
1
L:

F—J
I."
xii—J:

CI , O
C) Ox
1'")
3

1-.

,1
r.
F:
(1‘

\ '1

.. 7.5 51. .
(Q al.00 20.0 01.00 16.“ “0.50 32.9
a: .a.0t 1;_. 73.00 19.7 59.00 20.9
v' 1...: 71.: 92.,0 10.7 78.50 53.1
11 :a1t1t21. 1 ‘7 aa.r. 3r.03 77.30
'. 71 HO 20., “5.00 25.6 37.50 30.“
2‘ 53.10 11.: 53.00 17.8 “3.00 1“.7
L . .‘3 11.- 71.00 39.0 p6.50 31.“
:xvsa
halt-"<"e I'ET 11.50 J1.00 31.00
n3 7;.LJ 10.E 5;.00 29.3 37.50 21.0
(1 5:.00 12.; 59.~0 12.3 “5.50 3 .3
z' 100. 0 27.1 30.30 55.3 §~ 00 37.5
1«11a: 17%. “F 00 “0.50 29.50
'- 7L. r 13.: 07.50 17.3 35.00 15.6
23.1“ 12.: ”5.00 15.5 “0 50 15.7
*1 . . Q 1).: 05.00 18.2 50.00 23 5
Very :: :11? 5..»( 3:.01 :9.¢0
tn 1 . O 13.3 “5.00 15.“ 3:.L0 13.2
L ".-L 10.: 53.00 1T.é jU.'J 13.3
t H .00 2}.) 67.00 25.0 51.53 “1.1

IMWLT11‘331TVFRI.

,. .,.a “1 ,,
Cnicagc l”.: I..JC

I f'
H
C): (T. (T. x '1
‘-‘ a; ("J
I O
D (J
C; ' C)
r‘

(.7
c.
k4 H F4
1 (:1 ‘ ;
C
~J \,1 (L)
1.). .
I: ‘1
(I
C

01.00 17.1

Cincinnati 1'57 9?.UC “5 “U 35.90
:* 7;.00 13.: 5:.50 1A.“ A0.00 12.7
0, i .30 17.! (3.50 1“.“ 7.50 18.8
" 10’.00 23.0 73.50 25.2 9.00 29.2

1:131) \f‘. 1: .

Cleveland 1"§7 ::.CO “9.50 9,30
:0 r3.:0 20.6 59.00 10.2 5.50 10.7
:3 v3.00 13.“ 67.50 1“.“ 52.50 ;5.“
': 1LU.‘J ;2.§ 77.00 10.1 50.00 3.0
Iinncapolis- 19V? €8.EJ “.00 2.00
St. Paul r3 8’ 00 r. V 50 .

3.00 16.
9 50 10.

0.50 12.

.00
r

I,
)0 13.

*4 ”IKE!“ K,“
1:211 P.)

P...)

‘Obufl
5117
UJWN

r.
)-
._ k
I
C)
O
{-1 ',_1 1“
(NH
0
3U; F1)
‘Ntflfiufi
‘

1.5.1,; 3 A

Los Angeles- 1957 71.00 2.50 A .50

Long Beach 00 85.00 19.7 5.5. 2“.8 5 .00 20.0
63 QS.00 11.8 2.50 10.7 6 .00 0.3
66 110.00 22.1 8.50 22.1 7 50 21.8

Portland 1957 50

2 .50 17
.50 8.
50 20

.50

.OO 23 1

.00 7.1
5 8

INS

C
k:

(7.

(7ka ' ‘
F—J

\D

O

1...:

CD‘O

to

.C‘\

.50 1'

\D O (3"le U1 T»)*\1\1

(I) (13,ij
mmkfl J:

C) CI.) ‘J T‘\

r: 0- '
\fi
O
h)
'._J
\3

\O\JCT‘1\I' \J CV4“ KI": CD\I (DMD

13k? ‘JN (33 EKG O
O
0

San Francisco- 1957 79.00 57.00
Oakland 60 33.50 16.0 .5: 18.“ 6“.50 13.2
63 95.50 1“.“ .50 11.9 73.00 13.2
06 120.00 25.7 .00 2“.5 85.00 16.“

 

Source: Bureau of Labor Statistics, Bulletins 1210, 129“, 1“09, and 1553.

21

substantial gains on registered nurses in 10 instances,
and nursing aides made substantial gains on registered
nurses in 16 instances, while the converse was true in
only 2 and 6 instances, respectively.

On the whole, lower-skilled groups have evidently
been gaining on registered nurses with respect to narrow-
ing wage differentials; it appears, therefore, that the
demand for auxiliary personnel has increased relative to
the demand for professional nurses in hospitals. An ex-
planation for this phenomenon may be indicated in the
trend of implicit "upgrading" of auxiliary personnel in
hospitals, whereby auxiliary personnel have been perform—
ing more and more tasks once performed exclusively by
nurses.8 Such upgrading, achieved by redefining the
technical aptitudes of auxiliary personnel and thus serv-
ing to increase the technical substitutability of auxili-
ary personnel for nurses in production, would increase
the demand for practical nurses and nurses aides and
result in the narrowing wage differentials observed. In
addition, various newly created occupational categories

for which wage data are not yet available have further

 

8For commentary on the role of the nurse vis-a-vis
auxiliary and related personnel see: The Surgeon Gen-
eral's Consultant Group on Nursing, Towards Quality in
Nursing: Needs and Goals (Washington, D.C., 1963); R. A.
Kurtz and D. E. Saathoff, "General Duty Nurses and Aides
A Study of Roles," Hospital Management, July, 1963, pp.
60-68; Edna L. Fritz, Undergraduate Nursing Education,
National League for Nursing, Council of Member Agencies
of the Department of Baccalaureate and Higher Degree Pro-
grams, 1966. (Mimeographed.)

22

reduced the exclusive domain of the nurses' role in the
production of patient care. Such new "para-medical"
occupations as inhalation therapists, surgical, ortho-
pedic, and obstetric technicians are assuming special-
ized functions once under the general province of the
"nurse."

Writers contemplating the appearance of new tech-
nical specialties and the rapid increase in the ratios of
auxiliary nursing personnel to registered nurses in
short-term hospitals have attributed the changes to
several factors. The trend toward increased utilization
of lesser skilled personnel is attributed in one view to
technological change presumed to have allowed hospitals
to extend the division of labor and make better use of
the available range of skilled personnel.9 On the other
hand, the wisdom of the substitution of auxiliary person—
nel for professional nurses has been questioned on the
grounds that the observed personnel ratios appear to be
economically inefficient when viewed in the light of pre—
vailing relative wage rates.10 Still another view ex-
plains the substitution of auxiliary personnel for

registered nurses as an attempt by hospitals to temper

 

9Dale L. Hiestand, "Research Into Manpower for
Health Service," The Milbank Memorial Fund Quarterly,
XLIV (October, 19665, p. 173.

lOMark s. Blumberg, "Men, Machines, and Hospitals,"
Hospital Progress, November, 1959, p. 72.

 

23

the rate of increase of hospital cost. However, this
strategy has evidently been self—defeating, for, in re-
ducing qualifications for certain positions, hospitals
have also reduced the flexibility with which these person-
nel can be used.ll’l2
The latter two views imply that hospitals are not
cost minimizers. It has been suggested that the increas-

ing ratios of auxiliary to professional nursing personnel

indicates a hospital preference for quantity over

 

llHerbert E. Klarman, The Economics of Health (New
York: Columbia University Press, 1965), pp. 123-2 .

12The importance of maintaining a flexible produc-
tive process (employing factors of production of the type
that can produce efficiently over a wide range of output)
arises from the fact that hospital average daily census
approximates a Poisson distribution [Commission on Hos-
pital Care, Hospital Care in the United States (New York:
The Commonwealth Fund, 19H77, p. 279].

Rather than being a "natural law" as is commonly
supposed, the Poisson distribution of average daily cen-
sus reflects a fundamental aspect of hospital behavior.

In a queue-theoretic perspective, the distribution of
units in process cannot be independent of the strategy
employed by the server. The appropriate queueing model
views the hospital as serving random arrivals requiring
randomly distributed service times; a Poisson distribu-
tion of units in process can be obtained only if units in
process is viewed as the relevant queue, i.e., if hospital
strategy is aimed at eliminating the probability of a
waiting line developing. Given this criteria upon which
capacity is determined, flexibility and adaptability is.a
necessary condition for economic efficiency over the wide
range of utilization encountered.

The alternative strategy, which would allow special-
.ization and division of labor, would be to schedule arriv-
vals to achieve a constant rate of utilization of facili-
ties. This could be accomplished through, e.g., delaying
elective admissions and interhospital shifting of admis-
sions.

 

24

"quality" in terms of personnel per patient.13 Only im—
pressionistic evidence has been brought to bear on the
question of efficiency of personnel utilization by hos-
pitals; meaningful inferences cannot be made in the
absence of information about the nature of technological
change in the production of nursing care as it relates to
changes in the elasticities of substitution of auxiliary
personnel for registered nurses. However, the data are
not inconsistent with the hypothesis that hospitals are
cost minimizers and that technical change has been of
such a nature as to allow them to extend specialization
and division of labor in the production of patient care.
From the evidence reviewed so far, it must be con-
cluded that there is little or no indication of an eco—
nomic shortage in the hospital market for nurses' ser-
vices. Wages appear to be responding in the manner
predicted by economic theory when demand increases rela-
tive to supply and forces are generated to bring the
market into equilibrium. The wages of hospital nurses
are increasing faster than the national trend of wages in
general, and have increased relative to other fields of
nursing. At the same time, the wages of auxiliary nursing
personnel are increasing at a faster rate. The rate of
increase in demand for nurses has apparently been tempered

by implicit upgrading of auxiliary nursing personnel and

 

13Hiestand, "Manpower for Health Services," p. 173.

25

transfer of some specialized nursing functions to other
occupational categories.

Before accepting the conclusion that there has not
been an economic shortage of nurses in hospitals, it is
necessary to examine the market for nurses' services for
signs of imperfections that would render movements in
wages inadequate as indicators of a shortage. If nurses
were immobile between labor markets, wage movements would
not serve their rationing function and therefore could not
be used as indicators of scarcity. Imperfections on the
demand side of the market which prevent wages from rising
to attract supply would also negate the usefulness of
wage movements as an indicator of a shortage.

Imperfections in the Market
for Nurses' Services

Donald Yett has advanced an hypothesis relating the
"shortage" of nurses to the monopsonistic position enjoyed
by hospitals in local labor markets.

the hospital sector of the market for nur-
ses is more monopsonistic than the other sectors.
In addition, the short-run supply and demand
curves for nurses are highly inelastic, and the
market reacts only slowly to changes in demand
relative to supply.

It is not surprising to find that hospital

administrators, facing a situation in which
salary competition produces no appreciable in-

increases in the number of nurses that can im-
mediately be employed, and possessing the power

26
to restrain such competition, have not been will-
ing to raise salaries.l

In addition, Yett has found evidence of wide-spread
collusion between hospitals in local labor markets to
prevent wage competition; he supposes this collusion to
be a response to inelasticity in the short-run supply of
nurses under which circumstances "hospital administrators
must be well aware of the futility of bidding against each
other for the local supply of nurses."15

Monopsony power within labor markets is made pos-
sible by impediments to the mobility of factors between
markets. When employers do not face competition from
outside of their local labor markets, they have consider—
able control over the wages they must pay; monopsony power
based on factor immobility implies that employers face
inelastic factor supply functions. Yett's position as I
have recounted it here is based essentially on his belief
that the supply function of nurses is highly inelastic.
This assumption, together with the evidence of collusion,
is used to rationalize perceived wage rigidities in the
presence of a "shortage."

While it is true that 65 per cent of the total num-

ber of registered nurses are married and might therefore

 

114Donald E. Yett, "An Analysis of the Causes and
Consequences of Salary Differentials in Nursing," Western
Economic Journal, V (December, 1966), p. 103.

 

15Donald E. Yett, "The Supply of Nurses: An Eco-
nomist's View," Hospital Progress, February, 1965, p. 100.

27

be immobile with respect to movement between labor mar-
kets for their own employment purposes, it is also true
that one—third of the total number of nurses, and A3 per
cent of the married nurses, do not practice nursing. It
is therefore improbable that immobility between markets
could be a factor making for inelasticity in the supply
function; large numbers of inactive nurses within markets
who would respond to economic incentives would make the
immobility argument inapplicable. The notoriously high
turnover rates of hospital nurses indicate that local
nurses are quite mobile with respect to the choice of
accepting or rejecting employment. A 1956 Public Health
Service survey of general hospitals revealed that the
average annual turnover rate among professional staff
nurses was 67 per cent.16
These facts suggest that the "shortage" is related
to hospital ability to induce nurses to remain employed
rather than ability to hire them initially. If collusion
exists between local hospitals to restrict wage competi-
tion between them, wages would be somewhat rigid; indi-
vidual hospitals would be reluctant to raise wages uni—
laterally. However, the collusion or oligopsony argument,
in the face of high turnover rates, has untenable impli-

cations for the rationality of the cartel. The objective

 

l6Eugene Levine, "Turnover Among Nursing Personnel
in General Hospitals," Hospitals, September 1, 1957,
p. 51. ‘

 

28

of a cartel is presumably to prevent turnover resulting
from wage competition between members; if the cartel is
effective, the observed turnover must be caused by fail-
ure of the cartel to respond to market forces, i.e.,
failure of the members to do collectively what each
wishes to do individually in response to shifts in the
market supply curve or increases in their needs for nur-
ses.

In conclusion, the "shortage" of nurses appears to
be a phenomenon of inadequate effective demand relative
to expressions of "need." Although hospital nursing
wages have been increasing rapidly, the high proportion
of the nurse force that is inactive, and high turnover
rates in hospitals indicate that many more nurses might
be willing to work if sufficient inducement were offered.

Although hospitals complain of a "shortage" of nurses

--..\

me .“_.~_._. ..... 1

they appear unwilling to offer adequate rewards to nurses

— “

 

.4“
My“: ball-Jar“ M. H.
pm“ w- -hw.‘_ ml“ ,

to keep them actively employed. Invocation of the collu-WM

sion or oligopsony argument to explain inadequate demand
in the face of such circumstances is not logically accept—
able. To provide further insight into the "shortage"
phenomenon, analysis must turn to the internal mechanisms
of the industry wherein the demand for nurses' services

is derived (see Chapter III). Before consideration of

the economic organization of the hospital industry is

undertaken in Chapter III, however, the responsiveness of

w-n
"C
I

29

the inactive portion of the nurse force to changes in
wage rates will be examined in the following section.
The Elasticity of Supply
of Nurses' Services

As the "shortage" of professional hospital nurses
has grown worse, attention has turned toward the large
number of trained nurses who are not actively engaged in
nursing.17 Investigators have tried to determine the
characteristics of this pool of inactive nurses in order
to find ways to attract them back into the active nurse.
force. Surveys of inactive nurses have "revealed" that
the primary factors.in their reluctance to re-enter the
work force include family responsibilities, poor working
conditions and inadequate opportunities for advancement
in hospitals, and lack of confidence in their abilities
to perform the required tasks. Results of questionnaire
surveys of inactive nurses show that the salary level in
hospital nursing is not an important factor in the deci-

sion to leave, or not to re-enter, nursing.18

 

17See, e.g., AMA Committee on Nursing, "285,000
Inactive Registered Nurses Could Turn the Tide," Journal
of the American Medical Association, Vol. 20, No. 9 (May

29, 19677: pp. 119720.

18For the results of several surveys of inactive
nurses, see I.Deutscher, "Keep Nurses in Nursing," Hospi—
tal Managemgnp, Vol. 86 (July, 1958), pp. AA-AS; A. E.
Barker and E. E. Staton, "Inactive Nurses: An Untapped
Recruitment Source," Public Health Reports, Vol. 80 (July,
1965), pp. 637-N5; J. Stacey, "RN's Tell Why They Took Off
Their6Caps," Modern Hospital, Vol. 108 (January, 1967),
pp. 7 -77. '

 

30

However, the apparent insignificance of the wage
variable should not be taken at face value. For the wage
level represents the cost to an inactive nurse of pursu-
ing other activities, and is the fulcrum upon which the
alternatives are balanced when the choice oflaction is
made. There is a wage that will draw every trained nurse
into the work force; that wage is the one which will make
nursing more attractive than any other alternative open
to the individual. When a respondent replies, "I chose
to stay at home and raise children rather than work in a
hospital because working conditions are poor," or "because
working leaves me no spare time to spend with my family,"
she in fact means "the wage rate is not high enough to
make nursing more attractive than the alternative activi-
ties I could pursue."

The results of various questionnaire surveys of
inactive nurses have led to the belief that the inactive
nurse force is not responsive to changes in wages. Yett's
hypothesis on the causes of the "shortage" discussed
above incorporates this assumption. However, the elastic-
ity of supply has never been estimated, the reason prob—
ably being that adequate data has not been available.

Some data now exist which may be adequate for esti-
mating the elasticity of supply. In renewing nursing

licenses, the Michigan Board of Nursing asks each appli-

cant to indicate her activity status and field of practice

31

at the time of her application for renewal of license.

In 1965, the MBN published data from applications re—
ceived during the period January 1, 1964 to December 31,
196”, showing the total number of licenses renewed during
the period by residents of each county in Michigan, their
indicated activity status, and their fields of practice.19
These data may be used to estimate the proportion of the
nurses licensed to practice in each county who were active
in 196“.

In July, 196“, the Michigan Nurses Association con-
ducted a wage survey of all hospitals in Michigan; the
data reported by each responding hospital were minimum
and maximum salaries paid to general duty professional
nurses at the time of the survey.20 These data can serve
as estimates of the average wage level for nurses pre-
vailing in each county during 1964. In a cross-sectional
study of the elasticity of supply, the estimated propor-
tion of licensed nurses in each county who were active in
196“ can be regressed on the estimated average wage rate
that prevailed in each county in 196A.

Estimation of the parameters of the supply function

from cross-sectional data must allow for differing income

 

19Michigan Board of Nursing, Annual Report 196u-65
(Lansing: Michigan Board of NursingY.

2OSalaryListings for General Duty Staff Nurses,
Michigan Nurses Association, August 6, 196A. (Mimeo-
graphed.)

