Sectoral trends in employment and shifts in the Phillips curve

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Sectoral trends in employment and shifts in the Phillips curve
Dalton, Thomas Richard, 1946-
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xii, 123 leaves. ; 28 cm.


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Economic inflation ( jstor )
Employment ( jstor )
Labor ( jstor )
Labor markets ( jstor )
Labor supply ( jstor )
Unemployment ( jstor )
Unemployment rates ( jstor )
Wage rate ( jstor )
Wages ( jstor )
Workforce ( jstor )
Dissertations, Academic -- Economics -- UF
Economics -- Mathematical models ( lcsh )
Economics thesis Ph. D
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Thesis -- University of Florida.
Bibliography: leaves 118-122.
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The author wishes to express his appreciation for the

assistance of the members of the dissertation committee:

Dr. Milton Z. Kafoglis (Chairman), Dr. ClementH. Donovan,

Dr. Norman G. Keig, Dr. Madelyn L. Kafoglis, Dr. Ralph B.

Thompson and Dr. Sanford V. Berg. In particular, I am

grateful to Professor Berg, who suggested the hypothesis

and encouraged my work on a day-to-day basis. His editorial

and analytical assistance was invaluable. Dr. George Perry,

Dr. James Hosek, and Dr. Frank Sloan provided data and

assistance. Lu Dalton improved the style and exposition of

the paper.

The material in this project was prepared under

Grant No. 91-12-73-10 from the Manpower Administration, U.S.

Department of Labor, under the authority of title I of the

Manpower Development and Training Act of 1962, as amended.

Researchers undertaking such projects under Government

sponsorship are encouraged to express freely their professional

judgement. Therefore, points of view or opinions stated in

this document do not necessarily represent the official

position or policy of the Department of Labor.

Any errors and omissions are the responsibility of the



Acknowledgements.................................... ii

List of Tables........................................ v

List of Figures ............................ ........... vii

Key to Symbols........................................ viii

Abstract .............................................. x


1 INTRODUCTION.................................. 1


2.1 Phillips Curve Theory.................... 9
2.1.1 R.G. Lipsey: nonlinearities and
frictional unemployment.............. 10
2.1.2 G.C. Archibald: dispersion and
aggregate unemployment.............. 12
2.1.3 J. Vanderkamp: sectoral Phillips
curves................................ 14
2.1.4 C.C. Holt: job-search theory......... 14
2.1.5 E.S. Phelps: accelerationists and
unstable Phillips curves............. 16
2.1.6 J. Tobin: disequilibrium dynamics... 18
2.1.7 Lucas and Rapping: rational moti-
vation for money illusion............ 21
2.1.8 R.J. Gordon and G.L. Perry: data
adjustments and demographic studies... 22
2.2 Sector Analysis........................... 24
2.2.1 W. Baumol: unbalanced growth......... 24
2.2.2 V. Fuchs: goods and services as
identifiable sectors.................. 25
2.2.3 M.L. Wachter: interindustry wage
structure............................ 29
2.3 Labor Force Participation................ 30
2.3.1 Simler and A. Tella: discouraged
worker effects....................... 30
2.3.2 M.L. Wachter: the neoclassical labor
supply model......................... 32

Chapter Page

"PRIMARY" WORKERS............................ 34

3.1 Labor Market Boundaries and Labor
Force Mobility.......................... 34
3.2 Labor Force Participation in Heterogeneous,
Segmented Labor Markets ................. 38
3.3 Empirical Results for Two Broad
Industrial Groups........................ 49
3.3.1 General versus specific labor
market indicators................... 51
3.3.2 Money illusion and expectations..... 53
3.3.3 Prolonged high unemployment effect.. 56
3.4 Discouraged Worker Effect............... 58
3.5 Crossover Effects....................... 60
3.6 Conclusions ............................... 62

AGGREGATE PHILLIPS CURVE..................... 64

4.1 Disaggregation Into a Two Sector Model.. 66
4.1.1 General aggregation issues.......... 67
4.1.2 Industrial labor force composition
and pivots in the naive Phillips
curve............................... 76
4.1.3 Price expectations and shifts in the
Phillips curve...................... 79
4.2 Empirical Analysis of the Two Sector
Model................................... 81
4.2.1 Sector unemployment rates and wage
rates............................... 82
4.2.2 Complications in the estimation of
Phillips curves...................... 86
4.2.3 Aggregating sector Phillips curves.. 89
4.3 Conclusions............................. 95

5 SUMMARY AND CONCLUSIONS ..................... 100

5.1 Pivots in the Phillips Curve and Wage
Price Controls........................... 101
5.2 Implications for Future Research......... 104


References................ ............................. 118

Biographical Sketch................................... 123


Number Page

1 Labor Force Participation Functions for A
Neoclassical Model, For Industrial Data--
1958:1-1971:1................................ 52

2 Labor Force Participation Functions Combining
Neoclassical and Discouraged Worker Models.... 57

3 Discouraged Worker and Crossover Effects on
Labor Force Participation-1958-1971:1......... 59

4 Linear Phillips Curves 1958:1-1971:1.......... 85

5 Nonlinear Phillips Curves 1958:1-1971:1....... 85

6 Phillips Curves with Autocorrelated Disturbances
Removed....................................... 87

7 Aggregate Phillips Relations with Different
Sectoral Weights................................ 92

8 Aggregate Phillips Relations with Different
Sectoral Weights................................ 92

9 Estimated Phillips Tradeoffs (assuming PCR = 0) 97

10 Estimated Phillips Tradeoffs (assuming PCR = 3%) 97

A-1 Percent Composition of Non-agricultural Employ-
ment, by Sector ............................... 109

A-2 Average Rate of Change in Employment During
Business Cycles, by Sector.................... 110

A-3 Effect of Changing Distribution on Average Cy-
clical Volatility of Total Non-agricultural
Employment.................................... 110

A-4 Average Rates of Change in Output During
Business Cycles, by Sector .................... 114

A-5 Percent of Non-agricultural Employment by
Occupation .................................. 115



A-6 Average Rate of Change in Wages During
Business Cycles, by Sector--1958-1970......... 115

A-7 Average Rate of Change in Productivity During
Business Cycles, by Sector.................... 116


Number Page

1 Movement in Relative Wages and Unemployment
Rates 1958-1971 ................................ 83

2 Sectoral Phillips Curves 1958-1970........... 94



a constant

A aggregate sum of the squares of the residuals

B coefficient of explanatory variable

C coefficient of price change variable

E number employed

G, g Goods sector variable or parameter

I productivity related index

k fixed labor force weight

L, LF labor force

LF/N demographic labor force participation

LF/R industrial labor force participation

m,n number of observations in sample

N population.

P prices (consumer price index)

PCR rate of change in prices

p number of parameters

R population deflator for industrial labor force

S,s Service sector variable or parameter

U unemployment rate

UN,V number unemployed

W wages (compensation per man-hour)

w rate of change in wages


Key to Symbols--continued

Term Definition

X any variable quantity

a variable labor force weight

y sector proportion of employment (Chapter III);
Price expectations index (Chapter II)

6 relative wages

p relative unemployment

p variable weighting applied to the rate of change
in wages

a2 dispersion of unemployment rates


A aggregate figure

g Goods sector figure

i industrial data

j demographic data

p permanent variable

s Service sector figure

T Transitory variable

t time

Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctory of Philosophy



Thomas Richard Dalton

August, 1973

Chairman: Dr. Milton Z. Kafoglis
Major Department: Economics

This dissertation develops and tests a "segmented

markets" Phillips curve model which is based on the demand-

oriented industrial distinctions noted by Victor Fuchs,

and is related to recent models emphasizing both excess

demand and price expectational influences. The paper first

presents and critiques the theoretical and empirical con-

tributions which are used to develop the segmented markets

model. Three areas of concern are stressed: Phillips

curve theory, industrial sector analysis, and labor force

participation research. In order to evaluate the applic-

ability of sector,analysis cyclical labor force participation

movements are studied with the general conclusion

that these "labor supply-oriented" influences reinforce the

sectoral differences cited by Fuchs.

Finally, the segmented markets model is derived

and tested. The information provided by Fuchs' research and

the analysis of labor force participation in this study serve

as bases for the hypothesis that sectoral Phillips curves

possess different values for the intercept and coefficients;

resulting from differences in the output and labor markets

of the sectors. Further, with the assumptions that the

independent variables are exogenously determined, and that

no aggregation problems (such as dispersion of unemployment

effects) are present, the two sector curves are combined to

form an aggregate Phillips tradeoff. Tests of the model show

that sectoral Phillips curves exist, but that the assumptions

underlying the aggregation process limit the interpretation

of the aggregate function. However, trends in employment

are shown to have "pivoted" the aggregate curve in the wage

change-unemployment rate plane, such that the curve using

1970 employment weights is more steeply sloped than the

curve using either 1950 or 1960 weights.

The paper concludes that, although higher wage rate

increases can be expected at low rates of unemployment using

the 1970 employment mix, less additional unemployment will

accompany policy measures aimed at reducing the rate of wage

inflation. In addition, the difficulties encountered in

interpreting the influence of price changes, suggest that

present research should be supplemented by cross-sectional

analyses and multi-equation models. In any case, the findings

of this paper support the use of disaggregative analysis

to develop a model which can be used by policy makers in

dealing with the complex issue of inflation-unemployment




Since the end of World War II, the experience of gradual

inflation and the development of disequilibrium macro-economics

have caused increased attention to be focused on the infla-

tionary process and its relation to unemployment.1 During

the nineteen fifties this interest was expressed in a series

of theoretical explanations ranging from the demand-pull

theory to models based on disaggregated market behavior (29)

(42a). These theoretical models gave way to broader empirical

approaches during the sixties, led by the pathbreaking work

of A.W. Phillips (39).2 The seventies seem to be a time for

reassessing the significance of the major empirical contri-

butions, reconciling major theoretical approaches, and, hope-

fully, finding viable policy mechanisms for dealing with

these problems.

Positive and fairly steady growth in wages and prices

has characterized the post-war period. However, during the

periods of 1946-48, 1950-51, and 1965-1971 the rate of

1This paper will discuss the history of wage inflation, in
the United States, as well as the evolution of thought on
this matter, for the period since nineteen fifty-eight. For
a thorough treatment of the preceding. period see Perry (37a).

2For a discussion of the theory characteristic of the fifties,
as well as an early presentation of the Phillips relationship
for the United States see P. Samuelson and R. Solow (41a)


increase accelerated. Accentuating the problem is the fact

that during most of this period a condition of excess supply

has existed and that unemployment has been very unevenly

distributed. In addition, prices and wages have tended to

move concomitantly since nineteen forty-six. Therefore, it

is understandable that the central issues in recent inflation

discussions have been the relationship between money wages

and prices on the one hand, and money wages and excess supply

on the other.

This study is primarily concerned with the labor market

conditions underlying the apparent wage change-unemployment

rate tradeoff. This observed relationship has been labeled

the "naive" Phillips curve and is generally assumed to be an

inverse relationship. The approach, which is characteristic

of a pattern established by Phillips, does not directly

consider the issue of price determination, but concentrates

on explaining the nature of the wage determination mechanism.

Therefore, in this discussion the term "inflationary process"

refers to wage inflation.

Since the Phillips curve is viewed from a labor market

perspective, we seek to develop a model which incorporates

major labor market trends. This study departs from much of

recent Phillips curve work by formulating wage determination

and labor supply models based on industrial, instead of

demographic, data to demonstrate the existence of different

labor market characteristics. To the extent that institutional

barriers, geographical circumstances, and employment pre-

ferences curtail the perfect mobility of labor between

heterogeneous sectors, different labor supply and wage

determination patterns will exist. If, in the segmented

labor markets making up these sectors,wage bargaining is

conducted on an individual basis, and there is internal

labor mobility, wage levels and changes will be determined

in a competitive manner. Further, the voluntary unemployment

in these sectors will not be correlated with money wage rate

changes. However, adjustment lags and job-search behavior

give rise to frictional unemployment, and institutions such

as unionization can cause involuntary unemployment, both of

which may be negatively correlated with money wage rate

changes. Sectoral Phillips curves can be hypothesized in

this case, and to the extent the differences in these sector

curves can be explained in terms of labor market differences,

insight into the Phillips curve will be gained by studying

these relationships. At the same time, the existence of

partially segmented, and differentiated labor markets produces

disequilibrating influences causing other aggregate Phillips

phenomena.. While the influence of sector differences on the

Phillips curve has been hypothesized previously, this paper

represents the first attempt to comprehensively test a

sectoral model.3

Phillips curve thought, theoretically and empirically,

has developed rapidly, with earlier studies assuming that the

3Vanderkamp (47) provided an early test of a sectoral model,
based on organized and unorganized sectors. His discussion
is weak, however, lacking both a rigorous justification for
segmenting markets and comparable tests for Phillips phenomena
in the two sectors.

curve existed independent of other economic conditions.

Recent research has taken a broader perspective by including

other parameters and variables in the analysis. In particular,

the inclusion of a price term, interpreted as representing

the influence of expectations on wage inflation, has resulted

in renewed understanding of the Phillips relationship. More

recently, disaggregation of demographic data has resulted in

increased understanding of the possible causes of and influ-

ences on the Phillips curve. The present sectoral examination

extends the recent trend toward increasing emphasis on

changing economic conditions in studying the complexities

underlying the Phillips tradeoff. This analysis concentrates

on the sector differences in the cyclical fluctuations and

secular trends of key market parameters, and takes the

position that the examination of labor market structure yields

insight into the nature of the inflationary process. Since

this study uses a multi-market approach, it must consider both

demand and supply differences among sectors. The paper builds

upon Victor Fuchs'(18) valuable analysis of differences in

demand. In addition, the labor supply model developed here

tests for supply differences which may also affect the

Phillips relationship.

