Journal of Monetary
UTILITY
Economics 4 (1978) 687-713.
0
North-Holland
Publishing Company
MAXIMIZATION,
AGGREGATE LABOR FORCE
BEHAVIOR, AND THE PHILLIPS CURVE
John J. SEATER*
Fnirrctl
Reww
Bmk
qf PAiludelpkicl. Plriiadelpkiu. PA 19105,
C.S..4.
I. introduction
In this paper. 1 examine aspects of the Phillips curve using a microeconomit model of labor force behavior developed elsewhere [Seater (1977)]. The
model is a unification of the two major approaches to the microfoundations
of labor force behavior. The first approach, exemplified by Dale Mortensen’s
work (1970a). assumes the individual is an income maximizer with fixed
leisure time and examines how the individual divides nonleisure time between
labor and job search; the second approach, exemplified by Robert Lucas and
Leonard Rapping’s work (1970). assumes the individual is a utility maximizer
not engaging in job search and examines how the individual divides his time
between labor and leisure.
Each of these approaches
ignores an aspect of the individual’s time
allocation decision and is therefore deficient when applied to aggregate
analysis. The first approach, assuming leisure time fixed, ignores the participation decision and implicitly assumes that the size of the labor force is fixed,
an assumption contradicted by empirical observation. The second approach.
ignoring job search, implicitly treats unemployment
as an unpr0ductiv.e
leisure activity, a treatment contradicted by recent theories of job search and
which renders difficult a workable definition of unemployment.
By combining these two approaches, the unified model overcomes the
deficiencies of each taken separately. In brief, the individual is assumed to be
deriving utility from consumption
and leisure and
a utility-maximizer,
capable of engaging in labor. search, and leisure simultaneously.
Under
certain restrictions on labor supply, the model yields natural and mutually
*This paper is based on the second part of my Ph.D. dissertation at Brown University.
I
thank Herschel I. Grossman, Harl E. Ryder, and John Kennan, who constituted my dissertatron
committee, and also Robert A. Jones for many helpful comments and suggestions on my
dissertation. 1 al:. thank Anthony M. Santomero for comments and suggestions on earlier drafts
of this pape-. The views expressed herein are not necessarily those of the Federal Reserle
System or the Federal Reserve Bank of Philadelphia.
688
J.J. Seatcv. Utility
maximixtiort
consistent definitions of employment, unemployment,
and nonparticillill icjn.
These definitions help illuminate aspects of the Phillips curve heretofore not
examined and also show the relationships among the earlier contributions.
In section 2, I summarize the model and the pertinent results. In section 3,
I use the model to analyze the response of aggregate employment, unemployment, and nonparticipation
to certain exogenous changes. I show that, even
though the response of any given individual to an exogenous change may be
ambiguous because of income and substitution effects, this ambiguity does
not carry over to aggregate employment, unemployment,
and nonparticipation. The responses of employment and nonparticipation
are determinate
for the exogenous changes considered herein. The response of unemployment
generally is ambiguous but not because of income and substitution effects.
The ambiguity arises from unemployment’s
position as a ‘middle’ state
between employment and nonparticipation.
Changes which tend to induce
some people to leave unemployment
for employment also tend to induce
other people to leave nonparticipation
for unemployment,
leaving the net
change in unemployment ambiguous in general. In section 4. I use the model
to examine the Phillips curve. 1 show that, under appropriate assumptions
about perceptions, the model can generate a negatively-sloped
short-run
relation between inflation and unemployment.
Under most sets of assumptions used in earlier contributions,
such as those of Friedman (1968) and
Mortensen (1970a). the long-run Phillips curve is vertical. However, under
the assumptions used by Lucas and Rapping (1970), the relation between
inflation and unemployment is ambiguous in both the short run and the long
run, although the relation betwecsn both employment and nonparticipation
and inflation is unambiguous in both the short and long runs. The results on
inflation and unemployment
differ from those obtained by Lucas and
Rapping. In section 5. I summarize the results.
2. Summary of the individual model
The individual derives utility from consumption and leisure. Consumption
at any moment t, denoted C(r), is nonnegative and measured in goods per
week, Leisure is all time not spent in labor and job search. The rate of
leisure at any moment t. measured in hours per week, is 168 -L(f)S(t),
where 168 is the number of hours in a week and L(r) and s(t) are the rates
of labor and search at moment t, measured in hours per week. Labor is time
spent working on a job, and job search is time spent looking for a higher
paying job than that currently held. The rates of labor and search, and also
the sum of these rates, must be between zero and 168.
The assumption
that the individual gets utility from consumption
and
leisure implies that his utility depends only on C and the sum L + S, and not
on the sizes of the individual terms L and S. Consequently, utility at time r
J.J. Seutcr. Utility
muximizntion
6X9
can be expressed as U[C(t),L(t)+
S(r)]. I assume that C: is concave in
consumption and leisure, is additively separable in C and L + S, and satisfies
the usual Inada conditions; thus:
c’, >o,
U,
u2 <o,
L’zz co.
c’,2=&*
-0.
lim C,=+
(‘_-0
lim
(,+ :‘-a*
* -=o,
Y.
lim U, =c).
(’ * I
Lr2=0.
The indi\tduiri’s
lim
Lrz= - x.
I.+S--lhn
lifetitne budget constraint.
as perucited
by him at time T.
IS
d
.4(r)
it L i
I’*
-4(r)+cr.(f’
1
=;
P
I,
L(f)--C‘lf).
(1 1
Au-)=.-I,.
(2)
.4(D)=O,
(3)
.4(t ) =espected total assets at time t. measured in current dollars,
r* = the expected real interest rate at time 1. which equals
intcrest rate r minus the expected rate of inflation rr.
I’*=).--
the
nominal
.
and which in the ahsencc of inflation is assumed by the individual to
be constant.
\\*(II = the expected notninal hourly wage rate at time r, measured in current
dollars,
It==the expcctcd price of consumption
goods at time 1, which in the
absence of inflation is assumed by the individual to be constant.
7’= the present moment.
D = the moment of death, known by the individual.
,4,- = the initial value of assets, known by the individual.
assume that all assets are inside. cariable interest rate assets earning the
current market rate. I’.
The individual has some control oier the future value of his wage through
job search. Assume that:
1
B
J.J.
690
Seater.
Utility
nwxinrization
(a, There is a distribution of nominal wages over vacancies, denoted
S* be the density function associated with F*:
F*. Let
(b) The individual has a perception, denoted by F, of F*. Let -1‘ be the
density function associated with F.
(c) The individual adjusts F to F* with a lag. I leave the precise method of
adjustment unspecified.
(d) The individual’s nominal wage will not change unless he searches.