32

levels between labor markets that cause shifts in the
supply curve in the wage-quantity plane between markets.
Differences in income levels between counties may be taken
into account by including as a regressor the average in-
come of each county. The latest information available on
income levels is that from the 1960 census, which provides
median family income by county. In using the 1960 census
data, it must be assumed that relative income levels
between counties did not change between 1960 and 196A.

In estimating the elasticity of supply with the
county data provided by MBN and the 1960 census, it was
necessary to include only those counties which could be
reasonably identified as distinct labor markets. Thus,
the Detroit area, for example, could not be used as an
observation because it was contained in three counties
which contained other labor markets. Of those counties
which were classified as distinct labor markets, several
were rejected because of inadequate or no response by
hospitals within them to the MNA wage survey. Forty of
the 83 Michigan counties were ultimately selected for the
sample.

Regressions were run using four alternative wage
rates reported in the MNA survey: the minimum of all
hospital wages reported in the county; the maximum re-
ported voluntary hospital wage; the minimum government

hospital wage, if higher than the maximum voluntary

33

hospital wage; and the maximum of all hospital wages re—
ported in the county. The latter wage variable gave the

best results, which were as follows:

A3 = 0.515130 + 0.0003913 wi — 0.0000118 Yi (1)
(0.0u6106 (0.0000772) (0.0000079)
R2 = .uioi
log A; = -o.5375 + 0.2728 log wi — 0.1ou1 log Y1 (2)
(0.2588) (0.0596) (0.0697)
R2 = .361u

where A: the number of nurses reported active in the
ith county in 196“ divided by the total number
of nurses who renewed their licenses in that
county during 196“;

W = the maximum hospital wage rate reported in the
ith county in July, 196A;

Y = the median family income of the ith county in
1960.

The standard errors of the regression coefficients
appear in parentheses below them. The wage coefficient
was significant at less than the 0.05 per cent level in
both regressions. It appears therefore that the maximum
hospital wage is a good proxy for the general nursing wage
level in the market or the wage to which the local nurse
force responds. The results show that a A per cent in-
crease in the wage level, on the average, produces about
a l per cent increase in the proportion of the licensed
nurses who are active.

In order to calculate the elasticity of supply from

these regression results, it is necessary to assume that

34

the total number of nurses in each county or labor market
remains static as wages are increased, i.e., that nurses
are perfectly immobile between markets. On this assump-
tion, the wage coefficient of regression (2) becomes the
elasticity of supply; the elasticity of supply calculated
from regression (l) using the wage coefficient and the
means of the observations on W1 and A; is 0.275”. If,
however, it is assumed that nurses are not immobile
between markets, the elasticity of supply will be greater
than indicated by the calculation above, for, as nurses
move into a labor market and become actively employed,
the numerator and denominator of A; both increase by the
same amount such that the increase in A; is less than if
the source of active nurses were solely the immobile
residents of market i. It may be concluded, therefore,
that 0.275“ is the lower bound of the elasticity of
supply of nurses in Michigan, the exact magnitude depend-
ing on the extent of movement of nurses between markets

in response to wage changes.

CHAPTER III

ECONOMIC STRUCTURE OF

THE HOSPITAL INDUSTRY

Profile of the Hospital Industry

 

Table 6 presents some data on the hospital industry
gathered by the American Hospital Association in 1966.
Hospitals are generally classified according to ownership
and type of service, but for statistical purposes the AHA
does not adhere strictly to this stratification. All
federal hospitals are lumped together because they are
maintained primarily for charges of the government. Most
non-federal long-term beds are in psychiatric and T.B.
hospitals controlled by state governments. The long—term
segment of the industry rivals the short—term only in num-
ber of beds and patient-days because long-term hospitals
are generally of a custodial nature and have relatively
little patient turnover. Of primary interest are the
short—term hospitals which dominate the labor market, and
dominate the product market in terms of the supply of hos-
pital services related to episodes of acute illness within

the population at large.

35

36

 

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cam opmum
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mm a: mm om mm mm m: Asusosa-gosv
asapcdao>
mw mm mu m: mm m: Hm Emmelphonm
ma ma NH a: m 2: ma enmeumsoq
Hammommucoz
ma :H OH HH m OH m Hahmumm
Rooa $QQH «OOH Rooa gooa Rooa Road Hmpoe
wwwmwm ”WWW” 32.823 Emmi 22322 as £33.21 mmmmwgmmm

 

.mmma .mppmsocfi Hmpfiomon on» mo maamooo Hmofipmflumpmnl.m mqm<9

37

The nation's short-term general hospitals are
organized under several types of ownership. The proprie-
tary hospital is a private enterprise owned by physicians
or lay investors and operated for profit. Accounting for
only 12 per cent of the total hospitals and 6 per cent of
the admissions, they are found mostly in sparsely p0pu-
lated rural areas, with a few heavy concentrations in
high-income areas with rapidly growing populations such
as Los Angeles and New York City.

The next largest group are the state and local
government hospitals, which accounted for 21 per cent of
the total hospitals and 20 per cent of the admissions in
1966. In sparsely populated areas, a local government
hospital may serve the entire community, while in heavily
populated areas they tend to serve mainly lower-income
groups.1

The dominate ownership type is the voluntary non-
profit corporation which in 1966 accounted for over one-
half of the total hospital admissions, personnel, and
expenses in the United States. Because the voluntary hos-
pital dominates the industry, and becuase of its peculiar
organizational characteristics, the discussion will center

on it.

 

.1Anne R. Sommers and Herman M. Sommers, Medicare and
the Hospitals (Washington, D.C.: The Brookings Institu-
tion, 1967): p- ”9.

 

 

38

The Voluntary Hospital:
Organizational Structure

 

Voluntary hospitals are organized as non-profit cor-
porations; while they are "private" undertakings in the
sense that they are not operated by, or accountable to,
government, they are of a quasi-public nature in that they
are presumably maintained to enhance the communities which
they serve. Historically founded upon a tradition of
charity, the voluntary hospital is losing its eleemosynary
character as government takes on more financial responsi-
bility for medical indigents, the poor and the aged, with
the result that voluntary hospitals expect to be paid for
their services. The changing character of the voluntary
institution is exemplified by its loss of charitable
immunity in many tax Jurisdictions.

The legal responsibility for the operation of the
hospital rests with a board of directors or trustees.
Management of the hospital is undertaken by an administra-
tor chosen by the trustees. The board of trustees is
legally responsible for the quality of the hospital's
medical care; it has the authority to appoint physicians
to the medical staff and otherwise designate the limits
of their practice within the hospital. However, the by-
laws of most voluntary institutions oblige the trustees
to follow the recommendations of the medical staff with
respect to appointments and privileges. Some hospitals

have "closed staffs" whereby only those physicians chosen

39

by the medical staff may admit patients, while others
have "open staffs" making staff membership available to
any licensed physician in the community. In larger com—
munities, doctors may have privileges in several hospi;
tals.

Figure 1 presents an organization chart of the
"typical" voluntary general hospital, in the sense that
the chart reflects principles of organization outlined by
the Joint Commission on Accreditation of Hospitals as
standards for hospital accreditation.2 The following dis-
cussion will highlight the organizational philosophy of
the JCAH in the context of the organizational chart.3

The governing body, in bearing the legal responsi-
bility for the quality of care produced in the hospital
must adopt a constitution and by-laws defining rules and
regulations under which the professional work of the hos-
pital is conducted.” In discharging its responsibility,
the governing body delegates authority to two groups.

First, the governing body must appoint "as its official

 

2American Hospital Association, Hospital Accredi-
tation References (Chicago: The Association, 19575.

3As will become evident, the traditional staff-line
organizational diagram is limited in its ability to repre-
sent hospital organization. The physician-patient rela-
tionship precludes administrative control of the medical
staff, which exists within the hospital as a separate
organizational entity with its own by-laws and regula-
tions.

“American Hospital Association, Model Constitution
and Bylaws for a Voluntary Hospital (Chicago: American
Hospital Association, 1957).

HO

representative" an administrator who "is responsible for
the conduct of the hospital, and provides liaison among
the governing body, the medical staff, the nursing staff,
and other departments of the hospital."5 The administra-
tor is "to work with the medical staff and with all those
concerned with the rendering of professional service to

the end that the best possible care may be rendered to

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

all the patients."6
Board of Chief of
Directors Staff
_ i-‘ -o‘ 1 ‘
Joint \\\ Executive
Conference ‘\ Committee
Committee ’
II I II [I
[Administrator Clinical
Services
I I _.I I
General Ancilliary Nursing
Controller Personnel Services Services Services

Figure l.--Voluntary hospital administrative organization
chart.
Second, the governing body "must obviously delegate
the responsibility of medical functions to the medical
staff" which "is responsible for the quality of medical

care rendered to patients in the hospital."7 The

 

5Accreditation References, p. 57.

6Model Bylaws, p. 21.

 

7Accreditation References, p. 57.

Ml

governing body

shall appoint a medical staff. . ., shall see
that they are organized into a responsible admin-
istrative unit, and adopt such bylaws, rules and
regulations for government of their practice in
the hospital as the [board] deems to be the
greatest benegit to the care of patients within
the hospital.

While the governing body officially makes appointments to
the medical staff, it should "in no case"9 make an appoint-
ment without the staff's recommendations "as to the pro-

fessional qualifications of all who practice in the hospi-

tal."10

In order to carry out its responsibility for the

quality of medical care "it is incumbent on every medical

11

staff to be self—appraising and self-regulatory." Thus

the medical staff must adopt its own bylaws which are in-

cluded as a bylaw of the governing body.12 An Executive

Committee is elected by the medical staff to

coordinate the activities and general policies of
the various [clinical] departments, act for the
staff as a whole under such limitations as may be
imposed by the staff, and receive and act upon
the reports of the medical records, tissue and
other such committees as the medical staff may
designate.l3

 

8Model Bylaws, p. 22.

 

9Accreditation References, p. 61.
10 ll

 

Ibid., p. 57. Ibid., p. 72.

12Model Bylaws, p. 7.

 

l3Accreditation References, p. 65.

42

In addition, the staff elects a Chief-of—Staff who is "re-
sponsible for the functioning of the clinical organization
of the hospital and shall keep or cause to be kept a care-
ful supervision over all clinical work done in the hospi-
tal."lu
The official Juncture of the lines of authority in
the hospital is the Joint Conference Committee, a "medico-
administrative liaison committee and the official point of
contact among the medical staff, the governing body, and

"15 In the organization chart of Figure

the administrator.
l, the board and the medical staff are connected through
the Joint conference committee by dotted rather than solid
lines. For ex-post of the adoption of the medical staff
bylaws by the board, staff members are not subject to line
authority as long as they do not exceed the bounds de-
fined by those bylaws:

In the case of the individual patient, the physi—

cian duly appointed to the medical staff shall

have full authority and responsibility for the

care of that patient subject only to such limita-

tions as the [board] may formally impose and to

the bylaws, rules and regulations for the megical

staff adopted by the staff and [the board].1
"Fundamental" regulations to be embodied in the medical
staff bylaws are provisions relating to staff organization
and meetings, staff privileges, maintainence of clinical

records, consultation and recording of diagnosis and

 

14
16

Ibid., p. 83. 15Ibid., pp. 65-66.

Model Bylaws, p. 22.

“3

physician's orders, examination of removed tissue, and
prohibitions against fee-splitting.l7
The physician is not an employee of the hospital,
but an invitee of the hospital who is granted practicing
privileges by its owners. However, only the physician can
admit patients, order diagnosis, and prescribe therapy;
the hospital, even though it is a separate legal and pro-
ducing entity, is singularly dependent on the physician.
In the formal organization of the hospital, the medical
staff is outside administrative lines of responsibility
and does not have direct-line authority. But by virtue of
their professional status and power to admit and prescribe,
medical staff members command a great deal of power within
the organization, and are subject to minimal lay-authority.
The ambiguous formal lines of authority make hospital
government a "series of accommodations and compromises"
among the trustees, the administration, and the medical
staff.18
With respect to his own patients, a physician's

authority is almost supreme; because of his professional

relationship with his patients, the physician is generally

 

l7Accreditation References, pp. 76-77.

l8Edith Lentz Hamilton, "The Voluntary Hospital in
America--Its Role, Economics, and Internal Structure," in
Medical Care, Readings in the Sociology of Medical Insti-
tutions, ed. by W. Richard Scott and Edmund H. Volkart
(New York: John Wiley and Sons, l966), p. 395.

 

 

uu

free to cross administrative lines of authority when his
patients' welfare is at stake. These multiple lines of
authority within the hospital create difficulties for
its employees. While nurses are the hospital's employees
and are thus accountable to the administrator, they are
also responsible for carrying out doctors' orders and are
thus responsible to them for the welfare of their patients.
But the physician is not an employee and is free to cross
administrative lines of authority to which the nurse is
subject. When administrative restrictions on the nurse
are opposed by the desires of the physician, the nurse is
often caught in the middle of a conflict between two power
groups to which she is subordinate.19
The physician's professional status and technical
indispensability makes the medical staff the most power-
ful group in the hospital; although they are not employees
and have no direct financial stake in the institution, the
physicians on the staff influence virtually all decisions
'affecting the basic functions and policies of the hospi-
tal. The organizational structure of the voluntary hos—
pital, and the physician's status within it, has several
implications for the "shortage" of nurses. The ability
of an organization to develop and pursue a consistent set

of objectives will be limited when it is required to

 

l9Hans D. Mauksh, "The Organization Context of Nurs—
ing Practice," in The Nursing Profession, ed. by Fred
Davis (New York: John Wiley and Sons, 1966), pp. 116—30.

“5

function with a tripartite division of authority that is
the traditional hallmark of the voluntary hospital organ-
izational structure. Moreover, the dependence of the
hospital on private practitioners given wide latitude to
pursue their own self-interest has direct implications
for intra—hospital allocation of resources and the cap-

ability of other hospital groups to pursue their goals.20

 

20The implications of the traditional autonomy of
the physician in hospital-physician relationships have
been widely discussed in the literature. Rapid techno-
logical progress and centralization of production of
health and related services within the community hospital
have rendered the persistent traditional organizational
form obsolete and incapable of meeting the growing public
demand for effective and efficient provision of services.
Although one can perceive an evolutionary trend toward
more rational and efficient organizational forms, the in—
evitable integration of the physician's role into the
overall structure of the centralized organization is not
being accomplished without resistance. Primary emphasis
is now being placed on adoption of modern management tech—
niques and professional administration, salaried physi-
cians in clinico-administrative positions and explicit
requirements for physician participation in hospital
affairs, and area—wide planning of hospital construction.
A representative bibliography includes: Anne R. Sommers
and Herman M. Sommers, Doctors, Patients, and Health In-
surance, pp. 51-55, and pp. 102-106} Herbert E. Klarman,
The Economics of Health, pp. 131—136; Secretary's Advis-
ory Committee on Hospital Effectiveness, Report; Charles
Perrow, "Hospitals: Technology, Structure, and Goals,"
in Handbook of Organizations, ed. by James G. March, pp.
910-971; Robert N. Wilson, "The Physician's Changing Hos-
pital Role," in Medical Care: Readings in the Sociology
of Medical Institutions, ed. by R. Scott and E. H. Vol-
kart, pp. H064H19; Douglas R. Brown, "A New Administra-
tive Model for Hospitals," Hospital Administration, Vol.
12, No. 1 (Winter, 1967), pp. 6-2“; William W. Jack, "The
Functions of the Chief of Staff," in The Medical Staff in
the Modern Hospital, ed. by Wesley C. Eisele, pp. 35-A2;
James B. Osbaldeston, "The Functions of the Medical Direc-
torj'in The Medical Staff and the Modern Hospital, ed. by
Wesley C. Eisele, pp. A3-A7.

 

 

 

H6

The Voluntary Hospital: Demand
for Factors of Production

 

To draw the implications of the physician-hospital
relationship and the voluntary hospital's organizational
structure with respect to its function as a producer of
goods and services, we may, for convenience, dichotomize
the components of hospital care or output according to
those with which the physician has an individual interest,
and those with which he does not. Accordingly, two broad
categories of products are produced within the hospital

framework: medical care, defined as those processes of

 

diagnosis and therapy with which the physician has a

direct interest, and patient care, defined as those pro-

 

cesses carried on by the hospital qua hospital for the
patients of all staff members alike. The inputs in the
production of the former would include diagnostic and
surgical facilities, while the latter would include "hotel"
facilities and the hospital's nursing service department.
Whereas the hospital provides homogeneous patient care to
the clients of each staff member, it must be equipped to
serve the needs of heterogeneous groups of physicians,

each of which produces a different medical care product.21

 

21Physicians can be certified by the American
Specialty Boards in 26 specialties and subspecialties.
Pursuit of certification is voluntary; failure of a phy-
sician to be certified therefore does not imply that he
is not a "specialist" in the sense that he restricts his
practice to a single field.

Within the hospital, the medical staff is organized
around clinical departments on the basis of medical

A7

While the foregoing dichotomy has been utilized in analy-
sis of the hospital as a social system,22 it is being
applied here to analyze resource allocation by distin—
guishing between classes of products and their respective
inputs according as the economic benefit of their produc-
tion or maintenance accrues to special groups or to all
groups alike within the hospital. Thus, while only spe-
cial groups will benefit from the hospital's purchase of
heart-lung machines and electroencephalographs for pro-
ducing medical care, they are all assumed to benefit
equally from the hospital's maintenance of secretarial,
laundry, dietary, or nursing care facilities.

Given the community's demands for various "packages"
of hospital services (i.e., medical plus patient care for
management of various conditions) which determine the
budget constraints on its ability to produce care, the
hospital must establish priorities for allocation of re—
sources for their production; in terms of the dichotomy

established above, the hospital must determine the compo-

sition of hospital care according to the relative

 

specialties, and each physician works under the rules of
a particular department according to the practicing pri-
vileges granted him by the medical staff. The following
clinical departments are commonly found in most medium—
sized short-term general hospitals: Anesthesiology;
Pathology; Radiology; General Practice; Obstetrics and
Gynecology; Pediatrics; Internal Medicine; General Sur-
gery; and Surgical Specialty.

22See e.g., Mauksh, "Organization Context of Nurs—
ing Practice," p. 112.

M8

proportions of medical and patient care in its total out-
put. Due to the peculiarities of the market for hospital
care, consumer preferences play a secondary role in deter-
mining the composition of hospital output.23 Producing
in monopolistic markets, physicians and hospitals face
demands from consumers who are not technically competent
to evaluate the services they receive, or make marginal
decisions between alternative components of treatment.
Within wide bounds, composition of output is subject to
discretionary determination within the hospital; in the
market for hospital services, the hospital itself can be
viewed as the consumer or the arbiter of relative values
of output components.