Chapter 2 surveys previous research in three areas,

considering contributions with respect to the existence and

stability of the Phillips curve, the characteristics of

different sectors, and those aspects of labor supply research

pertinent to this discussion. While the first section

presents an overview of current Phillips curve thought, the

last two parts provide a basis for analyzing the demand and

supply characteristics of segmented labor markets, a necessary

prerequisite to developing a disaggregative Phillips curve

model. The first part, the Phillips curve survey, begins with

the unemployment dispersion explanation of the Phillips curve

presented by Lipsey and others who attempted to deal with

heterogeneous labor markets. Holt's job-search theory

presents another approach to disaggregative analysis and

precedes accelerationist and imperfections interpretations

of the Phillips phenomena. The second part, the examination

of sectoral characteristics,discusses different approaches,

ranging from Baumol's theoretical consideration of secular

trends to Fuchs' more empirical work. The third section,

labor supply, presents the results of tests of two opposing

views of labor supply response, the discouraged worker model,

and the neoclassical labor supply model.

Chapter 3 proceeds to develop two models to test for

labor supply response over industrial divisions. The chapter

analyzes the influence of the discouraged worker effect, the

significance of real wages as a basic argument of the labor

supply function in the short to intermediate run, and the

effect of relative wages on labor supply response. First,

a neoclassical model is contrasted with the discouraged

worker model to determine the applicability of the competitive

model in the short to intermediate run. Second, a relative

wage model is developed to test for the significance of

crossover effects, and differential wage and unemployment

patterns between sectors. These results offer evidence

regarding the nature of the Phillips tradeoff such as money

illusion and price expectations effects, and support the

tests conducted in the next chapter.

Chapter 4 develops and tests the sectoral Phillips

curve model, with the goal of determine the principle factors

influencing wage rate growth for the period 1958-1970.

First,we examine the theoretical aspects of sectoral dif-

ferences and establish the characteristics of sectoral

Phillips curves. Using the multi-market approach, we consider

two effects of market heterogeneity on the aggregate Phillips

curve. The first, and most important for the recent period,

is the influence of changing employment patterns; toward

service-producing employment. Of major importance here is

the consideration of the distinction between the imperfections

responsible for the sector curves and the market differentia-

tion factors, embodied in relative wages and unemployment

rates, which must be considered when aggregating these

separate curves. The meaning and significance of additional

influences on the relationship provide useful benchmarks for

interpreting the tests. These additional effects include the

price change variable, as well as the unemployment dispersion,

wage rate dispersion, and incomes policy effects. This

chapter concludes with a quantitative analysis of the effect

of changing economic conditions on the Phillips curve,

concentrating on the significance of the trend toward service


Chapter 5 presents some tentative conclusions concerning

the nature of the inflationary process in recent U.S. history

and develops policy implications from the theoretical and

empirical results presented in Chapters 3 and 4.

1) The evidence presented in the study suggests that
two sectors having different input and output structures
do posses different Phillips relationships, and that
the aggregate dynamic response, resulting in a short
run Phillips curve, is dependent upon institutional
arrangements and the size and makeup of individual

2) We find that the trend toward Service sector
employment has caused the aggregate Phillips curve
to pivot, resulting in an apparent outward shift
at high wage rate growth.

3) Sector disaggregation implies that a multi-equation
approach is needed to capture all of the relevant
relationships. The present, partial equilibrium
analysis can be viewed as a preliminary exploration
of a simple two sector model. However, the regression
results suggest that alternative statistical techniques,
and more complex models will reveal additional inter-
pretations of the aggregate Phillips tradeoff.

4) While the results of this paper support the
familiar "manpower" solution for improving the
tradeoff, (21b) (22) (25a) (25d), we conclude that
incomes policies, as presently administered, may be
relatively ineffective. This conclusion is derived
from the difference in policy visibility of the
sectors and the differences in market reactions to
the imposition of wage-price controls. Not only is
the Service sector less likely to be directly con-
trolled, but it is also less likely to be favorably
influenced by incomes policy. In addition, if
reference standards for wage adjustment depend on
relatively high wage rate growth sectors, incomes
policy may exacerbate the situation (31).

5) The comparison of demographic and industrial
studies suggests that not all the relevant effects
can be analyzed using either set of data alone. The
demographic data do not permit sectoral breakdowns,
while the effect of unemployment dispersion is not
fully captured by the industrial data. However, there
are more fundamental differences between the two
approaches. For example, the concomitant trends toward
service oriented employment and higher labor force


participation rates for secondary workers have had
different impacts. Because of the first trend, the
cyclical response in wages and unemployment has
changed. Due to the second, the dispersion of un-
employment has increased. While these trends are
reinforcing at low unemployment rates, they may be
offsetting as unemployment increases.

6) This study does not conclude with a single explan-
ation of the wage determination process, but it does
point out that sectoral differences are elements in
this process. Because of the importance of this
subject for policy purposes, it is necessary that
future study incorporate cross section data, as well
as more sophisticated models. But certainly, future
work should move away from the use of aggregate time
series data and the assumption of a single, homo-
geneous labor market. That research should capture
sectoral behavior in a meaningful way to reveal the
nature of the market forces creating the perceived
inflation-unemployment dilemma.



The sectoral Phillips curve model developed and tested

in this paper is derived from three broad areas of research:

theories and estimates of Phillips curves; labor market

studies stressing sector analysis; and studies of the

relationship between changing economic conditions and labor

force participation rates.

2.1 Phillips Curve Theory

Much of the importance of and interest in the Phillips

curve stems from its policy implications. Since basic goals

of modern society include the maintenance of full employment

and stable prices, any long-term negative relationship

between wage rate changes and unemployment rates suggests

that one goal must be "traded off" for the other.

The original Phillips curve was intended to be a

statistical study of the wage change-unemployment rate trade-

off. However, Phillips (39) broadly interpreted the results

of his tests by concluding that the observed relationship

supported a view that the rate of change in wages was function-

ally dependent on the unemployment rate. Although Phillips'

contribution was nontheoretical in nature, this conclusion

presents an early attempt to justify the tradeoff.1 Later

'Irving Fisher provided the first statistical study of an
inflation-unemployment tradeoff. Interestingly, he viewed
the direction of the causation of the functional relation-
ship differently than Phillips, claiming,

research has continued to examine the nature of the Phillips

curve in a number of ways. This section will consider some

of these additional topics.

2.1.1 R.G. Lipsey: nonlinearities and frictional unemployment

Lipsey (30) provides the first comprehensive theory of

the Phillips curve, basing his explanation on differences in

the relationship between wage rate changes and unemployment

rates for unemployment rates above and. below the frictional

level. According to this theory, wages rise in a sector only

when labor demand exceeds supply. Lipsey states that excess

demand exists when the unemployment rate is below the frictional

level and excess supply prevails when the unemployment rate

is above the frictional level. Assuming that the number of

vacancies remains constant when excess supply exists, excess

supply will increase linearly with unemployment. When excess

demand exists, changes in unemployment are associated with

other than linear changes in excess demand since the number

of vacancies are also variable at levels below frictional

unemployment. Assuming wages move linearly with excess demand,

then the resulting nonlinearity between unemployment and

excess demand will be transformed into a nonlinear relation-

ship between wages and unemployment.

If Lipsey's assumption regarding the assymetry of vacancy

movements is accurate, it is apparent that the rate of wage

"The fact that deflation causes unemployment has been
well recognized for many years in isolated instances,...
It has likewise been recognized that inflation carries
with it a great stimulation to trade and an increase
in employment." (16, p. 785).

change in the aggregate will be greater for a given level of

unemployment than the wage change which any sector with the

same level of unemployment would produce; as long as the

unemployment rate in one sector is below the frictional

level. For example, assume a two sector economy with a

frictional unemployment rate level of five percent, where

one sector has an unemployment rate of four percent and the

other a rate of eight percent, and the size of the labor

force being the same in each sector. An aggregate rate of

six percent would imply a simple linear relationship between

wage rate change and the unemployment rate, and the tendency

for the economy to equilibrate implies that the wage rate

change will be negative when the aggregate unemployment rate

is above five percent.

However, a more than proportionate (nonlinear) increase

in wage rates would occur in the labor market having only

four percent unemployment, which could outweigh the linear

decrease in the market with eight percent unemployment, and

cause increasing wage rate changes at an aggregate unemploy-

ment rate of six percent. The nonlinearity of the relation-

ship also suggests a Phillips curve convex to the origin at

aggregate unemployment rates ranging from those considerably

below the frictional level to those significantly above this

level. Lipsey's sectoral theory is the first comprehensive.

explanation of why wages tend to rise at overall unemployment

rates above the frictional level (or before "full-employment"

is reached). The Lipsey explanation suffers from its

reliance on a questionable assumption concerning vacancy

rate movements and the absence of a theory to explain why

money wage changes necessarily respond to excess demand

changes. However, as a technical explanation of the

observed tradeoff, the Lipsey model helps to link sectoral

behavioral differences with aggregate inflation and unem-

ployment behavior.

2.1.2 G.C. Archibald: dispersion and aggregate unemployment

Archibald (3a) (3b) has recently tested the Lipsey

notion of the effect of unemployment dispersion and expanded

this to a theory based on market structure. While noting that

he has no clear idea of what the "true" labor markets are,

Archibald contends that he has found that differences in

market structure affect the Phillips relationship.2 To

support this contention he theorizes that separate labor

markets exist, with different market characteristics which

give rise to different structures of excess demand. He

further notes that a theory based on such disaggregation

requires that the labor force be imperfectly mobile between

sectors (not, however, that it be perfectly immobile).

In such a case, he argues, a stable Phillips curve will

exist when the structure of excess demand between sectors

remains stable over time, (assuming, of course, that the

2 "the simple correlation between the rates of wage change
and the price change is fairly high,... If the former
depends upon excess demand in the labor market and the
latter on excess demand in the labor market and excess
demands for labor and goods are highly correlated, as we
should suppose, this is unsurprising. The question
however, is whether we can obtain more information about
the rate of change of wages from variables specific to
the labor market." (3a, pp. 124-25).

relationship between excess demand and the unemployment

rate is also stable).

To approach this problem he tests for the existence of

an effect of unemployment dispersion on the rate of wage

change. This involves two steps. First, he tests Lipsey's

assumption that the relationship is positive with a model

using geographical data for the U.S. and geographical and

industrial data for the U.K. The model used, neglecting

lags and additional variables, regresses the rate of change

in aggregate wages on the inverse of the aggregate unemployment

,rate and- the cross sectional variance in the unemployment


Archibald's tests support Lipsey's contention of a

positive dispersion effect. In addition he finds that there

is a significant correlation among the first three moments

in an expanded regression model including skewness of unemploy-

ment rates. Thus, any two of these variables can be removed

from the expanded model and the remaining variable will become

highly significant in the regression. This finding suggests

that both the aggregate level of excess demand and its

distribution, as reflected in dispersion and skewness, are

important factors in wage rate movements, and that the

stable distribution of excess demand offers a means of

shifting the Phillips curve by changing the distribution of un-

employment. While further testing is necessary Archibald

ventures another conjecture that,

"if our distributional hypothesis were accepted,
the whole debate over 'structural' versus 'demand-
deficient' unemployment would require reconsideration,
because the two would go together." (3b, p. 218).

While this analysis tests for an important influence of

heterogeneous labor markets, it provides only an indirect

view of labor market differences and captures only one

effect, the dispersion of unemployment rates.

2.1.3 J. Vanderkamp: sectoral Phillips curves

Vanderkamp's (47) two sector analysis seeks to examine

the effect of market differences more directly, by estimating

different Phillips curves for two industrial sectors. He

emphasizes the differences in unionization and divides the

labor market into organized and unorganized sectors. Although

he does not present a theoretical justification for segmenting

sectoral labor markets and considers only one aspect of

market heterogeneity, Vanderkamp's results are of interest

to the present research; he finds that, for Canada for the

period 1946-1962, wage changes are less sensitive to varia-

tions in unemployment in the unorganized sector. This analysis

is flawed by both the lack of a comprehensive disaggregative

model and the attempt to compare estimates containing different

explanatory variables. However, the study indicates that

more research, using disaggregated models, is needed before

the influences of market heterogeneity can be fully under-


2.1.4 C.C. Holt: job-search theory

Holt (25b) (25c) has recently developed an alternative

method of disaggergating market behavior with a job-search

theory of the inflationary process, the basis of which is

that job search requires effort due to informational and

other imperfections in the labor market. A new entrant into

the labor market will probably take some time to locate the

"best opportunity". The growth in population alone will

insure positive unemployment rates in such a case. However,

changes in aggregate demand provide the mechanism to generate

Phillips curves under this theory. As aggregate demand

expands there is a rise in the derived demand for labor

(indicated by an increase in vacancies in actual labor markets).