(e) The lndividual must accept or reject an offer as soon as he receives it.
(f) Similarly, if the individual quits his job, he loses all rights to it; should
he later want to return to it, he would have to compete with other
applicants for it.
(g) There is no cost to changing jobs.
(h) The only costs of search are foregone leisure and foregone earnings.
At any moment t, the rate at which the individual contacts vti:.ancies is a
function of the rate of search at moment t. Let N be this function, so that at
any moment the rate of contact is N[S(r)]. which has the units of vacancies
per week. Other possible arguments of N. such as the vacancy and
unemployment rates or transportation
technology, are suppressed. I assume
that I&’is concave in search:
N’(S)>O,
N”(S)<O.
and that N’ has the following limit properties:
lim N’(S)= + Y,,
S-O
lim !V’(S)=O.
s-+1
Under these assumptions, N’ is bounded away from zero for Ss 168.
Suppose an individual earning wage MI(~)decides to look into a vacancy
chosen at random. His estimate of the probability that he fails to improve his
wage is F[w(t)J. Suppose the individual searches for a length of time At, and
suppose N[S(t)J is constant over At. The total number of vacancies the
individual can conta,ct is N[S(t)]At. His estimate of the probability that he
will fail to improve his wage during the entire period Jr is
Denote
the density
function
associated
with (F[r~(t)])“l”“‘l“’ by js,,,[~(~
)].
J.J. Seater, Urility
maximizution
69 I
At time I, the expected improvement in the wage over the period dt. denoted
WWl, is
ECdw(t11=S~,r,Cw-w(t)l~.,,,(o)d~~
=j::,,,(l- [F(w)]Ni”“‘ld’
do ,
where G is the maximum wage attainable. The expected rate of change of
w(t) at time t, denoted E[r+(t)], is obtained by taking the appropriate limit as
dt goes to zero:
E[G(t )] = -N[S(t)]S~,,,lnF(o.,)dwhO.
I define
E[W )] = g[w(t), S(t)],
(4)
where
g&O,
g,,.2:0,
-
g&O*
gs, 5 09
g,,, 50.
Relation (4) is the individual’s best estimate of the ftiture rate of nominal
wage improvement. I assume that the individual treats it as the rate that
actually will occur and write’
The rate of change of real wages is simply’
g[H’(f).
SW]
N
-_n.
sip=1
d
w(t)
[
P
P
(5)
The individual’s utility over his remaining lifetime is3
(6)
J’:!U[C(t),L(r)+S(t)]dr.
‘This assumption implies certainty equivalence and Ignores behavior toward risk. In m) I
earlier paper (19771. I discuss the implications of this assumption and also show by an indirect
method how some of the stochastic elements of the individual’s maximization
problem can be
analyzed.
‘I assume rhar the rate of wage inflation
why R appears in (5).
always equals the rate of price inflation.
which is
‘Insertion into (6) of the usual discount factor e -” would not alter the results substantially.
However, when the time horizon IS hnown and finite. the discount rate neither is needed to
guarantee existence of the integral nor has the natural interpretation that arises when the time
horizon is infinite.
J.J. Seater, Utility
692
maximization
The individual’s problem is to maximize (6) subject to his budget constraint -.given by (l), (2), and (3)-and his real wage i,- lprovement constraint - given
by (5) together with the initial condition
W(T)=W,,
(7)
where M”~is known by the individual. The solution, or optimal control, is
obtained by applying Pontryagin’s maximum principle. The Hamiltonian is
A(t)
+ j&(t) __-____._
gCJ4f), w )I
w
_
P
P
(
L
)
w(t)
r* -j--+---j-
H=U[C(t),L(t)+S(t)]+9(t)
71
L(f)-C(t)
1
.
If a control is optimal. then
A(r) W(f)
_d A(t)
-...- = ?H
-_ = r*----+-L(t)-C(r),
cl)
dt P
P
P
.Y
.dj.(Il=
dt
An optimal
furthermore.
(11 I
=(-rH= -IL(f)L(r)-E.(t)(R,~[M,(1),S(f)]-~).
;(\yp)
control also must satisfy initial conditions
by the transversality cc>ndition, it must satisfy
(2), (3). and
/.( D ) = 0.
Finally. an optimal control must satisfy the following marginal condiiions:
(7);
(12)
J.J.
Seder,
Utility maximization
693
The Inada conditions imply that consumption and leisure always will be
positive. Consumption
continuously
rises such that the marginal utility of
consumption falls at a rate equal to r.
Because UL = Us = U2, equality in both (14) and (15) would imply that
However, the left side of (16) is bounded away from zero, so equality cannot
be attained for small values of \): ;ln particular, for M’equal to zero). In such’
cases, L is set equal to zero and S is positive. Thus in the early part of his
life, when \V is very low. the individual specializes in search (but still takes
some leisure).
When the individual is not working, (14) holds as an inequality. Relations
(13) and (15) hold as equalities; totally differentiating
then yields the
following implicit functions:
C=C($,,
f-1
S= S(i.
I+
(17)
iv).
N-- 1
(18)
where the sign ander a variable is the sign of the partial derivative with
respect to that variable. Small changes in +, i.. and 1%.have no effect on L. so
its partial derivatives are all zero.
A positive value of S implies growth of \v. As \V grows, equality tends to
come about in (16); but until it does, L remains equal to zero.’ At the
moment T* that ( 16) begins to hold as an equality, so does ( 14) and L
becomes positive, Relations (13).( 15) now ali hold as equalities and yield the
following implicit functions:
C-C(t),.
t-1
(19)
“This raises a complication
needing explanation.
It is clearly sensible t3 talk about the
indlvidtldis wage growmg when he is working. However, when the individual IS searching but
not working. he earns no wage. What sense. then. is there in talking about wage growth?
Consider an individual at‘ initial time T formulating
his optimal plan. Suppose he plans to
commence work at time T* and at an expected wage of w(T*). Consider a time T’ earlier than
TV. The wage w(T’I is the expected value of the wage the individual could earn if he followed
the same pattern of search but commenced work at i’:rne T’ instead of T*. Clearly, w(T*)
exceeds w(T’). It IS in this sense that the wage grows when the,individual
is searching but not
working. For further discussion. see my earlier paper (1977).
J.J. Seater. Utility
694
L= L (tj, i..
maximixtinn
M’).
(+w--I(+)
s=s
($b, i., M’) ,
(11)
c-)(+)(-4
L+S=(L+S)
($, M’).
(+)(+)
(22 )
Two regions have been defined :
Interior: Relations (13). (14), and (15) all hold as equalities, and C, L. and S
are all positive.
L=O Corner: Relation (IS) is a strict inequality and L =O; C and S are
positive.