The decision process of the voluntary hospital in-
volves three groups--the trustees, the administration,
and the medical staff--each of which may be motivated to
pursue diverse and conflicting objectives. The ordering
of alternatives obtained in their decision process will
reflect the personal objectives and professional opinions
of the individuals in each group. The outcome of the
decision, reflected in the hospital's composition of out-

put, will be determined by the preferences of each group

 

23Fordiscussion of the role of the consumer in the
market for medical services, see: Herbert E. Klarman,
The Economics of Health (New York: Columbia University
Press, 1965), pp. 10-19; Jerome Rothenberg, "Welfare Im-
plications of Alternative Methods of Financing Medical
Care," American Economic Review: Papers and Proceedings,
XLI (May, 1951), pp.3676-87.

 

"9

for alternative types of expenditure relative to their
power in the decision process. When the allocatory deci-
sion results in a ranking of priorities and a structure
of expenditure that is consistent with the preferences of
some but inconsistent with the desires of the other
groups in the hospital, the latter will be in disequili-
brium with respect to their "needs" for resources.

In hospitals with staffing arrangements that stress
the entrepreneurial role of the individual physician and
allow the medical staff to dominate the decision process,
the composition of output may be weighted in favor of
medical care components of hospital care at the expense
of patient care components. "Shortages" of resources for
the production of patient care would appear, reflecting
differential evaluation of those services by the various
factions of the decision—making body and unresolved con-
flicts in an environment of limited resources.2Ll

This analysis has implications not only for the de-
mand for nurses' services but for the supply as well.

For, if a hospital does not allocate sufficient funds to

 

2“It is interesting to observe that, while one hears
a great deal about "shortages" of nurses and other health
manpower, one also hears a great deal about underutilized
facilities and wasteful duplication of diagnostic and
therapeutic equipment between hospitals. For a discus—
sion of uneconomic use of capital by hospitals, see
Millard F. Long, "Efficient Use of Hospitals," in The
Economics of Health and Medical Care (Ann Arbor: Bureau
of Public Health Economics and Department of Economics,
University of Michigan, 1964), pp. 211-26.

50

provide the level of nursing care consistent with nurses'
professional standards or desires, the implied working
environment may affect the supply of nurses to that hos-
pital. The next chapter will develop the analysis in
terms of a formal theoretical model of the demand and
supply of hospital nurses' services. The analysis will
be restricted to the short-run whereby the stock of nur-
ses will be assumed fixed during the time period under

consideration.

CHAPTER IV

THE ANALYTICAL FRAMEWORK

In this chapter will be developed a formal model of
the demand and supply of hospital nurses' services. The
approach taken will view the hospital as an autonomously
reacting, multi-product, multi-factor firm-~an entity com-
bining inputs hired in factor markets in accordance with
a specific technology to produce outputs subject to a
budget constraint—-operated to optimize an objective func-
tion derived in an n—person decision process. The analy-
sis will proceed in a step-wise consideration of the vari—
ous elements in a model of the firm. The first element of
the construct to be derived will be the set of demand
functions for hospital output. The focal point of this
derivation will be the physician's economic behavior, for,
by virtue of his unique relationship to the consumer of
hospital services, his behavior is a primary determinant
of the demand for those services.

The demand for nurses' services will then be derived
from the demand for hospital services. However, the
mechanism which connects these two demands is not the

usual one postulated in the classical theory of the firm;

51

52

in this case the firm's behavior is not directed at maxi-
mizing a single-valued objective function so it cannot be
viewed as a passive reactor to forces originating from
the factor and product markets. Rather, analysis of the
hospital's supply of output and demands for factors of
production must consider its institutional structure
wherein objectives are formulated and productive decisions
are made with respect to the types and quantities of out—
puts that are produced. The institutional structure in-
vites the use of a total utility model of the decision
process. Under the assumption that the decision process
is such that a complete ordering over the firm's oppor-
tunity set is attained, the differential results of sev-
eral alternative general decision criteria will be in-
vestigated within the utility-maximization construction.
Next, the supply function of nurses' services will
be derived. Derivation of the firm's utility function
implies a complete specification of the product in terms
of the technical relationships between inputs and outputs.
Due to the discretionary nature of the decision process,
however, no unique product specification can be assumed
to exist. To develop the implications of differential
product specification between hospitals for the supply
function of nurses' services, working condition arguments
will be included in the individual's utility function in

addition to the traditional income and leisure variables.

53

Inclusion of the supply function of nurses' services
in the model allows solution of the system for optimality
of factor combination in production. The solution is
obtained by assuming that the nursing service department
maximizes output subject to a budget constraint determined
by the utility-maximizing allocation of funds yielded in
the hospital decision process. While the step—wise
approach abstracts somewhat from the simultaneous nature
of the solution, it provides the basis for the empirical
strategy developed in the following chapter.

Throughout the analysis it will be assumed that the
second order conditions insuring a relative maximum rather
than a minimum, or the converse when appropriate, are
satisfied. While this assumption is explicit in the pos-
tulate that the economic units in question behave so as
to optimize within the constraints facing them, that pos-
tulate also implies that economic units seek the optimum

optimorum. Thus it is also assumed throughout that con-

 

ditions for a global optimum are satisfied.
The Demand for Hospital Nurses

The Role of the Physician
Because the services of nurses are but one input in
the production of hospital care (as defined in the pre-
vious chapter), it is necessary to examine the product

market for hospital services in order to derive the demand

5“

function for nurses. To establish a framework for analy—
sis, we will view the physician as the organizer or coor-
dinator of production of hospital care. Within the con-
straints imposed by the availability of facilities and
the patient's willingness to pay and cooperate, the physi-
cian determines the particular combination of goods and
services that will be employed in the management of a
given medical condition. Although his services are but
one input in the production function of hospital care, his
rendering service is a prior condition for the existence
of demands for the other inputs with which this discussion
is concerned; the patient may become a consumer of hospi—
tal services only at the direction of a physician. Con-
sequently, analysis must begin by focusing on the physi-
cian's methods of organizing or utilizing other factors of
production to satisfy the demand for hospital services.
The purchase of a visit to the physician can be re-
garded as the purchase of information regarding the state
of one's health. The physician may make a diagnosis and
prescribe various treatments for a given medical condi-
tion. After a diagnosis is made, the patient and the
physician jointly determine the demand for additional ser-
vices according to the patient's willingness to pay, the
information provided by the physician, and the availabil—

ity of facilities in the community.

55

In a community of given size with given incidence
and prevalence of illness,1 there will exist some distri-
bution of illnesses each of which may be treated by a
variety of methods. Given the community income distribu-
tion, there will exist a set of demand functions for dif-
ferent services facing the physician per units of time.
Within the constraint imposed by his ability, the physi-
cian may choose to combine his labor with the services of
other inputs to produce diagnoses and treatments in any
combination and amount he desires. We will assume that
the physician's behavior is such that he acts to maximize
his utility, which is a function of income (Y) and leisure
(L):2

U = U(Y, L). (1)

We will define work as any rendering of medical ser-

vices that generates pecuniary income, and we will assume

 

1In the terminology of Epidemiology, the incidence
rate is a measure of the new cases of a disease in a pOpu—
lation, and the prevalence rate is a measure of all cases
current in a population, as a proportion of the population
per unit time. See John Knowelden and Ian Taylor, Princi-
ples of Epidemiology (Boston: Little, Brown and Co.,
1964), pp: 54-56.

 

 

 

2As general purchasing power over desired goods and
services, income affects utility indirectly. Let the
individual's utility be a function of his consumption of
goods and services G1, i=l,...,n, and his consumption of
leisure: U = U*(Gi, L). His budget constraint is given
'by Y = ZiPiGi where P1 is the price of the ith good or
service, so that his consumption of goods and services
are given by G1 = f1(Pi, Y). Substitution of the latter
functions into the utility function gives U = U*[f1(P1,Y),
L], which becomes U = U(Y, L) if the individual is
assumed to face constant prices in the market.

56

that the sole source of pecuniary income is work. Lei—
sure, accordingly, encompasses all other activity of the
physician, e.g., mowing his yard or providing free medi-
cal services. We are therefore concerned, not with the
temporal distribution of leisure and work within a given
time period, but with the total amount of leisure consumed
or work supplied during the period. If T is the total
time available per period, and H is the amount of time

worked,
L = T—H. (2)

The physician's income is the net revenue he earns
per period, the product of the average net revenue earned
per unit of working time and the total amount of time
worked per period. If R is the average revenue from the
sale of services per unit time, and g is the average cost

of production per unit time,

Y = H(R-C), (3)
where R = R(Xi)’ i=1,...,m (A)
x1 are services
and c = C(23), j=l,...,n (5)
z are inputs.

By substitution of (2), (3), (A), and (5), the

utility function becomes

57

C:
II

U{T-H, H[R(xi)-C(z )J}

J

V(xi, Zj’ H). (6)

The physician must choose the optimal quantities of the

xi, the zJ, and H such that his utility, U, is a maximum.
Intuitively, the argument is as follows. In Figure

2, income (Y) and work (H) per period are measured on the

vertical and horizontal axis, respectively. The physi—

cian's iso-utility loci, U, are convex to the horizontal

reflecting diminishing marginal utility to both income

and leisure. Within the relevant range, an increase in

net earnings for any given amount of time worked will re-

sult in an increased level of satisfaction. The further

an indifference curve lies from the origin, the higher is

the level of utility: U3>U2>Ul. There is an income func-

tion H(R-C) for each combination of services that can be

provided; they will be concave to the horizontal insofar

as the demand functions for services are negatively

sloped. Due to differentials in demand and cost for alter—

native services, however, they need not be non-intersecting.

To maximize utility, the physician must choose the optimal

combination of services, techniques, and work time that

puts him on the highest possible indifference curve. For

the preference pattern and alternatives represented in

Figure 2, the individual in equilibrium will produce the

combination of services that generates income function

58

H(R-C)", will work H* hours per period, and will make an

income of Y*.

      
 

 

 

YA
U3
H(R—C)"
H(R—C)‘
Y*---——-«- INR-C)
‘—>H

H*

Figure 2.--Determination of the optimal combination of
inputs, outputs, income and leisure.

Analytically, the xi, the Ed’ and H must be chosen
such that (6) is maximized. The necessary condition for

(6) to be a maximum is that V = V = V

l 2
the first partial derivative of V with respect to the k

3 = o, where Vk is
th

argument. Thus we must have

Vl = UY(5Y/5X1) = 0, i=1, .,m (7)
V2 = UY(6Y/6zj) = 0, j=1, ,n (8)
and V3 = UY(6Y/6H) - UL = 0. (9)

59

The solutions of (7), (8), and (9) will yield the Optimum
number and quantities of inputs and outputs, including
time worked, that maximizes the physician's utility.
Because H is a common input to all outputs, for any
given level of H it is impossible to increase any one
output without decreasing others. We therefore write the

factor-product transformation function in implicit form as

Q(zj, Xi) = 0, :%,...,m (10)

Since for any given set of factors H = [21...zn] there
will be a number of feasible sets of products, we can
assure a single-valued production function by assigning
arbitrary values to H2; products and determining the larg—
est value of the remaining product consistent with equa-
tion (10). I

To find the optimal combination of outputs H* =
[x*...x$] we must write cost as a function of output, C =

C(Xi)’ i=1,...,m, so that the income function becomes

Y = H[R(xi)-C(Xi)]
whence dY/dxi = H{(6R/6xi)—(GC/6xi) —

zrfll[(5R/5xr)—(50/axr)]}
rfii

so that the solution 0f equations (7) for any two outputs,

g and E, is

dY/dxs = (BY/6xt , s,t = l,...,m. (11)

60

Equation (11) shows that the optimal mix of outputs Hf is
obtained when the marginal rates of net return from pro-
ducing all outputs are equal.

To find the optimal combination of inputs Hf =

[zi...z:] we write the income function as

Y = H[R(x1)-C(z )]

J

whence GY/dz = H[21(6R/6x1)(6xi/62

J )- (CC/OZ

)]

J J

so that the solution of (8) for any input with respect to

any output is

60/62 = (GR/dxi)(6xi/Gz

J

j)' 5 (12)

Equation (12) shows that optimality requires the marginal
factor cost of any input to be equal to its marginal reve-
nue product with respect to any output, i.e., optimality
requires that inputs be combined in least-cost proportions
to produce any chosen combination of outputs.

To find the optimal conbination of income and lei-
sure, or the optimal amount of work, we solve equation (9)

and obtain

UL/UY = dY/GH. (13)

Equation (13) states that the Optimal amount of work is
obtained when the marginal rate of substitution of income
for leisure is equal to the rate of change of income from

an additional unit of work.

61

The general results of the analysis are as follows.
As long as the physician's utility function contains only
the arguments income and leisure, or as long as inputs and
outputs are valued only for their contribution to income,
the equilibrium solution will result in the least—cost
combination of inputs being employed for the mix of out-
puts produced, and that mix of outputs will be the one
which yields maximum net income for any given amount of

time worked.

The Supply of Hospital Services

Suppose that some of the demands facing the physi-
cian are for services requiring hospital facilities. In
such a situation, the physician faces the decision of
whether or not to meet those demands by hiring the neces-
sary inputs to produce those services. According to the
behaviorial assumptions of the preceding analysis, he will
undertake to supply those services only if, by so doing,
he can increase his utility, i.e., if the inclusion of
hospital-related services in his income function will
allow him to reach a higher indifference curve in Figure

2.

The Physician-Owned Hospital
In any given situation, the physician may or may not
face the alternative of utilizing existing hospital facili-

ties. Irrespective of this, however, he will provide his

62

own facility if the marginal utility of doing so exceeds
the marginal utility of proceeding with any other alter-
native. For example, consider the polar case of a single
physician in a community with no hospital. If the demands
and costs of hospital-related services are such that the
physician can undertake production of some combination of
these services and increase his income for any given
amount of work effort (or decrease work effort for any
given amount of income), he will do so. Alternatively,
consider the opposite extreme of many physicians in a
community with pre-existing hospital facilities. Like-
wise, they will undertake to provide their own facility,
either singly or jointly, if they can improve their wel—
fare by so doing. In any case, then, if the hospital is
maintained by the physician(s) for the purpose of enhanc-
ing his(their) utility, the demand for inputs follows
from the first—order optimality conditions of equations
(8) and (12). The physician-entrepreneur, in response to
market demand, combines the services of hired factors of
production with his own services to produce the most lucra—
tive set of outputs. Since its function from this point
of View is solely to improve the physician's welfare by
generating income, the physician-owned hospital is oper-

ated to maximize a single-goal objective function.

63

The Community Hospital

 

The community may find it more desirable to provide
itself with hospital facilities than to rely on the pri-
vate enterprise of physicians or others to do so. If a
hospital is provided by the community, physicians may
find it more desirable to use its facilities than to pro-
vide their own.

When the hospital is maintained independently of
the physician, its services may be viewed as intermediate
goods which the physician utilizes in his own productive
process, or alternatively, they may be viewed as final
goods consumed by the patient under the direction of the
physician. Both approaches point to the fact that in
this situation the composition of the hospital's output,
and its demand for factors of production, cannot be de-
rived only from a hypothesis on the behavior of the physi-
cian. Whereas the objective function of the physician-
owned proprietary form was easily derived from the entre-
preneur--utility-maximization hypothesis on the role of
the physician, the objective function of the non-profit
voluntary or publically financed form of organization
cannot be derived from the behavior of any single or homo-
geneous group of individuals.

We may suppose that a non-profit hospital exists in
a community and that it is controlled by a group of indi-

viduals charged with the responsibility of supervising its

64

Operations and the allocation of its funds toward the pro—
vision of various services to meet the needs of the inhab-
itants of the community. These individuals, together with
their administration and medical staff, will be responsi—
ble for determining the volume and composition of the hos-
pital's output.

Each individual involved in the hospital's decision
process3 will have a utility index ranking his preferences
for expenditure according to the amount of satisfaction
each item or class of items gives him. If H1, i=1,...,m,
are alternative hospital services or modes of expenditure,

then each individual 2, p=l,...,P, will have a utility

function denoted by

U =U x.
p 19(1)

The utility functions of the H individuals will be amal-
gamated through the mechanism of the decision process to
yield a utility function for the hospital, or the group
as a whole, ranking the overall expenditure preference

and denoted by

<
ll

V(Up), p=l,...,P

W(Xi), i=1,...,m. (1A)

 

3The term "decision process" as used here is not
restricted to description of a formal procedure, but in-
cludes all activity, formal and informal, that influences
and determines the final decision.

65

It cannot be supposed that all H individuals have
identical utility functions or identical orderings of
alternatives. By virtue of his particular motivation,
each may be assumed to favor a particular class of
expenditure at the exclusion or restriction of others.
Consequently, it is possible that the decision mechanism
may not yield a consistently ordered preference function
for the hospital; when the H individuals do not rank al-
ternatives in the same order, there is no presumption
that the group decision will be transitive under any type
of "democratic" decision process. Let us assume, however,
that the decision process is such that differential in-
fluence of individuals in the group, as well as intensity
of individual preference, is allowed for. In other words,
it will be assumed that the partial derivative of (1A).
with respect to any Hi does in fact represent the margi-

nal utility of the H to the hospital:

1

(SV/CSXi = Zp(6V/6Up)(6Up/6Xi) (15)

where 0V/6Up is the weight or influence of the pthindivid-

ual in the group's decision and (SUP/(8Xi is the intensity of

th th

the p individual's preference for the i mode of expen—

diture.“

 

”Thus it is assumed that the hospital can be treated
as a singular entity wherein the decision making groups
have achieved a complete ordering over their alternatives.
For each hospital, therefore, the utility function (lb)
gives a complete ordering of alternative services or

66

In a community of given size, income distribution,
prevalence of illness, etc., the hospital will face a set
of patient—physician determined demand functions for
various hospital related services, Hi, per unit time.

Let H be a vector representing the supply of hospital
services; then each possible situation is represented by

a vector H = [X ...Xm]. The hospital must choose the

i
optimal vector H* that maximizes its utility, subject to
the economic constraints imposed by the demand for ser-
vices and the supply of factors of production. Since
economic profit is not a goal of the non—profit hospi-
tal, it will be assumed that output is extended to the
point where economic rent is zero, i.e., where total cost
equals total revenue.