A high flow of labor into and out of the market relative to

the number employed introduces an element of uncertainty

for employers. An individual employer must guess at the wage

rate which will be offered by a competitor, and (due to the

technical heterogeneity of the labor force) the productive

contribution of the new employee. At the same time, the

employer tends to increase wages in this situation to retain

current employees. The combination of these factors gives

an upward impetus to wages which would not occur in a neo-

classical world, so that an expansion is characterized by

increasing vacancies, increasing wages rates, and less job-

search (i.e,, lower unemployment). However a counter tendency

occurs to partially or wholly offset this relationship. As

the unemployment rate declines, more labor is induced into

the market, with the attendent effect of holding wage increases

below what otherwise would occur.

In summary Holt concludes:

"It is the prime contention of the market search
theory of the Phillips relation that the rate of
wage inflation depends on the interaction between
the size of the labor force and the level of aggregate
demand," (25c, p. 230).

In addition, under conditions of low unemployment, the wage

level tends to drift upward.

"The inflow of new workers into the market through
increased labor participation that occurs when un-
employment declines tends to restore unemployment.
This allows greater increases in aggregate produc-
tion with less inflation response than would occur
otherwise." (25c, p. 231).

2.1.5 E.S. Phelps: accelerationists and unstable Phillips

Phelps (38a) (38b) draws on Holt's work and neo-

classical labor theory to advance a sophisticated version of

the accelerationist view of the inflationary process. First,

he states that during upswings, simply the expectation that

vacancies will increase beyond that desired by employers

can cause increasing money wage rates. However, such money

wage adjustment will, presumably, not occur without con-

comitant price adjustment, and therefore, real wages will not

change radically due to this reaction. Job searchers,

seeing an increase in money wages, accept positions not

previously acceptable to them because they are momentarily

fooled by the acceleration in money wage rates. (See McCall

(33) and Mortensen (35).)

At the onset of an expansion, increases in labor demand

can be considered a shock to the equilibrium situation. The

tendency is for firms to initially increase money wages and

to adjust as the uncertainty concerning wage levels and rates

of change dissolves through observation of market reaction.

At the same time, once a steady rate of money wage increase

is obtained, firms quickly attain their desired vacancy

levels. Employees, recognizing that all wage rates are now

increasing at a constant rate, in step with price increases,

will adjust their job-search behavior, and unemployment will

increase until the equilibrium level is reached. As long

as no other shocks occur, the equilibrium rate of wage

change will closely approximate productivity growth plus

the expected and observed growth in prices, and will be

unrelated to the unemployment rate.

Further, assuming a direct relationship between wage

and price inflation, all inflation in this steady state would

be expected and constant. The unemployment rate in such a

case would remain at what Friedman (17) has called the

"natural rate of unemployment". This rate is based upon the

institutional factors giving rise to the fictional and

structural conditions existing at any given time. If the

unemployment rate is held below this natural level, persistent

underestimation of the equilibrium value of the real wage

rate results, which causes, in turn, constant revision of the

wage expectations on the part of both employees and employers,

and a steadily accelerating rate of inflation (thus the term

"accelerationist theory"). This rise in the rate of inflation

will initially "buy" a lower unemployment rate. However, this

rate will increase and approach the natural rate as the

expectations of accelerating inflation develop.

Therefore, Phelps concludes,

"the Phillips curve, in terms of percentage price
(wage)increase shifts uniformaly upward by one
point with every one point increase of the expected
percentage price increase (or expected wage increase).
The equilibrium unemployment rate is independent of
the rate of inflation." (38b, p. 130).

He states that

"society cannot trade between steady unemployment and
steady inflation, on this theory; it must eventually
drive (or allow) the unemployment rate toward the
equilibrium level or force it to fluctuate around the
equilibrium level." (38b, p. 130).

Although Phelps' theory is highly developed, he leaves

two questions unresolved: is job-search behavior the only

major determinant of Phillips curve phenomena, and is the

short run stability of the Phillips curve sufficiently

long to permit it to be used as a policy frontier? Tobin

seeks answers to these questions with a disequilibrium model

of inflation and unemployment.

2.1.6 J. Tobin: disequilibrium dynamics

Tobin (45a) (45b) derives his theory from the same

basis that Phelps does, Holt's study, using elements of the

Lipsey-Archibald dispersion theory. He begins his argument

by making two points concerning the accelerationist view.

First, he states that the accelerationist view espoused by

Phelps assumes that employment beyond the natural rate is

socially inefficient since the time could be better spent

searching new jobs. Secondly, the job-search theory, on

which Phelps develops his theory, assumes that a job can be

more effectively searched when one is unemployed. Tobin

doubts whether either of these conditions is necessarily true.

Tobin theorizes that vacancies have a much stronger

upward effect on wage rate changes than unemployment has in

retarding wages. The fact that vacancies can be changing

constantly, and that the effect in markets with excess

demand outweighs the effect in markets with excess supply,

produces a nonlinear relationship between wage rate changes

and excess demand. This result has three central implications.

First, it provides an alternative to Lipsey's explanation of

nonlinear Phillips curves. Secondly, the variance among

markets in excess demand gives an upward bias to wage rate

changes. The greater the variance, with a given level of

aggregate demand, the greater the wage inflation. Finally,

since vacancies are more influential than unemployment on

the rate of growth in wages, full employment (equality of the

number of vacancies and unemployed), is incompatible with

price stability.

Tobin's view is that unemployment is basically a

disequilibrium phenomenon. The equilibrium component of

unemployment, which is pertinent to the accelerationist

viewpoint, is usually supplemented in actual markets by

a significant disequilibrium component. Disequilibria

continually arise because the structural conditions of the

labor market are in a continual state of flux, regardless of

the stability or instability of aggregate demand. Similarly,

so long as labor markets remain in disequilibrium, money wage

rate changes are also expressed through the action of a

strong disequilibrium factor.

Tobin accepts Keynes assumption that relative wages

form a basic argument for both labor supply and labor demand

in an equilibrium situation, and are conditioned by past

experience and the wage rates for those employed in each

sector. The "equilibrium" referred to here is a steady

state situation not envisaged by the neoclassical model,

since it is one in which aggregate demand can remain unchanged

while constantly changing "institutional" arrangements

produce Phillips curve phenomena.

"Reference standards for wages differ from market
to market. The equilibrium wage increase in each
market will be some function of past wages in all
markets, and perhaps of past prices too. But the
function need not be the same in every market."
(45a, p. 12).

The equilibrium concept based on the relative wage model

diverges from that predicated in terms of real wages:

"A system in which only relative magnitudes matter
has only a neutral equilibrium, from which it can
be permanently displaced by random shocks. Even when
a market is in equilibrium, it may outdo the recent
wage increases in related markets. A shock of this
kind, even though it is not repeated, raises perma"
nently the steady state inflation rate." (45a, p. 13).

The equilibrium situation is not defined in the same

manner in this system asinthe accelerationist system, since

the disequilibria which produce Phillips curves are constantly

arising. The possibility for a long term, stable Phillips

tradeoff exists in Tobin's model where it does not exist in

Phelps' model.3

3Lancaster (28) has recently developed a rigorous model
considering the interrelationships among segmented markets.
His model relies on a "demonstration effect" among markets
which requires cognizance of the fastest growing wages by
all sectors. He also shows under what conditions this leads
to a nonlinear Phillips curve which is convex to the origin.


2.1.7 Lucas and Rapping: rational motivation for money

Lucas and Rapping (32a) (32b) have constructed a

single market model which assumes that labor supply (in

terms of man-hours worked) is sensitive to short run price

and wage deviations. They find that labor supply movements

are positively related to price and wage movements. While

this finding means that a form of money illusion is involved

in labor's supply decision, they view this money illusion as

rationally motivated behavior, based on neither informa-

tional lags, nor behavioral distortions.

"money illusion results not from a myopic concentration
on money values but from our assumption that the suppliers
of labor are adaptive on the level of prices, expect-
ing a return to normal price levels regardless of
current prices, and from the empirical fact that the
nominal interest rate does not change in proportion
to the actual rate of inflation." (32b, p. 269).

Therefore, while Lucas and Rapping employ Holt's search

unemployment concept to explain Phillips phenomena, they

present evidence that the curve results from rational moti-

vation, and not from irrational behavior, uncertainty or

lack of knowledge. The model is neoclassical with the

exception that workers must search for new or better jobs and

in the process, weigh the costs and benefits of such a search.

The Lucas-Rapping study also draws a distinction which

will be of use to the present labor supply analysis, that not

all workers are equally well equipped to search for employment.

Those who have been "laid off" (as opposed to those who have

been "dismissed") are presumed by Lucas and Rapping to have

a better knowledge of "their" current wage rates than other

workers. While the authors use this distinction to draw

conclusions concerning the permanence of one's employment,

we will find it useful to make similar distinctions when

classifying the labor force by industrial structure. Yet

such classification also depends upon the nature and size

of individual labor markets. Lucas and Rapping are primarily

concerned with aggregate data and do not deal with problems

which arise when heterogeneous markets exist. Gordon and

Perry have considered some of these issues in a series of


2.1.8 R.J. Gordon and G.L. Perry: data adjustments and
demographic studies

Gordon (19a) (19b), and Perry (37b) (37c), in separ-

ate studies, have recognized that the heterogeneity of labor

markets can affect the interpretation of the aggregate

Phillips curve. Each has proposed data adjustments which

compensate for market differences.

Gordon's work on wage rate adjustment attacks the data

problems inherent in this type of research; he notes that the

compensation per man-hour data published by the Labor Depart-

ment has two basic weaknesses. These data are not corrected

for either overtime differences between periods or for

sectoral shifts in the employment mix. The result is that

when these data are left uncorrected they distort the rate

of change in wages for Phillips curve purposes. He contends

that this is basically an index number problem involving an

attempt to compare dissimilar data. When overtime and inter-

industry mix changes are not considered, fluctuations in

wages are possible with no cyclical- response in unemployment

rates. For example, a shift in employment from a high wage

industry to a low wage industry can result in the aggregate

wage rate falling in the presence of minimal frictional

unemployment. The change in labor force composition distorts

the theoretical interpretation of the results found when

using such data, and complicates the theoretical interpreta-

tion underlying these movements.

Also of major concern is a theoretically valid and

empirically useful measure of labor market tightness to

serve as an independent variable in regression analysis.

Different weighting schemes for obtaining an aggregate

unemployment rate have been suggested in recent years

(9) (11) (36) (43). These indices are not necessarily

mutually exclusive, but each has its own implications with

respect to underlying causal relationships and policy actions.

That is, no index can be expected to reflect all the subtle

changes in labor force composition or industrial mix.

Perry weights the unit of labor by hours worked and

hourly earnings, using age-sex groupings. With these weighted

units he computes both an unemployment and a dispersion index.

He finds that those groups with higher earnings have a

stronger influence on the rate of increase in wages than

those with lower earnings, and that the existence of dispersion

4Gordon's study has resulted in a recent addition to Labor
Department earnings data. Since 1971 the Labor Department
has published adjusted earnings figures in its publication,
Employment and Earnings.

among demographic unemployment rates reflects inflationary

pressures. He concludes that this weighted unemployment

rate-dispersion proxy for labor market tightness is more

useful in explaining wage rate changes within the Phillips

framework than the simple unemployment rate.

Perry's approach differs from Gordon's in that the

former's adjustment has a theoretical basis and the latter's

a technical basis. Perry hypothesizes that those groups which

contribute more to the economy through higher output per labor

input, also exert the greater pressure on the Phillips curve

relationship. He reasons that the loss of each unit of

labor input, as traditionally measured, is not equally effec-

tive in slowing wage rate increases. He used earnings as a

proxy for productivity and thus, his measure of excess demand

measures labor units in terms of their contribution to final

output and not in terms of individual workers.

2.2 Sector Analysis

The sectoral model has been the core of many studies of

unemployment, inflation, and Phillips curve phenomena. This

section considers three recent contributions to thought in

this area.

2.2.1 W. Baumol: unbalanced growth

Baumol (4a) (4b) presents one theoretical model

attempting to capture essential characteristics of an

observable trend toward increased employment in less techno-

logically progressive sectors.

This theory assumes that two sectors exist, that one

sector is technologically progressive and the other is non-

progressive, and that wages grow at the same rate in both

sectors, which is the rate of growth in productivity in the

progressive sector. If price and income elasticities of

demand for output are such that the proportion of final output

in both sectors remains constant over time, a fixed labor

force will shift out of the progressive into the non-progres-

sive sector. The equilibrium rate of this change will be

the rate of growth in productivity in the progressive sector.

Baumol concludes that this model suggests that balanced

growth in output, when unbalanced productivity exists, leads

to a declining rate of per capital growth in the economy.

Grossman and Fuchs (20) have recently challenged the empirical

relevance of this conclusion for the U.S. economy. They

find that since 1929, changing labor force composition between

Goods and Services has not affected the secular growth of

productivity in the economy. On the other hand, they observe

that the cyclical effects of such shifts on productivity can

be quite important.

2.2.2 V. Fuchs: goods and services as identifiable sectors

In his pathbreaking book, The Service Economy, Fuchs (18)

describes a two sector model, emphasizing the cyclical

movements in various labor market variables. He divides the

nonagricultural economy into two sectors, the Service sector

and the Goods sector, and notes that the Service sector has

experienced rapid growth in its relative labor force during

the last twenty-five years. In order to show the significance

of the changing sector mix in employmenton cyclical stability,

he discusses the broad interrelationships among each of four

areas of concern; employment, output, productivity, and wages.5

For the purpose of analysis, Fuchs defines the Service

sector as including wholesale and retail trade, finance,

insurance and real estate, and service industries and

government;6 and the Goods sector as including the industry

groups of mining, contract construction, transportation and

public utilities,and manufacturing.