There is no region in which S equals zero, so that the individual always
searches. Furthermore.
the individual never stops working once he has
started: in particular, he never retires. These results arise from the absence of
differential costs in the model. To make labor force nonparticipation
possible. consider a particular
differential cost a restriction
on hours
worked.
So far, the individual has been able to work any number of hours bctwecn
0 and 168. A consequence is that the individual nevzr sets both I. and S
equal to zero at once and therefore never is a labor force nonparticipant.
In
reality, however, most jobs require that an individual work some minimum
number of hours. For convenience, I take this minimum to be uniform at 40
hours because that seems to be about average. However, any number will do.
It is only the existence and not the value of the minimum that matters. This
restriction on hours worked makes retirement and nonparticipation
in the
labor force possible. It also leads to natural. precise definitions of cmployment, unemployment. and nonparticipation.
So assume now that the individual cannot work less than 40 hours a
week: if he supplies less than 40 hours of labor, no one will hire him. In
addition. assume that if an individual holding a job decides to supply less
than 40 hours of labor per week. he loses his job and his wage becomes zero.
For simphcity. continue to assume that the individual can work any amount
over 40 hours.
Under these assumptions, the wage earned depends on the number of
hours of labor supplied. Let I
be the wage rate associated with a terrain
job but which will be paid only if the individual works at least 40 hours a
week. Thc;n the wage actually earned, denoted M’,,is
N+,(t)=
i
n(t)
if
L(t)240
0
if
L(t)<40.
J.J.
Srarrr,
Utility
muximization
695
The model of individual behavior is changed somewhat by the presence of
the restriction on hours worked. The Hamiltonian becomes”
(
r*$+-(y
H=U(C,L+S)+l)
and eqs. (12~(
IS)
P
NJ
--_71
‘r
,
P /
become
A(t)
M’,
=r* -p--+-,-L(r)-C(t),
‘0
)I M II
= g[H’O
._- ._-.1.S(r
_--____
P
The original endpoint
(13) (IS) become
U,.=$(t
g(w,S)
)(
+;1
conditions
P
(2).
’
(3 ).
1.
(9’)
(7). and (12) still hold. Relations
(13’)
Suppose ~(r ) were large enough to satisfy (14’) as an equality if there were
no restriction on hours worked. The equality relation represents what the
individual would like to achieve: it is the relation that would m.lximize his
When the restriction on hours
utility in the absence of the constraint.
worked is present. however, equality in (14’) cannot always be attained-in
particular. whenever the individual would like to work a positive amount less
than 40 hours. The individual then must choose between working 40 hours.
which is more than the unconstrained
optimum. and not working at all.
which is less than the unconstrained optimum.” In either case. his utility is
‘The pertinent expression for making this choice is
ILrr,~~.:CI:!t!..S,rr)l-_C’[Clrl.JO+S,(rl]
40
where S,(r 1 is the amount of search that would be undertaken if L(t) were set equal to zero and
S?(r) 15 the amount of search if L(r) were set equal to 40. If the left side exceeds the right. the
individual bets L(t) equal to 40; if the right side exceeds the left. the individual sets L(r 1 equal to
0: and If the two sides are equal. he is indifferent between haling L(t) equal 40 and 0.
J.J. Seater, Urilit~
696
maximietition
less than in the unconstrained case. Also, (14’) is satisfied as an inequality. As
long as labor is positive, :arch is positive, too; when labor is zero, search
may be positive or zero. 6 Thus there are four possible states the individual
can be in:
Interior: L 2 40, S > 0. The hours restriction is not binding, and ( 13’)-( 15’) are
satisfied as equalities. The individual’s behavior is described by (19)-(22).
Type 1 Corner: L =40, S >O. The hours restriction is binding, and the
individual chooses to work. Small changes in +, i,, and w have no effect on
L, so the partial derivatives of L all are zero. Relation (14’) can be ignored
and the resulting system of (13’) and (15’) give the implicit functions (17) and
(18).
Type 11 Corner: L --0, S > 0. The restriction on hours worked is binding, and
the individual chooses not to work now but plans to work later. As at the
Type I Corner, L is not affected by small changes I,$, i.. and W, and eqs. (17)
and (18) again apply.
rvpe 111 Corner: L =0, S =O. The restriction on hours worked is binding,
and the individual chooses not to work now or in the future. Neither L nor S
is affected by small changes in 1(1,E,, or W; and all the partial derivatives of
both L and S are zero. Relation (14’) and (15’) can be ignored, and relation
(13’) gives ( 17) as the implicit function for C.
Solution of the individual’s problem provides optimal paths for C. L, and
S; together, these paths constitute the individual’s optimal plan. Should there
be unanticipated exogenous changes in the value of a parameter or variable.
the individual must formulate a new plan.’ The following equations show the
direction of the initial changes in C, L, S, and L + S in response to sew-al
exogenous changes for an individual in the interior?
CE=CE
‘The
indrvidual
(,4,
r--II,
N,
if.
p)
+
+(--I
+
+(+I
-
(23)
sets both L and S equal to zero (i.e., retires from the labor force) if and lmly
if
maxjyL[C,(r),
O]dt 2 max
j:’ b’[C~f).L(r)+ S(r)]dr,
where the maximum on the left side is taken over all paths of consumption (‘,, consistent HIIII
endpoint condition (3) mhen L and S are zero from T’ to D and where the maximum on the
right side is taken over all paths of C. L. and S consistent with (2). (3), (7). (8’). (1 I’) and (12). In
the absence of the hours restriction. the above inequality cannot be satisfied because the
individual always finds it worthwhile to devote at least a small amount of trme to labor and is
allowed to do so.
-One can think of the individual as making a new plan at every instant. If at time T all
variables have changed as anticipated at time T - dr, then the plan chosen at time T coincides
on the interval [T. D] with the plan chosen at time T -dr.
However. if some variable has
changed in an unanticipated way, then the plan adopted at Twill differ from that adopted at
7-- dt.
*See my earlier paper for the derivation of these relations.
J.J. SPuter. Utilif!, maxinlixtiorl
f!=L!
(.4,
-
s”=s”
I’---,
N,
~7,
p)
-
?(?,
?
-(+)
(A,
-
(L+S)“=(L+S)”
N.
r-Jr
-(+)
--(+I
(A,
-
r-;L.
-(+)
697
(24)
..
p)
N,
-
\r.
?(?)
?;‘-,?
(25)
p)
+
(26)
where
(0 the sign under a variable is the sign of the partial derivative with respe,-t
to that variable;
(ii) The variable N signifies all changes in the function N that change the
values of N[S(r)] and N’[S(r)] in the same direction; the sign outside
parentheses assumes dominance of the income effect of such changes and
the sign inside parentheses assumes dominance of the substitution effect;
. ..