The following relationships are used in the analy-

sis:
F(Xi, 23) = O, the production function,
where Xi =l,...,m) are services

ZJ (j=1,...,n) are inputs;

 

outputs in terms of not only the parameters that differ-
entiate classes of outputs but also the parameters that
define quality differences within classes of outputs;
i.e., determination of (1A) completely specifies the pro-
duction relationships for each alternative output Hi.
Equation (15) in turn implies that observed differences

in product specifications in terms of input-output rela-
tionships between hospitals may be rationalized by identi-
fying the preferences of the dominate group(S) in the
power structure.

67

P1 = P1(Xi)’ the demand for service H,

where Pi is the price of H;

R = XiPiXi = R(Xi), total revenue;

wJ = wJ(Zj), the supply of factor j,

where w

—j is the wage of l;

C = ZJwJZj,

total cost.
The production function H defines an isoquant in
the H—dimensional factor space for any given set of ser-

vices H. For given X = H (i=1,...,m), minimizing the

i i

Lagrangian function

L = ZJWJZJ + AF

gives the first—order conditions for least-cost factor

combination

and C' + AF' = O. (16)

For parametric H, the locus of least-cost points deter-

mines the expansion path which, in determining the Zj as
functions of the H, transforms the total cost expression
into a function of the Hi:

C = Z w ZJ = Z WJEZJ(X1)]'Z

J J J (X1) = C(Xi). (17)

J

At any point on the expansion path satisfying the

production function and condition (16), we have

68

dC = Z 'dZ = -A2 F' = A2 F'dX
101;) .13 iii

so that AFi is the partial marginal cost of producing ser-

vice H along the expansion path:

Ci = AF;; (18)

and the Lagrangian multiplier A = dC/ZiFidXi is the total
marginal cost along the expansion path.

It might be supposed that the governing body of the
hospital would wish to make each of the outputs Hi (i=1,
...,m) "as large as possible." Clearly, this problem is
not well defined. For, as the production function shows,
the outputs are interdependent; if there is no excess
capacity in the fixed factors, one of the outputs cannot
be increased without a reduction of others. In this case,
the output vectors H cannot be ordered unless weights are
introduced to define the relative importance of each of
their components.

In the case of the multi-product, profit-maximizing
firm, each product is weighted according to its contribu-
tion to net revenue, and output levels of each are chosen
so as to maximize the difference between total revenue
and total cost. However, this criterion cannot be applied
to the multi-product, non—profit firm; weights must be
assigned according to some other objective criterion, or

otherwise according to subjective evaluation of the rela-

tive desirability of alternative products. The general

69

case of the subjective selection process will be con-
sidered in the Utility Maximization Model below. But in
order to establish a base for comparison, we will first
consider the only objective selection criterion that is
meaningful in this situation: maximization of output

valued at factor cost.

Output Maximization Model

Maximization of output valued at factor cost by the
multi-product firm is analagous to the case of the single-
product firm that wishes to extend its output along its
total cost function to the point where total revenue
equals total cost, except that in the case of the multi—
product firm, the composition of output is also subject
to decision. By virtue of the interdependence of products
in production, there are an infinite number of possible
pairs of total cost and revenue functions, rather than
the single pair faced by the single-product firm. Thus
the multi-product firm must choose the optimal pair of
functions along which to operate.

Having derived the least-cost vector of inputs for
any given vector of services from the H equations of con-
dition (l6), and the cost function in terms of parametric
vectors of services, equation (17), we now wish to maxi-
mize output valued at factor cost subject to the con-
straint that total revenue equals total cost, i.e., we

wish to pick H1 (i=1,...,m) in order to

7O
maximize: C = C(Xi)

subject to: R(Xi) = C(Xi)°

Maximizing the Lagrangian L = C(Xi) + u[R(Xi) - C(Xi)]

gives the necessary first order conditions

and Ci + u(Ri — Ci) = 0. (19)

From equations (19), the following equivalent rela-

tionships are derived:

Ri = 01(1 — 1/u), (20)

which shows that optimality requires all services to be
produced in the region where their partial marginal cost

exceeds their partial marginal revenue;

Ré/Cé = Ré/Cé (s,t = l,...,m), (21)

which shows that the optimal mix of services is attained

when they are produced in quantities such that the ratios
of marginal revenue to marginal cost are equalized in all
product directions. It is instructive to note that this

is the same optimality condition that holds for a profit

maximizing producer, except that in this case the ratios

of marginal revenue to marginal cost are less than unity,
reflecting the extension of output beyond the profit—

maximizing point.

71

Finally, substituting Ci = lFi from equation (18)

into (19) gives

Ré/Ré = Fé/Fé (s,t = l,...,m), (22)

which shows that when the optimal mix of services is being
produced, the ratio of marginal revenues for any pair of
services must be equal to their rate of product trans-
formation.

We may now consider a situation where the hospital
receives a gift or grant of funds which will enable it to
extend production past the point where total cost equals
total revenue. Suppose that some amount of money, H, is

given to the hospital; the budget constraint becomes

R(Xi) + K = C(Xi).

Upon taking derivatives in the maximization operation, the
constant H drops out, so that the necessary conditions
(19) are undisturbed. It therefore follows that so long
as gifts are exogenous to the operations of the hospital,
the equilibrium expressions (20), (21), and (22) remain

valid.

Utility Maximization Model

Let us now turn to consideration of the decision
process implied by the derivation of the utility function
for the hospital, equation (14). According to that deriva—

tion, all the individuals influencing the decision need

72

not be motivated toward pursuit of a common goal as
assumed in the Output Maximization Model above. Rather,
they may have conflicting ideas about the optimal policy
to pursue, or they may be motivated by self-interest to
favor certain classes of expenditure over others. Con-
sequently, the amalgamation of the individual utility
functions in the decision process of the hospital's
governing body may not result in each output or service
being weighted by its potential contribution to the
attainment of a single goal, but rather by its potential
contribution to attainment of a number of (possibly con—
flicting) goals. The ultimate solution, constrained by
limited availability of resources and reflecting the
results of bargaining, coalition, and compromise between
the individuals involved, will be a subjective ordering
of alternatives for the group as a whole.

We have assumed that the ordering is transitive and
that it can be represented as a functional relationship
in equation (1A). We now wish to find the optimal combi-
nation Of services that maximizes the hospital's utility
subject to the constraint that total revenue equal total

cost, i.e., to pick H (i=1,...,m) in order to

i

maximize: W(Xi)

subject to: R(Xi) = C(Xi)'

73

Maximizing the Lagrangian L = W(Xi) + u[R(Xfi)- C(Xi)]
gives the necessary first—order conditions for maximum

utility

R(Xi) - C(Xi) = O
and Wi + u(Ri — Ci) = O. (23)

From equations (23), the following relationships

are derived by algebraic manipulation:

and W = W (s,t = l,...,m) (25)
S S

From (2“) and (25) we see that the larger (smaller)
is the marginal utility of any one output, the greater
(lesser) is the amount of it that will be produced. In
equilibrium, the output of lesser-valued services will be
restricted in order to provide surplus revenue to allow
extension of production of more favored outputs into the
region of absolute loss.

The Output Maximization Model is a special case of
the Utility Maximization Model. The solutions of the two
models are equivalent only if the utility of all outputs
are directly proportional to their values at factor cost.

If this is the case, the utility function becomes

7A
V = W[C(Xi)]
and the results of the Output Maximization Model follow.

Budget Allocation Model

In order to give the model some empirical substance,
it will be useful to rephrase the Utility Maximization
Model in terms of the budgeting process by which the
governing body allocates scarce funds to competing groups
within the hospital. The budgeting process can be viewed
as the vehicle through which the utility functions of the
various individuals concerned are amalgamated to produce
the utility function for the hospital, equation (1“). As
the allocation and coordinating mechanism of the hospital,
the budgeting process resolves conflicts between propo-
nents of various organizational goals to produce the ex-
penditure preference function for the group as a whole,
and the equilibrium budget reflects the optimal allocation
of funds between departments with respect to that prefer—
ence function.

By developing the model in these terms, each depart-
ment can be analyzed separately ex post of the determina-
tion of the budget. Once the governing body has deter-
mined the equilibrium allocation of funds, the budget
constraint on each department is established; thus, in
order to derive the demand for nurses, we may assume that

the budget for the Nursing Service Department has been

75

determined and confine our attention to that department
alone.

Suppose that the hospital anticipates a demand of
some amount HO for nursing service during the period, and
that it budgets an amount of funds equal to H for the
department's operation during the period. The director
of nursing must employ factors of production to produce
HO for a total outlay of less than or equal to H. If
the production function or the supply of factors is such
that HO cannot be produced for the given amount H, either
H must be increased or the quantity or quality of nursing
service (N) must be reduced.

The problem facing the director of nursing is to
find that combination of inputs which minimizes cost for
the desired output, or equivalently, which maximizes out-
put for the amount of funds available. Let the inputs be
represented by HJ (j=1,...,n) so that the production func-
tion for nursing service may be written N = N(ZJ). Total

cost is C = 2 w Z = C(Z ), where Ed is the wage of factor

J J J J
H. We wish to pick the Ed in order to
maximize: N = N(ZJ)
subject to: C = K.
Maximizing the Lagrangian function L = N(ZJ) + AEK —
C(23)] gives the necessary first-order conditions for max—

imum output

K - C(Z ) = O

J

and N5 - AC3 = 0. (26)

From equations (26), we see that factors must be
employed in quantities such that Nj/Cj is equalized for
all H, i.e., factors must be employed in such proportions
that the ratios of marginal product to marginal cost are
equalized in all input directions.

The Supply of Nurses and
Optimality ofHProduction

In the Budget Allocation Model above, the demand for
hospital nurses was derived under the assumption that the
nursing-service department is given a budget constraint
determined by the governing body of the hospital, and
attempts to maximize output subject to this cost con-
straint, the production function, and the supply functions
of the factors of production. In deriving the Optimality
conditions for factor employment, we made the assumptions
that (l) the supplies of all factors are functions of
price, and that (2) the production function for nursing
service is a relationship given to the organizer of pro-
duction and determined by purely technical considerations.
We now turn to consideration of these assumptions and
their implications for the analysis.

While the first assumption holds for non-human in—

puts, it can not strictly be applied to labor inputs.

77

For, in the case of human factors of production, "employ-
ers are sellers of conditions of work as well as buyers
of labor."5 Working conditions are partially embodied in
the technical relationship between inputs and output
given by the production function. Each possible factor
combination yields a distinct set of working conditions
under which the human factors must operate. When working
conditions are a variable in the supply function of a
labor input, the supply of that input will not be inde~
pendent of the particular input combination chosen; the
firm will face a family of labor supply functions, one
function for each set of working conditions implied by
each possible combination of factors employed.

According to the second assumption, we have viewed
the production function for nursing service as a descrip-
tion of a well—defined productive process in terms of the
specified inputs. We have discussed output in terms of
a single dimension-—quantity--implicitly specifying pro-
duct quality as a parameter in the model; the production
function has been defined as a functional relationship
between inputs and output that represents a satisfactory
level of quality to the producer. While the technology
of production is given to the producer, product quality
is a parameter of action which he can vary by changing

the intensity of factor application to a given number of

 

5Milton Friedman, Price Theory (Chicago: Aldine
Publishing Company, 1962), p._205.

 

78

patients with given characteristics. Within the same
technology, a varying range of quality levels can be pro-
duced by using more of some or all inputs for the same
quantity of output.

In the case of nurses or other "professional" per-
sonnel, the human inputs may have a conception of the
productive process with respect to the quality parameter
different from that held by the employer or manager of
the organization. When there is a difference of opinion
about the "correct" production function, the supply of
professional services will be a function of this diver-
gence as well as of the wage rate and the factor propor-
tions utilized in production. A nurse's education and
professional experience provide her with specific ideas
about her function and the related roles of other inputs
in the production of patient care. If she is hired by an
employer who does not share her views on "Optimal" patient
care or does not allow her to practice according to her
professional standards, a conflict will result. In order
to maintain her services, the employer will have to make

an adjustment in the wage rate or in working conditions.

The Supply of Nurses' Services
To derive the supply function of nurses' services

under the assumption that working conditions as well as

79

the wage rate are included as arguments, we write the

utility function of the individual as
U = U(L,Y,A) (27)

where H is liesure, H is income, and H is a parameter
representing working conditions in the particular insti-
tution where income is earned. Income is the wage rate

E multiplied by the amount of time worked, H:
Y = wH. (28)

If leisure is defined as that part of total time, H, per

period not spent working for a wage, then
L = T-H. (29)

We will assume that the utility associated with
working conditions is a function of a vector H of techni-
cal magnitudes utilized by the hospital in its production
of nursing care. We will specify the utility of working
conditions as a decreasing function of the parameter H;
treating working conditions as given to an individual

employed in a given institution, we have
A = A(N) = K (30)
and OU/OA < 0.

By substitution of (28), (29), and (30) into (27),

the utility function becomes

U = U(T-H, wH)] _ . (31)
A=A

80

To maximize utility, we set the derivative of H with re-

spect to H equal to zero:

dU/dH = -U' + wU' = O

and therefore w UL/UY]A=K . (32)

Equation (32) derived from the individual's maxi-
mizing behavior, is a relation in terms of E: H, and
the working condition parameter H. It thus defines the

offer curve of work, which can be written
W = W(H, A), (33)

giving the price of a nurse's services as an increasing
function of the amount employed and her discontent with
working conditions.

The implications of equations (32) and (33) can be
shown geometrically as follows. In Figure 3, income and
work are measured on the vertical and horizontal axis,
respectively. The iso-utility loci H are convex to the
horizontal reflecting diminishing marginal utility to
both income and leisure; the income functions 1 are
straight lines eminating from the origin, and their slopes
are given by the magnitude of the wage rate. The slopes
of the iso-utility loci are given by UL/UYJA=K' For every
value of H there will be a different indifference map, and
the larger is H, or the worse are working conditions, the
steeper will be the slopes of the indifference curves for

any given level of H.

81

Figure 3.-—Work-leisure choice

  

 

 

\
\\

Figure A.--The supply of labor

 

 

 

82

An offer curve of work (not shown) is the locus of
points of tangency between income functions for all wage
rates H and the indifference curves of a given indiffer-
ence map. The supply surve of labor, H in Figure A, is
obtained by transposing points of an offer curve onto the
wage-units of work plane. Since there is a different
indifference map for every value of H, there is a separate
offer curve and corresponding supply curve for every value
of H, as shown in Figure 4.

Suppose that a hospital wishes to buy H units of
work per period from a nurse whose indifference pattern
is represented in Figure 3. If working conditions are

"good," e.g., if A=A the hospital can obtain H units of

13
work for wage wate HI. On the other hand, if working con-

ditions in the hospital are "bad," e.g., if A=A2>Al,

hospital must pay wage rate H2 to obtain H units of work,

the

as shown in Figures 3 and A.

Optimality of Production
We now wish to derive the optimal conditions for
factor combination when the supply of nurses' services to
the hospital includes the working conditions variable de-
rived in the preceding discussion.
The technology of the production process is given

by the production function

N = N(Zi), i=1,...,n (3A)

83

where the Z1 are inputs. For a given quantity and quality
of output No’ (34) defines an isoquant in factor space
giving the technical range of substitution of inputs in
the production of No'

Letting Zl represent the quantity of nurses, we de-
rive the supply function of nurses' services to the hos-
pital by summing the supply functions of all the individ-
ual nurses in the hospital's labor market (equation 33),

obtaining

wl = wl(Zl, A). (35)

According to our argument, the working condition parameter
H is a function of the production process utilized by the
hospital; we therefore write A = A(N) = F(Zi), so that

(35) becomes

wl = wl[Zl, F(Zi)], i=1,...,n. (36)

The supplies of all other factors of production

will be assumed to be functions of prices, so we may write

wi = wi(Zi), i=2,...,n. (37)

Total cost, 9, is equal to the sum of the products
of the wage rates of the inputs and their respective rates

of utilization:

c = 2 21 = £1wi(zi)-zi, i=1,...,n.

iwi

8A

Given its budget allocation H for the eXpected number of
patients, the nursing service department wishes to maxi-
mize the quantity (or the quality) of nursing service

for those patients, i.e., it wishes to pick the Z in

i
order to

Maximize: N = N(Zi)

Subject To: C = K.

Maximizing the Lagrangian function L = N(Zi) = v(K - C)

gives the necessary first-order conditions for maximum

 

 

output
K - C 3 O, (38)
Ni - y{[wl + Zl(dw1/le)] + [(awl/5F)(5F/azl)le} = 0,.
and Ni - y{[w1 = Zi(dwi/dZi)] + [(6wl/5F)(5F/6zi)]zl} = 0,
i=2,...,n.
From equations (38) it is seen that optimality re-
quires the following condition to hold:
"1
Y 3 I
[wl + Zl(dwl/le)] + [(dwl/OF)(6F/dzl)]zl
":1
= [Hi + Zi(dwi/dZ1)] + [(5wl/5F)(5F/5zi)]zl
i=2,...,n,

i.e., the ratios of marginal product to marginal cost must

be equalized for all inputs. In this case, the marginal

1

85

cost of an input includes the effect of changes in its
rate of utilization on the supply function of nurses'
services. A change in factor proportions implies a
change in working conditions which in turn implies a
shift in the nurse supply function with respect to the
wage rate. For equilibrium to be reestablished, nurses'
wages must be adjusted even though their rates of use may
not have been changed.

The direction and magnitude of the required change
in nurses' wages for a given change in factor proportions
cannot be predicted a priori without further knowledge of
the function H. It was argued that the utility associated
with working conditions varies with the composition and
total amount of care produced, i.e., with factor propor—
tions and the ratios of factors to patients. To denote

this, we write

A = A(N) = F(Zi/Z Zi/P)’ i,j=1,...,n, (39)

J,
where H is the patient load.
The utility of working conditions is related to the
vector H of technical magnitudes through the parameter H
which is a magnitude summarizing the working conditions
in the hospital. While it can be assumed that more inputs
per patient will be preferred to less by the nurse and
therefore increases in Zi/P will reduce the magnitude of

H, the effects of changes in input proportions Zi/Zj on H

86

cannot be predicted a priori. For example, suppose that

Z are practical nurses; a decrease in Zl/Z2 might imply

2
greater supervisory responsibilities for the registered
nurses, while an increase in Zl/Z2 may imply that regis-
tered nurses spend a greater portion of their time in
direct care of patients. Whether or not greater or lesser

values of Zl/Z2 are preferred by registered nurses must

be determined empirically.

