THE DISTRIBUTION OF THE
UNEMPLOYED BY OCCUPATIONAL GROUPS:
A THEORETICAL AND EMPIRICAL ANALYSIS

- Thesis for the Degree of PIL D.
MICHIGAN STATE umvmsm
DUANE E. LEIGH
1968

.........

[HESIb

LIBRARY

., Michigan State
University

 

This is to certify that the

thesis entitled

THE DISTRIBUTION OF THE UNEMPLOYED BY
OCCUPATIONAL GROUPS: A THEORETICAL AND
EMPIRICAL ANALYSIS.

presented by

Duane Ernest Leigh

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in EconOmIgs

 

    

 

Majbr/ professor

Date @A/{g/ é/y/f

0-169

ABSTRACT

THE DISTRIBUTION OF THE UNEMPLOYED BY OCCUPATIONAL
GROUPS: A THEORETICAL AND EMPIRICAL ANALYSIS

By

Duane E. Leigh‘

This dissertation is an application of the tools of
economic theory to the problem of constructing a short-run
model which determines the distribution of unemployment by
occupational groups through time. The level of unemploy—
ment in a particular occupation is defined to be the differ-
ence between the number of workers supplied and the number
demanded at a given wage rate. This difference is, in
general, positive because unemployed workers cannot obtain
information on job opportunities instantaneously or at zero
cost.

The short-run demand for the members of an occupation
is specified to depend on the expected wage in the occu-
pation and on an index of industry product demand. The
short-run supply of workers to the occupation is a function
of expected wage rates, the probability of employment in
this occupation and in other occupations, and the level of

expected nonwage earnings. The probability of employment

Duane E. Leigh

in an occupation is hypothesized to depend on the ex—
pected unemployment rate in the occupation.

The model was tested using time-series data for six
major occupational groups and six major industries during
the 1958-66 period. A system of six demand and six supply
equations was estimated. Each equation was first esti—
mated by single—equation least squares for alternative
values of the parameter in a first-order autoregressive
process. The value which minimizes the sum of squares of
residuals and the corresponding coefficient estimates are
maximum likelihood estimates of the parameters of the
equation. The entire system of equations was also esti-
mated by a two-step Aitken procedure. This procedure is
intended to take account of possible correlation in con—
temporaneous disturbances across equations in addition to
autocorrelation in individual disturbances.

The most significant variables in the demand equa-
tions were the indices of product demand. This result is
expected from the theory of derived demand. However, a
given increase in aggregate demand does not improve em-
ployment opportunities in all occupations equally. The
evidence indicates that the low skill (high unemployment)
occupations benefit less than do the higher skill occu-
pations. A policy implication is that expansionary
monetary and fiscal policies are effective policy instru—

ments for reducing unemployment only if they are coupled

Duane E. Leigh

with retraining programs designed to increase the occu-
pational mobility of low skilled workers.

The results for the wage variables in the supply
equations are consistent with several long-run studies
which show that individuals respond to differentials in
present values of expected earnings in choosing among
occupations. In addition, significant coefficient esti-
mates were obtained for the unemployment rate variables.
With the exception of the unemployment rates for laborers,
the sign of these estimates verifies the use in the model
of "probabilistic" supply functions. The results for
laborers can be rationalized by consideration of the
probable effect of "hidden unemployment" concentrated

among the low skilled.

THE DISTRIBUTION OF THE UNEMPLOYED BY OCCUPATIONAL

GROUPS: A THEORETICAL AND EMPIRICAL ANALYSIS

By

Duane E. Leigh

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Economics

1968

ACKNOWLEDGMENTS

I would like to thank the College of Business and
the Department of Economics of Michigan State University
for making funds available for me to proceed with this
study. The University also allowed me the free use of
its CDC 3600 computer.

I was particularly fortunate in having the assis-
tance of a very able guidance committee. Professor James
B. Ramsey read the last two drafts of the study and made
numerous very helpful comments. The suggestions of
Professor Jan Kmenta were beneficial in all phases of
the study. I am also indebted to Professor Kmenta for
his stimulating and very useful courses in mathematical
economics and econometrics.

Finally, I gratefully acknowledge the invaluable
assistance and support of Professor Thomas R. Saving who
served as chairman of the committee. Professor Saving
initially suggested the tOpic, and as the study progressed,
he was an unfailing source of additional ideas and much
needed encouragement.

Of course, the author is solely responsible for
any errors, logical or otherwise, which appear in this

dissertation.

ii

TABLE OF CONTENTS

Page
ACKNOWLEDGMENTS . . . . . . . . . . . . ii
LIST OF TABLES 0 O O O O O O O O O 0 O V
LIST OF FIGURES . . . . . . . . . . . . vi
Chapter
I. INTRODUCTION. . . . . . . . . . . I
II. THE MODEL. . . . . . . . . . . . 9
I. Introduction . . . . . . . 9
II. The Demand for Labor. . . . . . 11
III. The Supply of Labor . . . . . . 16
A. Expected Wage Rates as Argu-
ments in the Labor Supply
Function . . . . . . . . 16
B. Incorporation of Short-Run
Unemployment Into the Model . . 21
C. Expected Unemployment Rates as
Arguments in the Labor Supply
Function . . . . . . 27
IV. The Complete Model . . . . . . A2

A. Determination of the Desired

Vector of Industry Output. . . AA
B. Determination of Firm and

Worker Expectations of Wage

Rates . . . . . . . . A5
C. Determination of the Vector of

Expected Unemployment Rates . . 48
D. Determination of the Vector of

Current Wage Rates . . . . . 50
E. Consolidating the Model . . . 51

iii

Chapter
III. THE DATA AND THE ESTIMATION PROCEDURE

I. The Data . . . . . . .
II. The Estimation Procedure . .

IV. THE EMPIRICAL EVIDENCE AND CONCLUSIONS.
I. The Results of the Estimation

A. The Demand Results.

B. The Supply Results. . . .
II. The Interpretation of the Results

A. Interpreting the Demand Results
B. Interpreting the Supply Results

III. Summary and Conclusion. . . .
APPENDIX . . . . . . . . . . .

BIBLIOGRAPHY. . . . . . . . . . . .

iv

Page

Table

LIST OF TABLES

Alternative Occupations for Members of
Each Occupational Group . . . . .

OLS Estimates of Parameters Appearing in

the Demand Equations Specified in (4.1).

Aitken Estimates of Coefficients Appearing
in the Demand Equations Specified
in (14.1) o o o o o o o

OLS Estimates of Parameters Appearing in

the Supply Equations Specified in (A.2).

Aitken Estimates of Coefficients Appearing
in the Supply Equations Specified
111(2402) 0 o o o o o o c o o

OLS Estimates of the Beta Coefficients of
the Standardized Variables Appearing
in (“‘0 l) o o o o o o

Page

71

80

83

86

87

94

LIST OF FIGURES

Figure

l. The Orthodox Theory of Work-Leisure Choice.

2. Time Paths of Adjusted Expected Wages of
an Employed and an Unemployed Worker in
the rth Occupation. . . . . .

3. Time Path of Adjusted Expected Wages in
Occupation q Viewed by a Member of
Occupation r. . . . . . . . .

A. Work- Leisure Choice Incorporating the

Possibility of Unemployment in an
Occupation . . . . .

vi

Page
20

32

33

36

CHAPTER I

INTRODUCTION

This dissertation is an application of the tools of
economic theory to the problem of explaining the short-
run distribution of occupational unemployment. At neither
the micro nor the macro level is the present state of
economic analysis entirely satisfactory with respect to
the labor market. At the microeconomic level of analysis,
the traditional theory of competitive equilibrium essenti-
ally precludes the unemployment problem because the attain-
ment of general equilibrium implies that all the marginal
conditions are met including those for full employment.
Thus, unemployment functions as a signal that the system
is out of equilibrium; but it is not clearly explained
how the unemployment comes about, nor is the mechanism
specified by which full employment is regained as the
system approaches equilibrium. Arrow neatly sums up the
problem in the following passage:

Neoclassical microeconomic equilibrium with fully

flexible prices presents a beautiful picture of

the mutual articulations of a complex structure,
full employment being one of its major elements.

[But] What is the relation between this world
. and the real world with its recurrent

tendencies to unemployment of labor . . .?1

At the aggregate level of analysis, excess supply
in the labor market is a stable solution to the general
class of macroeconomic models in which all markets but
the labor market are simultaneously cleared. But here
the inadequacy of the micro foundation is reflected in
the seemingly ad hoc assumptions which are employed to
arrive at the unemployment solution. Well-known examples
are the cases of rigid money wages, money illusion on the
part of labor suppliers, and the liquidity trap. Clearly,
the descriptive power of the standard Keynesian model
would be increased if the existence of unemployment could
be demonstrated on the basis of assumptions consistent

with economic theory.2

 

1Kenneth J. Arrow, "Samuelson Collected," Journal
of Political Economy, LXXV (October, 1967), p. 73A.

 

2Axel Leijonhufvud argues persuasively that Keynes'

theory, as distinct from the Keynesian model, is consistent
with economic theory. In his theory, Keynes discusses
wage rigidity as a policy recommendation rather than as a
behavioral assumption. Hence, to move from general
equilibrium theory to Keynes' world, it is sufficient
only to give up the assumption of instantaneous price
adjustments. Leijonhufvud notes that "The removal of

the [Walrasian] auctioneer simply means that the gener-
ation of the information needed to coordinate economic
activities in a large system where decision making is
decentralized will take time and will involve economic
costs. No other 'classical' assumptions need be relin—
quished." "Keynes and the Keynesians: A Suggested
Interpretation," Proceedings of the American Economic
Association, LVII (May, 1967), p. AOA. As will be seen
in the following paragraphs in the text, this is very
much the general approach taken here.

 

The purpose of this dissertation is to construct
and empirically test a model constructed from economic
theory which determines the occupational structure of
unemployment through time. The model is a short-run
model because it is primarily short-run fluctuations in
the unemployment vector in which we are interested. The
level of unemployment in an occupation is defined to be
the number of members of the occupation who are unem—
ployed. Hence, the level of unemployment is the differ-
ence between the number of workers willing to supply
their labor in the occupation at a given wage and the
number of workers demanded by firms at this wage. The
plan of attack is to develop market demand and supply
functions for each occupational group. Then at the market
wage rate, the quantity of labor supplied and demanded,
and hence the level of unemployment, is determined at any
particular moment.

Each occupational supply and demand function is con-
structed assuming rational decision making on the parts
of individual firms and labor suppliers. But because
product demand fluctuates unexpectedly and information
and mobility are not costless, wage offers by firms and
reservation prices of individuals will not in general
adjust with sufficient speed to assure that the number
of workers who desire to work will be equated to the

number of workers demanded by firms in the short run.

Therefore, a positive level of unemployment can exist

in the model without the assumption that labor unions or
other institutions enforce rigid wages. Rather than
serving as an indicator of disequilibrium, as in the
traditional theory of competitive equilibrium, a posi-
tive level of unemployment is inherent in the system
because of the costs involved in supply adjustments.

The labor economics literature related to the
topic of this dissertation is voluminous. Of the studies
examining unemployment as the dependent variable in the
analysis, a large number are concerned with determining
which of two contending hypotheses provides the better
explanation of observed unemployment in the past ten to
fifteen years. The two hypotheses are the inadequate-
aggregate demand hypothesis and the structural unemploy-

3

ment hypothesis. It is widely recognized that empiri-
cal information on the relative importance of the two
hypotheses is critical, particularly from the policy point

of View.“ The present model is not explicitly constructed

 

3The former hypothesis expresses the macro view—
point that unemployment rates throughout the labor force
rise and fall with changes in the total demand for goods
and services. The latter hypothesis is based on micro
considerations. It states that "structural" changes
have occurred in the economy which have resulted in sub-
stantial changes in the composition of labor demand.
Since workers are not instaneously mobile, unemployment
has become concentrated in particular segments of the
labor force while other segments enjoy a surplus of job
Opportunities.

“A widely quoted monograph supporting the inade-
quate-demand hypothesis is that by James W. Knowles and

to distinguish between the hypotheses; however, the
demand side of the model does provide evidence as to the
impact of changes in product demand on the occupational
structure of labor demand.

In developing the supply side of the model, exten-
sive use is made of two well-developed bodies of liter-
ature. These are the studies examining investment in
human capital and the studies analyzing labor force
participation rates. In the human capital literature,
an individual's effort to increase his earning capacity
is treated as an investment to raise the level of human

5

capital he possesses. As in the case of investment in

 

Edward Kalachek, Higher Unemployment Rates,l957-l960:
Structural Transformation or Inadequate Demand, Sub-
committee on Economic Statistics of Joint Economic
Committee, U. S. Congress (Washington: U. S. Government
Printing Office, 1961). Two brief statements of the
views of Charles C. Killingsworth, the chief prOponent
of the structural hypothesis, are found in Jack Stieber
(ed.) "StruCtural Unemployment in the United States,"
Employment Problems of Automation and Advanced Techno-
logy: A International Perspective TLondon: Macmillan
and—Company, Ltd., 1966), pp. 128:156 and Garth L.
Mangum (ed.) "Automation, Jobs, and Manpower: The Case
for Structural Unemployment," The Manpower Revolution:
Its Policy Consequences (Garden City, New York: Double-
day & Company, 1965), pp. 97—117.

5Gary S. Becker was instrumental in laying out the
theoretical framework upon which this literature developed.
See his Human Capital (New York: National Bureau of
Economic Research, 196A) and "Investment in Human Capital:
A Theoretical Analysis," Journal of Policital Economy,
LXX, Part 2 (Supplement: October, 1962), pp. 9-A9. In
this Supplement, the contributions of Jacob Mincer, Larry
A. Sjaastad, and George J. Stigler should also be noted.
An additional fruitful application of capital theory to
individual investment decisions is Yoram Ben-Porath, "The
Production of Human Capital and the Life Cycle of Earn-
ings," Journal of Political Economy, LXXV, Part I (August,
1967). pp. 352-365.

 

 

 

 

 

 

physical capital, investing in oneself yields a return,
but only at a cost. Therefore, it is postulated than an
individual will invest in himself up to the point at
which the present value of additional earnings equals
the additional costs.

The studies of labor force participation attempt
to isolate the variables which determine whether or not
individuals will offer their services in the labor market.6
Of special relevance to this dissertation is Mincer's
fundamental contribution examining the supply behavior
of married women.7

In the past few years, a literature has begun to

grow delving into the response of both employers and

workers to changes in product and labor demand.8 Because

 

6Two fine surveys of this literature are: Jacob
Mincer, "Labor-Force Participation and Unemployment: A
Review of Recent Evidence," in R. A. Gordon and M. S.
Gordon (eds.) Prosperity and Unemployment (New York:
John Wiley & Sons, Inc., 1966), pp. 73-112 and Anthony
Fisher, "Poverty and Labor-Force Participation," Research
Paper P-273, Economic and Political Studies Division,
Institute for Defense Analyses, February, 1966.

 

7Jacob Mincer, "Labor Force Participation of
Married Women: A Study of Labor Supply," Aspects of
Labor Economics, Conference of the Universities-National
Bureau Committee for Economic Research (Princeton:
Princeton University Press, 1962), pp. 63-97.

 

 

8A survey of this literature is found in Charles C.
Holt, "Job Search, Phillips' Wage Relation and Union
Influence, Theory and Evidence," Firm and Market Workshop
Paper 6705, Social Systems Research Institute, University
of Wisconsin, December 1A, 1967. (Mimeographed.) Of
particular use in this dissertation is the approach to
analyzing the costs and returns to information search

information cannot be obtained instantaneously or at zero
cost, some lag in response almost always exists for both
parties. In the development of the present model, the
lag in labor supply is utilized to demonstrate the
plausibility of an unemployment equilibrium situation.
The hypothesis proposed is that individuals view a
positive level of unemployment as the normal case rather
than as a transitory phenomenon which can safely be
ignored in making supply decisions. Consequently, they
consider the relevant set of unemployment rates in eval-
uating alternative occupations against each other. The
import of this hypothesis is that the past levels and
distributions of unemployment become crucial variables
determining workers' supply decisions in the current
period, so that past unemployment is an important determi-
nant of the characteristics of the present structure of
unemployment.

The dissertation is organized in the following
manner. In Chapter II the model is constructed. The
labor demand function for members of an occupation by a

firm is derived from the firm's production function, the

 

developed by Armen A. Alchian in his yet unpublished
paper "Information Costs and Unemployment" (Mimeographed)
and in University Economics (co-authored with William R.
Allen) (2d ed.; Belmont, California: Wadsworth Publish-
ing Company, Inc., 1967), Chapter 25. Special reference
should also be given the interesting application of
Markov processes by Martin David and Toshiyuki Otsuki

to the problem of predicting short-term movements between
the states of employment, unemployment, and nonpartici-
pation. See their "Forecasting Short-Run Variation in
Labor Market Activity," Review of Economics and Statistics,
XLX (February, 1968), pp. 68—771

 

 

definition of the profit function, and the profit-
maximizing constraints. Aggregation is performed first
over all firms in an industry and then over all rele-
vant industries to arrive at the total demand function
for a particular occupation.

The supply function to an occupation is the out—
come of a theory of short—run occupational choice. The
theory is developed on the hypothesis that individuals
behave as if they decide between occupations by compar-
ing the present values of the time streams of adjusted
expected wages in alternative occupations over a short-
run earnings horizon. The adjusted expected wage in an
occupation at any moment in time is the expected wage
adjusted by the probability of employment at that moment.
The expected unemployment rate enters the supply function
as the determinant of the probability of employment in the
occupation.

Chapter III is divided into two sections. The
first is a description of the data chosen to test the
model. In the second, the model is condensed for
statistical estimation, and the statistical techniques
used are considered. Finally, Chapter IV contains a
report of the empirical results and suggests some con-

clusions that may be drawn from the study.

