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Working Paper 9105
MAGNIFICATION EFFECTS AND ACYCLICAL REAL WAGES
by Charles T. Carlstrom and Edward N. Gamber
Charles T. Carlstrom is an economist at the
Federal Reserve Bank of Cleveland, and Edward
N. Gamber is an assistant professor in the
Department of Economics at the University of
Missouri. This paper was presented at the
winter meeting of the Econometric Society in
1989. The authors would like to thank Changyong
Rhee for helpful comments.
Working papers of the Federal Reserve Bank of
Cleveland are preliminary materials circulated
to stimulate discussion and critical comment.
The views stated herein are those of the authors
and not necessarily those of the Federal Reserve
Bank of Cleveland or of the Board of Governors
of the Federal Reserve System.
April 1991
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I. Introduction
Real business cycle (RBC) theory has been successful in
simulating the variability of and comovements among aggregate
variables, such as output, consumption, and investment.
However,
in order to generate the observed movements in employment over
the business cycle, RBC models have had to produce highly
procyclical real wages.'
This is inconsistent with data showing
that real wages are either slightly procyclical or acyclical.
This paper presents a one-period, two-sector model that
reconciles large movements in employment and output with
acyclical real wages.
The two sectors, which can be thought of
as durables and services, differ in their cyclical sensitivities.
The shocks to both sectors are positively correlated, but the
shock to durables has a larger variance than the shock to
services.
In this type of stochastic environment,
workers move
from the durables sector to the service sector during downturns
and from the service sector to the durables sector during
upturns.
The model presented here is motivated by Rogerson (1986), who
studies an infinite-horizon two-sector model.
One of the sectors
is high growth (low cyclical sensitivity, interpreted as
services), while the other is low growth (high cyclical
sensitivity, interpreted as durables).
Rogerson shows that this
.
As pointed out by Barro (1989, p. 8 ) , I t . . the (RBC)
models tend to overstate the procyclical patterns of hours,
productivity, real interest rates and real wage rates."
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type of economy experiences a sectoral reallocation of workers
from durables to services during downturns.
Empirical evidence
reported by Loungani and Rogerson (1988) supports this finding.
We modify Rogersonls environment to account for the acyclical
behavior of wages.
For simplicity, we present a one-period, two-
sector model that captures the sectoral reallocation process
discussed in the earlier study.
However, unlike Rogersonls model,
ours assumes that firms face a fixed cost of hiring workers,
which in turn generates a magnification effect.'
In other
words, the size of the sectoral shock needed to generate a given
amount of sectoral reallocation is smaller in the presence of a
fixed hiring cost.
This I1magnificationeffect1#causes wages to
be less procyclical, because additional workers flowing into the
service sector tend to depress wages there.
If the economy experiences a negative productivity shock,
workers move from the durable goods sector to the service sector,
and as they do, more firms in the service sector find it
worthwhile to incur the fixed cost of hiring some of the incoming
workers.
With an increase in the number of service-sector firms
hiring, each firm hires fewer workers, thus mitigating the real
wage decline in that sector.
Because the real wage in the
service sector declines by less than it would in the absence of a
fixed cost of hiring, additional workers find it advantageous to
Alternatively, this effect can be generated by assuming
that the number of firms producing is exogenous and that there
exists a fixed cost of entering into production (see Chatterjee
and Cooper [1988, 19891).
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move from durable goods to services.
Therefore, the increase in
the number of workers leaving the durables sector causes the real
wage in that sector to decline by less than it would have without
the presence of fixed costs.
The magnification effect generated by our model is similar to
that reported by Chatterjee and Cooper (1988, 1989).
Their work
is specifically aimed at generating large output effects from
small shocks in economies with endogenous entry and exit, and is
part of a growing body of literature that demonstrates how
economies can exhibit Keynesian-type features such as multiple
equilibria and magnification effects (see Diamond [I9881 and
Cooper and John [1988]).
Although our model exhibits magnification effects, it differs
from Chatterjee and Cooper's work in that we do not construct an
economy with multiple equilibria.
Our eventual goal is to embed
this type of model into an RBC model in order to generate data
that can be matched with real-world observations.
This paper is organized as follows. Section I1 describes the
model.
Section I11 presents simulations of the model and
analyzes the results.
Section IV discusses extensions of our
framework and concludes.