Since labor demand is derived from the demand for output,

output differences serve as a starting point for the discus-

sion. A major difference between sectors is that the Goods

sector, in general,produces "stocks" of consumer goods

(products characterized by durability), while the Service

sector produces a "flow" of consumables. If the commodity

in question may be purchased as a stock, with an indefinite

consumption life, its pattern of demand will be more variable

than one which must be purchased as a flow. In the former

case,consumption (the actual use of the product) and demand

for output may vary considerably in time. In the case of

services, consumption must coincide with output. At the same

SSee the Appendix for an empirical discussion of these
6The wage rate data for the government sub-sector is not
available, so this industry group is excluded from conside-
ration in the present study except for certain tests in the
Appendix. We believe that the inclusion of this group would
strengthen the case for the broad sector analysis used
in this research.

time, during downturns in the business cycle, inventories

of a stock decrease the necessity of current production.

Stockpiling is impossible in the case of a flow. Both the

consumption and production characteristics of the two

sectors indicate that the cyclical pattern foroutput should

be more volatile in the Goods sector.

If the demand for output is more cyclically stable in

the Service sector, the derived demand for labor should also

be more stable, ceteris paribus. Other factors which could

influence the cyclical behavior of employment and wages are

the wage determination process, the costs of hiring workers,

and the share of salaries paid in the form of commissions.

If wages are periodically fixed at given levels without

consideration of the demand and supply for labor, employment

will have to fluctuate to absorb shocks to the labor market.

Since the Goods sector is more highly unionized, we expect

the administered wage influence to be greater here. The

Service sector experiences greater hiring costs because there

are a larger number of firms competing in the market and very

little organization of the available supply (such as through

unionization). These cost and organizational differences

imply that the Service sector will lean more toward cutting

wages (or hours) than laying off workers during short reces-

sions, while the Goods sector will react in the opposite manner.

Finally, since wages paid by commission adjust rapidly

to cyclical changes in output demand, employment (in terms of

both hours worked and absolute numbers of employees) for

such workers should be relatively stable.' The wages should

fluctuate significantly to absorb changes in output demand.

The salesmen and brokers to which this is most applicable

are found overwhelmingly in the Service sector. All of the

above point to greater cyclical, stability in employment,

but more volatility in wages in the Service sector. These

points suggest that the cyclical patterns differ between the

two sectors with respect to unemployment and its effect on

wages changes: they also might differ with respect to the

relationship between price changes and wage changes.

In addition, job search characteristics, job definitions,

market power, and mobility are all very different between the

two broadly defined sectors. Job search is affected since

it is more difficult to apply and be interviewed at a large

number of heterogeneous firms than at a single, large manu-

facturing establishment. Since many Service sector industries

are highly competitive, owner-operated, or are related to

professionals, information regarding the "going wages"

should be readily available to those making offers. Yet a

person looking for work will have only a rough idea of how

various skills are weighed in the different occupations--and

thus he may reject a "good" offer on the basis of ignorance.

Mincer notes that for secondary workers, there is competition

of non-market work with market work, and a lower percentage

of time normally is devoted to market labor (34). Thus, the

7Fuchs attributes this "flexible" wages argument to Jacob

net gain of moving into the labor force is small, as is the

net loss from leaving it. Women, in particular, will tend

to enter the market when job search costs are low and labor

market conditions "attractive", explaining the greater

volatility of unemployment rates for certain demographic

groups. The changing character of the labor market is

further complicated to the extent that certain demographic

groups tend to be employed in different industrial sectors.

2.2.3 M.L. Wachter: interindustry wage structure

A recent study by Wachter (48a) provides a useful means

of simplifying some of the complex relationships between

sectors. He hypothesizes that the gap in relative industrial

wages fluctuates cyclically. If it is first assumed that

all wages only move upward (for ease of explanation), then

Wachter's thesis can be stated as follows: wage rate changes

in low wage industries will be greater during expansions; and

these increases will be greater during contractions for high

wage industries. He bases his explanation of this phenomenon,

in part, on market power. High wage industries are character-

ized by unionization and greater market power than low wage

industries. Therefore, high wage industries are better able

to obtain wage increases during recessions. On the other

hand, a certain amount of competition in wages exists between

industries, so that during expansions low wage earners benefit

from the existence of excess demand in the labor market;

competition among firms causeswage increases which close the

wage rate gap.

2.3 Labor Force Participation

The question of labor force participation was touched

upon in the previous section. New entrants are induced

into the labor market as employment opportunities increase

(8) (12). However, they do not join the labor force only

in response to the creation of new job vacancies (34). The

wages (real and relative) associated with these vacancies

are also important. These "hidden unemployed" tend to be

composed of secondary workers (the young, the old, and married

women). Since the specific employment shortages rarely

coincide exactly with these workers' "qualifications", secon-

dary workers tend initially to swell the unemployment ranks

with their entrance into the labor market. The two studies

described in this section provide insight into the movement

of the secondary workforce. In addition, these studies

provide a basis for studying labor supply functions sectorally;

a necessary analysis if sectoral Phillips curves are to be


2.3.1 N.J. Simler and A. Tella: discouraged worker effects

Simler and Tella (43) have formulated and tested the

hypothesis that the Phillips curve model, adjusted to take

account of unreported labor reserves, will have improved

predictive capacity. The labor supply model upon which this

estimation is based is called the "discouraged worker model"

and has as a basis the belief that the marginal worker times

his labor force participation to coincide with periods of low


8In contrast, Lucas and Rapping (32b) emphasize the real wage
effects on labor force participation.

In constructing the revised Phillips model several

theoretical and empirical points are noted. In the first

place, some groups experience more stable participation rates

than other groups. Prime age males have extremely stable

participation rates while females, teenagers, and older

workers have more volatile rates. This implies that some

labor force statistics for the latter group (secondary

workers by definition) are more dependent upon changes in

aggregate demand. When demand increases and job opportunities

improve, unemployed. primary workers accept jobs and

secondary workers enter the labor force. As full employment

is reached the labor reserve shrinks and strong upward

pressure is exerted on wages. The concomitant tendencies for

wages to be flexible only in the upward direction, and for

productivity changes to be passed on in the form of higher

wages (rather than lower prices) means that general wages

tend upward over time. If aggregate demand remains unchanged

and the labor force participation rate of secondary workers

tends to increase over time, the labor reserve for this

group will also grow. If the labor reserve (as well as the

measured labor force) affects wages within a Phillips curve

framework, this secular growth will tend to retard the growth

of wages.

Simler and Tella draw the following conclusions from

their tests:

"(a) the rate of increase in money wages will be
approximately equal to the growth in productivity
so long as there are unemployed primary workers and
reserves of secondary workers; (b) that wages will
begin to increase faster than productivity as un-
employment approaches a frictional minimum and the
participation rate of secondary workers a cyclical
maximum; and (c) wage increases will accelerate once
full employment is reached." (43, p. 47).

2.3.2 M.L. Wachter: the neoclassical labor supply model

Wachter (48b) takes exception to the use of the

"discouraged worker" model as an exclusive explanation of

labor force behavior. He favors the use of real wages as

determinants of labor force participation.

Wachter tests both the neoclassical and discouraged

worker models for the period 1948-1968 using demographic

data representing the various segments of the secondary work

force.9 He concludes from his tests that three major areas

of concern with respect to Phillips curve theory are illumina-

ted by this study.

"First, participation behavior is primarily explained
by real wages." (48b, p. 141).

"Secondly, the supply of labor responds positively
to a variable that reflects the rate of inflation.
The inclusion of this variable follows a formulation
proposed by Friedman (1968). He conjectures that a
form of money illusion in the supply function of labor
is the foundation of an empirically observable, short
run Phillips curve. Thirdly, the labor supply is
found to respond to changes in excess demand conditions
in the labor market only during the period of chronic,
high unemployment, 1958-1966 and even during that
period, the 'effect observed is considerably smaller
than that noted in earlier studies." (48b, p. 141).

9The explanatory variables are hourly earnings and the
consumer price index, representing wages and prices,


It is to these conclusions that we turn in the next

chapter, which uses industrial sectors, instead of demo-

graphic classifications, to examine the labor force

participation of stably employed workers; the primary work




Industrial sector analysis provides a potentially

useful method of examining Phillips curves, as long as

industrial labor force participation movements can be

explained in terms of cyclical fluctuations in the market

variables; wages, prices and unemployment.' If such

movements are unrelated to market characteristics, we cannot

predict that different sectoral Phillips phenomena will

arise for structural reasons, even when sectoral market

differences exist. This conclusion is drawn from the

presumption that Phillips curves are based on the inter-

action of demand and supply phenomena (15). It follows,

that if the labor force participation movements can be

explained in terms of underlying market structures, we will

be able to develop a theory of sector Phillips curves.

based on Fuchs' demand oriented industrial classifications,

since the demand and supply considerations will be rein-


3.1 Labor Market Boundaries and Labor Force Mobility

The differences in cyclical labor force response by

industrial structure have not been intensively examined

'The additional, necessary requirements for the existence
of a segmented markets model are discussed in Chapter 4.

because true labor market boundaries are ambiguous and

considerable labor market crossover is possible (2) (26).

We must assume that the industrial classifications used in

this study give a good first approximation to actual markets;

if so we can develop a labor force participation measure

reflecting this market segmentation. The advantage of

approaching labor supply from this perspective is that we

have a better estimate of the real wage argument of the neo-

classical theory of labor supply. Data exist for wages by

industries, but have to be estimated in the case of demo-

graphic studies, or as with Wachter (48b), the aggregate

wage serves as the proxy for all demographic groups. This

chapter will concentrate on market segmentation when con-

sidering the question of the cyclical response of the labor

force, with the purpose of developing an industrial labor

force participation variable, and of using this variable

to test labor supply behavior on an industrial basis for the

period 1958-1971.

The first approximation to separate markets used in

this study is based on the Goods-Services distinction

developed by Fuchs (18).2 Fuchs has shown that the two

sectors vary in their labor market characteristics. Although

his analysis is concerned with employment and wage differences

arising from differences in the demand functions, sectorally,

2These include a Service sector composed of wholesale-retail
trade, finance, insurance and real estate, and services, and
a Goods sector composed of manufacturing, contract construc-
tion, transportation and public utilities, and mining.

this classificatory system provides a basis for also comparing

the influence of different market structures on the supply

of labor. The structural differences of concern here center

on wage levels and cyclical wage movements, unemployment

rate movements, and the degree of unionization and demographic

composition. Fuchs found that wages are higher and less

volatile cyclically in the Goods sector due to a greater

degree of unionization in this sector and the relatively

larger number of workers paid on a commission basis in the

Service sector. The relatively greater swings in output in

the Goods sector, coupled with relatively smaller swings

in wage rate changes,cause the relatively larger shifts in

derived demand to result in larger swings in unemployment in

this sector. Finally, the Service sector has a larger pro-

portion of women workers, and can generally be more closely

identified with the secondary work force. Therefore, we

expect this sector, ceteris paribus, to have labor supply

characteristics more closely associated with this demo-

graphic group.

It is important to note that industrial data exclude a

segment of the measured labor force included in demographic

studies. This group is composed of the newly entering and

reentering unemployed workers. These are primarily the job

seekers who possess neither adequate technical nor job

search skills. While not all secondary workers are included

in the above group, its composition is primarily of secondary

workers. The assumption is made that by excluding this

cyclically volatile group a major influence of the secondary

work force on labor supply is removed. The remaining group

is stereotyped as the primary workforce and a labor force

participation model based on the primary force is hypothesized.

While some of the relative labor supply movement can be

explained in terms of the demographic composition of the

various industry groups, much of the explanation lies in

different production structures.

The general results of the chapter are:

(1) Labor markets differ along industrial lines, and

can be analyzed in terms of Victors Fuchs' industrial


(2) The neoclassical model provides more insight into

the supply phenomena of industrial labor markets than does

the simple discouraged worker model for the short to inter-

mediate length period. In other words, wages and prices are

more important market indicators than unemployment rates for

the industrial labor force.

(3) Labor force participation responds positively to

price changes in the short run. Also, labor overcompensates

for this short run response to the rate of increase in prices

in the intermediate run, supporting the neoclassical theory

for the existence of short run Phillips curves which shift

over the intermediate period. However, the money illusion

appears to be strongly motivated by rational behavior and

dependent on the given labor market structure; a result

which is not considered by neoclassical theorists.

(4) When real wages change, substitution effects are

more important than income effects in determining the

reaction of the industrial labor force. That is, the indus-

trial labor force participation curves are upward sloping.

3.2 Labor Force Participation in Heterogeneous, Segmented
Labor Markets

The central proposition of this research is that different

labor markets do exist and that the labor force participation

in each is dependent both on the demographic characteristics

of the group and the structural characteristics of the specific

sector. Segmented markets possessing different structures,

skills, and job characteristics should possess different

supply functions and real wage rate arguments. It follows

from this assumption that the labor supply for any given

industrial group can be predicted better in terms of the

real wage for that industry than for an aggregate real wage

rate, and that each labor supply function can be interpreted

in terms of the characteristics of its respective market.