CHAPTER II

THE MODEL

I. Introduction

The model presented in this chapter is an attempt
to explain short—run fluctuations in the occupational
structure of unemployment. We proceed under the assump-
tion that individuals and firms act so as to maximize
utility and profits, respectively. However, supply and
demand decisions in occupational markets must be made in
an uncertain and rapidly changing environment. The effects
of external events and shifts in consumer tastes result in
changes in the level and composition of product demand.
These changes are reflected in the demand for labor, and,
after a lag, in the vector of wage offers. However, in-
formation on wage rates in alternative occupations is not
available to workers instantaneously or at zero cost. Nor
is mobility costless after information is obtained. As
information is collected, the market works toward equating
supply and demand, but, in general, this process is not
completed in a short-run period. Consequently, a positive

level of unemployment can exist in every occupational

10

group. There is no need to place institutional or other
constraints on wage flexibility to demonstrate the V
existence of unemployment.

Suppose we describe the occupational structure of
unemployment at a particular moment in time by the

following m-dimensional vector:

(2.1) (U U ... U

lt’ 2t’ ’ mt)’

where th (q=l,...,m) is the number of unemployed workers
in the qth occupational group at time t. Each component
of this vector is defined to be the difference between

the quantity of labor supplied and the quantity demanded
at a given wage rate. We denote the number of workers who

are willing to supply their services in occupation q by

tat and the number of members of occupation q demanded by

d
qt’ qt’

the unemployment vector at time t may be written:

firms by A At a given wage w the qth component of

" ”d
(2.2) th = tat - tqt (q=l,...,m).

Our approach is to construct supply and demand functions
for the qth occupation at time t. Using (2.2) we are then
able to solve for the level of unemployment in the occu-
pation at a given wage.

This chapter is divided into three sections. In
Section II, static general equilibrium theory is utilized

to construct a short-run demand function for workers in

11

the qth occupation. Section III is devoted to the develop-
ment of the corresponding short-run supply function.

These functions are expressed in terms of the vectors of
expected wage and unemployment rates and the endogenous
vector of industry output.

Section IV contains hypotheses specifying how
expectations are formulated and how the other endogenous
variables are determined. To complete the system, a set
of relationships is introduced to determine the vector of

current wage rates.

II. The Demand for Labor

We begin the construction of the demand side of the
model by deriving the short-run labor demand function for
an individual firm. Then aggregation is performed over
all firms in the industry and over all industries to ob-
tain the total short—run demand function facing the mem—
bers of the qth occupation. Each multi-product firm is
viewed as a combination of two or more single-product
firms. Furthermore, each single-product firm is assumed
(l) to be perfectly competitive on both the product and
the factor markets, and (2) to employ the same factors of
production as the other firms producing the same product.
An implication of these assumptions for the multi-product
firm is that the level of output of any single product
does not affect the output of its other products. We

define an industry to be the number of single-product

12

firms producing a distinct product. The model is con-
structed for a short-run situation in which there are m
variable inputs (types of labor) and one fixed input
(the stock of capital) in the economy.

Consider the ith firm in the jth industry,
i=l,...,nJ and j=l,...,M. The firm's demand for the
qth labor input is derived from its production function,
the definition of profit, and the profit—maximizing
constraint. The following general production function

is employed:1

(2.3) yij = fiJ(Al,...,£m,kJ) (i=l,...,nJ;j=l,...,M),

where yiJ denotes the level of output, £l""’£m denote

levels of the m variable (labor) inputs, and k denotes

J
the quantity of the fixed input capital in the jth in-
dustry. The definition of expected total profit for the
firm is

(2.A) w*

= a _ x s a
13 pjyij (wlfil + ... + wmim + w k ),

k 3

where p3 is the expected market price of the jth product
and (w§,...,w;,wfi) is the (m+l)—dimensiona1 expected input

price vector facing the firm. Differentiating (2.A)

 

1Since the analysis in this and the following
section is static, the time subscript on all variables
is omitted to simplify the notation.

l3

partially with respect to each variable input, setting
the resulting equations equal to zero, and introducing
a random disturbance term yields the following m profit-

maximizing conditions:

3y
*__£l.= * =
(2.5) pjalq wq + eqij (q 1,. ,m)
A rationale for the disturbance term (eqij) is that

entrepreneurs modify their profit-maximizing input de-
cisions in response to essentially random disturbances
occurring outside the system which are not reflected in
the eXpected wage and price parameters. With the m+2
equations of (2.3), (2.A), and (2.5) in the unknowns
yij’flIj’zl""’£m’ we can solve for the levels of profit,
output, and labor inputs in terms of the expected para-
meters given to the firm. The profit-maximizing level

of the qth labor input is

~

= * * *
(2-6) £qij hqu(pJ:wls°'°swm3€qu)3

~

where lqij is the number of members of occupation q which
the firm desires to employ.

To derive the labor demand function for the industry,
we cannot simply sum the demand functions of the individual
firms for the reason that the product price is not fixed
to the industry. The industry product demand function is

based on the results of individual consumer utility

1A

maximization aggregated to the industry level. For our
purposes, it is specified that the desired level of out-
put of an industry is a function of the own expected
price and the expected prices of all other products.
Hence, the demand function for the jth product may be

written
(2.7) §, = gj<p§,....p§> (i=l,---,M),

where §J is the desired level of output of industry j.
We assume that the Jacobian of the system of functions
designated in (2.7) exists and is nonsingular for the

relevant intervals on the pJ's, that is,

5p1 5p2 5pM
3g2 3g2 3g2 # O
apl¥ 3p2¥ O O O 3pM¥ O
BgM BgM agM

 

 

Appeal to the Inverse Function Theorem allows us to

rewrite (2.7) as

(2.9) p3 = hj(§l,...,§M) (j=l,...,M).

15

Substituting, the labor demand function of the jth in—

dustry is

I

(2.10) 1

go
I

_ ~ ~ * *
qj quEhJ(yl,...,yM),wl,...,wmeqj

= a x ” "
nqj(wl’°"’wm’y1"'°’yM’€qj)’

where A is the number of members of the qth occupation

qJ
which the firms in industry j desire to employ, and e

qJ

is the sum of the disturbances for the individual firms.
The total demand function for the members of the

qth occupation is obtained by summing over all the in-

dustries employing members of this occupation. The total

demand function is

~d M
(2.11) A = Z n 3
q 3:1 q
= Gq(w§’...’W;,yl,...,yM,Eq) (q=l,ooo’m),

with the partial derivatives2

3G 8G. 3G
(2.12) W3 < 0, WA > o (rat'q), 5-37—91 > o (j=l,...,M).
.q r J,

 

2The sign of the partial derivative of G with re-
spect to yJ is due to the assumption that

 

 

8G M 3G a~ a *

__9 > 2 ~ 5:; _g_

ay i=1 8y p1 3y
J #3 i 3

That is, the direct effect of a change in the quantity

16

III. The Supply of Labor

In this section, the supply side of the model is
developed from a theory of short-run occupational choice.
Since it is a short-run model, we consider only the be-
havior of individuals who are in a position to move be—
tween occupations or between market and nonmarket activity
within a short period of time. That is, we are interested
in those individuals whose supply decisions have a shorte
run impact on the occupational distribution of the labor
force. Here, the labor force is defined as the total
number of workers either employed or unemployed in an
occupation. Unemployment in the short run comes about
because the time period selected for analysis is frequently
too short to allow an individual to both choose an occu-
pation and choose a job within the occupation.

In the first part of this section, the individuals
whose supply behavior is relevant to a short-run model are
identified, and then we supply a rationale for the in-
clusion of current expected wages in the supply functions
of these individuals.

A. Expected Wage Rates as
Apguments in the Labor
Sppply Function
It is first assumed that occupational groups may

be ranked by the stock of human capital that must be

 

demanded of product j on the demand for workers of the
qth type exceeds the indirect effect appearing via
substitute and complement relationships in the product
markets of all other goods, even in the most extreme case.

17

possessed by a worker in order to enter the occupation.
Secondly, it is assumed that an individual possessing a
given stock of capital may enter any of the occupations
(if such occupations exist) requiring a lower stock.
Upward mobility, however, requires that he first invest
in himself in order to increase his level of skills.
Examples of pertinent investment in human capital are
information gathering, education, migration, and on-the—
job training.

The costs of the investments described above may
be separated into two components: (I) the direct costs
of purchased goods and services, e.g., tools, tuition,
moving costs, etc., and (2) the earnings foregone, that
is, the present value of productive services withdrawn
from another occupational group. The individual will in-
vest in himself up to the point at which the present value
of additional earnings from investing equals the present
value of the additional costs.

To acquire a higher level of skills for upward
occupational mobility, an individual must normally under-
take an investment over a long—run period. The direct
and opportunity costs of this type of investment are
large enough that in order to justify such investments
the present value of prospective earnings over a long-
run horizon (perhaps a lifetime horizon) must normally

be considered. Because of the length of time required

18

to complete the necessary investment, we ignore upward
mobility as a possible short-run supply adjustment.
Therefore, the short—run sources of additional members
to an occupation, say occupation q, are: (1) members
of occupations which require higher levels of skills
than does the qth occupation, and (2) workers currently
outside the labor force (i.e., workers not currently
members of any occupation) who possess at least the
minimum level of skills to enter occupation q. For
these individuals, the costs of investing in occupation
q involve only the costs of collecting job information
and moving costs. Since their investment costs are
relatively minor, they are in a position to enter
occupation q in response to favorable job conditions
which may prove to be only "temporary." That is, these
individuals may make their supply decision with respect
to the qth occupation on the basis of the present value
of expected returns in the occupation for a short-run
earnings horizon. Over a short—run horizon, it is
reasonable to assume that the current expected wage is
a reliable measure of future expected wages. The work-
leisure analysis of traditional wage theory provides a
useful point of departure for developing a theory of
short-run occupational choice.

Suppose that the decision to work in the short-run
is an all—or—nothing decision, meaning that an individual

anticipates either working full time, say, eight hours

19

per day, or specializing in leisure, where leisure
refers to all forms of nonmarket activity. Further,
assume that an individual may be a member of only one
occupation at any moment in time. In Figure l, we
depict an individual's indifference map with income
per unit of time on the vertical axis and leisure per
unit of time on the horizontal axis. The distance OLm
represents twenty-four hours per day of leisure and OLO
represents sixteen hours per day of leisure. The level
of income OY is the income received other than that

O
earned from supplying labor on the market, and Y Y is

O T
wage income. Points A and B are assumed to be the only
alternatives available to the individual.

Conceptually, it is possible to distinguish between
the following two decisions for an individual: (1) whether
to choose the qth occupation over all other relevant
occupations; and if occupation q is selected, (2) the
choice between this occupation and full-time leisure.

He makes the first decision by picking out the set of
occupations for which he is qualified, and from the
corresponding set of eXpected wage rates selecting the
highest. Suppose that the expected wage in the qth
occupation is the highest. This expected wage is repre-
sented in Figure l by the slope of the line segment BC.

Any lower wage is represented by a line segment, such

as BD, of slope less than BC in absolute value.

20

Y/

A

 

 

 

 

Figure l.--The orthodox theory of work-leisure
choice.

The individual's second decision depends on whether
the indifference curve passing through point A is higher
than the indifference curve passing through point B. In
Figure l, I2I2 exceeds IlIl so that the individual will
supply his labor to the qth occupation. However, if the
expected wage in occupation q should fall to a level
lower than the wage rate represented by the slope of BD
and still remain the highest of the set of available

expected wage rates, the individual will choose to

specialize in leisure.

21

The analysis depicted in Figure l is deficient in
that attention to expected wage rates may not be sufficient
to evaluate expected earnings in alternative occupations
if conditions of less than full employment prevail. In
the next part of this section it is argued that short-
run unemployment arises because of the time involved in
the adjustment process required to move from one occu-
pation to another or to move into or out of the labor
force. The essence of the argument is that the adjust—
ment process may be carried out most efficiently while a
worker is unemployed. Differences in demand conditions
across occupations give rise to the occupational distri-
bution of unemployment. The discussion is carried out in
a framework of individuals' reservation prices.

B. Incorporation of Short-Run

Unemployment Into the
Model5

 

The reservation price represents a worker's evalu—
ation of his market alternatives. Consider an individual
employed in an industry which suffers a decrease in pro-

duct demand. Given that the labor supply function is

 

3Many of the important concepts in this discussion
of reservation prices are developed in Alchian, "Infor-
mation Costs and Unemployment" and in Alchian and Allen,
University Economics, pp. A9A-509. Other papers dealing
with the topic of job search are George J. Stigler,
"Information in the Labor Market," Journal of Political
Econom , LXX, Part 2 (Supplement: October, 1962), pp.
95-105; Albert Rees, "Information Networks in Labor Mar-
kets," Proceedings of the American Economic Association,
LVI6(May, 1966), pp. 559-5663 and Holt, op. cit., pp.
59- 5.

 

 

22

not perfectly elastic, he can be employed in this in-
duStry only at a lower wage. Suppose, however, he feels
that he has alternative employment opportunities in his
occupation (or in occupations requiring a lower level

of skills) at a higher wage than that now offered him.
That is, his reservation price exceeds the wage his
employer is offering. Rather than lowering his reser-
vation price, we expect that he will make an effort to
obtain information on job vacancies in other industries!4
Since this information is not available instantaneously,
time is consumed in the search process. As the worker
continues to search out information, he will acquire an
ever larger sample of the wage offers being made by em-
ployers. Finally, he will terminate the job search when
the increment in earnings by which his best offer exceeds
his next best offer suggests that the expected increment
from further search is less than the cost of the addi-
tional search.5 At this time he will adjust his reser-
vation price if he concludes that an adjustment is neces-
sary to secure employment. There is a limit to the
length of the search process because the "law" of

diminishing returns suggests that increments in earnings

 

“The principles outlined here also apply to the
case of a worker who revises his reservation price up-
ward and quits his job even though he could continue
to work at his previous wage rate.

5Alchian, 0p. cit., p. 12.

23

will begin to decline after some positive level of
investment in search. The costs to be considered are
the earnings foregone during the period of search, the
direct costs of search (e.g., the costs of using the
services of employment agencies and of traveling to
job interviews), and the costs of moving.

The individual in the above situation has the
following short-run alternatives Open to him: (I)
continue working at the reduced wage and engage in job
search during leisure hours, (2) begin working in the
highest—wage job immediately available and engage in
job search during leisure hours, or (3) devote himself
full time to searching for a job. Except in the unlikely
situation that an immediately available job is a global
optimum, the second alternative is more costly than the
first because it involves two moves, whereas the other
alternatives involve only one. The first move is to the
immediately available job, while the second is to the
job chosen at the end of the search period. Consequently,
the second alternative will never be selected over the
first unless the increment in earnings exceeds the addi-
tional cost of an extra move.

The third alternative would seem to be the highest
cost in terms of foregone earnings, but because the un-
employed worker specializes in job search, he can, in

general, accumulate more information about wage offers

2A

in a given period of time than an employed worker is
able to acquire. Consider two workers who possess
equivalent levels of skills. If the above proposition
holds, the unemployed worker is able to make his choice
from a set of alternatives and begin work some time be-
fore the employed worker is in a position to choose
among a comparable set of job offers. For this reason,
it is likely to be the employed worker who is at a net
disadvantage with respect to foregone earnings. If so,
it would be completely rational for a worker to select
unemployment as the best alternative state during his
adjustment period.6 The fact that information is not
available instantaneously or at zero cost implies, in
this case, that a positive level of unemployment is con-
sistent with optimal individual behavior. Thus, unem-
ployment may be said to exist in short-run equilibrium
where supply adjustments are a part of the unconstrained
functioning of labor markets. However, unemployment is
not consistent with long-run equilibrium which occurs
only when all adjustments have been carried out.
Returning to Figure 1, if a worker determines that
his highest expected wage is less than the expected wage
rate represented by the lepe of line segment BD after

his period of search is completed, he will leave the

 

6The result that it is rational does not imply that

unemployment is painless to the worker and his family.
Indeed, every effort should be made to increase the flow
of job information and hence shorten the period of ad-
justment.

25

labor force and specialize in leisure, either investing
in himself to upgrade his level of skills or devoting
full time to home work. This expected wage may there-
fore be defined to be the worker's reservation price
for remaining in the labor force.

The above analysis implies that except in the case
where changes in product demand are always positive,
there will exist a positive level of unemployment con-
sistent with short-run equilibrium in any occupational
market. The level of unemployment depends on the nature
of fluctuations in product demand faced by the industries

which employ the members of the occupation.7

The greater
are the frequencies and magnitudes of the fluctuations,
the larger is the number of workers placed in a position
where they may choose to be unemployed during their ad-
justment period rather than to accept a lower wage.
Consequently, the level of unemployment in the occupation
increases, even in the case in which the fluctuations
average out to zero across industries.

In the case of a downward shift in the entire vector
of industry product demand, workers do not, in general,
immediately recognize that the distribution of wage

ovvers has shifted downward. This realization occurs

only after they have collected a sufficiently large

 

7This discussion abstracts from the unemployment
impact of changes in supply due to long-run forces such
as changes in the demographic composition of the pOpu-
lation.

26

sample to infer that the reason wage offers are lower
than anticipated is a decrease in demand rather than
simple bad luck. Hence, while the market eventually
forces workers to adjust their reservation prices down-
ward, the length of the average adjustment period in-
creases so that the level of short-run unemployment is
higher in each occupational group.

To conclude the discussion of short-run unemploy-
~ment, the special cases of fixed proportions in pro-
duction and downward rigid wages are incorporated into
our theory. These are the two cases usually pointed
out as the causes of unemployment.

In a full-employment situation with fixed pro-
portions, a shift in the composition of product demand
results in an excess supply of the members of some occu—
pations. The marginal product of these workers falls to
zero so that there is no positive wage at which employers
find it profitable to retain them on the payroll. Simi-
larly, effective minimum wages remove the option for some
workers of working at reduced wages in the face of a de-
crease in demand.