CHAPTER V

EMPIRICAL PROCEDURE AND RESULTS

Statement of Hypotheses

A theoretical model of the demand and supply of hos-
pital nurses' services was developed in the previous chap-
ter. The demand for nurses' services was derived from a
conStruction based on preference function maximization
wherein the utility functions of the individuals involved
in the hospital's decision process were amalgamated to
yield a ranking of preferences for expenditure on alterna-
tive productive resources. The supply of nurses was de-
rived from a construction based on individual utility max-
imization. In addition to income and leisure, the indi-
vidual's utility function contained working conditions as
an argument assumed to be functionally related to the in-
put combination utilized by the hospital in its production
of nursing care.

To simplify the analysis and increase its tracti—
bility, the model was developed in terms of the depart-
mentalized structure of the hospital whereby it was

assumed that each department or producing unit within the

87

88

hospital is a separate argument in the group preference
function and that funds are allocated to each department
so as to maximize the hospital's utility subject to a
budget constraint determined by the community's demand
for hospital care. The utility-maximizing allocation
established the budget constraints on individual depart-
ments; the nursing service department's budget and its
production function for nursing care thus establish the
hospital's demand for nurses. The solution for factor
employment determines the magnitude of the working condi—
tions parameter operating on the supply function of nur-
ses' services to that hospital.

In its present form, the model developed in Chapter
IV and summarized in the preceding paragraphs is perfectly
general and devoid of empirical content. Imposition of
motivational assumptions on the logical structure of the
model will yield empirically testable hypotheses.

In Chapter IV, it was noted that nurses may not be
indifferent between the various alternative combinations
of inputs among which the hospital may choose to produce
nursing care. Inclusion of input combinations in nurses'
utility functions led to the theoretical result that the
working conditions implied by the vector of input combina—
tions utilized by the hospital affect the supply of nurses'
services to the hospital. In order to determine the em—

pirical significance of the theoretical result and to

89

estimate the effects of the proposed working condition

variables on the supply function, a first empirical hypo-
thesis is formulated: The sprly of nurses' service to a
hospital is affected by the technical magnitudes1 utilized

in its production of nursing care.

 

For an empirical investigation of the determinants
of the hospital demand for nurses, three groups may be
defined as the relevant participants in the decision pro-
cess--the administration, the medical staff, and the nurs-
ing service department. A conceptual framework of the
decision process can thus be established viewing the ad-
ministration, by virtue of the power vested in it by the
Board of Trustees, as the arbitrator of relative values
of alternative input combinations proposed by the medical
and nursing staffs.

Each of the latter two groups may be assumed to

have its own preferences for expenditure based on its

 

1In Chapter IV, the supply of nurses' services to a
given hospital was derived as a function of the wage rate
and the working conditions in that hospital. The supply
function of nurses' services may be written as the in-
verse of equation (35) of Chapter IV; taking working con-
ditions as a parameter, and setting Wil = S, we obtain

Z = (W

l A)

l,

as the supply function of nurses (Z1) to that hospital.
The working condition parameter H =1A(N) is a function of
the vector (N) of technical magnitudes utilized by the
hospital in producing nursing care [equation (39) of
Chapter IV]. Thus the magnitude of H will be partially
determined by the various ratios describing the hospi-
tal' s nursing service staffing (nursing service personnel
ratios and ratios of personnel to average census).

9O

particular role in the production of hospital care. The
medical staff, when composed of private practitioners,
can be assumed to favor expenditure on medical care in-
puts. Each field of medical practice requires special
equipment and personnel to assist the physician in pro-
ducing his own particular product. In some of the more
specialized fields, the extent of the physician's practice
is often determined by the availability of facilities and
equipment in the hospital. In addition, a high degree of
uncertainty prevails in medical diagnosis. The more
specialized or extensive the diagnostic equipment avail-
able to the physician, the higher the probability that
his prescribed therapy will be "correct." Moreover, in-
ternal pressure on physicians generated by medical audits,
tissue reviews, etc., would make for a united effort of
the medical staff to reduce the uncertainty of diagnosis.
The nursing staff may be assumed to prefer expendi-
ture on patient care inputs when the working conditions
in the nursing service department are determined by the
volume of these expenditures. Superimposed on the struc—
ture of professional groups is the administration which,
although motivated by the necessity of balancing revenues
and expenses, may be aligned with either of the other
two groups. From the proposition that the demand for
nurses' services arises from a bargaining process between

these three groups is derived an empirical hypothesis

91

upon which estimation of the demand function for nurses

will be based: A hospital's demand for nurses relative

 

to its patient load will vary with the influence of the

 

nursing staff in its decision process.

Testing the Hypotheses
The basic analytical proposition of this disserta-
tion is that the hospital's composition of output is
determined by a bargaining process between the various
formally and informally defined groups within the hospi—
tal. Observed differentials in factor employment can

thus be explained, ceteris paribus, by differential in-

 

fluences of these groups in the decision process between
hospitals. The analysis suggests that the problem of

the "shortage" of hospital nurses is related to inade-
quate effective demand relative to expressions of "need;"
within the organizational structure of the hospital, the
relationships between the groups participating in the
decision process and determining the hospital's alloca—
tion of resources and composition of output may be such
that some of them may be able to dominate the allocatory
decision without regard for the preferences of the others.
In this section, the empirical techniques used to test the
hypotheses will be presented following a discussion of the
procedure in which data was obtained for the statistical

analysis.

92

Collecting the Data

Data was collected from a sample of fourteen short-
term general hospitals in Michigan. The primary consid-
eration in choosing hospitals for the sample was their
willingness to participate in the project. Those hospi-
tals from which data was solicited were approached either
through Michigan State University or through the cooper-
ation of their area hospital council. All hospitals
included in the sample were accredited by the Joint Com-
mission on the Accreditation of Hospitals and were partic-
ipating Blue Cross Hospitals. Four of the hOSpitals were
church related, and six were community, voluntary insti-
tutions; four were county owned but were self-sufficient
in that they received no operating funds from tax reve-
nues--the only governmental support these institutions
received was for establishment and expansion of their
physical plants. Although the fourteen hospitals ranged
in size from 55 to A50 beds and were found in large met-
ropolitan industrial and educational centers as well as
in isolated rural areas, no primary teaching hospitals

were included in the sample.2

 

2The Association of American Medical Colleges de—
fines a teaching hospital as "an institution with a major
commitment in undergraduate, post-doctoral, or post-
graduate education of physicians." [Association of
American Medical Colleges, Council of Teaching Hospitals,
Rule and Regulations (The Association, 1965), p. l]. A
member hospital of the Council of Teaching Hospitals must
either be a major affiliate of a medical school or must
have approved internship programs and full residencies in

93

Two types of data were collected from the hospitals.
First, quantitative information was obtained on size and
occupancy rates of nursing units; staffing, wage and turn—
over rates of nursing service personnel; and on the size
and clinical distribution of the medical staff. Second,
general information about the organizational structure of
the hospitals, their decision-making mechanisms, and their
budgeting procedures was obtained in personal interviews
with the hospitals' administrators. '

Although various means were employed to make the
data as comparable as possible between hospitals, some
measurement error is still present in the figures used in
the statistical analysis. With respect to the quantita-
tive information, each hospital kept these data in vari—
ous forms and levels of disaggregation, and definitions
of some variables differed between hospitals. Patients
are assigned to nursing units according to type of con—
dition and need for care. Nursing service areas typi-
cally encountered were Obstetrics, Newborn Nursery,
Pediatrics, Psychiatry, Medicine, Surgery, and Rehabili-

tation. Some nursing units were not common to all

 

three of the following five clinical departments; Medi—
cine, Surgery, OB—Gynocology, Pediatrics and Psychiatry
[Ibid., p. 2]. Although one of the hospitals was a mem-
ber of the Council of Teaching Hospitals by virtue of its
internship and residency programs, it was not a primary
teaching hospital of a medical school. None of the hos-
pitals had major programs for undergraduate clinical
medical education.

9U

hospitals and service area proportions of total patient
load varied widely between hospitals. Analysis of nursing
service staffing was therefore restricted to medical—
surgical units in order to maintain a degree of homo-
geneity in patient characteristics between units of ob-
servation. However, some hospitals further segregated
patients within the medical-surgical category according
to their need for care: One-half (7) of the hospitals
had intensive care units (ICU), and five had Special car-
diac or cardio-pulmonary units. Since the patients
treated in these units would otherwise be in medical or
surgical wards, and since some hospitals did not have
separate statistics on these special units, the general
unit of analysis was average census (patient load) and
nursing service staffing of medical, surgical, ICU and
heart units. In a few hospitals, however, some medical
units were used for types of patients that would have
been excluded in other hospitals (e.g., pediatrics or
chronically ill patients); in computing ratios of nursing
personnel to patients, these nursing units were omitted.
Nursing service personnel staffing ratios were
computed as averages over a period of time, without ad-
justment for seasonal variation. Because the periods of
observation were not of the same length or over the same
months of the year, some bias may be present in these

ratios. The relevant measure of personnel is full—time

95

equivalents of full-time plus part—time employees; al—
though most hospitals could provide data on full-time
equivalents employed on each unit, some could provide
only the numbers of full-time and part-time personnel of
each occupational category on a per-unit basis. Thus it
was necessary to estimate the full-time equivalent mea-
sure of these part—time personnel. In most cases the
administration was able to indicate how many personnel of
each category per patient were normally maintained, so
that no serious difficulties were encountered.

Most hospitals could provide the turnover rate of
general-duty registered nurses only for the hospital as a
whole. However, when the turnover rate was available or
could be computed for the units in question it was used
instead of the hospital-wide figure.

With respect to the collection of qualitative in-
formation about the hospitals' organizational and
decision—making structures, initial ideas about hospital
organization were acquired by reading the hospital liter-
ature. The interviews, however, served as much as an
educational process as a data gathering device, with the
consequence that the original questionnaire was revised
several times as the interviews progressed and a pattern
of responses emerged which ultimately formed the frame-
work of a conception of hospital organization and Opera-

tion.

96

This conception necessarily contains some subjec-
tive and non—quantifiable elements: the outcome of a
group decision depends as much on the personalities of
the individual participants as on the mechanisms of com—
munization and hierarchy of authority employed. However,
the objective of this dissertation is to determine if an
analytic model can predict economic behavior in the hos-
pital industry, and the credibility, relevance, and use-
fulness of the dissertation can be served only by the
employment of methods which allow quantitative estimation
of the laws of the system. Thus the empirical methodology
demands that subjective evaluations and qualitative data
be transformed into objective and quantitative magnitudes,
or otherwise ignored. The rationale for identifying the
variables used in the analysis will be explained in the

appropriate places below.

The Supply of Nurses

The supply function estimated in "The Elasticity of
Supply of Nurses' Services" in Chapter II with county
cross-sectional data indicated that the responsiveness of
the inactive nurse force to changes in wages is of a low
magnitude, and that income from the practice of nursing
may be an inferior good to the family unit. Data col-
lected from a sample of individual hospitals will not
allow further pursuit of estimates of the market supply

function of nurses' services, for use of quantity supplied

97

as the dependent variable requires that all the nurses
supplying services in a given market be observed.

However, the limitations of the data in this re-
spect pose no problems for an attempt to determine the
significance of the variables postulated to affect the
supply of nurses' services to hospitals. It was sug-
gested in Chapter II that the primary problem facing hos—
pitals in dealing with nurse "shortages" is inducing nur—
ses to remain active once they have been employed rather
than hiring them initially, and the theoretical structure
of Chapter IV suggested that variables other than the
wage rate--"working conditions" variables--may be sig-
nificantly related to nurses' decisions with respect to
employment. The nature of the data and the hypothesis on
the variables to be included in the supply function imply
that the appropriate dependent variable for the analysis
is the turnover rate of nurses in hospitals.

Clearly, dissatisfaction with working conditions is
manifested in labor turnover: a voluntary separation from
employment is an adjustment from a disequilibrium position.
A given wage rate is an equilibrium one for the factors
employed at that rate; it was high enough to attract those
factors in the first place. A voluntary termination,
given that same wage rate and conditions of employment,
reflects an adjustment to a change in parameters facing

the individual, either exogenous or endogenous to the

98

hospital. The former may include changes in family in-
come, pregnancy, etc.; the latter, however, would be an
increase in information available to the individual about
working conditions in the hospital. Holding the former
conditions constant, it can be said that after an indi-
vidual accepts employment at a given wage rate, his gain—
ing additional information about working conditions
through working may place him in disequilibrium at that
wage, and result in his separation from employment. A
high frequency of turnover, ceteris paribus, would thus
indicate unfulfilled expectations with respect to working
conditions.

Labor turnover thus indicates that some of the work—
ing condition magnitudes determined by the hospital may
be disequilibrium quantities with respect to the prefer-
ence of employees. The prOportions of turnover attribu-
table to dissatisfaction with working conditions can be
separated from the prOportion due to exogenous factors;
turnover rates may be regressed on the wage rate, working
conditions variables, and other variables indicating dif-
ferences in environmental factors between labor markets
from which observations were taken to determine the abil-
ity of hospitals to prevent turnover of nurses.

Turnover rates of Registered Nurses in the fourteen
hospitals included in the sample ranged from 15% to 100%

annually. Administrators of hospitals in communities

99

with colleges or universities or military bases expressed
the Opinion that a large proportion of their nurses were
wives of students or military personnel and that they

were therefore dependent on a transient labor force. A
binary variable classifying the nurse fOrce as "transi-
tory" or "permanent" was used to separate observations on
hospitals which were in close proximity to colleges, uni-
versities, or military bases from those which hired nurses
from a relatively stable population.

An attempt was made to classify hospitals according
to whether they were in "urban" or "rural" communities
and according to whether or not they competed with other
hospitals for personnel. However, the nature of the sam-
ple was such that these classifications corresponded
closely to the classification of the nurse force as trans—
itive or stable; these two additional classifications were
therefore redundant and were abandoned in favor of the
nurse force classification.

An additional dummy variable was employed to indi-
cate whether or not General Duty Nurses were shifted
between services with changes in patient loads. While
most Administrators and Directors of Nursing expressed
the opinion that erratic shifting of personnel between
services was harmful to employee morale as well as to
quality of patient care, only a few took explicit measures

to avoid such shifting. Those which did not maintain a

100

complement of extra nurses ("float pool") relied on super-
visors and extra part—time help to take care of above-
average patient loads in some services. The majority of
hospitals, however, shifted nurses between services with
regularity, although it was admitted that nurses were not
enthusiastic about being moved about in the hospital.

The remaining variables used in the analysis follow
directly from the model of Chapter IV: ratios of General
Duty Registered Nurses, Practical Nurses, and Nursing
Aides to average daily census in Medical, Surgical, In—
tensive Care and Cardiac Units; ratios of General Duty
Registered Nurses to Practical Nurses and Nursing Aides;
and the wage rate of General Duty Registered Nurses.

Only a few hospitals could supply the average wage
rate paid to General Duty Registered Nurses. Therefore
two alternative measures of the wage rate were available:
the monthly starting wage and the maximum attainable
monthly wage, which was a function of the length of ser-
vice. Each measure of the wage rate was used alterna-
tively as an independent variable in every regression to
determine which was the best proxy for the "true" wage
rate.

The following is a list of the variables used in
the analysis of the supply of nurses' services:

T = the turnover rate of General Duty Registered
Nurses, per cent per year.

R/C =

P/C =
A/C =

R/P =

R/A =

W1 =

W2 =

D1

D2 =

The

101

Average Daily census (numbers of patients) in
Medical, Surgical, ICU, and Cardiac nursing
units.

General Duty Registered Nurses per average
daily census.

Practical Nurses per average daily census.
Nursing Aides per average daily census.

Ratio of General Duty Registered Nurses to
Practical Nurses.

Ratio of General Duty Registered Nurses to
Nursing Aides.

Minimum or starting monthly wage of General
Duty Registered Nurses.

Maximum attainable monthly wage of General
Duty Registered Nurses.

A binary variable coded 0 to 1 according as
the nurse force was "permanent" or "transitory."

A binary variable coded 0 to 1 according as
nurses were or were not shifted between ser-
vices.

following matrix shows the simple correlations

between the variables:

T

C
R/C
P/C
A/C
R/P
R/A
W1
W2
D1
D2

H
1.00
.02
-.26
—.01
.52
.15
-.58
-.06
.17
.62
-.52

Two

C R/C P/C A/C R/P R/A W1 W2 D1

1.00
.34-1.00
.33 -.10 1.00
-.34 .03 -.52 1.00
-.22 .43 -.82 —.74 1.00
.35 .57 .28 -.48 -.13 1.00
.75 .59 .32 -.17 -.04 .38 1.00
.63 .54 .13 -.11 .09 .28 .81 1.00
.53 .30 .16 .32> .09 -.19 .62 .66 1.00
.19 .16 .20 -.28 -.16 .25 .40 .05 -.19

groups of regressions were run, each group using

a different set of staffing ratios as independent variables

102

together with the wage and binary independent variables.
The first group was run with the set of ratios of nursing
personnel to patients (R/C, P/C, A/C) and the second with
the set of ratios of registered nurses to axuiliary nurs-
ing personnel (R/P, R/A). Apart from the fact that inter-
correlation precludes the use of these two types of ratios
in the same regression, the theoretical ground for sepa-
rating them is clear: the ratios of nursing personnel to
patients determine the position of an isoquant in factor
space and thus have implications for the perceived "qual-
ity" of patient care along a ray from the origin; while
the ratios of nurses to axuiliary nursing personnel have
implications for working conditions as substitution takes

places along an isoquant.3

 

3Confining the illustration to two-space, let the
number of Registered Nurses (R) and the number of Practi-
cal Nurses (P) be measured along the vertical and hori-
zontal axis, respectively.
B“ The Euclidean distance
from the origin to a
point on an iso-quality
locus (assumed convex)
implies a certain "qual-

 

ity" of care for a given
0 number of patients; as H
Q2 and H are increased equa-
proportionately for the
Q1 same number of patients,
:P the Euclidean distance

 

increases along the same
ray from the origin. When the ratio of H_to H is changed,
"working conditions" change but the direction of the im-
plied change in "quality" is indeterminate since no infor-
mation about the number of patients is contained in that
ratio (except in the restricted sense that it implicitly
assumes the quality function to be homogeneous of degree
zero in patients and personnel).