The present model is derived from the labor force

participation work by Wachter (48b).3 The starting point

for his model is neoclassical labor theory which holds

that labor supply is a function of real wages. In comparative

statics this relationship is instantaneously adjusting. How-

ever, for empirical purposes it is generally recognized that

only in the long run will the supply of labor be able to

3One difference in data source between Wachter's work and
this research is pertinent. The wage variable in this case
was drawn from compensation per man-hour under the assump-
tion that pecuniary fringe benefits are relevant to a
primary worker's marginal decision regarding employment.

respond fully to wage and price changes. It is for this

reason that Wachter derives the comparative static supply

function and the equilibrium real wage rate in terms of

permanent wages and prices. Wachter assumes that in the

long run the coefficient of the price term is exactly that

of the wage term and excludes consideration of the price

term. While this study uses the terms permanent and

transitory, following Wachter's nomenclature, the definition

of permanent wages and prices differs from Wachter's.

Wachter considers permanent money wages to be equivalent to

long run real wages. Due to data limitations, the present

study is constrained to a period of twelve years, thus

precluding statements on the long run association among the

various market variables and parameters. Therefore, the

term permanent refers to intermediate run variables and no

a priori assumptions can be made concerning different indust-

rial labor force responses under long run conditions.4

The relevant equation for the intermediate run supply

function is

(1) (LF/R) = a + B (W* y P*)
19 p p p
where: (LF/R)i = labor force participation (variables

described below),

'The permanent real wage used in this study is found by
taking the three year average of wages and prices. This
proxy is developed to preserve both the size of the sample
used and the concept of intermediate run adjustment.
Presumably, a longer period for the average would eliminate
some of the expectations effect noted in the present study.
Since lagged responses could conceivably be distributed
over the period studied, a model incorporating such consider-
ations could improve the present results.

a = constant,

W* = intermediate wages,

P* = intermediate prices,

B = the coefficient of the real wage term,

A = an index of price expectations in the intermediate

All variables are in logarithmic form." When A = 1 expecta-

tions adjust instantaneously, when A > 1, overcompensation

occurs, which is expected in the intermediate run.

The labor force participation variable, (LF/R)i, is

calculated by dividing the labor force, LFi, in each industry

group by a population deflator, R.. The deflator is cal-

culated by multiplying the proportion of the total employment

for both men and women in industry group i, E../E, by their

respective total population, N.. When LF. is divided by R.

the following obtains:
(2) (LF/R)i = LF.i E (Eij/E) N.

where: LF. = labor force in industrial sector i,
R. = population of demographic group j,

E.. = employment of group j in industry i,

E = total employment,

N. = total population of group j, and

j = is divided into men and women in this study.

5Note that the specification of the supply function is such
that the slope (in wage-quantity space), rather than the
intercept, is affected by intermediate price levels. An
alternative functional form with the reverse property is:
(LF/R) i= a + B' log (--r)

The logarithm is used in estimations of the labor supply

function. These calculations are necessitated by data

considerations, since labor force participation rates by

sex-age, and industrial groupings are not available. The

assumption is made,that the population for the industrial

group is proportional to the employment in that group, which

does not consider non-labor force jobs and makes a very

restrictive assumption regarding prospective preferences of

the secondary workers. However, it does permit the formula-

tion of a deflator which removes average supply changes due

to population growth.

In the present study we wish to consider separately

the wage and price reactions in the intermediate run. There-

fore we will consider an equation of the form,

(3) (LF/R)ip = ap + B (W*) B2(P*).

The expected sign of B1 is positive if an upward sloping

labor force participation function prevails. If the value

of p > 0 there should be a negative value of the coefficient,

B2, when B2(P*) is separately considered, where B2 = Bpp

from (1). Similarly, as long as y > 1, IB2 >Bl.

Like Wachter, we examine three short run topics: short

run real wage rate changes, money illusion, and the discouraged

worker effect. The first two are used to measure the response

of the labor force to short run divergences in real wages

from the equilbrium (long run) level. This effect could be

examined by an equation of the form,

(4) (LF/R)iT = aT + BT (W yTP)

where: aT = constant,

B = coefficient of the real wage term,

W = transitory wages,

P = transitory prices,

YT = money illusion index
All variables are logarithmic. If no expectations

existed in the intermediate run, the simplest measure of

the effect of transitory wage rate changes could be found in

equation (4). At the same time, when the steady state

neoclassical solution exists, the short run and intermediate

run supply functions will coincide with the long run function.

When the steady state is disrupted by a transitory divergence

of real wages, the real wage rate will diverge and the

possibility arises for money illusion in the short run. As

the system equilibrates, the further possibility exists for

intermediate run overcompensation. We use (W W*) and

(P P*) to determine the effect of the divergence when

adjustment lags and overcompensation occur. For example,

assume a disequilibrium situation where y > 1 andyT < 0.

The total labor force response when this short run diver-

gence is included in the labor force participation equation

will be measured as,

(5) (LF/R)i = a + BI(W*) B2(P*) + B3(W -W*) + B4(P -P*)

This equation will be the first tested in this paper.

If the value of B3 is zero, there is no short run

divergence from equilibrium due to wage rate changes. We

have assumed a positive supply function and B3 should,

therefore, be greater than zero, when there is a disequili-

brium movement in wages. In the present case, the transitory

effects occur in a disequilibrium situation, so both the

effect of the disequilibrium caused by the short run shock

and the prevailing disequilibrium situation must be considered

when evaluating the effect of money illusion. In this case

B4 has three possible influencing factors, short run diver-

gence in prices, money illusion, and expectations adaptation.

For the present case we know that P is always greater than

P*. With our previous assumption of a positively sloping partici-

pation function this would, ceteris paribus, indicate that

B4 should be less than zero. When expectations exist,

y > 1 and the value of the variable will increase, ceteris

paribus, and B4 < 0. B4 will be greater than zero given an

upward sloping supply curve, only if YT < 0 and its absolute

value is greater than the combined effect of the trend

growth in prices and expectations adaptation.

The coefficient of the wage and price variables can be

compared to reveal sector labor supply characteristics. For

example,Wachter has shown that the relative wage variable

coefficient, B3, can be compared to the permanent wage

variable coefficient, B1, in orderto.determine the predomi-

nance of substitution or income effects. If B1 > B3 we can

assume that labor reacts to increasesin wages by taking more

leisure (cutting back labor) and the income effect will

dominate. While we expect that B3 > B1 for all of the indus-

trial labor force, we can also use demographic differences,

sectorally, to predict differences in the magnitude of the

dominance of the substitution effect. Wachter has found

that women of childbearing years are more affected by the

income effect than other groups. Since we expect more of

these workers in the Service sector, we also expect it to

show less predominance of substitution effects, ceteris


The relationships among coefficients can also be used

to evaluate the money illusion effect. The reaction of the

industrial labor force to unexpected wage and price movements

is a central feature of the monetarist explanation of Phillips

curve phenomena. Search unemployment theory, as interpreted

by Phelps (38a) (38b), relies on money illusion by workers

to account for the short run actions of workers facing:

change in aggregate demand. Phelps views the reaction as

an informational lag problem, and assumes that workers

will finally adjust their expectations to future changes.

The adaptation of expectations occurs over time and requires

that some workers leave their present positions to search

for better jobs as money wages fall and that some unemployed

workers accept jobs at previously unacceptable wage rates as

wages rise. When these workers realize that all wages are

changing similarly, in step with price and productivity

changes, they will adjust their behavior accordingly, and

6The percentage of women in the Service sector increased
from 72% to 75% between 1960 and 1970. During the same
period the percentage of men in the Service sector grew
from 45% to 52%.

the natural rate of unemployment will be obtained. As

long as future price and wage changes are expected, this

unemployment rate will prevail. Since we expect that the

informational problems concerning current money wage levels

will be more evident in the less structured Service sector,

we also assume that "informational lag" money illusion will

be most evident in this sector.

Lucas and Rapping (32a) (32b). suggest that money

illusion on the part of workers is rational behavior, moti-

vated by a desire to maintain real income at a constant level.

This paper also assumes that money illusion may have a rat-

ional basis. We associate the character of money illusion

with demographic and job characteristics. First, we assume

that labor force sensitivity to cyclical changes is inversely

related to the degree of market organization. The Goods

sector, with more market organization, is expected to be less

influenced by both wage and price changes. This result is

due to the worker's view of union membership as a condition

of employment, which carries both costs and benefits. One

cost is that the worker cannot move from firm to firm and

industry to industry seeking better terms of employment. The

benefits include higher wages, seniority rights and effective

exclusion from the labor force of non-union members (see

Alexander (2) ). The inherent value of retaining this member-

ship acts to maintain labor force participation when real

wages fall (with the worker realizing that wage gains will

be made at the next bargaining session). If real wages rise,

the effective exclusion of non-union members maintains the

labor force size. On the other hand, to the extent that

workers who are identified with Wachter's secondary workers

are included, to a greater degree, in the Service sector we

might expect stronger Lucas-Rapping effects here. This

conclusion is based on the previously mentioned finding

that certain secondary workers possess stronger income effects

than the general labor force. Lucas and Rapping would predict

that as real wages fall the labor force would increase, a

result calling for roughly the same motivation. Therefore,

we cannot predict a priori whether the Service or Goods

sector will exhibit stronger money illusion effects. However,

we can use distinctions discussed here to interpret empirical

tests in order to determine the relative importance of demo-

graphic and industrial factors.

Finally, the discouraged worker effect can be added to

explain short run divergences not explained by the rest of

the model (Simler and Tella (43) ). As explained by Wachter,

this effect should be most prevalent during times of high,

prolonged unemployment and should, therefore, be represented

by an unemployment variable, UD, during such periods. A

universal application of the unemployment rate, U, in the

neoclassical model can yield deceiving results since in

many cases U and W overlap in explaining labor supply changes.

Assume, for example, that population remains constant so that

LF = E + UN .

where i

E is the number employed and

UN, the number unemployed.

For a movement along the supply function LF is constant,

so that an increase in E means a decrease in UN. If the

function is upward sloping and elastic, this implies that,

(W/P) = f(UN) = f(U)

where i

(W/P) is real wages and

U is the unemployment rate.

and the relationship between real wages and unemployment or

the unemployment rate is negative. This relationship provides

a mechanism for "discouraged worker" models to explain

neoclassical labor supply phenomena. Unless the labor force

reserve is unresponsive to real wage rate changes, the two

are also related for shifts in labor force size. If it is

assumed the reserve labor force responds to real wage changes

in the same way as the current labor force,then the relation-

ship is roughly the same as noted above. In this case,

LF + ALF = E + UN + ALF,


LF + ALF = E + AE + UN + AUN'

As long as AUN # 0, a negative relationship between real

wages and unemployment can be hypothesized. It is for this

reason that the unemployment rate variable, U, should be

included in the Wachter model only during times of prolonged

unemployment. It is during these periods that the greatest

probability of unresponsiveness to real wage rate change

exists. By adding UD and the independent variables in

equation (5), we form the second model tested in this


(6) (LF/R)i = al + Bl(W*)+B2(P*)+B3(W-W*)+B4(P-P*)+B (UD)

where B5 represents the effect on (LF/R) for those periods

when the rest of the equation is less effective. UD is the

logarithm of the unemployment rate during periods of pro-

longed, high unemployment.7 B5 will be negative in the case

of positive sloping labor force participation functions,

indicating that the labor force contracts when prolonged

high unemployment exists and expands as the unemployment

rate falls.

Here we argue that the "discouraged worker" effect is

associated with labor market structure in the case of the

primary work force. As mentioned previously, the discour-

aged worker effect is only a useful adjunct to the neo-

classical model where labor responsiveness to real wage rate

changes is minor. Assuming that,as economic conditions

change, labor demand shifts causing concomitant changes in

real wages, and the labor supply function is stable over

the business cycle, there are two major circumstances when

the neoclassical model will not accurately predict labor

force participation movements. The first is the case of job

7The unemployment rate, as measured industrially, is used in
this study as the unemployment variable, and is effective
during the period 1958:1 to 1964:2.

seekers whose reservation wage is below the minimum wage

rate. Their supply must be governed by some other market

parameter, presumably the duration and rate of unemployment.

This situation can be permanent as long as the value of the

marginal product for the worker is less than the minimum

wage (deflated by prices). The other case occurs during

recession when the value of the marginal product of the

unemployed worker falls below his reservation rate. While

this condition cannot last indefinitely, its existence is

prolonged by unemployment insurance, savings, etc. It is

quite conceivable that the discouraged worker effect would

be evident during short recessionary periods (those long

enough to permit a prolonged period of high unemployment,

but short enough so the reservation wage does not adjust

downward). In the present study a large number of the first

group of discouraged workers are excluded. Therefore, not

only should the discouraged worker effect be less pronounced

than found by Simler and Tella (43) and Wachter (48b), but

it should be significant only in prolonged, high unemploy-

ment periods.

3.3 Empirical Results for Two Broad Industrial Groups

Empirical analysis using time series data and seeking

to determine specific functional relationships has the problem

of distinguishing between movements along the curve and

shifts in the curve. In this study we make the assumption

that we are analyzing the labor force participation of

primary workers, implying cyclical stability in the functional

relationships. Therefore, unless a secular movement in

labor force participation is evident (a trend toward greater

or less labor force participation) we can interpret our

results in terms of movements along a supply function, and

not in terms of shifts in the function. The two sectors

studied here have exhibited trends toward increased labor

force participation for the period under consideration, 1958:1-

1971:1. While we will not dwell on this point, these trends

do give a slight positive bias to the coefficients of the

estimates of the functions, which should be kept in mind

when interpreting the results.8

The first task of this study is to examine the assump-

tion underlying the earlier discussion, that markets for

labor, with different characteristics do exist. Unless the

two sectors examined here behave in different ways, much of

the interest in a sectoral markets model disappears. To

test this assumption a Chow (10) test was conducted, based

on equation (5), for the Goods and Service sectors, for the

period 1958-1971:1 (all regressions cover this period). The

null hypothesis that the two markets operate within similar

structures was rejected at the .01 confidence level.9 This

eWith the exception of the results shown in Table 3 the
inclusion of a trend term had little affect on the regres-
sions used in this section.