(111)the sign under r - n outside parentheses assumes dominance of the
income effect of changes in r -n and the sign inside parentheses assumes
dominance of the substitution effect;
(iv) the sign under w outside parentheses is the result for an equiproportional change in all wages when the individual correctly perceives that
wages other than his own have changed, and the sign inside parentheses
is the result when the individual believes that only his own wage has
changed.”
The superscript
E’s are a reminder that the results shown pertain to
exogenous changes in the variables in question.
Note that when the individual is in a corner, some of the changes
indicated in (23H26)
may not occur. For example, suppose the individual is
in the Type II Corner when his assets unexpectedly fall. The individual has a
tendency to increase his labor, as shown by the negative sign under A in eq.
(24). However. in order to increase his labor at all, the individual must
incrcasc it to at least 40 hours a week. He may not be willing to do this and
consequently may continue to supply no labor at all, in which case L(T) will
not have been affected by the change in A(T). Similar results hold for labor
in the Type I and Type III Corners and for search in the Type III Corner.
Thus, for any pivcn indi\,idual in a corner, the effects described by (23). (26),
tend to csror but these effects may not be realized if their realization requires
“When the individual correctly perceives that wages other than his own have changed
equiproportionally
to his own, he perceives no change in the position of his nominal wage
relatrve to other nominal wages. whereas when the individual does not percelke that other wages
have changed. he does perceive a change in the relative position of his nominal wage. The
individual’s perception of his returns to search depends on the relatke position of his nominal
wage. SO it is necessary to distinguish between the two cases.
698
J.J. Seuter, Utility
masimizntinn
moving across the boundary of a corner. However, if we consider the total of
all individuals in a particular corner, it seems safe to assume that an
exogenous change that tends to push individuals across the corner boundary
in fact will do so for some individuals, Thus if we consider a ‘representative’
individual, functions (23)-(25) should apply.
Note that if individuals are assumed to maximize income with leisure time
fixed, the model reduces to that of Siven (1974), which is a continuous time,
variable search and !abor version of the McCall (1970)-Mortensen
(1970b)
model. If instead individuals are assumed to engage in no job search, the
model reduces to that of Friedman (1968) and Lucas and Rapping (1970).
Thus the model developed above is quite general and contains most earlier
models as special cases.
3. Aggregate behavior
The foregoing model yields natural
ment, and nonparticipation:
definitions
of employment,
unemploy-
(i) Employmen?: L >O, S ~0. An individual is employed if he is either in the
Interior or the Type I Corner.
(ii) Unemplo_rment: L=O, S >O. An individual is unemployed if he is in the
Type II Corner.
(iii) Nortparticiparion: L=O, S =O. An individual is nonparticipating
if he is
in the Type III Corner.
Aggregate employment, unemployment, and nonparticipation
are simply the
collections of all employed, unemployed, and nonparticipating
individuals.
respectively.
In this section, I examine the qualitative
responses of employment.
unemployment.
and nonparticipation
to various exogenous shocks to the
economy. The procedure is first to examine the effects of a shock on
individuals within each state and then to sum over states to obtain the net
aggregate impact of the shock on each state. This procedure treats labor
market phenomena
as strictly supply determined;
demand is ignored.
Undeniably, such a procedure is deficient. However. this deficiency is shared
by virtually all papers in this field; they, too, treat the aggregate labor
market phenomena
as supply determined.“-) Because the purpose of the
‘“See Friedman (1968), Gronau (1971). Lucas (1971. 1973). and McCall (1970). for example.
Lucas and Rapping (1970) mention demand. but do not use it in their analysis of the Phillips
curte. Mortensen (197Oa) is the only author to attempt a genuine full analysis of the labor
market. However, his demand side is flawed in several ways. and in any case, employment still
turns out to be supply-determined.
Moreover. the restrictions simplified by Mortensen’s
formulation of labor demand apparently do not alter the qualitative behavior of employment.
unemployment. and nonparticipation.
J.J. Srotcr.
G’iilirj,mffrim
xliorl
699
present paper is to synthesize the earher contributions and then examine how
their results depend on their particular assumptions. I make no attempt to
extend the analysis in the direction of including demand; I confine myself to
examination
of supply. Inclusion of demand would be a worthwhile
extension.
.r
An exogenous change may hate different effects in the early and later
periods of individuals’ lives. For example. an increase in the interest rate may
cause individuals to increase their labor supply in the early period of their
time horizons but to reduce it later. I confine my discussion to the earlier
period. W’irhirl this early period. I will distinguish between long and short
runs. during which certain adjustments have or have not taken place. The
adjustments concerned will be clear from context.
Subsections 3.1. through 3.h. contain a detailed analysis of certain exogcnous shocks of interest in examining the Phillips curve; the results are
collected and discussed in subsecticjn 3.7.
Because ali assets are inside. there can he no changtz in aggregate asvzt
holdings. Assuming that creditors and debtors are equally distributed among
emp,loyment. unemployment. and nonparticipation.
there are no asset effects
on the three states of participation.
’
_3._.
Sowimd
raft' (?I illic*rcW t
Suppose that I’ falls at time T and
rate I** falls. Because all wealth is
cflects. Ho\vc\er. there are aggregate
that individuals increase C( 7’) and
The effects on the apgrcgate states of
x is unchanged. so that the real in+e&.est
inside. there are no aggregate income
substitution effects. Eys. (23) -(Zh) shou
decrease L( T1. S(T). and L(T) + S( T 1.
participation are as folhwvs:
(il Employed indiiiduals reduce both labor and search. They may continue
to suppYy enough labor to remain employed. may reduce labor en!.qh
to become unemployed:
or may reduce labor and search enough to
become nonparticipatinp.
On average. there will be people reacting in
each of these ways so that wme people shift from employment
to
unemp1oymcnt and nonparticipation.
(ii) Unemployed individuals reduce time devoted to search. They may keep
search positike and remain unemployed. or they may stop searching
altogether and become nonparticipating.
On average. some people shift
from unemployment to nonparticipation.
(iii) Nonparticipating
individuals have no tendency to increase either labor
or search and therefore remain nonparticipating.
There is no shift out of
nonparticipation.
The net results are a decrease in employment, an ambiguous change in
unemployment, and an increase in nonparticipation.
from
arises
of unemployment
in the response
The ambiguity
and nonunemployment’s
being a ‘middle‘ state between employment
participation.
Changes which cause some people to enter unemployment
from employment also cause some people to leave unemployment for nonparticipation.
This same ambiguity in the response of unemployment
will
arise in most of the subsequent exogenous changes to be examined.