In periods of a general decrease in demand, effec-
tive minimum wages and/or fixed proportions reduce the
total number of positive wage offers that employers can
make. Thus, an individual finds that he must increase

his investment in search in order to obtain a given

27

sample of wage Offers. TO the extent that these con-
straints on firm behavior are more significant in some
occupational markets than in others, they serve to
accentuate inter-occupational differences in unemploy-
ment rates. Indeed, the least—skilled unemployed
workers may find employment Opportunities entirely
closed Off, with a consequent rise in hard-core unem-
ployment.

C. Expected Unemployment Rates

as Arguments in the Labor
Supply Function

 

 

The analysis presented in Figure 1 does not take
into account the existence of unemployment. The inclusion
Of unemployment in the system means that occupational
choice must be made under conditions of uncertainty. A
particular job does not guarantee a certain time path of
earnings, even over a short—run horizon. Consequently,
the vector of expected wages is not the only factor in—
volved in short—run decision making. The rational indi-
vidual will also take into consideration the possibility
that unforeseen changes in demand may occur which result
in his unemployment. At each moment in time he will com-
pare his current position (whether employed or not) with
the information he has on the conditions existing in the
occupations he is qualified to enter. Consider his
evaluation at time t=tO on the assumption that if he

selects a particular occupation he expects that he will

28

be a member of this occupation for at least the duration
of his short-run earnings horizon, which we suppose to
end at t=T. In what follows, a theory is developed in
which the individual first chooses among occupations,
taking into account the possibility that he may be un-
employed for a period of time in any one of the occu-
pations. Then he decides whether to enter or to remain
in the occupation judged to be the best among those con—
sidered.

An individual belonging to a particular occu—
pational group is either employed or unemployed in that
group; hence, at any time t, his employment position in
the occupation may be described by a binomial probability
distribution. Moreover, it is expected that the proba-
bility of employment in occupation q at a future moment
in time for a worker currently employed in the occupation
is not the same as the probability Of employment for a
worker currently unemployed in the occupation.

Suppose that an individual is employed in occupation
Viewed at t

q at time t the conditional probability

0' O’
Of being employed at the expected market wage in the qth

occupation at time t (tO<tsT) may be written as

(2.13) P(EtIEtO) = g(t,ua),

where u; is the expected unemployment rate in the occu-

pation at t It is assumed that the worker anticipates

0°

29

that the wage rate and the unemployment rate in occu-

pation q expected to exist at time t will continue

0
unchanged over his short—run horizon. In the same
manner, the probability Of being employed at time t
(t0<tsT) in occupation q given that the individual is
unemployed in occupation q at tO is

= *
(2.1A) P(Et]UtO) h(t,uq).
The signs of the partial derivatives of (2.13) and (2.1A)

are postulated to be

3g(t,u*) 8g(t,u*)
(2.15) W < O and ————3—3t < O,
and
3h(t,u*) 3h(t,u*)
(2.16) < O and ‘——————9— > 0.
Bug at

The negative sign of the second of the two partial
derivatives in (2.15) is rationalized as follows: the
further in the future is t, the less certain is the indi-
vidual that he will continue to be employed. On the
other hand, the sign Of the second of the partial deriva-
tives in (2.16) is positive because the individual may

be more certain of finding a job the longer the period

in which he engages in search.

30

At any time t, it is hypothesized that a worker
adjusts the expected wage rate in occupation q, denoted
by x3, by the conditional probability Of employment at
t--either (2.13) or (2.1A) depending on the worker's
current employment state. We define the adjusted ex-
pected wage in occupation q at time t to be x3 times the
conditional probability Of employment in occupation q at
t. Thus, if a worker is employed in the qth occupation

at time t the present value of the time path Of ad-

0’
justed expected wages in occupation q is given by

T
(2.17) pvq = {O[g(t,ua)-Xa]e

i(t—to)dt

3

where the expression in brackets is the adjusted expected
wage of an employed worker at time t, and i is the rate of
interest. The interest rate is assumed constant during
the short-run horizon.

Conversely, the present value of adjusted expected
earnings in occupation q as viewed by a worker currently
unemployed in the occupation is

T

= , -i(t-t )
(2.18) qu I [h(t,ua) xale 0 dt.

to

Finally, the present value of adjusted expected
earnings in occupation q evaluated by an unemployed

individual outside the qth occupation is

31

T
(2.19) PV = I [h(t,u*)-x*]e’i(t'to)dt - $[1-e‘i(t1’to)]
q to q q 1

3

where c is the direct cost Of investment in occupation q
at time t (toststl), and t1 is the end of the investment
period. The individual's choice among the set of occu-
pations available to him depends upon which one Offers
the highest present value Of adjusted expected earnings
net of any direct investment costs.

Figure 2 presents two time paths of adjusted ex-
pected earnings drawn for i; and E: which are assumed to
be the current values Of the expected wage and the ex-
pected unemployment rate, respectively, in occupation r,
an alternative to occupation q. The function AA repre-
sents the time path of adjusted expected earnings for a
member Of occupation r employed at time to, while BB
represents the time path for the same worker should he
currently happen to be unemployed in the occupation. The
vertical axis measures adjusted expected wages, denoted
by A(x;), and time is measured on the horizontal axis.
The second partial derivatives with respect to t of the
conditional probabilities of employment (2.13) and (2.1A)
are not specified so that the time paths AA and BB could
be re-drawn in several alternative ways consistent with
E; and 5; so long as the SIOpes of the functions are

negative and positive, respectively, in the interval

32

(tO,T].8 However, the partial derivatives with respect1
to us in (2.15) and (2.16) imply that for any fig>fi¥,
each time path would shift such that every point on the
new function is lower than the corresponding point on

the old function for any t (tO<tsT).

 

 

 

*
A(xr)
A\
i-* L
I" l
AN
| A
I B
|
I
I
I
I
I
O r I >t
T
t 0

Figure 2.——Time paths of adjusted expected wages
of an employed and an unemployed worker in the rth occu-
pation.

 

8The particular time paths depicted in Figure 2
are drawn on the assumption that at any time t, a cur-
rently employed worker never evaluates the probability
Of retaining his job to be less than the probability
he would assign to Obtaining employment were he currently
unemployed. A further assumption that might be made is
that in either case the worker views his probability Of
employment to be asymptotic to (l-u*). On this assumption,
the_timg paths AA and BB would be dann asymptotic to
(l-u;)-x;.

33

As mentioned previously, the sources of short—run
change in the relative quantities of labor supplied to
occupations are (1) members of higher occupational groups
who switch to lower occupations, and (2) individuals who
move into and out of the labor force. We examine first
the considerations relevant to a worker deciding between
occupations.

Figure 3 illustrates the position of a member Of

occupation r, either employed or unemployed, who is

 

 

Figure 3.——Time path Of adjusted expected wages in
occupation q as viewed by a member of occupation r.
considering the possibility of entering occupation q.
For this worker, one may conceptually distinguish the
process Of selecting an occupation on the basis of
general information on wage and employment conditions

from the process of selecting a particular job within

3A

the chosen occupation. In the figure, it is assumed
that the time required to complete investments in infor-
mation and/or geographical mobility in selecting occu-
pation q is the interval [t0,tl]. The direct cost of
these investments charged against expected earnings in
the occupation is shown by the rectangle (chtotl).

In addition, further investment in job search may be
necessary to sample the industry wage Offers being made
to members of the occupation. If this investment has a
direct cost, the net expected wage in occupation q is
negative for an additional time period, say (t1,t

2).

For tat however, the individual can anticipate a

2:
positive adjusted expected wage. A portion of total
short—run unemployment in an occupation therefore arises
because the time interval considered is long enough to
allow a worker to select an occupation, but it is too
short for him to search out the best available job.

The Opportunity cost Of investing to enter occu-
pation q is the present value of the time path of ad-
justed expected earnings in occupation r--either AA or
BB in Figure 2. But it is unlikely that a worker who
is dissatisfied with his present job in occupation r
can Obtain the information necessary to locate the best
job in an alternative occupation with instant search or

while working at the old job to avoid unemployment.

Hence, the time path AA in Figure 2, the present value

35

Of which is calculated by (2.17), does not represent the
relevant Opportunity cost of investment in occupation q
for most individuals. In what follows, we consider
explicitly only the case of workers who are unemployed
for some positive period of time. The decision between
any two occupations is therefore made by comparing pre-
sent values calculated by (2.18) and (2.19).

It is reasonable to assume that an individual's
utility function includes the following arguments: the
rate of consumption Of goods and services, the rate of
consumption of leisure, and tastes for particular occu-
pations. Define the total present value of expected
earnings in an occupation (TPV) to be the sum of the pre-
sent value of expected nonwage earnings (PVO), which is
assumed to be invarient between occupations, and the
present value Of adjusted expected earnings from working
in the occupation (PV). Then in the two-occupation case,
the utility function may be rewritten in the arguments
TPVq, TPVr, and leisure, since tastes for occupations
exist. Each argument may be measured on one axis of a
three-dimensional diagram. Assume, as in Figure 1, that
an individual anticipates working either eight hours per
day or not at all during his short-run horizon, and that
he works in either occupation but not in both. To choose
between the occupations, he will select the one which

puts him on the higher indifference curve at a level Of

36

leisure equal to sixteen hours per day. This will neces-
sarily be a corner solution.

Suppose that occupation q is preferred to occupation
r. The indifference curves presented in Figure A are
slices of the three-dimensional indifference map at

TPVr = PV As in Figure l, the distance OLm represents

0'

twenty-four hours per day Of leisure and OL represents

0
sixteen hours per day Of leisure. The vertical axis
measures TPVq; the distance OPVO is the present value

of expected nonwage earnings, while OPVq—OPVO is the
present value of adjusted expected earnings in occupation

q. Given the assumptions stated above, points E and H

TPV

PV

PV

 

 

 

>L/t

 

Figure A.-—Work-1eisure choice incorporating the
possibility of unemployment in an occupation.

37

are the only possible solutions. Since point H lies on

a higher indifference curve than does point B, market
labor in occupation q is preferred to specialization in
leisure. The higher is PVq, in general, the more likely
an individual is to enter the qth occupation rather than
to devote full-time to leisure. In this way, the level
of PVq enters an individual's supply Of labor function to
occupation q by determining the choice between this occu-
pation and others, and, if occupation q is selected, it
also determines the choice between the occupation and
full-time leisure.

Now suppose that the ith individual Obtains wage
and unemployment information for mi alternative occu-
pations (mism), including the qth occupation. Then the
following mi-dimensional vector is included as an argu-

ment in his supply function to the qth occupation:

(2.20) (PV .,PVm ).

,..
l 1

To simplify further, the following assumptions are made:
(1) the direct costs of investment are a minor consider-
ation in inter-occupational mobility; (2) the discount
rate applied to the time streams Of adjusted expected
earnings is the same for all occupations; and (3) an
unemployed worker assigns the same conditional proba-
bility distribution to all occupations, so that if

ua=u;, the worker views the probability Of being

38

employed in occupation q at time t to be the same as in
occupation r. Under this set Of assumptions, (2.20) may
be rewritten as

(2.21) (x§,...,x;i,u§,...,u;i).

It is mathematically equivalent to express this vector

in the following manner:

x* Xx * u*
(2.22) (fin-~56} ,xgm WES ,ua).
1 mi 1 mi

Up till now, no attention has been given to how
the level Of nonwage earnings is determined. Clearly, a
number of variables are involved including the level of
nonhuman wealth an individual possesses. In what follows,
we continue to ignore the effect of fluctuations in non-
wage income except for the important special case of
"secondary workers," i.e., males younger than 25 years
and Older than 5A years of age and all females. Exactly
the same principles of occupational choice outlined above
apply in this case, except that one additional feature--
the level Of nonwage earnings—-is given explicit consider-
ation.

Most secondary workers are assured Of a positive
level of nonmarket income simply by virtue Of being a

family member and supplying their services within the

39

family.9 This is true except during periods in which
the "primary" wage earner is unemployed. Therefore,

the present value of expected nonwage earnings of a
secondary worker over his short-run horizon depends on
the expected employment position of the primary wage
earner during this interval. It is assumed that the
expected employment position is an inverse function of
the current unemployment rate of married males, up. In
terms of Figure A, an increase in up is shown by a de-
crease in the distance OPVO, and, hence, a downward
movement Of point E on the vertical line drawn perpendi-
cular to the leisure axis at OLm. The higher is up, the
more likely it is that there will exist a wage Offer
which has a present value that exceeds the secondary
worker's reservation price for market labor.10

The ith individual's supply function to the qth

occupation may now be written as

 

9The inclusion Of family income in the labor supply
functions Of married women, the major component of total
secondary workers, is theoretically and empirically
treated in Mincer, "Labor Force Participation of Married
Women: A Study Of Labor Supply," pp. 63—97.

lOThis type of supply behavior is referred to in
the literature as the "additional worker" hypothesis.
According to this hypothesis, as the level Of economic
activity falls, labor force participation increases as
secondary workers enter the market in an attempt to
Offset the loss Of income by primary wage earners.

AO

X* X* u* u*
= *
(2.23) lqi fqi(xls'°°s§%iaxqsfi%a°° Wagg’: qu)

where nqi is a random disturbance term reflecting the
short—run impact Of random nonmarket variables on the
individual's labor market behavior.

Equation (2.23) is not an individual supply
function in the usual sense Of a worker supplying his
services in a particular occupation if the expected
wage rate exceeds his reservation price for entering
the occupation. Instead, joint consideration is given
the expected unemployment rate in the occupation.

Viewed in this manner, the equation is correctly labeled
a "probabilistic" supply function since it is the ex-
pected wage rate adjusted by the probability of employ—
ment through time in each occupation that is the crucial
variable to the individual.

A worker either supplies his services to the qth
occupation or he does not. Hence, equation (2.23) may
=1 if the worker

qi

enters occupation q, and fiqi=0 if he does not. Aggre—

gating across individuals, the probabilistic supply

be regarded as a step function where A

function to the qth occupation takes the following form:

~ x* x* u* u*
S
(2.2“) Qq = Hq(xl,...,-X%,Xa,ul’oo.’-‘lfi’ué’up’nq) (q=l,ooo,m),
' m m

Al

where I: is the number of workers who are willing to
supply their services in the qth occupation, and nq is
the sum Of the individual disturbances.ll If we assume
that equation (2.2A) is a continuously differentiable

function, the partial derivatives are assumed to have

the following signs:

8H OH

> O (isq); 53%> 0; u
q

3 a?

i

(2.25) < 0;

Q)
0)
9:4...“ ==

8H 3H

. __3
THU? < 0’ Eu > 0'
q p

The vector Of expected wage rates and the variable
up are representative of arguments similar to those fre-
quently found in ordinary supply functions. The test of
the probabilistic supply function specified here is
whether or not the vector of expected unemployment rate
variables is significant in the empirical analysis of

the model.

 

llThe aggregation process used to Obtain (2.2A)

involves the assumption that all individuals' short-run
time horizons are approximately the same length. In
addition, the aggregation assumes that each individual
calculates the present value of adjusted expected earn-
ings using the same discount rate. This would be the
case if all individuals could borrow and lend in the
capital market at the same rate of interest.

A2

IV. The Complete Model

 

In this section, the model is formulated in terms

of distinct time periods so that it is readily amenable

to empirical testing using discrete data. The variables

in the model are now defined as follows:

~d
iqt

number of members of occupation q which
firms desire to employ at the beginning of

period t;

number Of positions filled by individual

members of occupation q in period t;

number Of workers who desire to provide
their services in occupation q at the be-

ginning Of period t;

number Of members Of the qth occupation

employed in period t;

number of unemployed members of occupation
q in period t;
wage which firms expect to pay members of

occupation q at the beginning of period t;

wage expected in occupation q by labor

suppliers at the beginning of period t;

market wage in the qth occupation in

period t;

expected unemployment rate in occupation q

at the beginning Of period t;

A3

C
I

pt - unemployment rate of married males in period

t; and

§jt desired level of output Of industry j at

the beginning Of period t.

The model develOped thus far for the qth occu-
pational group consists Of the following system of
equations for period t:

~d

= x * ~ ~
(2.26) gqt Gq(wlt"°"wmt’ylt"’°’yMt’€qt)

I

p

X*t X*t "*t u*t
S = * x
(2.27) qt Hq(§%"°"§%€’xqt’fi%€""’ng’uqt’upt’nqt)

(2.28) Uq

III
p
I
A
Q
N
H
U
U
3
v
V

_ ~s .
where uqt - th/th' Equation (2.26) is the market demand

function, equation (2.27) is the market supply function,

and (2.28) is a definitional equation. The relationships

between 2d and Ad and between is and As are the
qt qt qt qt
following:
, ~s ~d .
(i) If th > gqt (i.e., th>0), then
”d _ d ~s s _
qt - £qt and gqt - zqt th.
~s ~d
(ii) If zqt < th (i.e., th<0), then
is = 1 and A - 1d — U

AA

It is clear that zit a sat.

In Part A of this section, a set of equations
determining the desired vector Of industry output is
specified. Then in Parts B and C, expectations mechan-
isms-are formulated for the vectors Of expected wage
and unemployment rates. A set Of equations determining
the current wage vector is described in Part D. In the
final part of the section, Part E, the complete model
is drawn together.

A. Determination Of the
Desired Vector of Industry

Output

The firm simultaneously determines its desired rate
of output and its desired level Of employment; therefore,
a set Of equations determining the desired output vector
must be developed. For our purposes, a very simple out-
put determination model is specified. However, it is
recognized that a more detailed treatment of this problem
might be desirable.

Because the firm must Operate under conditions Of
uncertainty, we assume that it utilizes a bit of infor-
mation it does possess, namely, last period's sales, to
determine its desired output level. At the beginning of

period t, this assumption may be written as

(2.29) yth = fij(sijt-l) (i=l,...,nj;j=l,...,M),

A5

where Sijt—l is the sales volume Of the ith firm in the

jth industry in period t-l. Assuming a fixed composition
Of the industry, the desired level Of output for industry

j at the beginning of period t is

(2.30) th = fj(sjt_1).

where s. is the sales Of industry j in period t-l.

jt—l

B. Determination of Firm
and Worker Expectations
Of Wage Rates

 

Firm Expectations.—-Given a change in the level or
composition of product demand, there are two cases to be
considered from the point of view of firms in the jth
industry. First, suppose that the demand for the "own"
product increases. Each firm in the industry now finds
it desirable to increase output, and, consequently, ex—
pand its labor force in order to maximize profits. One
alternative facing firms which find it necessary to attract
additional workers is to increase their wage offers.12
Hence, a change in the wages offered in industry j may
be assumed to be a function of the change in the demand
for the product produced by the industry.