103

The maintained hypotheses, in simple linear form,

are

T = a + d (A/C) + d (P/C)+ a D1 +

o (R/C) + auW = a

1 2

3 5

O6D2 + ua (l)

T = 80 + Bl (R/A) + 82 (R/P) + 83w + BuDl + 85D2 + u8 (2)

A priori, relations (1) and (2) appear to justify direct
regressions of T onto the staffing ratios and the other
independent variables. However, such regressions will be
justified only if the values of the independent variables
used in the regressions were generated independently of
T, i.e., if the independent variables in (l) and (2) are
truly exogenous.

While it was assumed that the staffing ratios and
wage rate were parameters facing the individual contem-
plating employment in a given hospital, it was shown in
Chapter IV that the cost minimizing hospital, which
determines the magnitudes of these variables in its own
best interest, must be aware of the effects of variations
in their magnitudes on the supply function of nurses'
services when determining the least—cost combination of
inputs for production of nursing care. On the cost—
minimizing assumption, the dependence of A, P, R, and W
must be taken into account when factor employment is
determined; consequently the values of A, P, R, and W are

not determined independently Of the value of T.

104

If hospitals are assumed to be cost minimizers,
estimation of equations (1) and (2) must be conducted in
the context of a simultaneous equation model, as implied
by the equilibrium conditions for optimality of factor
combination derived in Chapter IV. Thus the observed
(equilibrium) values of T, A, P, R, and W should be
treated as determined simultaneously. However, the opti-
mality conditions of the cost-minimization model presented
in Chapter IV [equation (38)] yield demand functions for
the inputs A, P, and R of such a form that the structural
equations (1) and (2) are underidentified for estimation
purposes. Equations (1) and (2) cannot be estimated in a

simultaneous equation context.Ll

 

”Solution of the first-order optimality conditions
for factor employment yields demand functions for factors
of production in terms of their marginal cost, the margi-
nal costs of the other inputs, the cost of turnover, and
the quantity of output. Assuming linearity, we have the
following system of supply, demand, and turnover rate
equations:

3 _ .
A — 00 + 01WA
D _
A - 20 + A(l+—— 6A) + 22wp(1+—%) + £3 wR(l+% —) + 24TH + 25C
3 _
P _ 0o + pin
PD = v + W(l+ 1) + V2W(1+l) + v3 W(l+;L) + v T + v C
0 wR 6 4 R 5
EA 8P R
S _
R ‘ ¢0 + ¢le

105

In the absence of identifiability all that may be
done is to estimate (1) and (2) directly realizing the
limitations of such a procedure if it is assumed that
they are structure equations of a simultaneous equation
system. If (1) and (2) are believed to be single-equation
models, i.e., if the independent variables are believed to
be determined independently of the dependent variable of
the equation, a least-squares multiple regression is
appropriate. If, however, (1) and (2) are structure equa-
tions, least—squares estimators are not consistent because

the disturbance terms are not then independent of the

 

:13
II

no + “l V(l+ 8A) + p2WP(l+— %) + u3 WR(1+e R) + u4TR + uSC

*3
l

R - $0 + wlA + w2P + w3R + puwR + wsc

where €(A, P, R) is the elasticity of supply of A, P, R
respectively.

The necessary (order) condition for identifiability
of an equation in a system of n linear equations is that
the equation exclude at least n- 1 of the variables in the
system. In this system of seven _equations, the turnover
rate equation excludes two of the eight variables in the
system; the turnover rate equation is therefore under—
identified.

The order condition for identifiability equivalently
requires that for an equation containing J exogenous and
H endogenous variables in a system containing a total of
H exogenous variables to be identified, the following must
hold: K-J : H-l [Carl Christ, Econometric Models and
Methods, pp. 326-27]. It follows that for the turnover
rate equation to be exactly identified, at least four more
exogenous variables (in addition to C) must be added to
either the demand or supply equations in the model. Even
if four such variables could be found, the regression re-
sults would be dubious since degrees of freedom would be
insufficient to obtain meaningful estimates of the reduced
form parameters.

 

106

explanatory variables. The implications of this inconsis-
tency will be dealt with after the estimated equations are
presented.

Evaluation of the statistical results required two
judgments to be made. The first involved the choice be-
tween alternative functional forms of the regression equa-
tions. The second involved the decision to eliminate inde-
pendent variables from the regression equations, i.e., to
restrict some of the coefficients of the explanatory vari—
ables in (l) and (2) to zero. Linear, semi-logarithmic,
and logarithmic functional forms were employed in regres-
sions for all combinations of the explanatory variables in
order to find the most precise relationships. Only the
"best fit" equations will be reported. The definition of
"best fit" is based on the fact that the major interest
is the reaction of the dependent variable to changes in
each independent variable. Thus the significance levels
of the regression coefficients are of primary importance,
and the "best fit" functional form is that which gave the
highest confidence levels on the estimated coefficients of
the explanatory variables.

The significance levels of the regression coeffi-
cients are affected by degrees of freedom, which in this
case are precious; obviously, extra degrees of freedom may
be obtained by dropping variables from the regression. In

view of the limited degrees of freedom available, a

107

significance level of 10 per cent or better for an esti-
mated coefficient was provisionally acceptable. In the
search for the best fit regression, independent variables
whose estimated coefficients had a significance level of
worse than 10 per cent were dropped and the regression
re—run.5

In a few instances, it was necessary to include a
statistically "insignificant" variable in a regression to
obtain acceptable significance levels for coefficients of
other variables. In most cases, however, dropping insig-
nificant variables did not radically change the basic re-

sults in terms of the magnitudes of the obviously important

variables or their significance levels. Radical changes

 

5This pragmatic solution to the problem posed by a
large number of explanatory variables relative to the
number of observations may seem dubious. If the inde-
pendent variables were chosen from among all the vari-
ables in the world on purely empirical grounds, then the
results would indeed be questionable. [Mordecai Ezekiel
and Karl A. Fox, Methods of Correlation and Regression
Analysis, pp. 297-98.] However, as the original variables
were chosen on purely logical grounds, eliminating some of
those variables from the regression equation because they
prove to be unimportant when viewed in the light of the
observed facts is analogous to reformulating the hypothe-
sis within the same theoretical structure. Insofar, then,
as this technique is aimed only at testing the various
elements of a single hypothetical structure, it is per-
fectly legitimate. Since the general hypothesis yields no
a priori information about the functional forms of the re—
lationships between the dependent and independent vari-
ables, and since some of the dependent variables are cor—
related with each other, the technique of comparing
alternative functional forms of a regression equation with
the coefficients of alternative variables restricted to
zero yields useful empirical information about the under-
lying structures. [Carl F. Christ, Econometric Models and
Methods, p. 537.]

108

were observed, however, in the values of some of the mul—
tiple coefficients of determination (R2) when variables
were dropped. Since there are a large number of indepen-
dent variables relative to the number of observations, R2
probably contains an upward bias. Therefore, the multiple
coefficient of determination adjusted by degrees of free—
dom (R2), which gives an unbiased estimate of the per cent
of true variance in the universe associated with the inde-
pendent variables, will be reported in addition to R2 and
the associated F statistic for each regression.

The sample correlations between some of the explana-
tory variables indicated that colinearity would be a prob—
lem. The results of colinearity--increasing the standard
errors of the estimated coefficients--was most evident
when El was included in a regression with either El or
EE. Regressions will therefore be reported using El, El,
and E3 separately.

For the first group of staffing ratios--proportions
of personnel to patients--the regression results are
shown in Table 7. The standard error of each regression
coefficient is shown in parenthesis below the coefficient.
In the regressions that included El (the labor force
classification variable) the linear function gave the
best fits but only the coefficients of El and 519 were
significant at a level of 10 per cent or better. Step—

wise deletion of the least significant variables improved

109

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A=F.Num.mmv

me. u mm AHH.ov Amoo.ov Am=.ov Aos.ov Amm.ov Ame.ov

on. u m we am.o . a: moo.o + Ao\<v=m.o + onmvmm.o + onmvmm.a n as.ou u a .mHmH

. "m: can as sea: .mH

Aom.suaa «my

mm. a mm . Amm.ov Aoa.ov Ama.ov

mm. u mm onmvoa.a . Ha oz.o + No.0 u e .N<H
Aem.aum.mmv

me. u mm Aoa.ov Ao=.ov Aom.ov Awm.ov Ama.ov Asm.ov

mm. a m we ma.o . AQ\«VHm.o + onmvom.o + onmVHH.H . an om.o + m=.o n a .H4H

"Ha spa: .aH

a.mu:oapwa on Hoccompoo no moapmm you madamma codmmommomln.w mqm<e

110

the significance levels of the coefficients of El and 51E
without appreciable reduction of R2.

Use of the wage rate instead of El in the regres-
sion makes the estimated coefficient of ALE significant
at the 5 per cent level or better. The semi-logarithmic
form gives the best fit when EE is used while the simple
linear form gives the best fit when El is used as the
wage rate variable. Use of El instead of Eg_makes the
estimated coefficient of El significant at a level of
10 per cent or better. This differential effect on the
significance level of EE is interesting: Evidently, the
closer the maximum wage comes to measuring the "true"
wage (which in itself indicates that the nurse force is
more permanent), the less important is the fact that nur-
ses are shifted between services. Thus there may be a
trade-off between higher wages and less stable working
conditions, as one would expect.

The positive sign of the coefficients of the wage
variable is curious. That the turnover rate varies posi-
tively with the wage rate may lend support to the hypo—
thesis that the supply curve is "backward bending." On
the other hand, the wage rate is positively correlated
with El, the transitory labor force indicator, which is
in turn positively correlated with the turnover rate.
Thus the wage rate is also a proxy for the transitivity

of the labor force (the consequence of which is the

lll

colinearity problem which precluded the use of El with
El or EE in the same regression equation). If their
separate effects could be isolated, the turnover rate
might well be found to vary inversely with the wage rate
in View of the latter's effect on the significance level
of the estimated coefficient of EE.

The results for the second set of staffing ratios—-
proportions of general duty registered nurses to auxiliary
nursing personnel—-are shown in Table 8. In the regres—
sions using El, the coefficients of E13 and Eg_were not
significant at the 10 per cent level. Their deletion
from the regression equation left the magnitudes of the
estimated coefficients of El and Ell substantially un-
changed but resulted in a slight improvement of their
significance levels with only a slight reduction of R2.

Use of the wage rate variable in place of El im-
proved the significance level of the estimated coefficient
of EE. The estimated coefficient of 34E, however, re-
mained insignificant. Deletion of ELE from the regres-
sion equations left the results substantially unchanged.

Although the regression results appear to confirm
the hypothesis that "working conditions" as indicated in
staffing ratios significantly affect the supply function
of nurses' services to hospitals, no conclusions may be
drawn about the implications of the regression results

until the question of simultaneous equation bias raised

112

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Amm.: H OH mmv

on. u mm Amo.ov Aaoo.ov Amo.ov AH©.QV

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Awe.a H OH mac

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me. u mm mm mm.o . H3 moo.o + Aaxmvmm.o . mfi.o- n e .ammHH

on. u mm Aoa.ov Aaoo.ov Amo.ov Aomo.ov goo.ov

me. H mm mm aa.o : m3 moo.o + A<\mvmm.o I Ad\mvmoo.o I mm.o- u awn .nHmHH
Aea.m u m.:mv

mm. H mm Ama.ov Aaoo.ov Aoa.ov Aomo.ov Amw.ov

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113

earlier is investigated. For, if simultaneous equation
bias exists--if the single equation models are misspeci-
fied--the least squares estimates are inconsistent.

To shed light on the question of simultaneous equa-
tion bias, three tests for specification error develOped
by Ramsey6 were performed on several of the regression
equations. The tests are sensitive to misspecification
of one or more of the following types: errors in vari-
ables, incorrect functional form, omitted variables, and
simultaneous equation problems. Although no specifica-
tion error will be detected if several offsetting mis-
specifications are committed, the power of the tests is
increased if misspecifications reinforce each other.
Since each test approaches the effect of misspecification
from a different point of view, i.e., as each test in-
volves a different alternative hypothesis against the
null hypothesis of no specification error, the tests are
complementary.

The three tests involve the null hypothesis that
the least equares residuals are distributed as N(O, o2IN)
and are stochastically independent, i.e., that the data
were generated under the ideal conditions necessary for

valid application of least—squares regression analysis.

 

6J. B. Ramsey, "Tests for Specification Errors in
Classical Linear Least Squares Regression Analysis,"
Econometrics Workshop Paper No. 6601, Michigan State
University, 1968.

114

Since the actual least squares residuals are not stochasti-
cally independent, the tests are made operational by trans-
forming the least squares residuals into a subset of resid-
uals which are independently distributed. The residuals
employed in the tests are Theil's Best Linear Unbiased
Scalar Covariance Matrix Estimator. Thus there are n-k
independent transformed residuals ui used in the tests,
where n and k are the number of observations and regres-
sors, respectively. Under the ideal conditions of the null
hypothesis the transformed residual vector u is distributed

as N(O, o2

In_k); under the alternative hypothesis, u is
multivariate normal but with a non-null mean vector, de-
noted by C

The first of the tests, named KOMSET for Kolmogorov
Specification Error Test, considers the distribution of

the squared residuals wr = ug/ui, s # t, where the s, t

are chosen according to the rule

 

Wr = , r, i = l, 2,..., 935, so that the wr are inde-

pendent as assumed under the null hypothesis of no speci-

fication error. Under the null hypothesis, Wr is distri-

buted as F Under the alternative hypothesis of

l,l'
specification error, wr is distributed approximately as

F where vl,v2 > 1. KOMSET is therefore a comparison

vl,v2
between two F distributions with (1,1) and (vl, v2)

115

degrees of freedom, accomplished by application of the
Kolmogorov test on the cumulative distribution of the Wr
The test RESET, for Regression Specification Error
Test, is based on the fact that under the alternative
hypothesis, the mean vector ; of the disturbance u is
non—null. Since C is not known it is approximated by a
function derived from the least squares estimates of the

dependent variable. Specifically, it is assumed that m
th

is
the mean of the i residual, can be expressed as a poly-
nomial expansion of the conditional moments about the
origin of yi, the least squares estimator of the condi-
tional mean of yi; thus a linear sum of vectors {qJ},
J=l,2,3, whose elements are qij’ i=l,2,...,n-k, is used
to approximate the non-null mean vector C of u. RESET
is performed by calculating the F statistic defined by

the ratio of the regression sum of squares to the error

sum of squares obtained from the regression
u = a0 + alql + a2q2 + a3q3 + e.

Under the null hypothesis, e is distributed as normal
with null mean vector and the multiple correlation coef-
ficient is zero, so that the null hypothesis is rejected
for high values of F.

The test RASET, for Rank Specification Error Test,
is based on the alternative hypothesis that a monotonic

relationship exists between the second moment of ui and

116

qil’ i=l,2,...,n-k. RASET is carried out by applying
Spearman's rank correlation test on the rankings of the

ui and qil’ Under the null hypothesis the ui are distri-
buted independently of the qil so that the value of
Spearman's rank correlation coefficient R8 is zero. The
statistic used to test the significance of R8 is distri-
buted as "t" with (n-k-2) degrees of freedom.

Table 9 presents the results derived from applica-
tion of the specification error tests to six of the re—
gression models. KOMSET is performed only at the 5 per
cent significance level; the computer program used to
perform the tests is such that acceptance or rejection of
the null hypothesis at the 5 per cent level only is indi-
cated to the user. For RESET and RASET, however, the
user is given the F and t ratios, respectively, with the
corresponding degrees of freedom. The table indicates if
the null hypothesis HO can be accepted at a 10 per cent
or better level of significance for the indicated F and
t ratios.

Only two of the models tested are suspect of speci-
fication error according to the results of the tests.
Model IB3 failed both KOMSET and RASET, and model IIB2b
failed RASET. Since both of these models contain W2 as
an independent variable, one might suspect that a measure—
ment error is associated with W2, i.e., W2 is not a good

proxy for the true wage rate and is consistently biased.

117

TABLE 9.--Results of specification error tests (Ho: no
specification error).

 

Specification Error Test

 

 

Regression
MOdel KOMSET RESET RASET
1A2 F4,7 = 0.6647 t9 = 1.1375
Accept Ho Accept Ho @ Accept Ho @
5% level 10% level 10% level
IB2a FH,5 = 0.392 t7 = 0.9885
Accept Ho Accept Ho @ Accept Ho @
5% level 10% level 10% level
1B3 FH,6 = 2.0690 t8 = 1.9300
Reject Ho Accept Ho @ Reject Ho @
5% level 10% level 5% level
IIA2 F4,7 = 0.3704 t9 = 0.7001
Accept Ho Accept Ho @ Accept Ho @
5% level 10% level 10% level
F = 1. 1 t = 0. 62
IIB2a 4,6 37 7 8 3 9
Accept Ho Accept Ho @ Accept Ho @
5% level 10% level 10% level
F = 0.u8 t = 1.6462
IIB2b u,5 95 8
Accept Ho Accept Ho @ Reject Ho @
5% level 10% level 10% level

 

118

Evidently, the tests picked up an errors-in—variables
problem.

As for the question of simultaneous equation bias,
one is faced with strong evidence that this type of mis-
specification is not a problem in the accepted models.

If one discounts the possibility that a variety of off-
setting misspecifications have been committed such that
the tests are rendered incapable of detecting dependence
between the disturbance and the independent variables,
the conclusion can be made that no simultaneous equation
bias exists in the estimation of the turnover rate func-
tion, and that the regression coefficients are not incon-
sistent.7

The implications of this analysis of the turnover
rate of nurses for the supply function of nurses' services
to hospitals can be summarized as follows. Although part

of the turnover of nurses is due to factors exogenous to

the hospital, a significant part of turnover is traceable

 

7Some preliminary information about the small sam—
ple properties of the specification error tests have been
obtained from Monte Carlo experiments on regression equa-
tions known to be misspecified in specific ways [James B.
Ramsey and Roy Gilbert, "The Small Sample Properties of
Some Statistics Used in Specification Error Tests: Some
Preliminary Results," pp. Hl-H2]. When the tests were
performed on regressions of a single equation of a simul-
taneous equation system with a sample size of 15 and
(“,8) degrees of freedom for the F statistic, RESET was
shown to have a probability of 99 per cent of rejecting
the null hypothesis at a significance level of 5 per cent.
Thus the power of RESET to detect simultaneous equation
bias appears to be quite high, even under small sample
conditions.