9The Chow test with a null hypothesis of similar regression
characteristerics is run using the following equation:
S (A S G)/p'(S + G)/(n + m -2p)
distributed as F(p,n + m -2p). Where A is the aggregate, S
the Service sectors' and G the Goods sectors' sum of the
squares of the residuals. The value of A is found by pooling
S and G. n and m are the number of observations in S and G
respectively and p is the number of parameters, so;that

suggests that the two broad markets are sufficiently dif-

ferent so that conclusions concerning differences in their

supply functions may be interpreted in terms of these


The segmented markets model is next used to analyze

the following four questions.

(1) The relative labor supply response to general

versus specific labor market indicators.

(2) The presence of money illusion in the short run

supply curves, and an expectations effect in the intermediate


(3) The relative magnitude of the discouraged worker

effect in each sector.

(4) The magnitude and nature of cross effects.

3.3.1 General versus specific labor market indicators

We will initially consider the four equations of Table 1.

The first facet of these results which is of interest is

that, despite the separate workings in each broadly defined

market, both supply functions can be explained at least as

well in terms of general as specific market parameters.

Since we would expect that segmented markets would be most

sensitive to changes in their specific market variables,

this result suggests some overlap between sectors. The

section dealing with cross effects suggests that while the

for this test, using equations (1) and (2) of Table 1.

A = .00146 S = .00056
G = .00045 p = 4 n = m = 45.
The Chow ratio is 9.15 and when this is compared to
F(4,82)=3.56 the null hypothesis is rejected, since 9.15>3.56.

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labor force overlaps sectors, its response to relative wage

and unemployment changes is related to changes in aggregate

demand. To the extent that this relationship prevails, we

expect the importance of cross effects to be diminished.

For example, we see that for equations (1) and (2)

(using general arguments for the Service and Goods sectors,

respectively) the coefficients of determination, standard

errors of estimate and Durbin Watson statistics, are approx-

imately the same as those for equations (3) and (4) (using

specific arguments). While these results are not sufficiently

good to establish'the superiority of either general or

specific arguments, we must question any assumptions of

complete market (sector) autonomy. An alternative hypothesis

was tested that workers respond to general conditions in the

short run, but adjust their supply over time to specific

market indicators. The results of this test were similar

to those shown in Table 1.

3.3.2 Money illusion and expectations

The second finding of significance is that money illu-

sion and expectations are important in the short and inter-

mediate runs, respectively, in the Service sector. The

signs of the coefficients of both the money illusion variable,

(P P*), and the expectations variable, P*, are those we

expect from the discussion of the proceeding sections,

assuming yp > 0 and YT < 0; the case where money illusion

is present in the short run and over compensation exists as

workers adapt their expectations. On the other hand, only yT

is significant in the Goods sector.

Search unemployment theory as developed by Phelps (38a)

(38b), leads us to expect that the Service sector, with less

market organization, and therefore, poorer communications,

than the Goods sector, would be most affected by the

recognition problems implicit in the money illusion inter-

pretation. However, we find that while the expectational

adaptations influence is more important in the Service sector,

money illusion is more important in the Goods sector (yp

is relatively larger in the Service sector and YT is relatively

larger in the Goods sector), supporting a different inter-

pretation of the phenomena.

The expectations term, y equals IB21/ B1, while the

money illusion term, yT, equals B4/B3. For the Service

sector, the value of y is approximately 1.5 while its value

is approximately 0.9 in the Goods sector. The value of yT

in the Service sector ranges from 0.7 to 1.4 (depending upon

whether specific or aggregate figures are used to compute

YT) and from 2.7 to 4.0 in the Goods sector. Although all

of the coefficients in these equations are important for

labor supply analysis,we are especially interested in the

values of expectational terms, since these are also important

to Phillips curve interpretation.

We have assumed that the Service sector would be more

susceptible to neoclassical money illusion. The fact that

the valuesof y and yT are approximately equal in the

Service sector suggests that the:neoclassical explanation

of money illusion is applicable in this sector. We will use

the Lucas-Rapping idea of rationally motivated money illusion

to explain why the Goods sector results deviate from the

Service sector findings.

If the Service sector can be characterized as composed

of many small firms and many worker bargaining groups, with

poor informational flows, the Goods sector might be typified

as having a few large firms and few worker bargaining units.

Eurther, the Goods sector is characterized as having

administered wages which mitigate the job-search explanation

of money illusion.

One hypothesis supported by this research, is that

union membership is maintained during price inflation and

the labor force is, effectively, not permitted to fall with

the drop in real wages. This effect does not need to arise

through coercion or even be explicit union doctrine. The

recognition that wage rate change must await the next

bargaining session, and the inherent value of the union

membership that might be lost by deciding to withdraw from

the labor force could maintain the level of sector supply.

Likewise, as real wages improve in the Goods sector, as a

result of bargaining at the next negotiating session, we

expect to see relatively less labor force participation

fluctuation since labor supply is dependent upon union

membership. Therefore, although the labor force participation

rate might grow while real wages fall in the short run, it

will not adjust over time, even when the real wage losses are

evident. In such a case a value of y of approximately one

is expected.

The Service sector appears to fit the neoclassical labor

supply model better for primarily structural reasons. As

equations (1) and (2), or (3) and (4) of Table 1 show, the

coefficients and t-statistics for the wage variables are

more significant in the Service sector. The greater flexi-

bility in wage rates and the relative lack of significant

market organization suggests a more elastic supply function

for the Service sector. At the same time, we see that the

value of the relative wage coefficient, B3, is greater than

the permanent wage coefficient, B1, supporting our contention

that strong substitution effects affect the industrial labor


3.3.3.Prolonged high unemployment effect

In Table 2 we add a dummy unemployment rate variable,

UA for aggregate data and Ui for sector data, for 1958-

1964:2, the period of high unemployment industrially. First,

it will be noticed that this additional variable is negatively

related to labor force movements (the coefficients of UA and

U. are negative), and is relatively significant. Our earlier

discussion led to a conclusion that unemployment rates should

be negatively related to labor force participation, if the

labor force is sensitive to this market indicator. This

reaction has been found by Wachter to be applicable to

secondary workers. This research suggests that primary

workers also respond significantly to extreme unemployment

conditions by adjusting their labor force participation.

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At the same time, the addition of the dummy unemployment

rate variable reduces the coefficient of the permanent

real wage variable. Notice that the values of B1 and B2

are lower in each equation in Table 2, than they are for

the same equations in Table 1 (where the equations with the

same reference number represent equivalent data bases). This

reduction in the coefficient of real wage variables suggests

some overlap between the discouraged worker and neoclassical

model in explaining labor supply movement.

However, the values of the coefficients of B1, B2,

and B5 in Table 2 only partially tell the story of the magni-

tude of the discouraged worker effect. First, it should be

noted that regressions in which the unemployment rate variable

was operative for the entire period showed a negative relation-

ship between labor force participation and unemployment rates

and considerable distortion in the permanent supply function


3.4 Discouraged Worker Effect

Separate regressions testing the "discouraged worker"

effect, as specified by Wachter, were also run (see equations

(1) and (2) Table 3). Most of the labor force participation

is explained by the constant and trend term in the dis-

couraged worker model, which leaves considerable room for

1'The addition of the unemployment rate variable for the
entire period, 1958-1971 caused the sign of the coef-
ficients of permanent prices in the Service sector and of
permanent and transitory wages in the Goods sector to
change. Considerable interrelationship between real wages
and unemployment rates for the majority of the sample
period is suggested by these sign reversals.

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improvement in explaining labor force participation. It

appears that much of this is explained by the neoclassical

model. When the present results of testing for the dis-

couraged worker effect are compared with Wachter's results,

it appears that this effect is most applicable to the

secondary work force (excluded in large part in the present

case). As would be expected, the results in this case are

less significant than comparable demographic studies

;(6)' (15) (43) (48b), with respect to the discouraged

worker effect, and the results in the Goods sector suggest

that labor supply is relatively more constant, cyclically,

where unionization is strong (whatever the cyclical movement

in employment, unemployment or real wages may be).

3.5 Crossover Effects

The final question considered by this chapter concerns

crossover effects. Crossover effects occur when workers in

one sector base their labor force participation decisions in

part or totally on movements in the variables in the other

sector. It is most often assumed that such behavior results

in migrations from one market to the other, so that when

these effects are sufficiently strong the labor force

participation in one market might change perceptibly without

any change in its real wages or unemployment rate arguments,

when these arguments change in the other market.

Tables 1 and 2 show results that support the assumption

that labor supply functions for primary workers are upward

sloping. It seems reasonable, therefore, that workers

will react to changes in relative wages or unemployment in

such a way as to migrate from the sector with falling

relative wages or rising relative unemployment, to the sector

with rising relative wages and falling relative unemployment.

The model may be described as:

(7) (LF/R)i = a + B6(Us/U ) + B7(Ws/Wg/).


s = Service sector,

g = Goods sector.

and all variables are as previously defined, but are not

in logarithmic form.

If there is a significant crossover effect the signs

of B6 and B7 will be positive and negative, respectively,

in sector g, and negative and positive, respectively, in

sector s. Table 3, equations (3) and (4) show the results

for regressions testing this model in both sectors. Although

the coefficients of determination are high in both: sectors,

the signs of the unemployment rate and wage rate variables

cast doubts on the significance of the correlation for

crossover effects.

The signs of both coefficients in each sector are

positive. This result is most easily explained in terms of

the relationship between these relative movements and the

cyclical changes in the aggregate. For the period studied,

wages in the Service sector increased, relatively, during

expansions and declined, relatively, during contractions.

Similarly, Service sector unemployment rates grew, relatively,

during expansions and fell relatively during contractions.

Assuming that the labor supply function is positively sloped,

we would expect increased labor force participation during

expansions and decreased labor force participation during

contractions. This hypothesis is supported by the results

of Table 3.

We are unable to conclude that there is no crossover

effect between sectors. However, since the analysis of

crossovers can be explained in terms of aggregate changes,

we find support for the contention that crossover effects

are not cyclically exogenous phenomena. We conclude that

the crossovers that occurred during the sample period are

due to aggregate cyclical changes.

3.6 Conclusions

We have found support for the theory of segmented

labor markets. The Service sector market is characterized

by neoclassical market mechanisms and its labor supply

function can be best interpreted using this model. The

Goods sector has a market characterized by more rigid

institutional arrangements, which constrain the movement

of the labor force, and produces a less steeply sloped

function (one which is less responsive to price or wage

changes). The result is that the sector with better infor-

mation transfer mechanisms, the Goods sector, displays more

money illusion and expectation adaptations problems. Since

this behavior is related to institutional arrangements it

can be expected to be of a longer duration, and, thus, more

important to Phillips curve phenomena, than the money

illusion problems arising from informational limitations

and lags.

The discouraged worker model, employing the unemployment

rate as the principle explanatory variable, is much less

useful in explaining industrial labor force participation

behavior of primary workers than is the neoclassical model.

This result would be expected due to the fact that the

primary workforce represented in the industrial data is

stably employed and does not view unemployment as a relevant

market parameter, except during periods of prolonged, high

unemployment. The overlap in explanation between unemploy-

ment and real wage variables is therefore more a result of

concomitant movements in the two, than a result of a strong

functional relationship between primary labor force participa-

tion and unemployment rates.

While this research indicates that significant differences

in price expectational behavior patterns exist between sectors,

more cross sectional analysis, aimed at studying the complex

interrelationships among occupational, demographic and

industrial groups is also suggested.



We have seen that the two sectors differ with respect

to labor force reactions to wage and price changes. While

these differences imply different neoclassical-expectational

Phillips relationships in the two sectors, we must more

fully explore labor market heterogeneity before the labor

market tightness influences are evident. This chapter serves

to develop such an analysis and to verify the expectational

conclusions found in the previous chapter.

This chapter develops a two sector model based on the

production-employment characteristics described by Fuchs (18)

estimates expectational Phillips curves for Goods and Services,

and contrasts the present industrial estimates with those

presented by Perry (37b). We establish the existence of

sectoral Phillips curves which possess predictable struc-

tures. In addition, the estimates support the contention

that disaggregative analysis is a useful tool for explaining

observed aggregate Phillips curves.

Although the model and conclusions derived in the present

paper provide new information concerning the observed trade-

off, a primary function of this chapter is to introduce an

alternative method of examining inflationary problems. The

disaggregation we employ is based on a general equilibrium

system, which involves the complex interdependences of wage

rate changes, price changes and labor market tightness, among

the major variables. However, this first attempt at such an

approach is limited to a partial equilibrium analysis, which

restricts the depth of the study and limits the inferences

we can draw from the results. Nevertheless, the single

equation model captures some essential differences between

behavior in the Goods and Service sectors.