The results for an increase in I’ are not merely reversals of those for a
decrease. Although individuals may leave employment instantly, they cannot
enter it instantly; they must spend some time searching for a job. Consider
the immediate effects of an increase in I’.
(i) Employed individuals increase their labor supply and therefore
employed, There are no shifts out of employment.
remain
(ii) Unemployed individuals increase their search and desire to increase
their labor. The increase in search means that no unemployed people
become nonparticipating.
The desire to increase labor means that
unemployed individuals want to start work sooner than before the
increase in r: however, in the first instant. none of them can start work
because they have not yet found jobs. Therefore, at the initial instant
that r increases, there is no shift out of unemployment
into either
employment or nonparticipation.
(iii) Nonparticipating
individuals may remain nonparticipating
or may commence searching and become unemployed. Like unemployed individuals,
they do not become employed immediately because search is required to
obtain
employment.
There is a shift from nonparticipation
to
unemployment .
The initial results are no change in employment, an increase in unemployment. and a decrease in nonparticipation,
However, as soon as time begins
to pass, the flow from unemployment to employment increases because of the
increased desire of unemployed individuals to commence work. This increased flow tends to reduce unemployment.
Eventually, the equilibrium
levels of employment.
unemployment,
and nonparticipation
are reached.
Employment
will be higher than before the increases in I’, and nonparticipation will be lower. The change in unemployment will be ambiguous,
depending on the relative magnitudes of the initial shift into unemployment
from nonparticipation and the total flow out of unemployment into employment. These final results are the opposite of those for a decrease in r.
A\suming that the new equilibrium levels of the three aggregates are reached
L)uickIy. these final results can be considered the aggregate effects of an
increase in I’.
J.J. Serrw. I'filifvnmxirnixtion
701
Henceforth, 1 examine exogenous changes in one direction only. The final
results for changes in the opposite direction are always exactly the opposite.
although
the paths followed may not be simple reversals of each other.
Changes in the complicated g function can arise in many ways and can be
quite difficult to analyze. I discuss only two of them. The first kind arises
from changes in the function IL’ such that both N[S(r)] and .%“[.S(r)]
increase for all values of S(r) .. in other bvords. from any change that
increases both the number of vacancies and the marginal number of
tacancies that an individual can contact with a given z:mount of search. An
improvement in information or transportation
technology ~;.~rlld be such a
change. The second kind of change arises from an equiproportional
increase
in all images; such a change ‘expands the density function of tvages ,f’*. I
discuss the second kind of change in the next subsection.
Suppose .4,’ changes such that ,V[Slt )] and .Y’[S(r )] both increase. The
aggregate effects are the following:
(i) Some employed individuals, perceiving an incre;ise in the return to
search relative to the return to labor, may quit work to search for a
better job and thereby become unemployed.’ I There is a shift o\;t of
employment to unemployment.
No one becomes nonparticipating.
t,f
course, because to do so would make it impossible to capture the
benefits of the change in S.
(ii) Unemployed individuals remain unemployed. Like employed individuals.
they do not become nonparticipating.
They do not become employed
because their wage is still zero. There i:re no shifts out of
unemployment.
(iii) Nonparticipating
individuals may be induced by the improved returns
to search to become unemployed. Like unemployed individuals. they do
There is a shift from nonparticipation
to
not become employed.
unemployment.
The net results are a decrease in employment, an increase in unemployment.
and a decrease in ilonparticipiltion.
One could argue that these results are not the final ones. The change in 3’
mukcs it easier to find a job paying any given wage rate. Therefore, does not
the change in N reduce the duration of unemployment. implying Ibat as time
begins to pass the flow from unemployment to employment increases. leaking
and unemployment
amthe final new equilibrium
le\,els of employment
biguous’? It is true that the change in N makes it easier to find a job paying
any given wage: ho\vever, as P have shown in my earlier paper. the change in
.V also induces people to increase their acceptance wage. which tends to
increase the duration of unemployment. The net change in the duration of
unemployment is ambiguous. For simplicity, I assume tlxre is no change in
the duration of unemployment so that the results of the preceding paragxph
are the final results of a change in N.
Suppose there is an equiproportional
increase in all nominal wages. The
reactions of employment, unemployment.
and nonparticipation
depend on
whether or not individuals perceive the general nature of the wage increase.
Suppose first that they do.
41) Employed individuals perceil e equiproportional
increases in their real
’
,’
Some
employed
individuals probably
\vage and real returns to search.
would be induced to lea\-e employment for unetnployment. but it seems
safe to assume the number of people so induced to bc negligible. No one
becomes nonparticipating
because to do so would make it impossible to
capture the benefits of the wage increase. There are no shifts out of
employment.
(ii) llnemployed
individuals percei1.e an increase in their real returns to
search. Whether untmplqed
individuals increase or decrease their
search time is ambiguous because of income and substitution effects:
but. as I ha1.e argued irl ml- earlier paper. the duration of unemployment
can be expected to fall becau>e of the increased attractivcncss of holding
a job. Ho\ve\-er. unemployed indil,iduals do not become employed
immediateI>- because their own ~.age is still zero: an 1. like employed
individuals. they do not become nonparticillatiny.
There are no shifts
out of unemploxnient.
(iii) Nonparticipating
indi\,iduals also percei\,e
an increase
in their
real
returns to search and may become unemployed.
Like unemployed
individuals. they do not hccomc rmplo!~cd immcdiatcly. Thcrc is a shift
from nonparticipation
to unenip~oymcnt.
The initial results arc no chanpc in emplo~mcnt. an increase in uncmplo>ment. and a decre;r?;c in nonpal.ticipation.
As time passes. howcvcr. there is
an increased fiou from unemployment
to employment
because of the
decreased duration of unemployment. Consequently. employment ultimately
J.J. Secrtrr. L’tiliry
maximi.xrtion
703
rises. Whether unemployment
ends up higher or lower than before the
equiproportional
increase in wages is ambiguous because of the shift into
unemployment
from nonparticipation.
Therefore, the final results are an
increase in employment,
an ambiguous change in unemployment,
and a
decrease in nonparticipation.
Now suppose individuals perceive only the increase in their own nominal
wage.
(i) Employed individuals perceive an increase in their real wages and a
decrease in their real returns to search.13 They remain employed. and
there is no shift out of employment.
(ii) Unemployed individuals feel no impact of the wage increase because
their own wage of zero is unchanged and they perceive no change in
their returns to search. They are completely unaffected by the wage
increase initially, and there is no shift out of unemployment.
(iii) Nonparticipants
are in the same position as unemployed individuals.
There is no shift out of nonparticipation.
The initial results are no changes in employment. unemployment,
or nonparticipation.