Now suppose that the product demand facing the jth

industry is constant or declining, but other industries

 

12Examples of nonwage alternatives are increasing
expenditures on search, revising productivity standards
downward, upgrading existing employees, and expanding
on-the-job training programs.

A6

are enjoying an increase in demand. It is likely that
some Of these industries employ members Of the same
occupations as are employed in industry j, or that some
other "spill—over" relationship exists between the wages
paid in these industries and in industry j. If so, the
firms in industry j may find that they have to raise the
wages paid to workers they desire to keep on their pay-
rolls in order to match wage offers made by industries
in more favorable demand situations. Consequently, the
wages Offered in industry j are not only a function Of
the "own" change in product demand, but they are also a
function of the changes in product demand facing other
industries.

An increase in demand for the product produced by
an industry is observable in a decrease in inventories
and/or an increase in product price. The volume of
sales Of an industry is measured in nominal terms. Thus,
a positive change in sales may measure either the drawing
down Of inventories, i.e., an increase in the physical
quantity of output sold, or an increase in the price at
which each unit Of the product is sold. Both situations
indicate to the profit-maizimzing firm that a larger
level of output, and, hence, a larger labor force, would
be desirable. Using sales as a proxy for industry
demand, we specify that the wage firms in industry j
expect to pay the members of occupation q at the beginning

of period t is

A7

* =
(2.31) wqjt wqjt_l + qu(Aslt_l,...,AsMJt_l),
where wqjt—l = wage paid by firms in the jth industry
to members Of occupation q in period t-l;
M3 = number of industries whose sales affect
the wage paid by firms in the jth industry
to members of the qth occupation, léngj;
th_l = sales Of industry j in period t-l; and
ASjt-i = Sjt-l ‘ Sjt-2'

Assuming a given industry composition Of the economy,

aggregation across all industries yields:

(2.32) wét = wqt-l + gq(Aslt—l’°"’ASMt-l) (q=1,...,m).

In this equation, the variable wét

an average of the distribution Of industry expected wage

may be interpreted as

rates and wqt-l as an average of industry wages paid in

the last period.

Worker Expectations.--Turning to the supply side Of

 

the model, it is simply assumed that workers set their
reservation prices equal to the wage they last earned in
the occupation of their choice. They have every reason
to believe that at this wage they were receiving the
value of their marginal product. Hence, they believe
that other employers will be willing to Offer them the

same wage. This expectation is justified except in a

A8

situation Of a general decrease in demand. In this

case, the worker perceives the necessity of reducing
his reservation price only after he has invested the
time to obtain information on his alternative employ-

l3

ment Opportunities. As a short-run first approxi-

mation, it is assumed that workers expect the wage

structure existing last period to carry over into the
* = =

current period, that is, xqt wqt—l (q l,...,m).

C. Determination of the Vector

Of Expected Unemplpyment
Rates

 

 

It is hypothesized that at the beginning Of period
t, an individual adjusts his expectation of the unemploy-
ment rate in the qth occupation in proportion to the
discrepancy in the previous period between the market

determined unemployment rate (u ) and the rate he

qt-l
expected to exist at the beginning of the period (uét-l)

In addition, we assume that the ratio Of the expected
unemployment rate in occupation q to each Of the expected

unemployment rates in the other m-l occupations is

 

13In his study of unemployed Minnesota workers,
Hirschel Kasper found that for each month Of unemployment,
workers were willing to reduce their reservation prices
by only 0.3 per cent. In fact, Kasper suggests that
workers who have been unemployed less than six months
Often have reservation prices which exceed their former
wages. "The Asking Price of Labor and the Duration Of
Unemployment," Review Of Economics and Statistics,
XLVIV (May, 1967), pp. 165—172. For a summary of this
and other studies Of the time path Of reservation prices

see Holt, Op. cit., pp. 59-65.

 

A9

determined in the same manner. This hypothesis may be

written as

(2.33) uat - uat-l = (1 _ dq)(uqt-l _ uat_1)’
and
11* 11* u 11*
(2.3A) 3;"; - 1jgizzl ... (1_ 5) ugt-l _ uqt-l
it it-l q it-l It-1

(i=l,...,m;i#q),

where 0<6q<l. The coefficient (1 - Sq) determines the
speed at which the expected unemployment rate (ratio Of
unemployment rates) is adjusted to the difference be—
tween the actual and the expected rate (ratios) in the
previous period. Equation (2.3A) may be equivalently

written as

u*t [u t 1I u t 2‘
(2.35) —§— = (1 — 6 ) —3—:—- + a —9—:—
[uit] q ‘uit-IJ q uit—2J
{u U
+ 6 2 ~9£Z§. + + 6 n —9A3121l +
q u1t—3 q ui,t—n—1

The level Of unemployment of married males (Up) is

an endogenous variable determined by the relation
m
Upt = q:lcthqt, where th is the proportion Of married

males in occupation q in period t. Since we are not

50

particularly interested in the time path of U some

pt’
occupations are conveniently excluded from the empirical

analysis in Chapter III so that thEUt’ where U is

t
total unemployment in period t. Therefore, the unemploy-
ment rate of married males (up) is assumed to be exo-
genously determined in Chapter III. TO simplify the
presentation of the model, up will also be assumed to

be exogenous in this chapter.

D. Determination Of the Vector
Of Current Wage Rates

 

 

To complete the model, all that remains to be done
is to specify a set Of relationships determining the vector
of wage rates in period t. On the basis of the previous
discussion, it is hypothesized that the rate Of adjust-
ment in the quantities of labor demanded in occupational
labor markets exceeds the rate of adjustment in the cor—
responding wage rates. Hence, we assume that the change in
a market wage rate is inversely proportional to the change in
the level of unemployment in the occupation. That is, we

specify the following relationship for occupation q in

period t:
(2.36) Awqt = kq(Ath) (q=l,...,m;kq<0),
where Awqt = wqt - th_1,

Ath = th - th_l, and

kq is defined to have the appropriate dimension.

51

E. VCOnsolidating the Model

 

Consider first the demand side Of the model which

consists of the following 2m+M equations:

~d _ x * ~ ~
(2.37) zqt — Gq(wlt’°'"Wmt’ylt""’yMt’€qt)
(2.38) yjt = fj(sjt_l) (j=l,...,M)

(2.39) w* = w

qt "ASMt-l) (q=1,...,m).

qt-l + gq(ASlt—l"‘

Substituting equations (2.38) and (2.39) into (2.37)

yields:

(2.A0) A mt-l’slt-l’°"’SMt—l’

A .,A

s1t-1’” SMt-l’eqt)°

After assuming a linear approximation of this set Of

equations, we have

~d -
(2.A1) Aqt ‘ ago + aqlwlt-l + "° + aqmwmt-l + bqlSlt-l
+ ... + quSMt-l + fqlASlt-l +
+ quASMt-l + eq.

The supply side Of the model is comprised by the

following system of 3m equations:

52

A ”s x*t x*t u*t u*t
_—_ it It
(2. 2) Q’qt Hq(§%;,...’§r%;_’xqt,$’...,{l-%-t_’uqt,upt,nqt)
it =
(2.A3) xqt wqt-l
* _ ii- : _ _ it
(2.AA) uqt uqt-l (l Sq)(uqt-l uqt—l)

(A - (£3 = . — (at) - [L]
it-l

(i=l,...,m;i#q).

Linearizing equation (2.A2) and then substituting equation

(2.A3), we Obtain:

”8 " t-l W t 1
(2.A6) A t = c 0 + c 1 W9——— + ... + c m WET:—

 

+ d + e u + n .

*
qm+lu qt q pt qt

Now substituting equations (2.AA) and (2.A5) into (2.A6)
and applying the Koyck transformation, the following

equation is obtained:

(2.A7)

The
equations

~d ~s
tqt, tqt,

(2.A8)

... W
s = _ s t-l
A t (l (Sq)cqO + aqfiqt-l + cql fi5———
lt-l
w t 2 W t 1
_5cl_9_‘_+ C _9._:__
q q w1t—2 qm Wmt-l
wgt-2
- échm w + cqm+lwqt-l achm+lwqt-2
mt-2
u t 1
+ (1 - 5 )d —9—:—- +
q ql u1t—1
+ (1 — 5 )d Eflill. + (1 5 )d u
q qm u q qm+l qt-l
mt-l
+ e u 6 u + - 6 .
q pt q pt-l nqt qnqt-l

complete model now consists Of the following 3m
and m definitional equations in the variables

U and w

qt’ qt:

Id = a + a w + + a w + b 5

qt q0 ql lt—l qm mt-l ql lt-l
+ + quSMt—l + fqlASlt—l +
+ quASMt-l + eq

' w
s = _ s gt-l
(2.A9) Aqt (l (Sq)cqO + 6,2qt-l + cql w
lt-l
W W
_Scl—QELZa-I- +0 E.
q q w1t—2 qm wmt-l
wgt-2
- q qm wmt—2 + Cqm+1wqt-l - dchm+lwqt-2
u t—l
+(l'5m1E—q— +.
q q 1t-l
ugt 1
+1-5d ' +1 5d
( q> qm umt-l ( q) qm+luqt-l
+ e u 0 e u + n 0 n .
q pt q q t 1 qt q qt-l
(2.50) wqt — wqt-l = kq(th - th_l)
_ d
(2.51) th = tat - Aqt (q=1,...,m).

Equations (2.A8) and (2.A9) are already in reduced form.
Eliminating the identities, the system Of equations may

be written in matrix form as follows:

(2.52) fl = K (q=1,...,m),

where B
-_q

and

AH:

|><

I<I

 

 

 

(- "‘ I" "‘
”d
1 0 0 tqt
S
0 1 0 , 1 = tqt ,
k -k l w
q q qt
._ —l L_. _I
r— "—1
A B FIO 0 0 0 0 0 lo 0

0 0 0 5 c —5 c 1-5 D —5 0

l q q < q) eq qeql O ’
0 0 0|0 0 0 0 0 0 I1 -kq
.. _1.

w s AS '15 wR wR UR

 

 

I
wqt-l th—f] ’

 

 

E '7
qt
nqt dqnqt-l ’
0
.. J
(aqO’ aql’ ’aqm)
(bql, .,qu)
(fql,...,qu)

(CqO’cql’°°"Cqm’cqm+l)

(d )

ql,...,dqm,dqm+l

(l’wlt—l"°"wmt-l)

(Slt-l’°'°’smt-l)

__t-l t-l t-1l qt-l t—l t-2 t-l upt upt-1I

ASt-l - (Aslt-l""’Ath-l)
W W
WIS—1 (1,w—1——t'1,...,w—9_—t'l,wqt_l)
lt-l mt—l
W W
w5_2 = (1,fi9323,...,W9323,w t_2)
lt-2 mt-2 q
R ugt-l ugt-l
Ut-l = (u "°°’u ’uqt-l)
lt-l mt-l

The inverse of the coefficient matrix of the current

endogenous variables is

 

,
1 0
(2.53) pfl = 0 1
-k k

__ q

 

so that the parameter kq does not enter either Of the two

stochastic equations, (2.A8) or (2.A9).

CHAPTER III

THE DATA AND THE ESTIMATION PROCEDURE

The purpose Of this chapter is to construct an
empirical test of the model developed in Chapter II.
Our intent is to determine the extent to which the vari-
ables proposed in the theoretical analysis are able to
account for variations through time in the structure of
occupational unemployment. In Section I, we discuss the
data used in representing the variables Of the model.
Then in Section II, the model is condensed to make it
manageable for regression analysis, and the estimation

techniques used in testing are discussed.

I. The Data

 

The variables included in the model constructed in

the previous chapter are defined as follows:

2 = number Of members of occupation q desired by

employers at the beginning of period t;

iqt = number Of members of occupation q who desire
to work at the beginning Of period t;
th = number of unemployed members of occupation

q in period t;

57

58

wqt-l = wage rate in occupation q in period t—l;
uqt—l = unemployment rate in occupation q in period
t-l;
sjt—l = sales Of industry j in period t-l; and
upt = unemployment rate of married males in period
t.

United States time-series data for six major occupational
groups and six industries are collected to measure these
variables. The six occupational groups are clerical
workers, sales workers, service workers, craftsmen and
foremen, operatives, and laborers; and the six industries
are contract construction, durable good manufacturing,
nondurable good manufacturing, wholesale trade, retail
trade, and services. The time period examined is from
January, 1958 to December, l966——a total of 108 monthly
Observations on each variable.

In 1959 the six industries listed above employed
59.A per cent of employed clerical workers, 85.A per cent
Of employed sales workers, 8A.3 per cent of employed ser—
vice workers, 73.8 per cent Of employed craftsmen and
foremen, 8A.2 per cent of employed Operatives, and 76.6

per cent of employed laborers.l

 

lThese percentages were calculated from U. S.
Department of Commerce, Bureau Of the Census, U. S.
Census of Population: 1960, Subject Reports, Occupation
by Industry, Table l.

 

 

 

59

The Bureau of Labor Statistics (BLS) publishes
monthly seasonally adjusted level of employment and
unemployment rate data for the eleven major occupational
groups going back to January, 1958.2 It should be men-
tioned at the onset that there are at least two diffi—
culties inherent in using these occupational data.
First, the major occupational groups are composed of a
large number of specific occupations so that in using
these data, we are not examining supply and demand
decisions in well defined labor markets. Second, in the
collection of these data, the BLS places an unemployed
worker in a particular occupation according to his last
job. However, there are likely to be numerous cases in
which in his last job the worker did not work as a mem-
ber of the occupation for which he is trained and of
which he considers himself a member. Consequently, these
unemployment data may not accurately reflect the true
distribution Of the unemployed by their chosen occu-
pations.

The BLS publication Employment and Earnings pro-
vides monthly seasonally adjusted data measuring the
unemployment rate Of married males.

In every time period, the unemployment rate in

each occupation considered is Observed to be positive.

 

2U. S. Department of Labor, Bureau Of Labor

Statistics, Employment and Earnings and Monthly Report
on theALabor Force, Vol. 1A (July, 1967).

 

 

60

Therefore, we assume that the desired quantity of labor

demanded at the beginning of period t is always satis-

~d _
fied during the period so the Aqt — Aqt, where lqt is

the number of employed workers in occupation q in period

t. It follows from our definition Of unemployment that

~

5 = A + U . Using BLS data on the level of un-
qt qt qt
employment and the unemployment rate in the qth occu-
pation in period t, the desired labor supply in the

occupation at the beginning Of period t is calculated by

~ 8
t
(301) lat = fl (q=1,...,6)o
qt

Data published by the Office of Business Economics
(OBE) are collected to measure the sales of the six in—

3

dustries specified above. Monthly seasonally adjusted
estimates Of sales are used for the durable and nondurable
manufacturing sectors and for wholesale and retail stores.
The final sales of services in the OBE estimate of GNP by
major type are employed to measure the sales Of the ser—
vices sector. Since these data for the services sector
are published only quarterly, it is assumed that the
changes in the series between quarters are linear so

that monthly estimates can be Obtained.“ The F. W.

 

3The sales series are taken from U. S. Department
of Commerce, Office of Business Economics, Business
Statistics, 1967.

 

“The monthly estimates obtained on the basis of
this assumption involve measurement errors so that

’

61

Dodge Company seasonally adjusted index Of the value Of
construction contracts in A8 states is used as a proxy
for the sales Of the contract construction sector.
Published time-series data measuring wage rates in
occupational groups are not available. Consequently,
the wage rates specified in the model must be estimated
from the earnings data that are available, namely,
monthly estimates Of gross average weekly earnings of

5

production and related workers by industry and median

annual earnings Of the experienced labor force who
worked 50 to 52 weeks in 1959 by detailed occupation.6
As noted previously, the 1960 Census Of Population pro-
vides industry employment data cross-classified by
occupational groups.7

A number of estimators of the wage rate in an

occupation, say the qth occupation, may be constructed

 

regression analysis applied to these data yields incon—
sistent parameter estimates. It is assumed that the

- inconsistency introduced by interpolating is small
enough to be ignored.

5U. S. Department Of Labor, Bureau Of Labor
Statistics, Employment and Earnings Statistics for the
United States--l909-l967, Bulletin NO. 13I255.

6

U. S. Department Of Commerce, Bureau Of the
Census, U. S. Census of Population: 1960, Subject
Reports, Occupational Characteristics, Table 30.

7U. S. Department Of Commerce, Bureau of the
Census, Occupation by Industry, Tables 1 and 2.

 

 

 

 

 

62

from these data. The estimator presented here seemed to
require the least restrictive assumptions of those con-
sidered.

The following assumptions are employed in the con-
struction of the estimator: (l) the wage paid to members
Of the qth occupation by firms in the jth industry changes
in proportion to the average wage paid by the industry,
and (2) the number Of employed workers of the qth type
per dollar of output (AqJ/yj) is constant for the jth
industry. The assumption that lqj/yj is constant over
the 1958-66 period implies that the average product Of
the qth labor input is fixed for each industry. For all
six variable inputs, this in turn implies that if the
output of a particular industry doubles, its rate Of use
of all inputs must also double. But this can be true
only if each firm produces according to a linearly homo-
geneous production function. Assuming linear homogeneity
does not seem too unreasonable.

The output measures are constructed as follows for
each industry. The measure employed for durable and non-
durable manufacturing and wholesale and retail trade is
current sales plus the change in inventories from the end
of the previous period, this sum deflated by an appropri-

ate price index.8 The sale Of services deflated by the

 

The source Of the inventory series and the price
indices is U. S. Department Of Commerce, Office Of
Business Economics, Op. cit.