Of the various central issues of stabilization policy

during the past decade, few have been subject to more research

and controversy than the observed relationship between the

percentage change in the aggregate wage rate and the aggre-

gate unemployment rate. Phillips (39) interpreted the aggre-

gate tradeoff as reflecting a functional relationship between

money wage rate changes and the aggregate demand for labor.

The monetarist writers of the sixties took exception to this

view, claiming that no permanent Phillips tradeoff existed

(17). A third interpretation, by Lipsey (30), is that not

only is the aggregate unemployment rate a surrogate for the

aggregate excess demand for labor, but it is also a proxy

for the inflationary influences of labor market hetero-

genity (3a) (3b). Here we examine the effect of structural

differences among industrial sectors on this aggregate


'Archibald (3b) has examined the effects of unemployment
dispersion, an index of product and labor market hetero-
geneity, over both geographical and industrial divisions;
his results show a positive relationship between unemploy-
ment dispersion and wage inflation.

Labor market heterogenity can be examined in terms of

demographic, industrial, or occupational characteristics.

This study examines industrial differences in contrast to

Perry (37b), who recently examined the influence of labor

supply heterogenity on wage rate changes, focusing on the

effect of more youth and women in the labor force. Perry

concludes that the influx of these groups into the labor

force has caused the Phillips relationship to shift out

when one uses a conventionally measured aggregate unemploy-

ment rate. The sectoral model developed in the present

research demonstrates that when the labor force is imper-

fectly mobile, differences in labor demand functions produce

different Phillips curves for the resulting segmented markets.

The analysis of the estimated sectoral "Phillips curves"

suggests that for zero price inflation a 4 percent unemploy-

ment rate corresponds to a 2.8-3.0 percent rate of change of

wages for 1950, but a 3.2-3.4 percent rate for 1970. However,

this study indicates that the shift is not uniform, but is

the result of a pivoting of the aggregate Phillips curve.

4.1 Disaggregation Into a Two Sector Model

Research using disaggregative functional relationships

may be required due to two basic problems of aggregation in

a diverse world. The first is the famous paradox of com-

position, in which the whole is something more or less than

the sum of its parts. Because of this problem, Lipsey and

Archibald suggest that unemployment rate dispersion should

be included with the aggregate unemployment rate in equations

explaining wage rate changes.2 The second is the difficulty

encountered in attempting to aggregate over different func-

tional relationships, when such aggregation obscures the

underlying economic structures. Perry addressed this problem

from the labor supply side, via demographic differences

while we focus on industrial sector differences, as well as

on the supply characteristics of the primary work force.

4.1.1 General aggregation issues

The problem of identifying sectoral contribution to an

aggregate functional relationship has both a theoretical and

a technical (index number) basis. Perry's approximation of

demographic groups' contribution to excess demand is grounded

in a theory of the inflationary process. He contends that

differences in supply characteristics of eight demographic

groupings give rise to varying degrees of inflationary

influence. Perry's excess demand variable is:
8 8
(1) U* = (z (I ) (V ) )/(Z (I.) (L ) )
.=1 .=1


U* is the weighted aggregate unemployment rate,

I. is the productivity index for demographic group j,

2The problem of dispersion effects is treated in section
4.2.3. Since the dispersion model we test is essentially
that formulated by Archibald, we have not treated its
derivation in the present section. We assume in the remain-
der of this section that the paradox of composition is not
present. The additional consideration of dispersion effects
complicates the analysis, but it does not invalidate the
conclusions drawn in this section concerning aggregating
over different functional relationships.

V. is the number unemployed of group j, and

Lj is the total labor force for group j.

The Perry model emphasizes supply influences through weights

given the eight components of the unemployed portion of the

labor force.

In the present case, we use a simple two sector model

which assumes that two heterogeneous labor markets exist,

and that the movement of labor between them is restricted.

Such an approach, which may be contrasted with Perry's

weighting technique, provides a more direct test of sectoral

influences on the aggregate observed variables. The aggre-

gate Phillips curve equation in linear terms is:

(2) WA = aA + BA(UA) + CA(PCR).

where wA is the rate of change in compensation per manhour,3

UA is the aggregate unemployment rate, and
t-1 t-5
PCR is the rate of change in expected prices, ( ).
The intercept and the coefficients of the independent

variables are subscripted with A to distinguish them from

later, disaggregated versions of the model.

Of course, the estimate of the above aggregate relation-

ship will be biased if shifts occur in underlying components.

Gordon (19a) has shown that the aggregate value of the

compensation per manhour variable is subject to bias from

both secular and cyclical. shifts in both industrial work-

force composition, and changes in hours worked. Gordon

suggests that the employment and hours worked figures, which

3Although wage rate and compensation per manhour will be
used interchangeably, it should be understood that our
empirical work involves the use of the latter.

serve to weight wage rates over industries, be held constant

at the median value for the period under consideration. In

this way, fluctuations in aggregate compensation per manhour

will be due only to changes in the industry wage rates, not

to other secular and cyclical intersectoral shifts. For

example, a change in relative employment from high wage to

low wage industries would result in the observed aggregate

wage rate falling, yet Gordon would argue that the labor

market tightness variable (U or 1/U) could be unchanged.

Estimates that did not make this technical adjustment would

be biased.

Assuming two industrial sectors, Goods (g) and Services

(s), equation (2) can be modified in compliance with both

Gordon's and Perry's adjustments.4
n n
(3) A(ZYiwi)/( iwi) = al + B1 (UG) + C1(PCR)
iI i=i


y is the constant relative employment weight given
the wage rates of the individual sectors substituted
for the time variable weights used in official
aggregate statistics,

i is the ith industry group, and

Eyi = 1.

While Perry has analyzed a model similar to (3), such

analysis can be significantly extended by using data on

4The Perry model tests the reciprocal of the unemployment
rate against the rate of change in wages, which reflects
the belief that a nonlinear relationship exists between
UA' as a proxy for excess demand, and the rate of increase
in aggregate wages. Although, this paper estimates both
linear and nonlinear forms, the theoretical discussion is
limited to the linear case for ease of mathematical mani-

industrial categories. Perry compares his, esults'with those

using an unweighted unemployment rate to indirectly test a

specific sectoral influence: demographic differences in

productivity. Due to data limitations and the absence of

broad labor market characteristics for demographic groups,

sectoral Phillips curve analysis based on supply (demo-

graphic) categorizations are limited to these Perry-type

models. However, industrial categorizations remove the

data problems and permit broad labor market structures to

be used in developing sectoral Phillips curves. When

theoretical differences exist among industries, we can

hypothesize different sectoral Phillips phenomena, since

both w. and U. are classified by industries.5 We argue that

this separation is legitimate as long as there are basic

structural differences between sectors and there is partial

labor immobility among sectors.6
5It is important to note that industrial data exclude a seg-
ment of the measured labor force included in demographic
studies. This group is composed of the newly entering and
reentering unemployed workers. These are primarily the job
seekers who possess neither adequate technical nor job-search
skills. While not all secondary workers are included in the
above group, its composition is primarily of secondary workers.
Related research suggests that the aggregate Phillips curve
will be steeper when this cyclically volatile group is removed
from the data.
6The assumption of labor immobility is sufficient but not
necessary for the functional differences to have a meaningful
economic interpretation. The labor immobility assumption
is a useful simplifying assumption for developing a sectoral
model, and one that could be empirically tested. Initially,
we assume that perfect market segmentation exists. When this
occurs, the model described in equations (4) and (5) demon-
strates the problems involved in identifying aggregate
inflationary patterns in a multisector world. The assumption
of a homogeneous market model used by others, is that the
-functional relations in both sectors are the same and that
perfect labor mobility exists between sectors. The actual

If the above conditions are met, we can hypothesize

different Phillips relationships between industrial

sectors, such that for a two sector world,

(4) w = a + B U + C (PCR),
g g g g g

(5) w = a + B U + C (PCR)

where both equations are of the form of (2) above, so that

w is the rate of change in wages in the Service

w is the rate of change in wages in the Goods sector,

U is the unemployment rate in the Service sector,

U is the unemployment rate in the Goods sector, and

subscripts, g and s, designate the individual sectors. For

simplicity we will assume that U and PCR are independent,

and focus on the determinants of B and B As will be

seen, this approach overlooks essential interrelationships.

These two Phillips curves are the basis of the seg-

mented markets model. The differences in the markets

associated with the curves provide the means for predicting

different functional forms for equations (4) and (5). Fol-

lowing this interpretation, the aggregate function is only

an average representation of the various sectors (ignoring

the aggregation problems previously mentioned). Therefore,

situation, and the one more fully considered in the empirical
work in this paper, is that functional distinctions exist in
a world where partial labor mobility occurs between sectors.
This hedge does not nullify the model presented in equations
(4) and (5), but, as will be seen later, introduces additional,
complicating elements into the analysis.

the aggregate function is dependent upon both the cyclical

changes affecting each individual market and the secular

trends affecting the relationships among markets.

Four additional parameters are introduced to facilitate

the aggregation of the individual sector curves to obtain

the curve for the economy as a whole:

(5a) P = Ug/Us

where p is the changing proportionality factor
relating the observed unemployment rates of the
two sectors;

(5b) WA = y W + y W
A s s g g
where y provides fixed weighting for sectoral
wages following Gordon, and Zy = 1 (i.e.
Y = 1 );

(5c) 6 = W /Ws

where 6 is a changing proportionality factor
reflecting relative wage movements in the
sectors; and

(5d) UA = aU + (1 a) U
A g s
where a is the changing weighting factor for the
unemployment rates based on the size of the labor
force in each sector.

A listing of other labeling conventions also is presented to

make the analysis more accessible:

W = money wages,

w = rate of change in wages,

U = unemployment rate,

a = intercept for linear Phillips curve,

B = slope for linear Phillips curve, in the wage
change-unemployment plane,

C = slope for linear Phillips curve, in wage change-
price inflation plane,

A = subscript which indicates aggregate,

s = subscript for Service sector,

g = subscript for Goods sector,

i = subscript for industry i, example: retail trade,

Yi = employment in sector i divided by total employment,
fixed at some average value.

Thus, if we aggregate equations (4) and (5), we must define

the coefficients aA, B-, and CA in terms of the sector

values of the intercept and slopes. The four parameters

introduced above are necessary to relate the sector curves

to the aggregate Phillips curve. That is, the aggregate

must reflect changes in the relative unemployment rates (u),

wage rates (6), and labor force weights (a, 1-a), and the

fixed employment weight given wages in each sector (ys and

Yg). To illustrate how these parameters come into play,

let us derive the aggregate curve.

We have defined w and w as follows:

(6a) ws = (Ws0 Wso)/Ws,

(6b) w = (W g-Wg,)/Wg where 0, i are time periods


(7) WA = (WA WA)/WA = ((Ws + gW)-

(YWs + YgWg))/(YWs + Yg Wgo

Recombining terms in (7), and substituting 60, the relative

wage factor, into the denominator results in:

(8) (Wsi Ws) + (W W
Ys + Ygo)Wso (Yg + Ys/60)Wgo

Remembering that ys = 1 y and substituting, we obtain:

swso 7 wgo
Y, + 60-Y 60o g + 1/60-Y /So

w w
so + go
(1 + 60o/ -60) (1 + 1/60Y -1/60)

Now we can see that to obtain the rate of change of aggregate

wages, wA, the sector rate of change of wages will be

weighted by only the fixed factors ys, y (as in 5b) only when

60 = 1, a case when a sector analysis is rendered less interest-

ing, since wages in the sectors would be equal. Note that

the Gordon technical adjustment holds the y's constant over

the time period; so that instead of using the actual economy-

wide wA, for estimation purposed, another aggregate wage

variable is used which does not reflect changes in the com-

position of employment.

Pursuing this analysis further, we define

p = 1/(1 + 60o/s 60), and

Pg = 1/(1 + 1/6og 1/60).

so that we simplify the "rate of change" version of (5b) to

(10) WA = Pss + pgWg.

Summing equations (4) and (5), and utilizing (10) yields

(11) w = Pa + pga + p B U + pgBU + PsC (PCR)
A s s g g sss g g gss

+ pgC (PCR)

= aA + BA (aU + (1-a) Us) + CA(PCR).


(12) a = pa + pga
A s g g

(13) B = (p B U + pgBU )/((l-a) U + aUg),
A ss g9g g s g

and since Ug = IU ,

(14) BA = (psBsUs + pgB gUs)/((l-a)Us + t)Us),

= (p Bs + p gB )/(l-a + ap),


(15) C = PsC + pgC

Equation (11) and the underlying determinants of the observed

aggregate intercept, aA, the slope, BA, and the price expecta-

tions coefficient, CA, as shown in (12)-(15) indicate the

complex interrelationships which are hidden in the estimation

of an economy-wide expectations Phillips curve. The intercept

and the price expectations coefficient depend upon relative

wages, 6, and relative employment size, y, while the slope

also depends on relative unemployment rates, p, and relative

sizes of the labor forces in the two sectors, a. If the sectors

are independent and have different slopes and intercepts, a

trend movement in y, as well as the movement of 6, and a

over the period,will be reflected in a shift in the aggregate

curve.7 However, we must qualify this interpretation of CA,

since the aggregation process has involved strong assumptions,

including complete independence of price expectations and

labor market tightness.

1Imperfect labor mobility between sectors limits crossovers
in response to relative wages (6) or labor market tightness
(p). See Arthur Alexander's RAND study (2) which addresses
this problem using cross-section data for the period 1958-67.