119

to variables the magnitudes of which are determined by

the hospital. Insofar as turnover is a method by which
nurses express their preference with respect to these
variables, they become significant arguments in the sup-
ply function of nurses' services which the hospital should
consider in its attempt to achieve economic efficiency in
production of nursing care.

Within the observed range of their magnitudes,
several variables stand out as having significant effects
on the supply function of nurses' services. With respect
to ratios of nursing personnel to patients, nurses prefer

higher ratios of themselves to patients and ceteris pari-

 

REE: lower ratios of nursing aides to patients. With re-
spect to ratios of nurses to auxiliary nursing personnel,
nurses evidently feel that the services of nursing aides
are not substitutes for those of nurses. The evidence
indicates that in all respects, nursing aides are dis-
commodities in the opinion of General Duty Registered Nur-
ses. One further conclusion can be made on the basis of
the statistical analysis of the data, but with a higher
level of reservation: nurses evidently prefer not to be
shifted between services in the hospital.

If one is willing to take these significant staffing
ratios as indicators of the working atmosphere prevailing
in a hospital, one may conclude from the regression re-

sults that nurses' decisions with respect to hospital

120

employment are based primarily on working conditions
rather than the wage rate. What these ratios imply for
working conditions is a conjectural matter. However, it
seems reasonable to suppose.that lower ratios of general
duty nurses to nursing aides imply greater supervisory
responsibility, and less participation in direct care of
patients, for the nurses. The results are consistent

with the suggestion that requiring nurses to function in
supervisory and administrative roles may offend sensibili-
ties determined in professional training programs that
place primary emphasis on direct patient care.8 Also,

the estimated positive effect on the turnover rate of in-
creasing the ratio of nursing aides to patients while the
ratio of nurses to patients is held constant may imply
that nursing aides have a negative marginal product in

the opinion of nurses. This may derive from the implied
increase in supervisory responsibility, or nursing aides
may simply have an unpleasant connotation for professional
nurses.

Regardless of the interpretation given to the rela-
tionships between the significant staffing ratios and im-
plied "working conditions," the results of the statistical
analysis have direct implications for the cost of produc-

ing nursing care. For, although high turnover of

 

8Hiestand, "Research Into Manpower for Health Ser-
vice," p. 1&6.

121

professional nurses may be costly and inefficient, the
cost of reducing turnover by replacing nursing aides with
professional or practical nurses appears also to be high.
Thus the optimal or cost-minimizing solution for factor
combination in nursing service may yield a high turnover
rate in any given situation. We turn now to attempt to
isolate the factors that determine nursing service staff-
ing, or the demand for nursing service personnel in hos-

pitals.

The Demand for Nurses

This section will be devoted to a test of the hypo—
thesis on the hospital decision process as it affects the
demand for nurses' services. The rationale for identify-
ing the explanatory variables used to test the hypothesis
will be explained in a discussion of hospital organiza-
tion structures observed when data was collected. But in
order to estimate the demand function for nurses' ser-
vices and thereby test the hypothesis on the decision pro—
cess, it is first necessary to isolate factors not in-
cluded in the hypothesis that may account for some of the
observed differences in nursing service staffing between

hospitals.9 These factors may be divided into three

 

9The underlying operational assumption of regres-
sion analysis based on cross-sectional data is that all
units of observation are homogeneous except in the vari-
ables in the hypothesis and a ramdom error [Lawrence R.
Klein, An Introduction to Econometrics, p. 55]. In order
to avoid biased estimates resulting from mispecifica—
tion of the regression equation through exclusion of

122

categories: variables relating to (l) differences in
patient characteristics between hospitals; (2) differ-
ences in productive techniques utilized by hospitals in
producing nursing care; and (3) opportunity for factor
substitution within a given technology. The variation

in nursing service staffing between hospitals due to dif-
ferences in these variables must be detected in order
that their systematic effects may be separated from the
effects of the organizational variables which are of pri-
mary interest.

Variables Not Included
in the Hypothesis

 

 

Differences in Patient
Characteristics

As has been previously pointed out, control for
some of the differences in patient characteristics be-
tween hospitals has been achieved by limiting the analy-
sis to average daily census and staffing in medical, surg-
ical, Intensive Care and Cardiac units. However, the
nursing care requirements of these patients may be ex—

pected to vary with the variety of specialized procedures

 

variables which systematically affect the error term, it
is necessary to hold their effects constant. While unique
individual "firm effects" may be assumed to be random and
therefore not to introduce bias into the estimates by vir-
tue of their independence, the same does not hold for
errors that are persistent between firms (hospitals); the
systematic component of the error term must be extracted
from the omitted variable category and be included as ex—
plicit variables in the regression equation in order that
the equation will be specified more accurately.

123

performed in the hospital by its medical staff. Where the
proportion of physicians with special privileges is high,
nursing care requirements may differ from the situation
where the medical staff are predominately general practi-
tioners. The ratio of physicians with special privileges
to the total medical staff was used as an independent
variable to isolate variation in nursing service staffing
resulting from differences in the extent of medical staff
specialization in therapeutic techniques between hospitals.
Differences in Technology Implied
by Special Nursing Units

The significance of the effects on medical-surgical
nursing service staffing of the maintenance of special
Intensive Care and Cardiac units may be determined by the
use of binary variables in the regression equations. The
expected effect of special units on staffing requirements
is subject to speculation. It has been argued that main-
tenance of special care units necessarily indicates a
change in product specification with respect to the qual-
ity parameter of nursing care such that more intensive
staffing is required because of the specialization among

10 On the

personnel necessary to produce specialized care.
other hand, one might suspect that the division of labor

implied by special units would result in an increased

 

10Mark S. Blumberg, "Special Care Units," Modern
Hospital,lOH, No. 1 (January, 1965), pp. 69—71.

124

demand for specialized factors of production at the ex—
pense of demand for more versatile inputs. Further, main-
tenance of special units for care of patients with special
conditions may indicate that a hospital has been able to
achieve economies of scale or has been able to increase
the efficiency of utilization of nursing personnel and
consequently reduce its total requirement for general duty

nurses .

Utilization of Student Personnel

Many of the hospitals in the sample maintained
"diploma" schools of nursing or participated in training
students of professional nursing from colleges or univer-
sities. In addition, many of the hospitals participated
in training practical nurses. Although hospitals may not
include student nurses or practical nurse trainees in
their staffing plans, it is conceivable that students and
trainees could be substituted for some nursing personnel.
To test for effects on nursing service staffing, dummy
variables were employed to indicate the presence of pro-
fessional or practical nurse trainees in the hospital.

Organization Variables Relating
to the Decision Process

Hospital Organization for
Decision and Control
As represented by the organization chart in Chapter

III, the formal organization of the "typical" voluntary

125

institution does not provide a mechanism for managerial
control of the productive activities of all the groups in
the hospital. The hospital administrator, in the context
of the organizational chart, has no explicit authority
over the medical staff which is an independent entity
within the hospital organization subject only to the
Board's control. Moreover, the organization chart pro—
vides no information about the decision process of the
hospital whereby the opinions of the various groups in-
volved in production of hospital care interact to produce
a definition of the product in terms of the optimal mix
of inputs. The following discussion will review various
organizational situations encountered in the sample hos-
pitals under which decisions were made and control over
the production process was achieved.

In addition to direct line authority over the vari-
ous hospital departments, administrative coordination and
control within the hospital framework had at least two
other dimensions. The first consisted of a tacit recogni—
tion by the medical staff of the administrative function
which was generally maintained in the working relation-
ships between the administrator and the official hierarchy
of the medical staff. The second dimension of administra-
tive authority was the Administrator's control over the
budget; as the agent of fiscal control, the administration

exercises explicit power through control of the hospital's

126

budget. The discussion will take up these tOpics in the
following order: administrative authority in relations
with the medical staff; administrative authority implied
in the budgeting process; and the determinants of nursing
service staffing.

Administration-medical staff relationships.--The

 

Emechanism of communication and coordination utilized by
the Administrator with respect to the Medical Staff was a
function of the medical staff organizational structure
which in turn was generally (although not exclusively) a
function of the size of the hospital. In smaller hospi-
tals where there was no need for formally structured medi-
cal staff organization, the Administrator and members of
the Medical Staff maintained close, day-to-day, informal
working relationships. In larger hospitals with formally
departmentalized medical staffs, close working relation-
ships between the Administrator and the upper echelons of
the medical staff hierarchy—-the Chief-of-Staff and Chiefs-
of-Services——generally existed. In only one instance were
salaried physicians found in administrative positions (as
Medical Directors and Assistant Medical Directors); none
of the hospitals had salaried Service Chiefs.

In all the hospitals, the administration was repre-
sented at medical staff meetings. In some hospitals the
Administrator expressed the opinion that he was the main

instrument in maintaining medical staff organization. In

127

these hospitals, and some others, the Administrator was
an officer of the Executive Committee of the Medical Staff.
As an officer in the medical staff organizational struc-
ture, the Administrator was apparently able to provide an
element of stability when the official group was subject
to periodic change and was evidently able to maintain
organized medical staff functions at an acceptable level
(with respect both to the requirements of the Joint Comis-
sion on Accreditation of Hospitals and to the Administra—
tor's own standards).

In a few hospitals, the Administrator was a member
of the Board of Directors. Most felt that this position
increased their official credibility in the eyes of the
medical staff and gave them an advantage in the degree of
authority generally available to them.

While all the administrators expressed the opinion
that they had inadequate power within the organizational
structure, most felt that the lack of explicit authority
was partially compensated for by the existence of good
working relationships and mutual respect between them and
individual members of the medical staff. The primary
variable appeared to be medical staff appreciation of the
role of the Administrator as coordinator of the hospital's
activities. In the few cases where this recognition was
absent, the Administrators expressed the opinion that the

primary task they faced was to gain credibility in the

128

eyes of the medical staff and thereby achieve a dominate
position in the hospital authority structure.

Budgeting procedures.-—A wide variety of budgeting

 

procedures was utilized in the sample hospitals. No con-
sistent philosophy of budgeting prevailed among the admin-
istrators. Some maintained that, since reimbursement of
payment for services was based primarily on cost, formal
budgeting of operating expenses was superfluous as long

as costs were kept within acceptable limits. Thus the
primary concern of these administrators was maintaining

an acceptable quality Standard of care in terms of attract-
ing and keeping adequate numbers of personnel in employ-
ment. In these situations, formal budgets were not main-
tained for the purpose of control.

At the other extreme, some administrators would
tolerate no variance from the planned budget by individual
departments. In these cases, the budget evidently was in—
flexible and was used as a device for strict control of
fiscal operations. On the whole, however, the majority of
administrators were admittedly frustrated in their at-
tempts to use the budget as a control device. While bud-
gets were planned on the basis of past experience and
anticipated future changes, most administrators found that
wide tolerance limits for deviation from the formally de—
rived budget had to be set in order to maintain operations

at some minimum level of acceptance. Thus it may be

129

doubted whether a well—defined budget constraint applied
in the majority of hospitals in the sample; the overriding
objective appeared to be maintenance of a certain "qual—
ity" of patient care as perceived by the various groups in
the organization.

Although the formal mechanical procedures of deriv-
ing budgets were similar between hospitals it was in no
case clear that any objective criteria were employed in
allocating funds between departments. In general, the
allocation was determined by the administration on the
basis of perceptions of the "needs" of each department
individually. In several cases it was pointed out.that
an Administrator without at least some technical knowledge
of all the hospital activities was at a disadvantage when
determining the budget, for this situation might require
too much reliance on opinions of various vested interest
groups in the hospital. Almost universally, determination
of the budget was a jealously guarded prerogative of the
administration, and it was always pointed out that if
there were a single most important role for the adminis-
tration, it was determining priorities for resource allo-
cation in the hospital.

Determinants of Nursing Service staffing.--The Nurs-
ing Service Department is the largest in the hospital-—
both in terms of operating expenses and number of person-

nel. As opposed to the situation in the Clinical Services

130

where quality standards of medical care are determined by
the self-regulating medical staff, the standard of quality
of nursing care produced by the Nursing Service department
of the hospital is a parameter of action of the Administra—
tor.

Although "quality" is an elusive term subject to
individual subjective interpretation, maintenance of a
certain level of quality was the basic expressed objective
of hospital administrators in determining Nursing Service’
staffing plans. Most hospital administrators and direc—
tors of nursing used hours of nursing care rendered per
patient per day as the objective first approximation to an
index of quality of nursing care. In attempts to achieve
a certain pre—determined quality level of nursing care,
maintenance of specified staffing ratios was of first-
order importance; Nursing Service staffing ratios were the
primary magnitudes considered in planning for, and control
of, quality of nursing care. Observed staffing ratios
thus reflect quality standards determined in the hospital's
decision processes.

Administrators' descriptions of how staffing plans
were determined were generally vague, primarily because no
objective criteria could be brought to bear on the defini-
tion of quality. Consequently, staffing ratios were gen-
erally subject to discretionary determination within the

constraints peculiar to each institution. While several

131

administrators employed outside consultants to recommend
staffing plans, most staffing plans were determined in a
decision process internal to the hospital. The constrain-
ing conditions under which staffing ratios were deter—
mined in the sample hospitals can be generalized into
three categories as follows: the amount of administrative
influence in the staffing decision with respect to (l) the
degree to which the Administrator delegated authority to
subordinates, and (2) the degree to which budgetary con-
siderations influenced the staffing decision, and (3) the
degree of interdisciplinary influence in the staffing
decision.

Administrative control was imposed on nursing ser-
vice departments at two levels: through the budget and
through the administrative lines of authority. With re—
spect to the latter, authority was delegated to assistant
administrators or department heads according as the Admin—
istrator took a professional interest in the functions of
the Nursing Service department and as he judged the com-
petence of subordinates. The attitude of the Administra-
tor thus had direct effects on the way in which Nursing
Service staffing was determined.

Administrators of the sample hospitals had a wide
variety of backgrounds, including Professional Nursing;
thus some of the administrators had a direct professional

interest in planning nursing service staffing. In other

132

instances the professional autonomy of the Nursing Service
department was a function of the level of administrative
competence imputed by the administrator to his subordi—
nates in that department and the degree of budgeting con-
trol utilized. In some cases the Administrator relied
heavily on the Director of Nursing and staffing plans
recommended by the Nursing Service department were effected
without revision, whereas in other cases the ultimate
staffing pattern was the result of negotiation and compro-
mise between the nursing service department and the con-
troller.

In most of the larger hospitals where size limited
the informal flow of information between departments, a
number of interdisciplinary committees were maintained for
the purpose of quality control. In addition to some regu-
lar committees of the Medical Staff which included non-
physician participants, the most common was a "patient
care" committee of representatives from all the groups
involved in patient care. Such committees, in bringing
together various groups on a regular basis to review the
overall operations of the hospital, were designed to
broaden channels of communication and aid in solving prob-
lems that were of an interdepartmental nature. Although
several administrators had disbanded patient-care commit-
tees on the grounds that they were used primarily as forums

for individual character assassinations, interdisciplinary

133

committees generally functioned in larger hospitals as
substitutes for the informal methods of communication
prevailing in smaller institutions. Thus patient care
committees played an important role in the determination
and maintenance of the standards of nursing care provided
by some hospitals.
Empirical Formulation of
the Conceptual Framework

The problem of measuring the factors that determine
the hospital's choices for estimation of their effects on
the demand for nurses' services may now be considered. An
empirical approach to isolating quantifiable variables was
indicated in the establishment of the conceptual view of
the hospital decision process at the beginning of this
chapter. The conceptual development will lend itself
readily to empirical formulation within the framework sug-
gested by Marschak.ll Such a framework views an organiza-
tion as a set of rules—-a constitution--describing how
group decisions are made. Thus a value consensus is sub-
sumed in the definition; a requirement for the existence

of an organization is that the participants achieve a

transitive ordering over their alternatives. Two aspects

 

llJacob Marschak: "Efficient and Viable Organiza-
tional Forms," in Modern Organization Theory, ed. by Mason
Haire (New York: John Wiley and Sons, Inc., l96l), pp.
307-320; "Towards an Economic Theory of Organization and
Information," in Decision Processes, ed. by R. M. Thrall,
C. H. Coombs, and R. L. Davis (New York: John Wiley and
Sons, Inc., 195“), pp. 187-220.

134

of the organization are relevant for analysis of the deri-
vation of the ordering. First are the tastes of the indi-
vidual participants of the decision process; second is the
nature of the decision rule, i.e., the method by which
interpersonal utility comparisons are made. The theore-
tical analog to Marschak's organization model is contained
in equation (15) of Chapter IV, the first partial deriva—

tive of the hospital utility function:
6V 6X = 2 6V 6U 6U 6X.
xi p(/p><p/l>

th

where dV/dUp is the weight or influence of the p indi—

th

vidual, and (SUp/GXi is the intensity of the p individ-

ual's preference for the ith mode of expenditure.

In the application of Marschak's framework to des-
cription of a given decision process, two basic sets of
equations become important: equations describing the
information or communication system of the organization,
and equations describing the rules by which action is
undertaken in response to receipt of information. Thus a
description of the decision process will indicate how in-
formation is assimilated in the organization, reflecting
the manner in which interpersonal utility comparisons are
made, and how standards of performance are determined for
the component parts of the organization, i.e., how weights

are assigned to preferences in determining constraints on

the component parts of the organization.

135

Formulation of the conception of hospital methods of
decision—making and control in terms of Marschak's frame-
work suggests several variables as likely measures of the
determinates of nursing service staffing with respect to
the nature of the decision process. These variables fall
into two categories, the first categorizing the communica-
tion or information system employed in the hospital, and
the second categorizing the nature of the constraints
placed on the solution for nursing service staffing. The
nature of the data allows only a binary classification of
hospitals with respect to these variables; thus, insofar
as a continuum exists in these classifications, informa-
tion is lost and the results may in some respects be arbi-
trary.

As mentioned above, the need for a formally struc-
tured communications system was generally a function of
hospital size. In small hospitals information was circu—
lated in an informal manner such that the mechanisms of
communication afforded by formal departmentalization were
redundant. On the other hand, larger institutions re—
quired a more formally structured mechanism of communica—
tion such that departmentalization on the basis of tech—
nical or professional function became relevant and
interdisciplinary committees were maintained in some in-
stances to insure direct and constant communication

between groups. Thus two ways of classifying hospitals

136

on the basis of their mechanisms of intra—hospital communi-
cations presented themselves: First, hospitals were clas-
sified "large" or "small" according as their medical

staffs were or were not organized into clinical depart-
ments with Chiefs-of—Services. Secondly, a classification
was created to denote the existence of patient—care or
other hospital wide, extra—medical staff interdisciplinary
committees.