63

services component of the Consumer Price Index (CPI)
is the output measure used for the services sector.
Finally, the value of new construction put—in—place
(seasonally adjusted) deflated by the Commerce Depart-
ment's Composite Construction Cost Index is used to
measure the output Of the construction sector.

Based on the two assumptions listed above, the

estimate Of the wage in occupation q in period t is

 

 

 

 

 

? W (A
(3.2) Oqt =3“l €131 JB (q=1,...,6),
z 43.3.1.3.
J=llyJBI
where
B = base year 1959;
quB = number of members of occupation q employed by
industry j in the base year;
ij = output of the jth industry in the base year
measured in dollar terms;
wjt = average weekly wage paid by the jth industry
in period t;
ij = average weekly wage paid by the jth industry
in the base year; and
wqu = median annual wage paid to the male members

Of the qth occupation by the jth industry

in the base year.

6A

The 1960 Census of Population provides annual

 

earnings data by detailed occupations; but a significant
fraction of the workers in each major occupation group,
with the exception of service workers, is defined to be
"not elsewhere classified." Each Of these n.e.c. cate-
gories is broken down to a greater or lesser degree by
industry. Thus, for five of the six occupation groups,

we can utilize the variable W But for service

qJB'
workers, this variable must be replaced by qu' Here,
the year 1959 may be interpreted as an equilibrium period
so that the wage paid to service workers is the same
across all industries which employ them.

Within the services sector, time-series earnings
data are published for hotels, tourist courts, and
motels; laundries and dry cleaning plants; and motion
picture filming and distributing. Unfortunately, these
three industries employ only a small percentage of the
total number of workers employed in the services sector.

As a proxy for the ratio th/W , we use employment in

jB
the services sector in period t relative to the total
employment in the sector in the base period. The use Of
this proxy assumes that the elasticity of the aggregate
supply function of all types of workers to the services
sector is unitary over the relevant range.

The wage measure specified in (3.2) is in nominal

terms. Since individual workers and firms make decisions

65

on the basis of real variables, our wage measure should
be adjusted for changes in prices during the 1958-66
period. The CPI is intended to measure changes in the
prices of goods and services bought by urban wage earn-
ers and clerical workers. Hence, it is a particularly
appropriate measure of the price changes facing the
members Of the six occupations we are considering. De-
flating (3.2) by the CPI, our measure of the real wage
in occupation q as seen by labor suppliers in period t

is

(3.3) fizt = r6%%; (q=ls°°°:6)3

where (CPI) = 100.

1959
For the wage variables appearing in the demand
equations, the price deflators used are indices of pro—
duct prices for the six industries examined. The specific
indices are the Construction Cost Index (construction),
the Wholesale Price Index-—Manufacturers (durable and
nondurable good manufacturing), the Wholesale Price
Index--All Commodities (wholesale trade), and the CPI-—
Commodities (retail trade). The proxy used for the ratio
wjt/ij in the services sector makes it unnecessary to
use a price deflator since we assume that employment in
an industry adjusts to changes in real wages. The mea-

sure Of the real wage in occupation q viewed by employers

in period t is constructed as follows:

66

 

 

 

6 ) [ wJt ]
Z (A . /y. W
3:1 qu jB PIjt/PIjB qu
W.
J.ElULqJB/ij)

where PI is the relevant price deflator for industry

jt

j in period t.

II. The Estimation Procedure

In this section, a priori information is applied to
the model for the purpose Of reducing the number Of para—
meters to be estimated to a more manageable number. In
the process, we will hopefully remove some of the multi-
collinearity which is likely to be encountered in esti-
mation. After the model has been condensed, the esti-
mation techniques applied to the model are described.

From Chapter II, the system of equations to be

estimated is writen as follows for m=M=6:9

~d — A A
(3.5) tqt - aqO + aqlwlt_1 + --- + aq6w6t-1 + bqlslt-l

+ + 00.

+ bq6s6t-l + fqlASlt-l

+ fQ6AS6t-l 'l' eq.

 

9The d and s superscripts on the two vectors of
real wage variables are omitted for convenience. How—
ever, it should be kept in mind that different real wage
vectors appear in the supply and the demand equations.

 

 

~ ~ G
.6 15 = 1 - 5 c + 5 is + —932l
(3 ) qt ( q) q0 q qt-l qu alt 1
“Q ‘ G
- 0 c 1 79213 + + c 6 A t-l
q q wlt 2 q W6
I" 'J "t-1
rfitz‘ A A
- 6 c —9—:—- c w 6 c w
q q6 Q q7 qt-l q q7 qt—2
k 6t-2J
L1
+(1—5)d _th;_1_ +...
q ql u1t-1
L1
t-l
+ 1 — 5 d _A___. + 1 5 d
< q) q6[u6t-l] < q) q7uqt_l
+ e u — 6 e u + n - 6 n
q pt q q pt-l qt q qt-l

We expect that autocorrelation exists in both

disturbance terms a and nqt because it is likely that

qt
the effect Of random shocks on the system spills over

from one monthly time period into the next. In particular,

we assume that 6 satisfies the first-order autoregres-

qt
sive process

+ 3

(3-7> eqt = pqeqt—l qt’

where the aqt's are normally and independently distri-

buted, each with zero mean and common variance 03d,

68

2

that is, NID(0,0qd). Similarly, we assume that nqt

satisfies the first-order autoregressive process

(308) nqt = gqnqt_l + "qt,
where the n 's are NID(0,O2 )
qt qS

One method Of consolidating the wage vector in
equation (3.5) is to retain the own wage and construct
a weighted average Of the other five wage rates. The
Optimal weighting scheme would employ as weights the
marginal rates of technical substitution between the
members of one occupation and the members of each Of
the other occupations. However, in the absence Of
information on the marginal rates Of technical substi—
tution between the broad occupational groups employed
here, it is assumed that I: is a function only Of the

own wage rate in the wage vector, i.e., a =0 (i#q) in

qi
equation (3.5)-

Suppose that the components Of the sales vector
are numbered in the following order: construction, 1;
durable good manufacturing, 2; nondurable good manu-
facturing, 3; wholesale trade, A; retail trade, 5; and
services, 6. The number of arguments in the labor
demand function can also be reduced by constructing‘
summary measures of the sales and change in sales vectors.

Note, however, that the sales variable for the construction

sector is in different units than the sales variables for

69

the other industries; hence, it cannot be included in

a summary measure. Assume that

 

 

 

R A
= _AEE = .932
(3'9) bq2 B<q ygB] fq2 Fq YQB
b = B E f = F 336—2
q6 q y6s q6 q. y6s ’
where (fiqu/ij) (j=2,...,6) is the number of workers of

the qth type employed in the jth industry in the base
period per dollar of output Of the jth industry in the
base period. This is much the same weighting scheme
employed in the construction of the wage variables in
(3.2), and the same assumptions apply. Now equation (3.5)

may be rewritten as

~d _ . A — T -'
(3.10) th - aqO + aqwqt-l + quqt—l + Fq(°qt—l-Sqt-2)
+ bqlslt-l + fq1(51t—1'51t—2) + eqt’
6
where Sqt—l = j:2(£qu/ij)SJt-l' The variable Sqt—l

should be interpreted as an index Of the product demand
facing the industries which employ members of the qth
occupation. The sales variables for the construction
sector will be included only in the equations for crafts-
men and foremen, Operatives, and laborers since the in-
dustry is not a major employer Of white—collar and service

workers.

70

On combining equation (3.10) with the first—order
autoregressive process specified in (3.7), we have,

after rearranging,

A

(3.11) A —p A qt-l-pqwqt—2)

qt q qt—l = aq0(l-pq) + aq(w

+ Bq(sqt-l'pqsqt—2)

+ th(sqt-l-Sqtn2)"pq(sqt-2—Sqt-3)J

bq1(51t-1'pqs1t—2)

+ quE(Slt—l-Slt—2)-pq(slt-2—slt-3)J

+ eq-Qqélqt—l.

Turning to the supply side Of the model, we can also
reduce the number of variables appearing as arguments in
equation (3.6). One way of doing this is to rank the
occupations by the approximate skill level required to
enter the major components Of each occupational group.
The three blue-collar occupations may be roughly ranked
in the following order Of descending skill requirements:
(1) craftsmen and foremen, (2) Operatives, and (3)
laborers. Within the blue—collar group, we assume that
a worker can move down in the skill hierarchy but not up.
In addition, it is assumed that workers in the white-

collar occupations and service workers can become

71

laborers, and that both white-collar and blue—collar
workers can become service workers. The alternatives
relevant to a member of each occupation are shown in
Table l, where the occupational groups are numbered as
follows: clerical workers, 1; sales workers, 2; ser-

vice workers, 3; craftsmen and foremen, A; Operatives,

5; and laborers, 6.

TABLE l.--Alternative occupations for members of each
occupational group.

 

Current Occupational Group

 

 

U)
c c O

H (DC) > U)

are a) a)m E E H h

03-! S—I 0‘4 U30) 4-) 0.)

H0) (00) HQ) 4-354 CU $4

ex ex >x mo L4 O

01p PIP p a mun a) Q

PIC m o O o A O. w

0:?- C03 U13 0023 O Q

Alternative 2 l 6 5 6 3
Occupations 3 3 6 3

6 6 3

 

With respect to the supply equation for craftsmen
and foremen, one further assumption will be made. The
variable upt is included in the model because the supply
decisions Of secondary workers hinge on the employment
state of the primary wage earner in the family. In view

of the component occupations of craftsmen and foremen

and the fact that most Of these workers are males, it

72

seems likely that the vast majority Of the members of
this occupation are primary wage earners. Hence, the
variable upt will be excluded from this equation.
Consider now any one of the six supply equations,
for example, the equation for laborers which is written

as follows:

 

 

~ ~ W
s _ s 6t-l
(3.12) A6t - (1-06)c6O + 56£6t—l + 063 A
w3t—1
O
6t-2 A A
‘ 56063 g + C67W6t_1 ‘ 56067W6t—2
3t-2

 

+ d (l 5 ) u6t"l + d [(1 5 ) J
63 ‘ 6 63t_l 67 ’ 6 u6t—1

+ e6upt ‘ 66e6upt—1 + n6t ' 56A6t—1'

~s _
Note that u6t—l is a component Of £6t-l by the construc-

tion Of the latter variable (see (3.1)). Consequently,
in what follows, the own lagged unemployment rate is
omitted from each supply equation. The effect of this
omission on the estimated coefficients of the unemploy-
ment rate Of married males is discussed in Chapter IV.
As is usual in distributed lag models, equation
(3.12) is overidentified with respect to certain para-
meters. For example, an estimate of 56 may be Obtained

from an estimate of the coefficient of QEt-ls however,

73

yet another estimate Of 56 may be Obtained from estimates
of the coefficients Of w6t-l/w3t-l and w6t-2/w3t-2'

These two estimates will not, in general, be the same.

In particular, the coefficients of w6t-2/w3t—2’ w6t-2’
are nonlinear in the parameters

/u and u

u6t-1 3t-l’ pt-1
of the model. To estimate the parameters of this
equation, nonlinear restrictions must be placed on each
of these four coefficients (d67=0 by assumption).
Following Zellner g£_al., a nonlinear estimation techni-
que that could be applied is the Gaushaus method.10
An alternative nonlinear technique, which we shall

employ, is described most easily by first rewriting (3.12)

 

 

 

 

as
~ ~ w
s s _ 6t-l
(3.13) £6t — 6626t“l - (1-66)C60 + C63 A
w3t-1
lw6t-2 A A
‘ 56 Q + 067(W6t-l-56w6t-2)
I 3.-.
(u
6t-1
+ d (1—5 )
63[ 6 u3t_1U
+

86(upt-66upt-1) + n6t

‘ 66"6t-1'

 

10A. Zellner, D. S. Huang, and L. C. Chau, "Further
Analysis Of the Short-Run Consumption Function with Emphasis
on the Role of Liquid Assets," Econometrica, Vol. 33
(July, 1965),-pp. 571-581.

 

7A

Equations (3.11) and (3.13) are now expressed in a form
such that unique parameter estimates Of both equations
may be Obtained by single—equation application of ordi-
nary least squares (OLS) for selected values of the
parameters pq and éq, where 0<pq,6q<l and q=6 in (3.13).
The criteria for selecting the estimates Of pq and Sq
and the corresponding sets of coefficient estimates is

to choose pq and Sq for which the sum of squares Of
residuals is a minimum in each equation. The estimates
obtained are maximum likelihood estimates and are thus
consistent and asymptotically efficient.

Estimation of equations in the form of (3.13) in-
volves the assumption that the expectations coefficient
5g equals the parameter Eq in the first-order autoregres-
sive process specified in (3.8). This assumption is

commonly employed, but it must be noted that we have no

knowledge from economic theory from which to infer that
11

qe
A random shock may affect the contemporaneous dis-

€q=5

turbances of the set of demand or supply equations, or it

might simultaneously affect both sets of disturbances.

 

11The sensitivity of the inferences made from a
distributed lag consumption function model to this and
various alternative specifications of the disturbance
term is examined by Arnold Zellner and Martin S. Geisel
in their yet unpublished paper "Analysis Of Distributed
Lag Models with Applications to Consumption Function
Estimation." (Mimeographed.)

75

To handle this situation, Zellner has proposed a pro-
cedure which yields coefficient estimators at least
asymptotically more efficient than single—equation

least squares estimators.l2’l3

In this procedure,
regression coefficients are estimated simultaneously
by applying Aitken's generalized least squares tO the
system of equations. To construct the Aitken esti-
mators, Zellner employs estimates Of the disturbance
terms' variances and covariances based on the residuals
derived from an equation—by-equation application of OLS.
However, Zellner's method for estimating seemingly
unrelated regressions is constructed on the assumption
that individual equation disturbances are not auto-
correlated. To take into account both autocorrelation
and contemporaneous correlation in a system of equations,

the following two-step estimation procedure is prOposed:lu

 

12Arnold Zellner, "An Efficient Method of Esti—
mating Seemingly Unrelated Regressions and Test for
Aggregation Bias," Journal Of the American Statistical
Association, Vol. 57 (June, 1962), pp. 3A3-368}

l3Zellner, "Estimators for Seemingly Unrelated
Regression Equations: Some Exact Finite Sample Re-
sults," Journal Of the American Statistical Associ-
ation, Vol. 58 (December, 1963), pp. 977—992.

1“Richard W. Parks presents a similar asymptoti-

cally efficient technique for estimating the coefficients
of a system of regression equations. The difference be-
tween his procedure and the one presented here is that

he estimates the parameter p in a first-order auto-
regressive process as follow%:

 

 

76

Step 1: Find the OLS estimates of the parameters
6“ and 0q which minimize the sum Of squares Of residuals
for each equation in the system. Then use the associ—
ated estimates Of the regression coefficients for each
equations to estimate the contemporaneous variance-
covariance matrix.

Step 2: Form the Aitken estimator using the esti-
mated variance-covariance matrix. This step is equivalent
to applying Zellner's technique to the regression equa-
tions after the estimates of 5q and pq have been obtained.

In the next chapter, the results Obtained by OLS

and the modified Aitken procedure are presented for the

twelve—equation system.

 

 

where u t is the OLS residual for the ith equation in
period A, and n is the sample size. Parks proves that
his estimator is consistent and asymptotically more
efficient than the Zellner estimator when autocorre—
lation is present. "Efficient Estimation Of a System
of Regression Equations When Disturbances are Both
Serially and Contemporaneously Correlated," Journal Of
the American Statistical Association, Vol. 62 (June,
1967), pp. 500—509. 7

Parks' estimate Of p is the "first round" esti-
mate in an iterative procedure discussed by J. Johnston,
Econometric Methods (New York: McGraw—Hill Book Company,
Inc., 1963), pp. l93-l9A. In general, the first round
estimate of Pi will not be equivalent tO the maximum
likelihood estimate for finite samples.

 

 

CHAPTER IV

THE EMPIRICAL EVIDENCE AND CONCLUSIONS

This chapter is devoted to a discussion of the
empirical results obtained for the model as specified in
the previous chapter. In Section I, the parameter esti-
mates for the sets of demand and supply equations are
reported. Section II contains an economic analysis of
the results. Finally, in Section III, we suggest some

conclusions that may be drawn from the study.

I. The Results of the Estimation

 

The system of equations estimated is the following:

(A.l) git-pqigt—l = aqO(l-oq) + aq(wqt_l—pqwqt_2)
+ Bq(§qt—l- ngt-2)
+ Fq[(gqt-l_§qt-2)—pq(gqt-2'gqt-3)J
+ bq1(slt-l—pqslt-2)
+ fqlt(slt-l—Slt-2)_pq(slt—2_Slt-3)J
+ eqt-pqeqt-l

77

~s ~s figt l figt 2
A.2 . A -5 A = c 1-5 + c ' —5 A '
( ) qt q qt-l q0( q) ql p q w
lt—l lt-2,
G t l a t-2
. + c 6 79—:— - 5 ,9.—
W6t—1 W6t—2
+ A — A
Cq7(wqt-l aqwqt-2)
u
+ dqlfil-Oq)[fifi]] + ...
lt-l,
+ d (1-6 ) 393:; + e (u -6 u )
q6 u6t-l q pt q pt—l
+ nqt-éqnqt—l (q=1,...,m),
where Agt = number of members of occupation q employed
in period t;
Agt = number of members Of occupation q in period t;
fiqt_l = estimate of the real wage in occupation q in
period t—l;
Eét_l = index of sales of the industries employing
members of occupation q in period t-l;
Slt—l = index Of sales of the construction industry
in period t-l;
uqt—l = unemployment rate in the qth industry in
period t-l; and
upt = unemployment rate of married males in

period t.

79

A minimum of two and a maximum of four of the cq and dq
coefficients in equation (4.2) are assumed a priori to

equal zero in each supply equation.