However, as time begins to pass, two things happen. First,
people engaging in search experience unexpectedly high wage offers. Not
knowing that all wages have increased equiproportionr-illy and that the wage
distribution has been expanded, they belie1.e these wage offers to be relatively
high in the wage distribution and to be a ‘once in a lifetime’ bit of good luck.
Some unemployed people accept employment earlier than they had anticipated,
thereby
increasing
employment
and reducing
unemployment.
Second, people begin to learn of the equiproportional
increase in wages and
the increased returns to search. As this happens, the aggregate results
approach those of the case where people perceived the increase in all wages
immediately. Once perceptions have caught up to reality, the results for the
two cases are the same. Employment is higher, the change in unemployment
is ambiguous, and nonparticipation
is lower.
First suppose the price level rises once and for
returns to search are reduced equiproportionally,
same effects on participation
as if it were caused
decrease in all nominal wages. Employment falls.
ment is ambiguous, and nonparticipation
rises.
all. Real wages and real
This reduction has the
by an equiproportional
the change in unemploy-
lJln this cast. Individuals perceive no rxpanswn of the distnbution
F. Consquentl~.
eack
individual pcrcelvc~ an increase in his norn~nal wage relative to all others; this reduces the
return to search. as can be seen from (5 t.
704
J.J. Seater. Utility nmirnization
Now suppose there is an equiproportional
increase in all prices and
nominal wages. It seems reasonable to assume that the individual perceives
immediately the increase in his own nominal wage, if he is earning one.
However, he may or may not perceive immediately that all other wages have
risen by the same proportion
as his. He also may or may not perceive
immediately that the price level has risen, There are four possibilities to
consider. Individuals may perceive at the instant they occur:
Case (a ). Both the increase in the price level and the increase in nominal
wages other than their own. Perceived real wages and returns to search are
unchanged. and there are no changes in employment, unemployment,
or
nonparticipation.
CUW (6). Neither the increase in the price level nor the increase in nominal
wages other than their own. The only people to feel any immediate effects
are the employed. They immediately perceive the increase in their own
nominal wages: because they do not immediately perceive the increase in the
price lev,el. they perceive the increase in their nominal wages to be an
increase in their real wages. Consequently, there are no initial changes in
employment, unemployment.
or nonparticipation.
As time begins to pass,
two things happen. First. people engaged in search begin to receive unexpectedly high nominal wage offers. This inducts an increase in employment
and a decrease in unemployment.
Second, everyone begins to learn of the
equiproportional
increase in nominal wages and prices. Assume that all
participants revise their perceptions of wage and price levels at an equal rate.
Then it is reasonable to assume that nonparticipants
revise their perception
of wage levels more slowly than their perception of prices. Presumably,
nonparticipants
engage in as much consumption. on average, as participants;
therefore they acquire information on prices at the same rate as participants.
However. nonparticipants
engage in no search and acquire information on
wages more slowly than participants. Consequently,
during the period of
adjustment of perceptions, nonparticipants
perceive real wages to be 10~s.~
than before “the equiproportional
increase in nominal wages and prices,
Nonparticipants
therefore will have no incentive to leave the state of
nonparticipation.
and as a result nonparticipation
will not be affected by the
equiproportional
change in wages and prices, Eventually, everyone’s perceptions catch up to reality. and employment and unemployment
return to
their original levels.
Cuss 1~). The increase in the price level but not the increase in wages other
than their own. Employed individuals perceive no change in their real wages.
All individuals perceive a decrease in their real returns to search. Employed
individuals perceive that the real return to work has risen relative to the real
J.J. Sratrr.
Utility
nwxin~i~ution
705
returns to search: presumably,
they remain employed. Unemployed
individuals perceive only the decrease in the real returns to search, and some
become nonparticipants.
Nonparticipants
remain as such. Therefore, there is
initially no change in employment, a decrease in unemployment,
and an
increase in nonparticipation.
As time begins to pass, individuals engaged in
search receive wage offers higher than expected and accept employment
sooner than planned. Consequently,
employment rises and unemployment
falls still more. Eventually, however, people learn that wages have risen by
the same proportion as price; emplot-ment and unemployment return to their
original levels.
Case (d). The increase in wages other than their own but not the increase
in the price level. Before perceptions adjust, the effect is as if only nominal
wages were increased. As explained in section 3.4. the result is an increase in
employment,
an ambiguous change in unemployment.
and a decrease in
Once people learn of the increase in the price level,
nonparticipation.
employment, unemployment,
and nonparticipation
return to their original
levels.
Suppose there is an increase in the expected rste of inflation IL If t!le
nominal rate of interest I’ adjusts fully and instantaneously
to changes in T: so
that the real rate r* remains constant, then there are no effects on anyone’s
behavior. Consequently, there are no changes in employment, unemployment,
or nonparticipation.
Suppose instead that r dots not immediately make full
adjustment to changes in IL Then I * MS when 71 rises. As explained in
section 3.2, the result is a decrease in employment, an ambiguous change in
unemployment, and an increase in nonparticipation.
Consider now an increase in the actual rate of inflation z*. Initially.
people’s perceived rate of inflation II lags behind R*, so that people
continuously
experience unexpected increases in all prices and nominal
wages. The results for employment, unemployment, and nonparticipation
are
the same as when the levels of prices and wages unexpectedly increase once
and for all. as described in subsection 3.5. Thus if individuals perceive at the
moment they occur:
(a) Both the increases in the price level and the increases in nominal wages
other than their own, there will be no effects on employment, unemployment, and nonparticipation.
(b) Neither the increases in the price level nor the increases in nominal
wages other than their own, then at first employment rises, unemploy-
ment falls, and nonparticipation
is unchanged; ultimately employment
and unemployment return to their original levels,
v-1 The increases in the price level but not the increases in wages other than
their own, the results are as in case (b) above, except that nonparticipation increases.
wages other than their own but not the
Id) The increases in nominal
increases in the price level, then at first employment rises, the ‘change in
unemployment
is ambiguous,
and nonparticipation
falls; ultimately,
employment, unemployment and nonparticipation
return to their original
levels.
If the actual rate: of inflation IT* gradually increases f.om an initial level to
level. the results are again the same as for a once and for all
increase in the levels of wages and prices.
a higher
3.7. Summary
The following equations
changes analyzed above:
summarize
the net results
of the exogenous
EM=EM(W, p. zv,r-71).
+--
(13)
UE = C;E(w, p,N, r-n),
? ‘? +
?
(14)
NP=NP(w. p, NJ-71),
-++
(151
where EM, C’E, and NP stand for employment, unemployment,
and nonparticipation and where changes in variables are assumed to be in the same
direction and proportion for all individuals.”