4.1.2 Industrial labor force composition and pivots in the
naive Phillips curve

For the estimated parameters to have any meaning, we

must have some way of identifying different markets. Archi-

bald (3b) has commented that "true" labor markets are dif-

ficult to find. Yet, Fuchs (18) has provided a good first

approximation with his characterization of the Serivce and

Goods sectors. Fuchs' work on the trend toward a Service

economy indicates that important differences in employment

behavior exist between sectors. These can be summarized as

follows: Goods sector employment fluctuates more over the

business cycle than Service sector employment, affecting

both i and a over the cycles, but Goods sector wages are

relatively more stable cyclically, affecting 6. Fuchs cites

several reasons for the tendency of the labor demand function

in the Service sector to be less elastic than that in the

Goods sector, and for the demand function to shift less over

the business cycle in the Service sector. The numbers of

persons paid by commissions in the Service sector, plus the

greater hiring and search costs due to a lack of organization

of the market (many small firms and little unionization), imply

that the Service sector employers will lean more toward wage

and/or hours reductions than worker layoffs during short

recessions, while the Goods sector will have the opposite

tendency. This observation means that when a labor demand

shock of equal magnitude is applied to each sector, the

reactions will be different due to different labor demand


In addition, labor demand shocks are unlikely to be of

equal magnitude, so excess demand for labor will not be at

the same level or change at the same rate in the two sectors.

As Fuchs points out, the demand function for labor will tend

to shift more over the business cycle in the Goods sector

since output is more volatile here. In other words, the

actual shocks to each labor market will differ with any

given change in aggregate demand, as will the reaction to any

given shock.

In general, we could expect that for the linear model,

the absolute value of the slope in the Service sector, Bs,

will be greater than the value of B For example, assume

that for sectors s and g, g is a highly organized production

sector, producing a durable output, and s is a competitive

sales and service sector. The two are perfectly segmented,

g has no informational transfer problems, s has imperfect

information flows concerning available positions and workers,

and the sales personnel are paid on a commission basis. What

will happen if an aggregate demand shock occurs? If the shock

is recessionary, s will tend to maintain employment levels

and absorb downturns with effective salary cuts for employees

on commission. Following the monetarist writers (38b), a

short-run Phillips curve will arise due to search unemploy-

ment by workers seeking to improve their wage situation.

Assuming that the recession has equally affected all firms

in sector s, such unemployment will be short term, lasting

only as long as it takes for workers to discover that their

opportunities -are the same with each firm. In an upturn,

with wages and prices rising, unemployed job seekers accept

jobs with real wages which were not previously acceptable.

As the monetarists point out, such behavior on the part of

the unemployed betrays money illusion and the observed

Phillips curve can be expected to be short-run.

Now, assume that the firm and one union bargain for the

services of all labor in sector g, the firm and union in g

have agreed to bargain wages to last for considerable periods

of time, and money wages are based on the previous rate of

growth in productivity and previous prices, such that during

the period for which wages are bargained, wages will increase

proportionally to the average productivity plus price growth

for the previous period. In a downturn, money wages will

continue to grow at a given rate of increase, and unemploy-

ment will absorb the brunt of the recession. In upturns,

increases in productivity will increase profits, but will

not immediately affect money wage rates. Unemployment in

this situation can be expected to fall as long as marginal

revenue product exceeds the going real wage rate.

The Phillips curve in g will be a perfectly horizontal

line which will shift up (when the trend in the growth rate

of productivity is upward) or down (when the trend is downward)

with new wage negotiations. The Phillips curve in s will be

very steeply sloped, showing a tendency to absorb shocks in

money wage changes. The curve will not be perfectly inelastic

due to some search unemployment.

When the extreme assumptions of this example are relaxed,

we still predict different sectoral Phillips curves. How-

ever, partial mobility between sectors will tend to mitigate

the extreme results stated above, by permitting some of the

employed and unemployed in each sector to seek better employ-

ment or salary situations in the other sector. Similarly,

the lack of perfect organization in sector g will cause some

slope to its Phillips curve with the introduction of some

other elements, such as less organization and imperfect

information flows. Likewise, the slope of curve s will likely

be less steep since some wages in this sector are inflexible

and the workers paid these wages will be laid off when their

marginal revenue product falls and will be rehired at going

wages when aggregate demand increases. However, we can con-

clude that the inflation-unemployment relationship for each

sector is functionally distinct, is based upon labor and

industry structure, and that the sectors can be expected to

have different Phillips curves based on these functional

differences. To reiterate, as the weighting shifts from one

sector to the other, we can expect the aggregate Phillips

curve to pivot.8

4.1.3 Price expectations and shifts in the Bhillips curve

Phelps (38b), Lucas-Rapping (32b), and Eckstein-Brinner

(14), among many others, have shown that the inclusion of a

price change variable in the Phillips' equation helps to

8Vanderkamp (47) examines what amount to sectoral Phillips
Curves for Canada. However, the theoretical justification
for breaking the economy into organized and unorganized
sectors is weak, and his conclusions are not those expected
from the discussion above.

explain wage inflation. The addition of this variable

suggests that wages may rise independently of changes in the

demand for labor. The expectations interpretation of the

price change coefficient means that single equation models

fail to capture all the interrelationships involved in the

inflationary process. Prices are not exogenous phenomena

and cannot be interpreted as an independent influence on

wage adjustment.

In this chapter we focus on the effects of labor market

tightness and constrain the price change term. A priori we

have no basis for judging the sectoral differences in expecta-

tional influences. On the other hand, we have seen in the

previous chapter that the primary labor force responds to

price changes differently in the two sectors. We will use

these results when analyzing the estimates obtained in this

chapter. Although this method cannot substitute for a

simultaneous equation model, it does provide an initial

interpretation of some of the complexities underlying segmented

markets (36). Multi-equation models and other approaches

should improve the estimates of price change coefficients.

In summary, this analysis suggests that the source of

the shock to the economic system is of utmost importance.

For example, if the shock is due to a change in capital

investment decisions, the relative difference in the impact

of the shock will be more in evidence than if the shock

takes the form of a uniform change in consumer expenditures.

That is, the existence of partially segmented, heterogeneous

labor markets offers support for Tobin's (45b) contention

that significant Phillips phenomena can exist when there is

no change in aggregate demand. The permanence of an aggre-

gate Phillips curve becomes a stochastic problem in this

situation, dependent upon the actual number of relatively

separate sectors, and the size and frequency of disturbing

shocks to the system. In addition, the position of even

short run aggregate Phillips curves depends on the shocks to

and proportion of the labor force in each sector.

4.2 Empirical Analysis of the Two Sector Model

In this section we consider tests of the segmented

markets hypothesis and contrast this approach to Phillips

curve analysis with the approaches developed by Perry and

Archibald. The analysis presented here suggests that sectoral

breakdowns provide a potentially powerful mechanism for

analyzing Phillips' phenomena. By specifying functional

relationships at the sectoral level, we can predict secular

shifts in the Phillips curve, as well as potential short run

Phillips movements due to any given change in excess demand.

This section uses three variables; the rate of change

in wages, the unemployment rate, and the rate of change in

prices. The wage rate change and unemployment rate vari-

ables are considered in the aggregate and as sectoral values,

while price changes are in terms of aggregate price levels.

The rate of change in wages is computed both as the four-

quarter and as the one-quarter percentage change in civilian,

non-agricultural compensation per man-hour, adjusted for

interindustry shifts in labor force, among the seven indus-

trial groups comprising the Service and Goods sectors. The

aggregate unemployment rate, UA, is based on labor force data

for the wage and salary workers in the industrial groups

covered by this study. The rate of change in process, PCR,

is the four quarter percentage change in the consumer price

index, lagged one quarter.

4.2.1 Sector unemployment rates and wage rates

The unemployment rates for the Goods sector, U and

the Service sector, Us, are drawn from the same data as the

industrial rate, UA. During recessions, we expect the

unemployment rate to rise more in the Goods sector, and that

it will fall more rapidly in this sector during an expansion,

as both rates approach a minimum, frictional rate. This

prediction is based on Fuchs' observation that employment

fluctuates more over the cycle in the Goods sector.9 The

sector wage rate changes, ws and w for the Service and

Goods sectors respectively, are also drawn from the same

data as the aggregate.

Fuchs (18) predicts that wages will fall more rapidly

during recessions and rise more rapidly during expansions

in the Service sector. Wachter (48a) has shown that the

relative movement in wages, industrially, is dependent

upon the ability of workers in non-unionized industries to

exert upward pressure on their wage rates. This ability is

9This contention also requires that the labor force size
remain relatively constant in both sectors. Industrial
labor force data excludes newly entering and re-entering
workers who are unemployed. We assume that the major cause
of cyclical volatility in labor force size is removed with
the exclusion of these workers from the data base.

Relative Wages 6 = 9

r- tor m m V C4 C
S H H H H H H f
4 4

4 c





'' a)


''0 4'0
''0 a)
Hl d

n >

7H H

H -Hl


L" I


=n i ;uauI~o~dCaufl aArh5T2rI

restricted during recessions when each worker's job is

threatened. As labor markets tighten, these workers gain

confidence and demand and receive larger wage boosts. This

theory, if applicable to sector differences, supports Fuchs'

view and suggests that the turning point in relative wage

rate growth is related to labor market tightness.

In Graph I, we have traced the movement in relative

wages (6) and unemployment rates (V) for the period 1958:1-

1971:1. We find that in general, during recessions, the

unemployment rate in the Goods sector rises relative to that

in the Service- sector; and during the initial phase of

expansions, the Goods rate falls rapidly with respect to

the Service sector rate, until the two rates are roughly

equal. We also find, that during this period, Service

wages have tended to increase relative to Goods wages.

During recession and the initial phase of expansions, this

trend is not evident. Once the unemployment rates are

equalized, Service sector wages grow rapidly with respect

to Goods wages. This observed behavior appears, to fit that

predicted from the Fuchs and Wachter studies.

Turning to the regression results for the sectoral

Phillips curves, we find that, as expected, the wage change-

unemployment rate tradeoff in the Goods sector is flatter

than in the Serivce sector, usingalinear tradeoff. In Table

4, equations (1) and (2) show the results for Serivce and

Goods industries, respectively. Tests were also run using

the assumption of nonlinear Phillips curves. These tests


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a C) w) in ikD 0 '-0Hrl r

Ef) -4 C 0% C t- 0 (n r CD C)0 a 0 )
1-1 ON C) -0010 CODC1 mC a 4U
n r o~o meo r-o ] ro oo O
M. . CM .


I I U i pin N NI 0) N i I 4
p- O oo L14in O ) r 4
w HO r-O N ) m HO 40 (a
0 O to a n to ~ONk- NO :



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I-HIim N N I o IN r

+ N IN I N N a

H H Hi H 0I
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C (u

( -H4

0 4- r- r T
r-l 4) rq `4-1 0 -IT $ L l-
I I *- a)
N1 C4 0h 0 0-H)

4 -I I 1 a P

-- C *H ) 0) --

TO O I V 1 Oi ir O O-H
(l 4 4-) d o a
m 04

Cm D ~ a I1L
% l V m 0 r

H 4) t- 4 0 )
0 0 *-r 4-

S- --I N I CN -
H C B r0
rh 0 3 cN m) 4

rd LO ) to o C1 n rl mT oo(n ri 0 m m
H D U- 0Th 0) C) L o ol

l z r0T 0 r r. a) 4- rO
03 0 0 I I 0 ) 0

*rl 4 LflH 0 01 .0 0)
03 N
U 0. l a-1 40

4J 41) TO r

za 3 a) Hri

-H z NO iHt), Q F: f U) tn & 0 40
l-lI a) r 2 r-l Q) -r4 *4 fd (D
0. 04 0l OH O 4 Z H 4-]0m
fa a) rd! 0 ain) f
El Q > E- Q

yield slightly better fits, but the general conclusions

of this paper remain unchanged with this latter formulation.

The results based on a model of the form w = a + B(1/U)+C(PCR)

for the Service and Goods sectors are presented in equations

(1) and (2) of Table 5. For the linear curves, the coefficient

B is -.5692 or approximately three times the coefficient B .
s g
The coefficient of PCR is .6137 in the Service sector and it

is .5390 in the Goods sector. This result is consistent

with the finding of Chapter 3 that labor force participation

in the Services involves less "money illusion" than the labor force

participation in the Goods sector. Thus, increases in PCR

induce relatively fewer participants into the Service sector,

and are associated with relatively greater wage inflation.

A Chow (10) test conducted to determine whether or not

the two sectors have significant differences in their Phillips

behavior rejected the null hypothesis of similar structures

at the .01 level of confidence.10

4.2.2 Complications in the estimation of Phillips curves

Some of the problems of estimating complex relationships

with a single equation model, are apparent in the autocorrela-

10The null hypothesis that both sectors are governed by the
same relationship was tested with the equation (A-S-G)/p-
(S + G)/(n + m -2p) distributed as F(p, n + m -2p). In
this equation, A is the sum of squares of the residuals for
the pooled equation; S is the sum of squares of the resi-
duals for the Service sector; G is the sum of squares of
the residuals for the Goods sector; n and m are the number
of observations included in the Service sector and Goods
sector regressions respectively; and p is the number of
parameters. For this test, A = .02692, S= .004050, G =
.004803, p = 3 and n = m = 48. Using the above figures, the
Chow ratio is 28.6. Since F (3,90) at the one precent
level of significance is 4.04, the two sectors can be
reasonably assumed to operate under different relationships.
The null hypothesis is rejected.

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