A. The Demand Results

 

The parameters of the set of demand equations were
first estimated by OLS. The coefficient estimates of the

equations for craftsmen and foremen, operatives, and

""1

laborers suggested that the inclusion of the sales and
change in sales variables for the construction industry

adds very little to the explanatory power of the demand

 

side of the model. The equations were again estimated
excluding the construction sales variables, and the co—
efficient estimates and the corresponding standard errors
of the six demand equations are reported in Table 2. The
subscript q (q=1,...,6) refers to the equation in which
the parameter occurs. The coefficients of multiple
determination (R2) are given in the last column of the
table.

OLS estimates of each equation are obtained for
p =O.l, p =O.2,...,p =O.9 (q=1,...,6). The maximum like-

q q q

lihood estimate of pq (Sq) is that which minimizes the

sum of squares of residuals for each equation. The set

of pq's and the corresponding coefficient estimates are

reported in the table.1 The fact that pq is 0.6 in two

 

1The asymptotic variance of pq is calculated by

FL “is.

5. 1.. a .P

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.Hm>ma pcmo pod m on» pm opmm 509% pcmpmoMHo meQmOHchmHm

Q

.Ho>ma pcoo Loo H map pm opmm Eogm osmpommflo mflpcmOHchwfimm

.mpmoplp ooafimplozp ohm

mpmmp Ham paw mpcmfloflgmmoo opp ZOHmD mommzpcmhma Cw pmmoam mpopho opmocmpmx

 

 

 

Ammo.ov Amwmv Aomsv Ammm.fiav Ammv
memo.o mm.o 5oz- mmm :ss.mfiu mama mumpopmq
Aaao.ov Amaa.mmv Ammm.mav “moo.mmv Ammmv
mmma.o mm.o m:o.oan mzmm.mw mm:.m mmms.m mm>flpmcmao
Aaao.ov Azmmv Ammav “mam.mv Ammav swampom a
mmma.o no.0 mmHH.H- mamm.a mm: momm.m cmempoato
Ammo.ov Amma.fiv Azmm.av Amma.mmo game mtmxpoz
msmo.o mm.o :Hm.H- mmoq.m om:a.mm mmm: moa>pmm
Ammo.ov Ammqv Aoozv Azam.fiav AHOHV mcmxpoz
momfi.o mm.o mmm scam mam. . mmfie mmflmm
Ammo.ov Aozm.mv Ammm.:v “cam.mmv Ammav mp@&toz
mmoa.o mw.o ooma.mu mmom.mm mmm.m mmmw HmOHcmHo
mm Ga ANIwaV Aslwaxv Annmaxv .pmcoo COHpmasooo
,. a m
*.Aa.zv

CH oofimHoon meowpwzom ocmEmo who CH mcfipmoadm

mtmmemcma so mmpasapmm moo-n.m momaw

81

equations and 0.8 in the other four indicates that posi-

tive autocorrelation exists in the eqt's (q=1,...,6).

In addition, each estimate of pq is significant. The

Durbin-Watson statistiasfbr the disturbances e -p 8
qt q qt-l

(q=1,...,6) range from 1.91 to 2.50. This range is well

above the tabulated upper bound for the sample size and

number of explanatory variables. Hence, we do not re—

ject the hypothesis of random disturbances when a first—

“4‘ “‘9 _-..-

2
order autoregressive process is assumed.

For the set of OLS estimates of pq and Sq, the

 

Zellner procedure described in Chapter III was then

applied to the twelve equation system.3 These Aitken

 

1-8 2
S; = J— ’
pq n

where n is the sample size. This formula was derived
by Professor J. Kmenta.

2The Durbin—Watson test is derived for the case of
nonstochastic regressors; consequently, if the lagged
dependent variable Rat—l were considered a predetermined
variable whose coeffgcient is to be estimated, the con—
ditions required for use of the Durbin-Watson test would
not be met. However, all the regressors in (4.1) are
nonstochastic so that the Durbin-Watson test is appropriate.

3The OLS estimates of 6 (q=1,...,6) are obtained
in exactly the same way as the estimates of p . They
are discussed in Part B of this section. q

82

estimates of the demand equations are reported in Table 3.
The coefficients of multiple determination were not calcu—
lated for this procedure.

The coefficient estimates obtained by OLS and the
Aitken procedure differ because the data in the sample
are given identical weights equal to unity in the OLS
estimator; whereas, the elements of the inverse of the
variance—covariance matrix are utilized as weights in
the Aitken estimator.

As anticipated, the standard errors reported for
the Aitken procedure in Table 3 are uniformly lower than
the corresponding standard errors reported in Table 2.
This is also the case for the standard errors estimated
for the coefficients of the supply equations (see Tables
u and 5).

In general, the gain in efficiency obtained by
using Zellner's technique is a maximum for a given level
of correlation between contemporaneous disturbances if
the explanatory variables in different equations are un-
correlated. This is clearly not the case in the system
of equations presented here, particularly in that five
of the six supply equations contain the variable up.
However, it is also clear that we obtain a significant
gain in efficiency by using the Aitken estimator.

Turning to the coefficient estimates, the estimates

of the constant terms obtained by both estimation

 

lmf.
I

3

L.

83

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Q

.Hm>ma pcmo pod H onp pm opmm Eopm pcopmmwfio meQmOHchmem

.mpmmunp ooafimpuozp ohm
mpmmp Ham ocm mpcmHOfiwmmoo mg» soamp mommgpcmzmd cfl zmoddm whoppm osmocmpm*

 

 

 

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mw.o was: mmam.a mmo.m| mozm whopoowq
Aaao.ov Amflo.afiv Amm:.mv Amsm.aav Aommvr

«0.0 mmH.HHu mmmz.mm mam.ma- azao.m mmsfipmcmao
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m

gm mpsmHOHoumoo no mmpmsflpmm :mxpfl<--.m mamas

84

techniques are uniformly positive and highly significant.
The lagged indices of industry sales (Eét_l) also per-
formed very strongly. Each of the estimated coefficients
of sét_l is positive as expected, and five of the six OLS
estimates and all of the Aitken estimates are signifi—
cantly different from zero.

The lagged change in sales index (As ) was intro—

qt—l
duced into the model as part of the hypothesis determining
the wage rates expected by employers. The hypothesis

states that the greater is AEét_l,
expected to exist in occupation q in period t. Thus, it

the higher is the wage

is anticipated that the coefficients attached to the
change in sales indices will be negative because the
number of workers desired by firms is specified to be
inversely related to the expected wage rate. This is
the case for five of the six OLS estimates and for each
Aitken estimate. Two of the OLS estimates and three of
the Aitken estimates are significantly different from
zero. More of the estimated coefficients might be ex—
pected to be significant except that variation in Asét_l
very likely has a direct impact on the demand for labor
which partially offsets the indirect effect appearing
via the expected wage.

The performance of the lagged real wage variables

is somewhat disappointing in that only two of the OLS

coefficient estimates and three of the Aitken estimates

85

have the anticipated sign. Both the OLS and Aitken esti—
mates of a3 are positive and significant, while the only
negative estimate approaching significance is the OLS
estimate of a6.

Part of the lack of significance of the lagged
wage variables may be traced to the high correlation be—
tween the wage and sales indices. The existence of multi—
collinearity suggests that reliable estimates of the ef—
fect of changes in wage rates are not obtainable without
utilizing some prior information about the relationship

between the wage and sales variables.

B. The Supply Results

 

The OLS estimates of the parameters of the six
supply equations, along with the corresponding standard
errors and R2's, are reported in Table u. Table 5 con-
tains the coefficient estimates calculated using the two-
step Aitken procedure.

In all six supply equations, we assume that the
expectations coefficient éq equals the parameter Sq in a
first—order autoregressive process. The parameter Eq is
successively assigned the values 0.1,0.2,...,0.9 in each
equation; the estimates reported in Table 4 minimize the
sum of squares of OLS residuals. Again, there is signifi-
cant positive autocorrelation among the nqt's with
E (=8q) equaling 0.9 in four equations and 0.8 and 0.6

q
in the remaining two equations. Each of these estimates

86

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87

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Awao.ov Amzm.av Aoeo.av Annoy “ammo Amoa.omv Aammv Amway Aomm.mv cosotom a
cm.o mom on amflo.~n ama www.mH so: mw flow.au coEnpumLo
aweo.ov A=-.~V gamma Aoamv Amemv Rams nausea:
am.o m-.mu omms.a omem.fl mma mean ooa>tum
Ammo.ov Amma.av Aamav Aoomv Aweac Aaomv “away Amema hama.av ”mama "toxeoz
am.o th.Hu comm.a mafia- Hmfi- emm mo- am- am; aaom muaam
Awao.oo A-~.ma Amam.~v Aaaa.av gamma “mao.av flames Amam.av Amma.mv “woes ”amaze:
ca.o namm.en came.» eaam.a- gem- mom.H own- an». mm~.H ameH.H Haeateao
A onV .
co co can mac man man How :Mc woo mwo moo moo H.co .uncoo cofiuwasooo
‘ 1| ( ( ‘ ( ‘ o .I ( 4‘ .I l‘

(

-.A~.=V :H uvfiuauoan mcoaumscm zfianzm on» ca maunaoaam muCQHOauuQOo no noumeauwo coxufi<uu.m mqm<B

88

is significant.. The Durbin-Watson statistics for the
disturbances ”qt-dqnqt-l (q=1,...,6) all exceed the
tabulated upper bound.

Consider now the parameter estimates of the
supply equations. Five of the six OLS estimates of the
constant terms in the supply equations are positive, and
of these five, four are significantly different from VG“
zero. All five positive Aitken estimates are signifi-
cant.

Turning to the coefficient estimates for relative .

 

wage rates, eight ofthe thirteen OLS estimates have the £,£
expected positive sign, and two of the eight are signfi-
cant. It is interesting to note that all three relative
wage coefficients in the equations for clerical workers
are negative, and the only significant negative coefficient
(313) also appears here. Omitting this equation, the OLS
estimates for the other five equations are much more con—
sistent with the sign of the partial derivatives speci-
fied in the theoretical model. However, the Aitken co-
efficient estimates for relative wage rates in the equation
for clerical workers show Just two "incorrect" signs which
is also the case in the equation for sales workers.

Three of the six absolute wage variables have
positive OLS estimates of their coefficients. The only
OLS estimate which is significant (867) is also negative.

The Aitken estimates are much more consistent with the

89

theoretical model with five of the six coefficients
having the expected positive sign. One of the positive
estimates is significant, while the estimate of C67 is
significant but negative.

Only seven of the thirteen coefficients of rela-
tive unemployment rates are estimated to be negative by
OLS. 0f the six significant coefficients, however, four
have the expected negative sign. Again the OLS results
are more consistent with the theoretical model if the
equation for clerical workers is omitted. In this
equation, two of the three coefficients of relative un-
employment rates are positive, and one of these (816)
is also significant.

The Aitken coefficient estimates for relative un-
employment rates are arranged in an interesting but not
easily explicable pattern according to sign. The co-
efficients of the own unemployment rates relative to
the unemployment rates for white-collar and service
workers are negative, as expected, and each of the co-

efficients in the column headed by d is highly signifi—

Q3
cant. 0n the other hand, the own unemployment rates
relative to the unemployment rates for operatives and
laborers have positive coefficients, and four of these
six coefficients are significant. The pattern of these

coefficients will be considered further in the next

section of this chapter.

90

Four of the OLS coefficient estimates for the un-
employment rate of married males are negative, only one
coefficient having the positive sign specified in the
model. Two of the Aitken estimates are positive, and
one of the positive estimates and one of the negative

estimates are significant. These rather ambiguous re—

 

sults can be rationalized once it is pointed out that f..
the reformulation of the model for empirical estimation ;
leaves room for forces other than that specified in the 5
model to be reflected in the coefficient estimates cal-

culated for up. . gr

The elements of the unemployment rate vector tend
to fluctuate together in response to forces which shift
the entire structure of unemployment. The impact of such
forces affects both numerator and denominator of the un-
employment rate ratios and thus washes out, but the
impact is caught by the own unemployment rate in the
supply equations specified in Chapter II. However, as
noted in the previous chapter, the own unemployment rate
is omitted from each equation because it enters the con-
struction of the dependent variable. This means that the
impact of forces affecting the structure of unemployment
is reflected in the variable up since the level of un-
employment among married males in any time period is a
linear combination of the level of unemployment in each

occupation. Thus, a rise in the unemployment rate of

91

married males increases the incentive for secondary
workers to supply their labor in the market, as speci-
fied in the model. But since the own unemployment rate
is omitted from each equation, a rise in up also reduces
the incentive for workers to enter or to remain in any
particular occupation because of the lower present
values of adjusted expected earnings from market labor.
The estimated coefficients of up are considered in more

detail in the next section.

II. The Interpretation of the Results

 

A. Interpreting the
Demand Results

 

 

The sign of the constant terms in the six demand
equations is expected since a firm must employ a positive
number of workers if it is to operate. The fact that
each of the six constant terms is significant indicates
that some positive level of employment in each occu—
pational group is assured in the short run, at least for
the range of the product demand and wage variables ob-
served in the 1958—66 period.

The magnitudes of the constants give an indication
of the elasticity of demand for the members of the occu—
pations: the smaller the constant, the more elastic the
demand function in the observed interval. Perhaps the
most clear—cut case among the six occupational groups

involves the blue-collar occupations where the OLS and

92

Aitken estimates of the constant term in the equations
for laborers are much smaller than the estimated con-
stant terms in the equations for craftsmen and foremen
and operatives. The explanation for the differences in
elasticities in this case probably lies in the relatively
greater hiring and training costs embodied in the more
highly skilled workers.

It was noted in the previous section that there is
a significant positive relationship between the indices
of industry sales (Ed) and the occupational demand for
labor. To the extent that changes in these indices are
adequate proxies for changes in product demand, this re-
sult is expected from the theory of derived demand. Note
that the sales index in a particular demand equation is
constructed to reflect both changes in the composition of
the industry sales vector and shifts in the entire vector.
Therefore, a change in the structure of product demand,
as well as a change in the level of total demand, is re-
.flected in the set of sales indices.

Examination of the R2's for the demand equations
:indicates that the explanatory power of the demand side
(of the model is considerably less for two of the occu—
Ebations than for the remaining four occupations. In
IDarticular, the R2 for the equation for laborers is
Ebarely positive. To assist in evaluating the relative

ianortance of the explanatory variables in each equation,

93

beta coefficients were estimated, and the coefficients
and their standard errors are reported in Table 6. The
coefficient Bg, for example, is the beta coefficient of
the sales index in the equation for service workers.

The beta coefficients reported in Table 6 are

single equation estimates of the coefficients of the

 

independent variables standardized by their standard wqa
deviations. Within each equation, the beta coefficients 3
provide a measure of the individual contribution of

every regressor in explaining variation in the demand

for labor. Since the coefficients are pure numbers, §M*

they also allow comparisons of individual regressors
across equations.

The relative magnitudes of the beta coefficients
of the sales indices are important because they indicate
the employment response in each occupation to changes in
the vector of industry product demand. Only in the
equation for laborers is the beta coefficient of the
sales index exceeded by the coefficient of one of the
other variables in the equation. And while Bg is the
lowest of the six coefficients of the sales indices,
there is also a significant difference between the co-
efficients B*, B3, and B* and the two coefficients B*

2

and B*.

3

As summarized in Table l, the blue-collar occu-
pations were ranked in the following order of descending

skill requirements: craftsmen and foremen, operatives,

TABLE 6.--OLS estimates of the beta coefficients

standardized variables appearing in (4.1).

of the

 

 

* x *
Occupation aq Bq Fq
Clerical 0.0270 0.8281 —0.0983
Workers (0.1182) (0.120u) (0.0573)
Sales -0.0838 o.uu29 0.0756
Workers (0.1781) (0.1826) (0.0962)
Service 0.26u3 0.5536 —0.0530
Workers (0.1552) (0.1596) (0.0706)
Craftsmen 0.0058 0.8816 -0.17u9
& Foremen (0.0813) (0.0826) (0.0506)
Operatives 0.0“32 0.8U6O -0.0167
(0.1319) (0.1322) (0.0u68)
Laborers -0.1804 0.1585 -0.0510
(0.1149) (0.1216) (0.105“)

 

*Standard errors appear

coefficients.

in parentheses below the

95

and laborers. There was no attempt to rank the two
white-collar occupations, and it was assumed that both
blue-collar and white-collar workers could enter the
service occupations in the short run. This ordering
is consistent with the BLS ordering of the same occu-
pations, except that the BLS places clerical workers
above sales workers in the white-collar skill hier-
archy.

Suppose that fiscal and/or monetary policy were
applied such that every element in the vector of in-
dustry product demand were increased by a given per-
centage. The estimated beta coefficients of the product
demand indices reveal that craftsmen and foremen would
benefit most from such a policy in terms of expanded Job
opportunities and laborers would benefit least. It is
interesting to note, moreover, that within both the
white- and blue-collar occupations the beta coefficients
of the product demand indices rank the occupations in
exactly the same order as they are ranked by skill re—‘
quirements, assuming that clerical workers, in general,
invest more in acquiring skills than do sales workers.
Therefore, the relative magnitudes of the appropriate
beta coefficients indicate that the higher skill occu-
pations in both the white- and blue-collar groups would
benefit more from a policy induced shift in aggregate

demand than would the lower skill occupations.

96

It is also instructive to examine the structure
of unemployment rates during the 1958—66 period. Among
the blue-collar occupations, the levels of the time pro-
files of unemployment rates are inversely related to the
ranking of the occupations by skill, with the time pro-
file for craftsmen and foremen situated at approximately
the same level as the time profiles for clerical and
sales workers. The time profile of unemployment rates
for service workers lies below those for clerical and
sales workers but above the profile for laborers.

Consider now how these results compare with the
conclusions reached by Charles C. Killingsworth in his
study of the structure of unemployment. In a well—
known statement of his position, Killingsworth examines
the relationship between unemployment and the level of
education during the period from 1950 to 1962.“ He
argues that during the period a "twist" in the demand for
labor occurred such that there has been a long-run de-
cline in the demand for low skilled, poorly educated
workers and a long—run rise in the demand for high
skilled, well educated workers. The implication for
policy is that attempts to reduce the level of unemploy-
ment by increasing aggregate demand will increase Job
vacancies for well educated workers but will have rela-
tively little effect in providing additional Job oppor-

tunities for poorly educated Workers.