The most striking thing is the almost complete ambiguity of the behavior
of unefnploymcnt;
only improvements in the search process. through the N
function, have definite effects on unemployment.
The reasons the nther
changes have ambiguous effects is that unemployment
is a ‘middle’ state
between employment and nonparticipation;
changes which cause people to
leave unemployment
for employment
also cause other people to leave
nonparticipation
for unemployment,
and vice versa. The change in unemployment is ambiguous as a result. Note that the ambiguity in the behavior
of unemployment does not arise from any income or substitution effects. For
“Note
that (13H15)
give the final results only; temporal patterns are suppressed. For
increase in all nominal wages and prices
are the same irrespective of how people initially perceive these challges, whereas the temporal
patterns of EM. L’E. and .VP do depend on initial perceptions.
example.the ultimate results for an equiproportional
J.J.
Serrtcv. L:tilrt\.
mtl.rimixtion
707
example, the ambiguity arises whether one assumes dominance of the income
or substitution effects of wages. These results are not found in the earlier
literature. Earlier models. by not allowing the individual to choose his labor.
search, and leisure simultaneously and vary them continuously, were able to
define only two states of participation - either employment and unemployment, as in Mortensen (1970a). or employment and nonparticipation,
as in
Lucas and Rapping (1970).‘” There is no natural third state of participation.
obviously making it impossible for unemployment to be a middle state and
have the characteristic ambiguities of a middle state.
4. The Phillips curve
Recent microfoundations
models of the Phillips curve can be divided into
three groups. First. these models can be divided between those that assun:~
the individual to be an income maximizer whose leisure time is fised and
who does engage in search (Group I models)‘h and those that assume the
individual to be a utility maximizer whose leisure time is \,ariable but who
does not engage in search. This latter group can be divided between those
models in which the individual is concerned with current wages on1y (Group
2 models)’ _1and those in which the individual speculates on the future levels
of wages (Group 3 models).”
Phillips curves arise in these models when
certain assumptions are made about individuals’ perceptions of the levels and
rates of change of prices and nominal wages.
In this section. I examine what happens when these same assumptions are
applied to the more general model de\,eloped in this paper, which contains
the earlier models as special cases (see section 2). This exercise confirms the
results of the Group 1 models and therefore strengthens them by obtaining
them in a more general framework. modifies the results of the Group 2
models and therefore makes them more precise, and contradicts some of the
results of the Group 3 models and therefore corrects those resulth. As kvill be
seen quickly, all results are evident from the discussion in section 3.
708
J.J. Seater.
Utility
mtr.ximi:atiou
4.1. Group I models
Assume as in the Group 1 models that changes in individuals’ perceptions
of nominal wages other than their own lag behind changes in nominal wages
themselves. The analysis can be divided into two cases, depending on how
the individual is assumed to perceive changes in the current price level. It
may be assumed that the individual perceives immediately any change in the
current price level, or it may be assumed that his perceptions lag behind.
(The models of Group 1 make neither assumption, ignoring altogether the
problem of how people perceive changes in the price level. These models can
do SO because they assume people are income maximizers. Changes in the
price level affect real income, but real income is maximized if and only if
nominal income is maximized; and nominal income is independent of the
price level. Consequently, an income maximizer’s behavior -in particular, the
amount of search he undertakes -is independent of how he perceives the
current price level. Because employment and unemployment are assumed to
be functions of the amount of search undertaken, they, too, are independent
of the individual’s price perceptions.)
As it turns out, the qualitative behavior of employment and unemployment, but not nonparticipation,
is unaffected by how the individual perceives
changes in the price level, which is a somewhat surprising result, as I explain
momentarily.
The first possibility - that individuals
immediately
perceive
changes in the current price level -is case (c) of the discussion in section 3.6;
the second possibility- that individuals’ perception of the current price level
lags behind the actual level is case (b) of the discussion in section 3.6.
In both cases, an increase in the rate of inflation at first causes an increase
in employment
and a decrease in unemployment.
I_lltimately, however,
employment and unemployment return to their original levels once people’s
perceptions have caught up to actuality. Consequently, an increase in the
rate of inflation reduces unemployment in the short run, which is the Phillips
relation; however, in the long run, unemployment is unaffected by the rate of
inflation so that the long-run Phillips curve is vertical. These results agree
with and therefore strengthen those of the Group 1 models; in particular, see
Mortensen ( 1970a).
It is interesting that the qualitative results do not depend on the accuracy
of people’s perceptions. As 1 mentioned above, it is natural that price
perceptions do not matter in the Group 1 models because of income
maximization. However, in the present model the individual is assumed to be
a utility maximizer whose behavior has been shown to depend on real
income and therefore on perceptions of the price level. Why does the
behavior of employment and unemployment not also depend how individuals
perceive the price level? The reason is that these two states of participation
are not functions of the amount of time individuals devote to labor, search,
and leisure. If people misperceive the distribution of nominal wages, they
receive unexpectedly high nominal wage offers, which induce them to acct’p,t
employment. They may work fewer hours if they perceive that the price level
has risen than if they think it has not; but they have a greater tendency to
accept employment nonetheless, and that is all that matters.
Assume as in the Group 2 models that changes in the individual’s
perceptions of the current wage and price level lag behind changes in the
current price level. Then as actual inflation causes the current wage and price
levels to rise, individuals’ perceptions of the current wage and price levels lag
behind. The behavior of employment, unemployment, and nonparticipation
depends on whether or not people fail to perceive that nominal wages other
than their own are rising as theirs are. (The models of Group 2 make neither
assumption, ignoring altogether the problem of how people perceive changes
in other people’s nominal wages. These models can do so because they assume
people do not search and therefore do not care about the distribution of
nominal wages.)
Ctrse (i). Suppose that individuals do not perceive immediately that nominal wages other than their own have risen. This situation correspor.Js to
cast (b) of the discussion in section 3.6.“’ People receive unexpectedly high
nominal wage offers; and at first, employment rises, unemployment falls, and
nonparticipation
is unchanged. Eventually, people adjust their Derceptions of
thl; levels of wages and prices to the true values. Employment and unemploym::nt return to their original levels. Consequently, an increase in the rate of
inMion
reduces unemployment
in the short run. which is the Phillips
relation; however, in the long run, unemployment is unaffected by the rate of
inflation so that the long-run Phillips curve is vertical. These results agree
with those of the Group 2 models; in particular, see Friedman (1968).