As indicated earlier, the Administrator's perception
of his role determined to a great extent the autonomy of
the Nursing Service Department with respect to its ability
to determine its own quality standards for nursing care
and its ability to pursue those standards within a budget
constraint. The Administrator's perception of his role
varied with his background and With the degree to which
reliable subordinates were available. A third classifi-
cation of hospitals was created to indicate the degree to
which an administrator participated directly in planning
nursing service staffing. Administrators fell fairly
unambiguously into two categories according to whether
they adOpted an authoritarian attitude in their relation-
ship to the Nursing Service Department or whether they
were willing to delegate authority and responsibility for
determining nursing service staffing to subordinates.

A fourth classification of hospitals was employed

to designate the extent to which quality standards

137

formulated by professional groups were compromised by
budgetary considerations of the administration. While it
would be totally unrealistic to maintain that budget con—
siderations had no influence on staffing plans, particu-
larly when the Administrator participated personally in
staffing decisions, it was possible to delineate situa-
tions where budget considerations were secondary relative
to the maintenance of a given standard of patient care
from situations where staffing plans were determined in
budget negotiations. Hospitals in the sample were cate-
gorized according to whether staffing plans were deter-
mined in conjunction with determination of the budget, or
whether budgets were compromised to implement or maintain

given quality standards of nursing care.

Regression Results
The following is a list of the variables used in the
analysis of the demand for nurses' services:

S = ratio of physicians with special clinical pri-
vileges to total active medical staff.
ICU binary variable coded 1 or 0 according as the
hospital did or did not have an Intensive Care
Unit.

CPU = binary variable coded l or 0 according as the
hospital did or did not have a Cardio—Pulmonary
unit.

PNT = binary variable coded 1 or 0 according as the
hospital did or did not train practical nurses.

RNT binary variable coded l or 0 according as the
hospital did or did not participate in the train—

ing of professional nursing students.

138

D1 = binary variable coded l or 0 according as the
medical staff was or was not organized into
clinical departments with chiefs-of-services.

D2 binary variable coded 1 or 0 according as a

patient-care committee was or was not main-

tained.

D3 = binary variable coded l or 0 according as the
administrator was "Authoritarian” or a "Deli-
gator" of authority with respect to the Nursing
Service Department.

DU = binary variable coded 1 or 0 according as nurs-
ing service staffing was or was not determined
in explicit budget negotiations.

T/C = total nursing personnel per average daily census
in medical, surgical, ICU and heart units.

R/C = General Duty Registered Nurses per average
daily census.

P/C = Practical Nurses per average daily census.

A/C = Nursing Aides per average daily census.

R/P Ratio of General Duty RN's to Practical Nurses

(= R/C + P/C).

R/A = Ratio of General Duty RN's to Nursing Aides
(= R/C + A/C).

The matrix on the following page gives the simple correla—
tions between the variables.

Although relative wage rates were included in the
analysis, they are not included in the list of variables
above because they did not show up to have significant
effects on nursing service staffing. Two things must be
pointed out with respect to wage rates. First, starting
wage rates were significantly and positively correlated
with hospital size, and also with the classification of

hospitals according to whether or not they were in "rural"

139

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140

or "urban" communities. Secondly, there was almost an
exact relation between starting wages of Registered Nur-
ses, Practical Nurses, and nursing aides within hospitals:
the starting wage differential between R.N.'s, Practical
Nurses, and nursing aides were approximately in the ratios
1.00: 0.75: 0.50. Thus it appears that, while the abso-
lute level of wage rates may be subject to employer dis-
cretion and determined in relation to, among other things,
differentials in parameters of the supply function between
labor markets, the structure of occupational wage differ—
entials of nursing personnal is a function of industry
custom. If actual wages bore a proportional relationship
to reported wage scales, the appropriate model would view
hospitals as factor quantity adjustors facing pre-
determined (parametric) relative wage rates; but with no
variation in relative wage rates between units of observa-
tion, the system could generate no observation along the
demand functions such that the relation between employment
and relative wages could not be observed.

Due to the limited number of observations, no mean—
ingful regression results could be obtained if more than
four independent variables were included in a single re-
gression equation. Each dependent variable was therefore
regressed onto all pairs, and all 3-tuple and u-tuple
combinations of the explanatory variables to discern the

interrelationships among the variables and to discover

1H1

the "best fit" regression equations. In this instance,
"best fit" is defined in terms of the significance levels
of the estimated regression coefficients; the combinations
of explanatory variables which gave the highest acceptance
probabilities for the estimated coefficients of the in-
cluded variables were the best-fit equations, irrespective
of the values of the coefficients of multiple determina-
tion. Where more than one combination of explanatory
variables were equally acceptable under this criterion,
all acceptable combinations will be reported. Each regres-
sion will be accompanied by the coefficient of multiple
determination (R2) and the corresponding F statistic

(F ) by which to compute its level of significance,

vl,v2
and by the coefficient of multiple determination adjusted
by degrees of freedom (R2). The standard errors of the
regression coefficients appear in parentheses below them.
Each regression is based on 19 observations.

With the ratio of total nursing personnel to average

daily census as the dependent variable, the following best

fit equation was obtained:

(1) T/C = 0.75 - 0.2M CPU + 0.19 RNT + 0.81 01 - 0.10 on
(0.07) (0.11) (0.10) (0.08) (0.07)

‘2 2

R = .UO R = .58 (F = 3.1“)

3,9

Although it is not itself significant at the 10 per cent

level, the inclusion of D4 in the regression equation

142

improved the significance levels of the coefficients of
CPU and D1.

With the ratio of Registered Nurses to average daily
census as the dependent variable, two alternative combina-

tions of explanatory variables gave acceptable results:

(2a) R/C = 0.22 + 0.38 S - 0.08 ICU - 0.09 D4

(0.03) (0.08) (0.04) (0.03)
R2 = .74 R2 = .80 (F3’lo = 13.13)
(2b) R/C = 0.25 - 0.04 ICU - 0.09 D4 + 0.13 RNT
(0.03) (0.04) (0.03) (0.04)
R2 = .63 R2 = .72 (F3,lo = 8.49)

When S and RNT were included in the same regression equa-
tion, neither were significant; only D4 was significant
when S, RNT, ICU, and D4 were included in a single regres—
sion equation. Colinearity appears to be the main prob-
lem, for the most drastic change resulting from changing
combinations of independent variables appears in the
standard errors of the estimated coefficients rather than
in the magnitudes of the coefficients themselves.

For the ratio of Practical Nurses to patients as
the dependent variable, the following combination of vari-

ables was most satisfactory:

(3) P/C = 0.16 + 0.17 ICU - 0.14 RNT + 0.10 D3
(0.04) (0.06) ' (0.06) (0.0u)

E2 = .3A R2 = .49 (F = 3.18)

3,10

143

The estimated coefficient of ICU was significant only in
combination with D3; otherwise, only the coefficient of
RNT was significant in any combination of independent
variables.

For the proportion of nursing aides to patients, the
following variables defined the space in which the best-

fitting regression surface was found:

(4) A/C = 0.25 - 0.39 CPU + 0.23 RNT + 0.17 D1
(0.05) (0.09) (0.08) (0.07)

'2 2

R = .58 R = .68 (F = 7.00)

3,10

For the ratio of Registered to Practical nurses,
three combinations of independent variables gave good

fits:

(58) R/P = 1.05 + 2.63 RNT — 2.55 CPU

(0.17) (0.35) (0.37)
-2 _ 2 _ _ -
R - .82 R — .85 (F2,11 - 29.96)
(5b) R/P = 1.77 + 1.53 RNT — 0.82 01 — 1.27 D2
(0.36) (0.45) (0.45) (0.41)
—2 _ 2 _ _
R - .51 R - .62 (F3,10 — 5.43)
(So) R/P = 1.63 + 1.39 RNT - 1.37 D2 -
(0.35) (0.45) (0.44)
0.65 D3
(0.31)
R2 — 46 R2 = 59 = 4.70)

“3,10

144

Inclusion of D1, D2, or D3 in combination with CPU raised
the standard errors of their estimated coefficients such
that none were significant at the 10 per cent leve1..
Their use in separate regression equations appears to
radically alter the position and slope of the fitted re—
gression plane with respect to the intercept term and co-
efficient of RNT.

Finally, use of the ratio of Registered Nurses to
nursing aides as the dependent variable gave the following
fitted regression as the best fit with respect to alterna-

tive combinations of the explanatory variables:

(6) R/A = 1.66 - 0.53 ICU + 0.89 CPU — 0.51 01 — 0.76 D4
(0.29) (0.31) (0.23) (0.26) (0 26)

R2 = .53 R2 = .67 (FA 9 = 4.63)

Although the significance of its own estimated coefficient
is questionable, inclusion of ICU as an independent vari-
able brings the significance levels of the other included
explanatory variables within acceptable limits.

For convenient reference, the significant relation-
ships are summarized in Table 10. Inspection of the table
reveals that some distinct patterns prevail in the dif-
ferential effects of the explanatory variables on the

employment of alternative personnel.

145

TABLE ll.--Signs of the significant relationships between
explanatory variables and staffing ratios.*

 

Independent Variable

 

 

Dependent
variable 3 RNT ICU CPU 01 D2 D3 D4
T/C +' — +
R/C + _ _
H + .—
P/C — + +
A/ C + - +
R/P .
H _ _
H + — —
R/A + _ _

 

*The sign of the estimated relationship between the
dependent and independent variable appears in the body of
the table if the regression coefficient was significant
at a level of 10 per cent or better.

The regression results indicate that the variable
having the most pervasive influence on nursing service
staffing is the presence of professional nurse trainees
(RNT). As the hypothesis that professional nursing stu-
dents are substitutes for nursing service personnel pre—
dicts, the ratio of Practical nurses to average census is
negatively related to RNT. The positive realtion of A/C
and R/C to RNT may be explained by the fact that, while

professional trainees may perform nursing tasks under

146

supervision of Registered Nurses that would otherwise be
performed by Practical Nurses, these students would not
be expected to perform menial tasks which generally are
done by nursing aides or practical nurses. Thus profes-
sional nursing students will require more R.N. supervi-
sion in performing patient care functions of Practical
nurses for which they are substituted, but do not perform
the tasks which the Practical nurses performed jointly
with nursing aides.

The presence of special care units also has a per-
vasive effect on nursing service staffing. Segregation
of patients into special units appears to allow hospitals
to function with less total personnel per patient, with
differential effects of requiring less Registered Nurses
and Nursing Aides per patient and more Practical Nurses.
The observed relations are consistent with the hypothesis
that special care units allow hospitals to extend the
division of labor by affording opportunity to match nurs-
ing care needs of different groups of patients with the
skill hierarchy of nursing personnel.

With the effects of RNT and special nursing units
held constant, the organizational variables have differ-
ential effects on nursing service staffing of alternative
personnel. Of particular interest are the significant
negative effects of non-zero D4 on R/C and R/A, and the

positive and negative effects of D3 on P/C and R/P,

147

respectively. Evidently, when nursing service staffing
is determined in the context of an explicit budgeting pro—
cess, the demand for nurses is diminished. Although the
diminution is not accompanied by a significant compensat-
ing increase in P/C or A/C for non-zero D4, the appearance
of D3 as a significant determinant of P/C and R/P suggests
that when the administrator assumes a direct role in
determining nursing service staffing, budget considerations
may enter indirectly into the staffing decision and bias
the results toward less expensive personnel. One might
speculate further on causal relationships, but the fact
that variables indicating the assertion of administrative
influence bear significant relationships to nursing ser-
vice staffing is crucial to acceptance of the hypothesis.
For non-zero values of D1 and D2, the organizational
variables chosen as indicators of a relatively formal in—
formation hierarchy, nursing service staffing appears to
be weighted toward employment of less skilled, less ex-
pensive personnel. If one will grant that the more form-
ally structured relationship between groups implies a more
wide-spread participation of groups in the decision pro-
cess and a consequent reduction of the independence of
individual departments, one may rationalize the observed
relationships between the variables as the result of a
bargaining situation implied in the existence of such an

organizational device. Recalling that low values of R/A,

148

and high values of A/C, were not preferred by nurses (as
indicated in their effect on the turnover rate), one may
infer that in these situations the nursing service depart-
ment is the "loser" with respect to nurses' achievement

of their preferred position in terms of working condi-
tions.

On the whole, the results obtained in the statisti-
cal analysis of the data are consistent with the overall
hypothesis that nursing service staffing is affected by
the ability of that department to pursue a relatively
independent course of action within the hospital organi-
zation. Variables indicating the direct imposition of
constraints, and variables intended as proxies for other
constraining forces on the autonomy of the nursing ser-
vice department have significant effects on the utiliza-
tion of various types of personnel in production of nursing
care. Particularly, the demand for General Duty Regis-
tered Nurses relative to average census is significantly
affected by administrative imposition of explicit fiscal
controls on departments in the organization. Further,
the existence of other organizational devices employed for
purposes of information and control have significant
effects on other variable magnitudes of nursing service
staffing that were previously seen to influence the supply

of nurses to hospitals.

CHAPTER VI

CONCLUSION

The purpose of this dissertation is to place the
issue of the "shortage" of professional hospital nurses
in an objective framework. To do so, it is necessary to
conduct the analysis within the context of the market
system, as Opposed to the p0pular approach which empha-
sizes various arbitrary definitions of "need" rather than
effective demand for nurses' services. The justification
of the economic approach comes from recognition that in
the economy individuals are free to choose among activi-
ties as their interest dictates. Consequently, hospitals
must compete in the market for the services of these
individuals on terms set by the alternatives they may pur-
sue. In this context, the existence of a shortage can be
determined only with reference to the efficiency of the
market mechanism and to the forces determining the demand
and supply of nurses' services. Accordingly, a model of
the demand and supply of nurses' services is required.

Derivation of the demand function for nurses' ser—
vices required an approach based on less restrictive

assumptions than those which characterize the traditional

149

150

theory of the firm. The particular theoretical approach
to the problem of rationalizing hospital economic behavior
was necessitated by the nature of the industry which ren—
ders the conventional theory of the firm ill-suited to
analysis of the hospital as a producing unit. Since the
industry is dominated by non-profit firms, hospital objec-
tives are not easily described in terms of concrete, mea-
surable magnitudes. But more important, the links between
the producer and consumer are clouded by physician-patient
and physician—hospital relationships, as well as the exis—
tence of third-party payers. For these reasons, economic
analysis of the demand for hospital nurses must concen-
trate on the internal decision-making mechanisms of the
hospital. The requisite approach was thus a total utility
model of the firm.

Being perfectly general at the analytical level, a
total utility model of the firm requires formulation in a
specific organizational context to be operationally signif—
icant. The work of medical care sociologists, organiza-
tional theorists, and other researchers in hospital organi-
zation indicated that the stratification of authority
existing in the typical voluntary hospital organizational
structure could be used to advantage in making the model
Operational. Insofar as the preferences or objectives of
component groups of the decision-making body are known, it

is sufficient to identify the dominant coalition in order

151

to determine the outcome of a discretionary decision pro—
cess. Given the nature of the hospital decision process,
it was held that the demand for nurses' services could be
predicted by the use of variables indicating the relative
degree of influence of the professional nursing element
in determining the product specification. A field study
provided further insights into the nature of the hospital
decision process as well as providing the basis for a
limited test of the explanatory powers of the model.

From the methodological viewpoint, analysis of the
supply of nurses' services was straightforward. The
approach to derivation of the supply function involved the
inclusion of the traditional income and leisure arguments
in the individual's utility function, and the addition of
variables reflecting the individual's sensibilities with
respect to working conditions. Specifically, it was held
that the supply of nurses' services to a given hospital
would be functionally related to the vector of product
specification parameters determined in the hospital's
decision process, as well as to the wage rate.

In placing the problem in an objective perspective
from the economic point of view, the analysis indicates
that the "shortage" of professional hospital nurses cannot
be traced to imperfections in the labor market. Although
estimation of the wage responsiveness of the inactive nurse

force with county cross—sectional data from the state of

152

Michigan indicated that the short-run supply function of
nurses is inelastic with respect to the wage rate, nursing
wages are rising at a rate surpassing the national aver-
age. There is no indication that wages are impeded in
performing their rationing function when demand increases
relative to supply. Nor can it be held that the stock of
nurses is being fully utilized so that artificial barriers
to entry into the profession are relevant, or that immo-
bility is a factor restricting freedom of choice of the
members of a female-dominated profession. For, while a
large proportion of the licensed nurse force is inactive,
turnover rates of registered nurses in short-term hospi-
tals average more than 50 per cent annually.

Although the quantity of nurses' services supplied
in the short run appears to be relatively unresponsive to
changes in wage rates within the observed range, the
supply is not inelastic with respect to other hospital
parameters of action. Statistical analysis of data col-
lected from a sample of short-term general hospitals re-
vealed that turnover rates of professional nurses were
significantly related to the hospitals' product specifi-
cations in terms of the combinations of inputs used to
produce nursing care. This relationship suggests that
nurses' decisions to pursue active practice are influenced
heavily by their ability to find employment in situations

that appeal to their professional sensibilities. The

153

observed sensitivity of the supply of nurses' services to
conditions of their professional environment has direct
implications for the "shortage" of nurses.

Because product specifications are subject to dis-
cretionary determination in decision processes involving
divergent views of numerous professional groups, the out-
come in any given situation will depend on the dominant
professional view that prevails in the political structure
of the particular institution. Thus in one respect the
problem of the "shortage" of nurses reduces to one of hos-
pital politics rather than one of ability to achieve well-
defined objectives within a set of constraints. For,
whereas hospitals which relegate nurses' professional
environment to a second order of importance in the allo-
cating decision complain that nurses are not available in
the labor market, hospitals which pursue an explicit
strategy to minimize turnover by offering incentives to
which nurses respond experience no "shortage."

In another respect, however, an objective statement
can be made about the "shortage" of nurses. If one takes
the dominant professional View as the "correct" one, i.e.,
if the prevailing product specification of hospital care
reflects society's preferences, one may conclude that
there is a surplus of nurses. For, insofar as nurses re-
spond to incentives of a type which are not being offered
in the market, resources are being used to produce a

commodity for which there is no demand.

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