 

“Killingsworth, "Structural Unemployment in the
United States."

97

In a recent article, Killingsworth examines the
structure of the unemployed classified by educational
levels between March, 1962 and March, 1967.5 Although
unemployment rates fell uniformly during the period, the
decline for the lower educational levels arose only be-
cause labor force participation fell at a faster rate
than employment decreased. Killingsworth makes a con-
vincing case for the hypothesis that "discouragement"
among the least educated groups due to insufficient Job
opportunities led to the decline in their labor force
participation, even during this period of rapidly ex-
panding aggregate demand.

The results presented here for the 1958—66 period
using data for occupational groups rather than educational
groups strongly support Killingsworth's conclusion that
increasing aggregate demand does little to improve the
employment situation for low skilled workers. This is
especially true for workers who classify themselves as
laborers, the occupational group which had by far the
worst unemployment record during the period studied.
Indeed, expansionary monetary and fiscal policy may have
the effect of increasing inflationary pressures by creat-

ing excess demands in the markets for more highly skilled

 

5Killingsworth, "The Continuing Labor Market
Twist," Monthly Labor Review, Vol. 91 (September, 1968),
pp. 12—17.

98

workers. Probably the more effective way to deal with
hard core unemployment is through retraining and edu-
cation programs designed to assist workers to acquire
the skills necessary to enable them to move from the
low-skill occupations. At the very least, it is clear
that an Optimal strategy to combat unemployment must
include programs of this type in addition to the policy
instruments which expand aggregate demand.

B. Interpreting the
Supply Results

 

 

 

Now turn to the results for the six supply equations.
The R2's for the six equations range from 0.11 to 0.30.
Thus, the wage and unemployment variables in the model
presented here account for some 11 to 30 per cent of the
monthly variation in occupational labor supply. In View
of the empirical results obtained in other short-run
studies, these R2's are not unexpectedly low. A case in
point is the study by Peter S. Barth examining the quarterly
labor force participation rates for 21 age-sex classes of
the population over the period 1948-64.6 Barth included
a trend term in each equation to catch long—run changes

occurring during the period. In most of his equations,

the estimated coefficients for the trend terms were

 

6Peter S. Barth, "Unemployment and Labor Force
Participation," Southern Economic Journal, XXXIV (January,
1968), pp. 375-382.

 

99

highly significant. In the summary equations for all
males and all females, Barth reports extremely high
t-test statistics for the trend terms; indeed, he notes
that the partial coefficient of correlation of the
trend term for all males is 0.857.7 Since the model
presented here simply classifies the members of the
labor force into alternative occupational groups,
Barth's results imply that the equations of our purely
short-run model will not have high associated R2's.

As reported in Section I, five of the constant
terms in the supply equations are positive and signifi-
cant. This indicates that these supply functions are
elastic in the range of the wage variables observed in
the 1958-66 period. The constant term in the equation
for craftsmen and foremen is negative, but the fact
that this estimate is exceeded by its standard error
does not allow the inference that the supply of crafts-
men and foremen is inelastic.

The literature pertinent to the supply side of
the model may be divided into two parts. The first part
is composed of studies of the labor force participation
rates of alternative age and sex categories of the popu-

lation. These studies show quite clearly that labor

 

71tio., p. 379.

q mm. s
. '.
“.1

100

force participation is positively affected by increases
in the levels of the relevant wage rates.8

In addition, there is a scattered literature
examining the relationship between occupational choice
and the time paths of long-run earnings in alternative
occupations. Frequently, the relevant earnings horizon
is taken to be individuals' entire working lives. The
general conclusion drawn from the empirical evidence is
that there is a long-run occupational supply response to
differentials in the present values of expected earnings,
even though the response may occur only after a signifi-
cant lag because of the time involved in training.9

With the exception of the OLS estimates for the

equation for clerical workers, the results presented in

Tables A and 5 provide support for the hypothesis that

 

8See Fisher, Op. cit. for a summary of the empirical
evidence presented in some of the best known of these
studies.

9See the results reported in Bruce W. Wilkinson,
"Present Values of Lifetime Earnings for Different Occu-
pations," Journal of Political Economy, LXXIV (December,
1966), pp. 556-572 and the references cited therein.
Jacob Mincer provides an additional indirect piece of
evidence supporting this conclusion. He establishes
that the distribution of personal income in the economy
can be explained as the result of the market equalizing
the present values of lifetime earnings in alternative
occupations. "Investment in Human Capital and Personal
Income Distribution," Journal of Political Economy,
LXVI (August, 1958), pp. 281-302.

101

short-run occupational supply adjustments, just as long-
run adjustments, depend on expected wage rates in alter—
native occupations. Although the signs of the estimated
coefficients are quite consistent with the model, the
general lack of significance of the estimates is probably
due to violations of the fairly restrictive assumptions
required to construct the wage estimates.

The sharp division in the results for relative
unemployment rates may perhaps be rationalized by inter-
' preting the coefficient estimates in light of the "hidden
unemployment" in the United States economy. The hidden
unemployed are those workers who have dropped out of the
labor force due to lack of job opportunities. Because
the level of hidden unemployment is positive, there is a
discrepancy for some occupations between the BLS estimates
of occupational unemployment rates and the "real" unemploy—
ment rates. This discrepancy arises because the former
measures include only workers in the labor force, while
the latter also include discouraged drop-outs from the
labor force. Killingsworth's calculation of the real as
opposed to the "official" unemployment rates for alter-
native educational groups in 1957 and 1962 indicates that
the discrepancy is serious only for the lower educational

groups.10 In a subsequent paper reported on earlier,

 

loKillingsworth, "Structural Unemployment in the
United States," p. 44.

102

Killingsworth finds that this same discrepancy persisted
into the period from 1962 to 1967.11 In this connection,
it was noted earlier that the unemployment rates for the
lower educational groups declined between 1962 and 1967,
but this decline occurred only because labor force
participation fell faster than employment decreased.

Among the six occupational groups examined here,
laborers are, in general, the least skilled and the most
poorly educated, and there seems to be an important
parallel between the employment conditions encountered
by the poorly educated and by laborers. During the en-
tire 1958-66 period, the employment of laborers remained
fairly constant. In contrast, the employment of service
workers increased sharply. However, from early 1961 to
the end of 1966 the unemployment rate among laborers de—
clined steadily. As in the case of the poorly educated,
the explanation for this decline in the unemployment rate
must lie in an important fall in labor force participation.
And as with the poorly educated, a significant proportion
of the laborers who leave the labor force probably do so
because of discouragement. Hence, they are included among
the hidden unemployed.

To see how the level of hidden unemployment relates
to the interpretation of the positive coefficient esti-

mates, consider the estimate of dl6' During the period

 

11
Twist."

Killingsworth, "The Continuing Labor Market

 

103

from 1961 to 1966, the estimate of dl6 reflects the posi-
tive correlation between the supply of clerical workers
and the steady rise in the ratio ult-l/u6t-l caused by
the relatively greater rate of decline in the unemploy-
ment rate of laborers. A rational supplier evaluating
unemployment conditions in the two occupations will take
account not only of the number of unemployed laborers,
but he will also take into consideration the number of
discouraged laborers who have left the labor force.
Since the official unemployment rate for laborers de-
clined during this period while employment remained
relatively constant, it is reasonable to assume that the
hidden unemployment associated with a fall in partici-
pation increased among laborers. If this hypothesis is
correct, the increase in the supply of clerical workers
is not a positive response to the rise in the ratio
ult-l/u6t-l’ but it is rather a negative response to the
increase in the level of hidden unemployment among laborers.
This interpretation is of course, consistent with the
theoretical model if the relevant unemployment rate for
laborers is taken to be the real rather than the official
rate. For the five other occupational groups considered
here, it seems reasonable to assume that the discrepancy
between the two rates is of a second order of magnitude.
At this point, it might be worthwhile to repeat

that the data utilized in the empirical analysis are

104

collected for major occupational groups. Very probably,
however, a significant proportion of short—run inter-
occupational mobility is between specific occupations
within particular major occupations. If this is the
case, the fact that the relationships postulated in the»

model seem to exist for major occupational groups lends

 

additional credence to the model. 5“
To the extent that the unemployment rate ratios in the

supply equations tend to verify the use of probabilistic V

labor supply functions, they also imply that the structure _

of unemployment in past periods affects the current struc- é.r

ture by partially determining the current supply of
workers to alternative occupations. Using the estimates
of Gq (q=1,...,6), we can calculate the weights assigned

to the unemployment rate ratios in each period from

A
0*

equation (2.35). For oq = 0.9, the weights associated

With uqt-l/uit-l’ uqt-2/uit-2’ uqt-3/uit-3’ and uqt—4/
uit-4 (i#q) are 0.10, 0.09, 0.08, and 0.07, respectively.
The average lag is nine months.12 For Sq = 0.8, the

weights are 0.20, 0.16, 0.13, and 0.10, respectively.

The average lag is four months. Finally, for Sq = 0.6,
the weights are 0.40, 0.24, 0.14, and 0.09, respectively;
and the average lag is one and one-half months.‘ Hence,
there is considerable variation in the weighting patterns

in different occupations. In four of the occupations,

 

A 12; 2+38 3+...)
= a /(1—o ‘1

his is computed from (1-6 )(6 +25
) q q q
q q

105

individuals appear to consider the time paths of rela—
tive unemployment rates for a year or more in arriving
at expected relative unemployment rates. This is con-
sistent with the finding in studies of the short-run
consumption function that the weights applied to past
levels of disposable income fall off rather gradually
13

in the calculation of expected income. For laborers
and sales workers, however, the weights assigned to un-
employment rates in past periods fall off rather more
sharply.

One further implication may be drawn from the
estimates for the relative unemployment rates. These
results indicate that concentration of private of govern-
mental efforts to ease an unemployment problem in a
particular occupation is likely to be at least partly
offset by short—run movements of workers into the occu-
pation from related occupations and from outside the
labor force. Consequently, programs designed to reduce
unemployment by upgrading workers in all or most of the
lower skill occupations are to be preferred to programs
concentrated in any single occupation. The probable
effect of the latter type of program is to shift the

unemployed between occupations rather than to reduce the

total level of unemployment.

 

l3Zellner, Huang, and Chau, op. cit., p. 579.

106

The final variable in the supply equations to be
considered is the unemployment rate of married males.
As pointed out in Section I, an increase in the level
of up generates two Opposing pressures on the flow of
labor into an occupation. The flow of labor is in-
creased in accordance with the additional worker hy-
pothesis, described earlier. On the other hand, the
flow is decreased due to the general reduction in pre—
sent values Of adjusted expected earnings implied by an
increase in up. The latter effect of an increase in
unemployment is referred to as the "discouraged worker"
hypothesis. There have been a number Of attempts to
measure the relative impact of these two hypotheses on
labor supply behavior. W. Lee Hansen found that the
effects Of the two hypotheses are roughly offsetting,lu
while Kenneth Strand and Thomas Dernburg concluded that
the net effect is in favor of the discouraged worker
theory.15

In a study referred to earlier, Peter S. Barth

found an inverse and significant relationship between

participation rates and the overall unemployment rate

 

1“W. Lee Hansen, "The Cyclical Sensitivity Of the
Labor Supply," American Economic Review, LI (June, 1961),

pp- 299-309.

15Kenneth Strand and Thomas Dernburg, "Cyclical
Variations in Civilian Labor Force Participation,"
Review of Economics and Statistics, XLVI (November, 1964),

pp. 378-391.

 

 

107

for all groups of male workers classified by age, except
for the age groups 35-44, 55-64, and 65 and over. For
females, he found no consistent relationship for most
of the female age groups considered.l6 Thus, Barth's
results seem to indicate that within a number of the
age groups included in the category secondary workers
the discouraged worker hypothesis is roughly Offset by
the additional worker effect. However, among prime-age
males, the discouraged worker effect clearly dominates.

The OLS coefficient estimates for up presented in
Table 4 support the hypothesis that an increase in the
general level of unemployment rates (and thus in up)
leads to a decrease in the vector of present values Of
adjusted expected earnings which reduces the incentive
for workers to offer their services in the market. How—
ever, the discouraging effect of the shift in this vector
is offset by the entrance into the labor force by second-
ary workers motivated to attempt to maintain family in-
come. Except in the equation for clerical workers, the
offsetting impact of the additional worker hypothesis is
sufficient to render the coefficients of up statistically
insignificant for the relatively low-skill occupations
remaining.

The Aitken estimates indicate that the discourage—

ment effect dominates in the white-collar and the service

 

16Barth, op. cit., pp. 379-380.

108

occupations and is statistically dominant for clerical
workers. However, these results also reveal the addi-
tional worker hypothesis to be statistically dominant

for laborers.

III. Summary and Conclusion

 

On the theoretical level, we have utilized the
tools of economic theory to construct a model which
determines each component of the occupational vector of
unemployment as the difference between the number of
workers supplied and the number demanded at a particu—
lar wage rate. The supply and demand functions are
developed on the assumptions of utility- and profit-
maximizing behavior on the parts of individual workers
and firms, respectively. From the level of the indi—
vidual worker and firm, aggregation is performed to Ob—
tain the market demand and supply functions.

On the demand side of the model, the demand for
the members of the qth occupation depends on the desired
vector of industry output and on the vector of expected
wage rates. The supply to the qth occupation depends on
the vector of expected wage rates, the probability Of
employment in q and in alternative occupations, and
expected nonwage earnings. The probability of employment
in occupation q, in turn, depends on the expected un—
employment rate in the occupation. For secondary workers,

the unemployment rate of married males also enters the

109

supply function as the determinant of the level Of non-
wage expected earnings. To complete the model, equa-
tions hypothesizing the formulation of expected wages
and unemployment rates are introduced, and sets of
equations determining the vector of desired output and
the vector of current wages are specified.

On the empirical level, time-series data for six
major occupational groups and six major industries were
collected for use in testing the model. The time period
examined is from 1958 to 1966. As part of the hypothesis,
the six demand and six supply equations estimated were
formulated in such a manner as to incorporate a first-
Order autoregressive process in the individual distur—
bance terms. Single equation OLS was then applied to
obtain maximum likelihood estimates for each equation of
the parameter in the first-order autoregressive process
and the coefficients in the equation. In addition, a
two-step Aitken estimation procedure was applied to the
system of equations. This procedure allows the relaxation
Of the assumption that contemporaneous disturbance terms
in different equations are independent.

The results for the demand equations indicate that
the sales index representing the level and composition of
industry product demand is a significant determinant of
labor demand in every occupational market. In addition,

there is some evidence to support the expected wage

110

hypothesis prOpOsed in the theoretical model. The large
positive constant terms in the demand equations imply
that a significant number of the members of each occu-
pation are regarded by employers as fixed factors of
production in the short-run for Observed fluctuations

in wage rates and product demand.

The estimates of the beta coefficients for the
demand equations reveal that a given percentage increase
in each component Of the vector Of industry product de-
mand results in larger increases in employment oppor-
tunities in the high skill occupations than in the occu-
pations requiring a low level of skills. This result
for occupational groups strongly supports Killingsworth's
finding for educational groups that the demand for labor
has twisted such that the long-run employment opportunities
for the poorly educated have worsened while those for the
well educated have improved. An implication is that ex-
pansionary monetary and fiscal policy is a relatively in-
effective instrument for increasing employment in the
occupational markets which have the greatest unemployment
problem. A more effective policy would be programs de-
signed to increase the upward mobility of low skilled
workers. Such programs would necessarily be coupled
with expansionary policies intended to maintain a high
level of aggregate demand so that the demand for more
highly skilled workers is sufficient to allow for the

employment of retrained workers.

111

The supply results provide some evidence that
workers respond to differentials in the present values
of expected earnings in alternative occupations in
making their short-run labor supply decisions. In this
respect, the results Obtained here are consistent with
the conclusions drawn in studies examing long—run occu-
pational choice. In addition, these results show that
not only expected wage rates but also expected unemploy—
ment rates are significant in short-run supply functions
to occupational groups. Among the estimated coefficients
of lagged relative unemployment rates an interesting
pattern emerged. The signs of the coefficient estimates
for unemployment rates relative to the unemployment rate
for laborers were positive and significant, while the
signs for the other relative unemployment rates were
nearly all in accordance with the negative sign speci-
fied in the model. The rationale advanced to explain
this important perverse result focuses on the existence
of "hidden unemployment" in the economy. There is reason
to expect that hidden unemployment among laborers is
particularly severe relative to the other occupations
examined. Moreover, there is likely an inverse relation-
ship between the unemployment rate Of laborers and the
level of hidden unemployment among laborers for at least
a significant part of the time period examined. There-

fore, the significant positive coefficients may be

112

interpreted as an adjustment in labor supply to changes
in the relevant, but unreported, level of "real" unemploy—
ment. If this interpretation is accepted, the complete
set of estimates for the unemployment rate variables
verify the use of the probabilistic supply function
rather than an ordinary supply function in the model.
Because the expected unemployment rate in an occupation
is calculated using a distributed lag model, the past
distribution of unemployment helps to determine the cur-
rent structure Of unemployment by affecting relative
labor supply.

The signs and significance of the coefficient esti-
mates for the unemployment rate of married males were
mixed indicating that neither the additional worker effect
nor the discouraged worker effect dominates the other in
the occupational groups considered here.

To summarize, the results at both the theoretical
and the empirical level lead to the conclusion that short—
run fluctuations in the vector of occupational unemploy-
ment can be explained to a significant extent by a purely
economic model of supply and demand. Some Of the policy
implications of these results are the following.

A necessary condition for reducing short—run
unemployment is the direction of additional effort toward
shortening the supply adjustment periods of unemployed

workers who do not require additional training to locate

113

new employment. In particular, a good deal Of short-run
unemployment could be eliminated by simply increasing

the flow of public and private information on job oppor—
tunities so as to reduce the direct and Opportunity costs
of investment for these workers.