CNW (ii). Suppose individuals do perceive immediately that nominal wages
other than their own have risen. This situation corresponds to case (d) of the
discussion in section 3.6. People believe their real returns to search have
is
improved. At first employment increases, the change in unemployment
ambiguous, and nonparticipation
decreases. Ultimately. once peiceived and
actual inflation became equal again, employment. unemployment
and nonparticipation
return to their original levels. Consequently, in this case the
short-run effect of an increase in the inflation rate is ambiguous. There may
be the usual negative. Phillips-type
relation; there may be an unusual
positive relation: or there may be no relation at all. In any case, the long-run
result is a vertical Phillips curve. The short-run results differ from those of
the Group 2 models. The reason the short-run results in case (ii) imply that
both the unemployed and the nonparticipants
are affected by the increase in
tlhe rate of inflation, whereas in case (i) only the unemployed are affected.
The result is that in case (ii) the flows out of unemployment
into employment are offset by flows into unemployment from nonparticipation,
whereas
in case (i) they are not.
Thus the results depend on the assumptions about perceptions. The Group
2 models, by ignoring job search, suppress this dependence. Consequently,
the model developed in this paper modifies the results of the Group 2
models.
4.3. Group 3 nto&ls
Assume as in the Group 3 models that individual’s price expectations
are
based on a return to normality scheme,‘” that the individual misperceives the
normal levels of prices and nominal wages, and that the perceived real
interest rate is inversely related to the perceived rate of inflation.21 If the
actual rate of inflation rises and if this rise is not perceived immediately,
individuals at first expect deflation; therefore the perceived real interest rate
rises. As explained in section 3.2, a rise in the real interest rate causes a
decrease in employment. an ambiguous change in unemployment,
and an
increase in nonparticipation.
Ultimately. people learn of the higher rate of
inflation and come to expect inflation rather than deflation. In the long run,
the perceived real interest rate falls, causing an increase in employment, an
ambiguous change in unemployment,
and a decrease in nonparticipation.
Consequently, there is no clear relation between inflation and unemployment
‘“A return to normality scheme assumes that people believe there are normal levels to which
prices and wages return. The perceived normal levels themselves may be adjusted over time, but
onf) ,vlth a lag. Consequently. if prices unexpectedly rise. people then expect them to fall. If
prices persist at their new, higher levels. people slowly adjust their perception of the normal
lc\cl upward until the discrepancy between actual and perceived normal prices disappears. This
scheme has an intcrcstmg implication for changes in the rate of inflation. If the inflation rate
rises and this rise is not immediately
perceived. then people experience unexpected price
increases. However. as just explained. people believe for a while that prices will return to thetr
old normal le\cls and therefore will fall. Consequently. for some time after the onset of inflation,
people actually expect deflation. Eventually. of course. they learn of the inflation and their
expectations change according!y.
“This last assumption really cannot bc justified in the present model because people do WI
hold money. When people hold money. the perceived rate of inflation and the perceiled real
interest rate will be inversely related through the well-known effect of perceived inflation on the
real return on money. However. when there is no money. there seems to be no reason for such
an inverse relation to exist. It is extremely difficult analytically
to introduce money ir: any
meaningful wag into the model presented in this paper. Despite these difficulties, 1 will discuss
the implication% of an mlercc relation betnecn the perceived re;lI interest ruts and the perceived
inflation r.ite for the sake 01 comparison.
in either the short run or the long run.” However, there are unambiguous
relations between both employment and nonparticipation
and inflation in
both the short and long run.
These results on the behavior of unemployment are considerably different
from those obtained by Lucas and Rapping (1970), who concluded that
unemployment was inversely related to inflation in the short run. thus giving
a standard short-run Phillips relation. and unrelated to inflation in the long
run, thus giving a vertical long-run Phillips curve. The reason for the
difference is that the Lucas and Rapping model, like the Group 2 models,
ignores job search and therefore
has only two genuine states of
participation --employment and nonparticipation.
The Lucas and Rapping
model artificially introduces unemployment
in such a way that it is not a
middle state between employment and nonparticipation.‘”
The results of ttrlz
behavior of employment and nonparticipation
agree with those obtained b:,
Lucas and Rapping.
Thus the model developed in this paper contirms and therefore strengthens
some of the results of the Group 3 models but contradicts and therefore
corrects other results of those models.
5. Summary
In this paper, I have applied
to aggregate ailalysis a model of indi\idua‘.
behavior developed elsewhere. The model assumes the individual is a utility
maximizer who derives utility from consumption and leisure and who can
engage simultaneously
in labor, search, and leisure. This model unites two
common approaches to the study of the microeconomic
foundations
of
aggregate labor force behavior and contains the earlier models as special
cases. It is thus a useful generalization
of earlier
microeconomic
investigations.
In addition. the model offers significant improvements over earlier work in
It provides natural. mutually consistent
its macroeconomic
applications.
definitions of all three of the states of employment. unemployment.
and
nonparticipati~,n.
These definitions are given directly in numbers of people
rather than in terms of approximating functions of numbers of hours devoted to
“If thele should turn out empirically 10 be ;i relation in the short run. then there \vill be an
cjpi>cjsltc relation m the long run bccuuse the heha\ior of the perceibcd real Interest rnte in the
long run I\ the opposite of that in the <hart run.
“LUGI!, i\nd Rapp~np define ihc unemplqment
rate IO be ;i function of the difference bcturcn
actuiil and ‘normal’ employment. Normal employment is the employment that would preba’l if
is the employment
that
current real wages CqUi~lld normal real wages. Actual employment
pre\;lils at the actual current wage. Both normal and actual employment are functions of the
real interest rate. As It 1~1*ns out, v.hen one takes the difference .>f actual and normal
employment. the real interes; rate term xncels out. so thilt unemployment has the odd feature
of ncbt hcmg a function of tht‘ real interest rate e\en though both actual and nc>rmal emplqment
tit-c.
712
J.J. Seater, Utility maximization
search, or leisurli: by a representative individual. These more direct,
precise definitions have enabled clarification o; the nature and behavior of
the three states of participation and have permitted avoidance of assumptions regarding dominance of income and substitution effects. The simultaneous, mutually consistent definitions of all three states of participation
have resulted in recognition of unemployment’s position as a middle state
between employment and nonparticipation. This middle position generally
results in ambiguity in the response of unemployment to various exogenous
changes, even though the responses of employment and nonparticipation are
unambiguous.
The model also confirms the results of certain recent studies of the Phillips
curve-those that assume the individual speculates on the distribution of
nominal wages over vacancies, typified by Mortensen’s (1970a) work; modifies the results of others-those that assume the individual misperceiyes his
current real wage, typified by Friedman’s (1968) work; and contradicts some
of the results of still others-those that assume the individual speculates on
the future levels of real wages, typified by Lucas and Rapping’s (1970) work.
In general, it is possible to obtain an inverse relation between inflation and
unemployment in the short run and no relation between them in the long
run, but these results depend on the assumptions made about individuals’
perceptions.
labor,
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