Beyond this, the results for the demand equations
show that policy measures designed to raise the level Of
aggregate demand do not increase labor demand to the same
extent in all occupations. Members of low skill occu-
pations appear to benefit less in terms of expanded job
Opportunities than do members of higher skill occupations.
Since the low skill occupations are primarily those with
the highest unemployment rates, measures intended to main-
tain a high level Of aggregate demand will be successful
in reducing the level Of long-term unemployment only if
low skilled workers are assisted in receiving the addi—
tional training necessary to qualify for membership in
higher skill occupations. The results for relative un-
employment rates in the supply equations indicate, more-
over, that retraining programs spread across the low
skill-high unemployment occupations will be more success-
ful than programs concentrating on easing unemployment
in particular low skill occupations. This difference
between programs arises because a reduction in
unemployment in particular occupations encourages workers

in related occupations and outside the labor force to

114

enter the now more attractive occupations. Consequently,
the supply of workers to these occupations would increase

so that the previous level of unemployment persists.

APPENDIX

fiU

11

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CONSTRUCTION AND SOURCES OF SAMPLE DATA

The construction of the sample data used in the
regression analysis is described below and a listing of
the data sources follows. Monthly observations were ob-
tained for the period 1958 to 1966. The subscript 3
refers to the Jth industry, J=l,...,6. The six indus-
tries examined in the study are numbered as follows:
construction, 1; durable goods manufacturing, 2; non—
durable goods manufacturing, 3; wholesale trade, H;
retail trade, 5; and services, 6. The subscript q re-
fers to the qth occupational group, q=l,...,6. The six
major occupations considered are: clerical workers, 1;
sales workers, 2; service workers, 3; craftsmen and fore-
men, “; operatives, 5; and laborers, 6. It was decided
to report the empirical results in the text with clerical
workers labeled the first occupation and sales workers the
second. However, in the data fed to the computer, the
order of these two occupations was reversed. Hence, for
example, the data series labeled LDl above is the number
of employed sales workers, while LD2 is the number of

employed clerical workers.

128

202

Q:

129

Number of employed members of the qth occupational

group, thousands of workers.

~d _ =
zq (-LDq) (l)

Unemployment rate in the qth occupational group,

per cent.

uq (=Uq) = (2)

Unemployment rate of married males, per cent.

up (=UP) = (3)

Number of members of occupation q, thousands of

workers.

”8 _ _ (l)
"q (‘st ‘ T7137

Sales of the construction industry.

81 = (4)

Sales of durable goods manufacturing, billions of

dollars.
s2 = (5)

Sales of nondurable goods manufacturing, billions

of dollars.

86:

PI

PI

PI

PI“:

130

Sales of the wholesale trade industry, billions

of dollars.

Su"

(7)

Sales of the retail trade industry, billions of

dollars.

S5

(8)

Sales of the services industry, billions of dollars.

S6:
Price index for

PIl

Price index for

PI2 =

Price index for

1959:100.

PI3

Price index for

1959:100.

PIN =

(9)

the construction industry, 1959:100.

(10)

durable goods manufacturing, 1959:100.

(11)

nondurable goods manufacturing,

(12)

the wholesale trade industry,

(13)

PI

PI6:

CPI:

AI

AI

AI“:

AI

131
Price index for the retail trade industry, 1959:100.

P15 = (1“)

Price index for the services industry, 1959:100.
P16 = (15)
Consumer price index, 1959:100.

CPI = (16)
Change in inventories of durable goods manu-

facturing, billions of dollars.

A12 = (17)

Change in inventories of nondurable goods manu-

facturing, billions of dollars.

A13 = (18)

Change in inventories for the wholesale trade

industry, billions of dollars.
AI“ = (19)

Change in inventories for the retail trade industry,

billions of dollars.

AI5 = (20)

Ya:

Y6:

132

Output of the construction industry, billions of

dollars.

_ (4)
yl ' Tic?

Output of durable goods manufacturing, billions

of dollars.

= (5)4-(17)
y2 (lI)

Output of nondurable goods manufacturing, billions

of dollars.

= (6) + (18)
y3 (12f

 

Output of the wholesale trade industry, billions

of dollars.

= (7) + (19)
yu (13)

Output of the retail trade industry, billions of

dollars.

_ (8) + (20)
y5 ' (in)

 

Output of the services industry, billions of

dollars.

_ (9)
y6 ' TT§T

 

2

mI

>

0..

QJ

.Q

133

'8: Number of members of occupation q employed by

industry J in the base period, 1959.

1 . = 21
QJB ( )

qu: Wage paid to the members of occupation q by in-

dustry j in the base period, dollars.

w . = 22
qJB ( )

Wage paid in the Jth industry, dollars.

Wj = (23)

Weighted average of the sales of industries

employing members of occupation q.

6 2
's' (=3Hq) = z (.9153
q 3:2 ij J

Estimate of the real wage in the qth occupation

facing employers, dollars.

 

 

 

6 k W
z _ng. ] w
i=1 yJB PI; IJB QJB
W
a: (=EHQ) = 6 ‘z 33
z _Ql§
J=l yJB

)

l3“

Estimate of the real wage in the qth occupation

facing labor suppliers, dollars.

(1)

(2)

(3)

(A)

(5)-(8)

 

 

 

 

§[“qJB WJ w J ‘
i=1 5'38 WJB CUB

 

 

 

1 9. 1
Z Ly' BA

AS _ \ = 11:]. JB

Wq (‘WHq’ CPI

Seasonally adjusted employment of the members
of the qth occupational group, thousands of
workers.

Bureau of Labor Statistics, Employment and
Earnings and Monthly Report on the Labor Force,
vol. 1“ (July, 1967), pp. 107—110.

Seasonally adjusted unemployment rate in the
qth occupational group, per cent.

Bureau of Labor Statistics, Employment and
Earnings and Monthly Report on the Labor Force,
Vol. 1“ (July, 1967), pp. 114-115.

 

Seasonally adjusted unemployment rate of married
men, per cent.

Bureau of Labor Statistics, Employment and
Earnings and Monthly Report on the Labor Force.

 

 

F. W. Dodge Company seasonally adjusted index
of the value of construction contracts in 48
states, 1957-59leO. In the construction of
the output measure for the industry, the value
of new construction put-in-place (seasonally
adjusted), billions of dollars, is utilized.

Ofgice of Business Economics, Business Statistics,
19 7.

 

Seasonally adjusted business sales of the jth
industry (j=2,...,5), billions of dollars.

Ofgice of Business Economics, Business Statistics,
l9 7.

 

I I II. ..II I‘

 

(9)

(10)

(ll)—(12)

(13)

(14)

(15)

(16)

(17)-(20)

(21)

135

Seasonally adjusted final sales of services
in GNP by major type (monthly rates), billions
of dollars.

Office of Business Economics, Business Statis—
tics, 1967.

 

Department of Commerce Composite Construction
Cost Index, 1959:100.

Office of Business Economics, Business
Statistics, 1967.

Wholesale price index--manufacturers, 1959:100.

Office of Business Economics, Business
Statistics, 1967.

Wholesale price index--all commodities, 1959:
100.

Office of Business Economics, Business
Statistics, 1967.

 

Consumer price index--commodities, 1959:100.

Office of Business Economics, Business
Statistics, 1967.

Consumer price index-~services, 1959:100.

Office of Business Economics, Business
Statistics, 1967.

 

Consumer price index—-all items, 1959:100.

Office of Business Economics, Business
Statistics, 1967.

 

First difference of the end of period book
value of manufacturing and trade inventories
for the jth industry (j=2,...,5), billions
of dollars.

Office of Business Economics, Business
Statistics, 1967.

 

Major occupational group of employed persons
by major industry group, 1959, number of workers.

Bureau of the Census, U. 8. Census of POpu-
lation: 1960, Subject Reports, Occupation by

Industry, Table l.

 

 

 

(22)

(23)

136

Median earnings of males who worked 50 to 52
weeks in 1959, by occupational groups, dollars.

Bureau of the Census, U. S. Census of Popu-
lation: 1960, Subject Reports, Occupational
CharacteristiCs, Table 30.

 

 

 

Average weekly earnings in the jth industry,
dollars. For the services industry, total
employees in the current period relative to
the base period was used as a proxy for
relative earnings.

Bureau of Labor Statistics, Emplpyment and
Earnings Statistics for the United States-—
190941967, Bulletin No. 1312-5.

 

 

BIBLIOGRAPHY

SELECTED BIBLIOGRAPHY

Books

 

Alchian, Armen A., and Allen, William R. University

Economics. Second edition. Belmont, California:
Wadsworth Publishing Company, Inc., 1967.

Becker, Gary S. Human Capital. New York: National
Bureau of Economic Research, 196“.
Cain, Glen G. Married Women in the Labor Force: An

Economic Analysis. Chicago: University of
Chicago Press,'1966.

Goldberger, Arthur S. Econometric Theory. New York:
John Wiley & Sons, Inc., 196A.

Johnston, J. Econometric Methods. New York:

McGraw-
Hill Book Company, Inc., 1963.

Articles and Periodicals

 

 

Arrow, Kenneth J. "Samuelson Collected." Journal of
Political Economy, Vol. 75 (October, 1957), 785-737.
Barth, Peter S.

"Unemployment and Labor Force Partici-
pation." Southern Economic Journal, XXXIV
(January, 1968), 375-382.

Becker, Gary S. "Investment in Human Capital: A
Theoretical Analysis." Journal of Political

Economy, LXX, Part 2 (Supplement: October, 1962),
9" 90

Behman, Sara. "Wage—Determination Process in U. S.

Manufacturing." Quarterly Journal of Economics,
LXXXII (February, 1968), 117-1A2.

Benewitz, Maurice C., and Zucker, Albert. "Human Capital
and Occupational Choice--A Theoretical Model."

Southern Economic Journal, XXXIV (January, 1968),

138

139

Ben-Porath, Yoram. "The Production of Human Capital and
the Life Cycle of Earnings." Journal of Political
Economy, Vol. 75, Part I (August, 1967), 352-365.

 

Bowen, W. G., and Finegan, T. A. "Labor Force Partici-
pation and Unemployment." Employment Policy and
the Labor Market. Edited by A. M. Ross. Berkeley:
University of California Press, 1965.

Brehm, C. T., and Saving, T. R. "The Demand for General
Assistance Payments." American Economic Review,
LIV (December, 196A), 1002;1018.

Cain, Glen G. "Unemployment and the Labor-Force Partici-
pation of Secondary Workers." Industrial and Labor
Relations Review, Vol. 20 (January, 1967), 275—293.

 

Carol, Arthur, and Parry, Samuel. "The Economic Rationale
of Occupational Choice." Industrial and Labor Re—
lations Review, Vol. 21 (January, 1968), 183él96.

 

 

David, Martin, and Otsuki, Toshiyuki. "Forecasting
Short-Run Variation in Labor Market Activity."
Review of Economics and Statistics, XLX (February,
I9687,268-77.

 

Dernburg, Thomas, and Strand, Kenneth. "Hidden Unemploy-
ment 1953-62: A Quantitative Analysis by Age and
Sex." American Economic Review, LVI (March, 1966),

71—950
Eckstein, Otto, and Wilson, Thomas A. "The Determination
of Money Wages in American Industry." Quarterl
Journal of Economics, LXXXVI (August, 1962), 375—u1u.
Gallaway, L. E. "Labor Mobility, Resource Allocation,

and Structural Unemployment." American Economic
Review, LIII (September, 1963), 694-716}

 

 

Hansen, W. Lee. "The Cyclical Sensitivity of the Labor
Supply." American Economic Review, LI (June, 1961),
299-309.

 

Hildebrand, George H. "Structural Unemployment and Cost-
Push Inflation in the United States." Monetary
Process and Policy: A Symposium. Edited by George
Horwish. Homewood, IllinEIs: Richard D. Irwin,
Inc., 1967.

 

Johnston, Denis F. "Education and the Labor Force."
Monthly Labor Review, Vol. 91 (September, 1968), 1-11.

 

1A0

Kasper, Hirschel. "The Asking Price of Labor and the
Duration of Unemployment." Review of Economics
and Statistics, XLVIV (May, 19677, 165-172.

 

Killingsworth, Charles C. "Structural Unemployment in
the United States." Employment Problems of Auto-
mation and Advanced Technology: IA InternationaI
Perspective. Edited by Jack Stieber. London:
Macmillan and Company, Ltd., 1966.

 

 

 

"Automation, Jobs, and Manpower: The Case
for Structural Unemployment." The Manpower Revolu-
tion: Its Policy Consequences. Edited by Garth
L. Mangum. Garden City, New York: Doubleday and
Company, 1965.

 

 

. "The Continuing Labor Market Twist." Monthly
Labor Review, Vol. 91 (September, 1968), 12-17.

 

Leijonhufvud, Axel. "Keynes and the Keynesians: A
Suggested Interpretation." Proceedings of the
American Economic Association, LVII (May, 1967),

 

 

Mincer, Jacob. "Investment in Human Capital and Personal
Income Distribution." Journal of Political Economy,

 

LXVI (August, 1958), 281-302.

. "Labor-Force Participation and Unemployment:
A Review of Recent Evidence." Prosperity and
Unemployment. Edited by R. A. Gordon and M. S.
Gordon. New York: John Wiley & Sons, Inc., 1966.

 

 

. "Labor Force Participation of Married Women:
A Study of Labor Supply." Aspects of Labor Economics.

 

A Conference of the Universities-National Bureau
Committee for Economic Research. Princeton:
Princeton University Press, 1962.

. "On—the-Job Training: Costs, Returns and
Some Implications." Journal of Political Economy,
LXX, Part 2 (Supplement: October, 1962), 50-79.

Moore, T. G., and Rapping, L. A. "Dismissal Pay and
Flexible Wage Adjustments: A Theoretical Analysis."
Southern Economic Journal, XXXIV (July, 1967),
101-112.

 

Oi, Walter Y. "Labor as a Quasi-Fixed Factor." Journal
of Political Economy, LXX (December, 1962), 538—555.

1A1

Parks, Richard W. "Efficient Estimation of a System of
Regression Equations When Disturbances are Both
Serially and Contemporaneously Correlated."
Journal of the American Statistical Association,
Vol. 62 (June, 19677, 500-509.

Rees, Albert. "Information Networks in Labor Markets."
Proceedings of the American Economic Association,

LVI (may. 1966), 559-566.

Severn, Alan K. "Upward Labor Mobility: Opportunity
or Incentive?" Quarterly Journal of Economics,
LXXXII (February, 1968), 1&3—151.

Simler, N. J. "The Structural Hypothesis and Public
Policy." American Economic Review, LIV (December,
196A), 985—1001.

Sjaastad, Larry A. "The Costs and Returns of Human
Migration." Journal of Political Economy, LXX,
Part 2 (Supplement: October, 1962), 80—93.

Stigler, George J. "Information in the Labor Market."
Journal of Political Economy, LXX, Part 2 (Supple-
ment: October, 19627, 9A-105.

Strand, Kenneth, and Dernburg, Thomas. "Cyclical Vari-
ation in Civilian Labor Force Participation."
Review of Economics and Statistics, XLVI (November,
196A), 378-391.

Wilkinson, Bruce W. "Present Values of Lifetime Earnings
for Different Occupations." Journal of Political
Economy, LXXIV (December, 1966), 556-572.

 

Zellner, Arnold. "An Efficient Method of Estimating
Seemingly Unrelated Regressions and Test for
Aggregation Bias." Journal of the American
Statistical Association, Vol. 67 (June, 1962),
3A3-368.

 

 

. "Estimators for Seemingly Unrelated Regression
Equations: Some Exact Finite Sample Results."
Journal of the American Association, Vol. 58
(December, 1963), 977-982.

Zellner, A., Huang, D. 8., and Chau, L. C. "Further
Analysis of the Short-Run Consumption with Emphasis
on the Role of Liquid Assets." Econometrica,
Vol. 33 (July, 1965), 571-581.

 

142

PubliC'Documents

 

Knowles, James W., and Kalachek, Edward. Higher Unemploy-
ment Ratesyl957-1960: Structural Transformation
or Inadequate Demand. Subcommittee on Economic
Statistics of Joint Economic Committee, U. S.
Congress (Washington: U. 8. Government Printing
Office, 1961).

 

U. S. Department of Commerce. Bureau of the Census.
U. S. Census of Popplation: 1960. Subject Re-
ports, Occupational Characteristics.

. Bureau of the Census. U. S. Census of
POpulation: 1960. Subject Reports, Occupation
by Industry.

 

 

. Office of Business Economics. Business
Statistics, 1967.

 

U. S. Department of Labor. Bureau of Labor Statistics,
Employment and Earnings Statistics for the United
States--l909—l967. Bulletin No. 1312-5.

. Bureau of Labor Statistics. Employment and
Earnings and Monthly Report on the Labor Force,
Vol. 1“ (July, 1967Y.

 

Unpublished Material

 

Alchian, Armen A. "Information Costs and Unemployment."
(Mimeographed.)

Alchian, A. A., Arrow, K. J., and Capron, W. M. "An
Economic Analysis of the Market for Scientists and
Engineers." RM-2190-RC. Santa Monica, California:
The Rand Corporation, 1958.

Fisher, Anthony. "Poverty and Labor-Force Participation."
Research Paper P—273. Economic and Political
Studies Division, Institute for Defense Analyses,
February, 1966.

Holt, Charles C. "Job Search, Phillips' Wage Relation
and Union Influence, Theory and Evidence." Firm
and Market Workshop Paper 6705. Madison, Wisconsin:
Social Systems Research Institute, University of
Wisconsin, December 1A, 1967. (Mimeographed.)

1A3

Rees, Albert. "Remarks on the Nature of Our Unemploy-
ment Problem." Discussion paper for meeting with
the Board of Governors of the Federal Reserve
System, January 30, 1965. (Mimeographed.)

Zellner, Arnold, and Geisel, Martin S. "Analysis of
Distributed Lag Models with Applications to Con-
sumption Function Estimation." (Mimeographed.)

  
  
 

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