11. The Model
his section presents a one-period, two-sector, general
equilibrium model in which the firmls decision to hire and the
workerls decision to stay or to relocate are endogenous.
Labor
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moves freely from one sector to the other, but firms face a fixed
hiring cost.
The existence of this fixed cost produces a nonconvexity in
the firm's hiring decision; that is, firms will not hire
additional workers until the payoff exceeds the fixed cost.
Once
this threshold is exceeded, the firm hires workers until wages
equal the marginal productivity of labor.
This nonconvexity
leads to both the magnification effect and a real wage that is
less procyclical.
The timing of decisions in this economy is as follows.
Workers are initially allocated to one of the two sectors:
durables or services.
One can think of this initial allocation
as being determined by the demand conditions in the previous
period.
For simplicity, we assume that N workers are allocated
to each firm and that there are an equal number of firms in each
sector.
Prior to production, firms and workers observe the state
of the economy, i.e., they observe the productivity shocks as
Simultaneously,
well as the demand conditions in each ~ e c t o r . ~
workers decide where to work and firms decide whether to incur
the fixed cost of hiring.
Once these variables are determined,
Examples of a fixed cost of hiring are placing an ad in
Job Openinss for Economists, renting a hotel room for
interviewing at the American Economic Association meetings, or
hiring a personnel service.
Our model allows sectoral reallocation to take place
either as a result of productivity differences or of taste
differences between the sectors. The latter is what we refer to
as the demand conditions.
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production and consumption take place.
We consider types of
shocks such that, in equilibrium, workers will move from the
durable goods sector to the service sector, and only firms in the
service sector hire additional workers.
We repeat this one-period game for several different
realizations of the productivity shocks to each sector.
We then
compute the variances of wages, output, and employment and
compare these to the case in which firms do not face a fixed cost
of hiring.
Consumption
We assume that the economy is populated by a large number of
identical consumers, each of whom lives for one period.
A
representative consumer is initially located in one of the two
sectors: the S-sector (services) or the D-sector (durables).
Prior to production, the consumer observes the productivity shock
to each sector and decides whether to stay and produce or move to
the other sector and produce.
There are no fixed costs
associated with moving; however, the worker who moves faces an
exogenous probability of finding a production opportunity
(employment) in the other sector.
A representative worker chooses a sector to work in and the
quantities of the S-good (C,) and the D-good (C,) in order to
maximize the following utility function:
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where 0 5 6 I 1 and y 1 1. We restrict y to be greater than or
equal to one because we only consider movements from durables to
services.
The representative worker faces the usual constraint that the
sum of the quantities Cs and C, multiplied by their respective
prices is less than or equal to the wage.
For simplicity, we
assume that individuals in this economy have no utility for
leisure.
Production
Production in both sectors is carried out by a large number of
perfectly competitive firms.
Each firm is initially endowed with
N workers, and labor is the only input in the production process.
The production functions in both sectors exhibit diminishing
marginal product and are identical except for a multiplicative
shock.
A representative firm faces the decision of whether to produce
with its initial allocation of workers or to incur a fixed cost
and hire additional workers.
Formally, the profit function for
the representative firm in the S-sector that decides not to hire
any additional workers is as follows:
The implications of relaxing this assumption are explored
in section IV.
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where W, is the wage paid in the S-sector to existing workers, P,
is the price of output in the S-sector, and
E,
is a random
productivity shock.
Firms in the S-sector that decide to hire additional workers
have the following profit function:
where 8 is the proportion of D-sector workers who move to the Ssector, q is the exogenous probability of finding employment in
the S-sector, h is the fraction of firms in the S-sector that
decide to incur the fixed cost in order to hire the incoming
workers, and k is the fixed cost of hiring measured in units of
the S-good.
The quantity 8q/h is thus the number of additional
workers that will be employed by those firms in the S-sector that
decide to hire.
Since we consider only movements from the D-sector to the Ssector, the profit function for the representative D-sector firm
is simply:
where
E~
is the productivity shock to the D-sector, WD is the
wage paid in the D-sector, and PD is the price of output in the
D-sector
.
Since output and labor markets are perfectly competitive and
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consumers are all identical, this problem can be reduced to a
social planner's problem.
In order to maximize the utility of a
representative consumer subject to the production constraints,
the social planner chooses consumption in the S-sector (C,),
consumption in the D-sector (C,), the proportion of workers
moving from the D-sector to the S-sector (0), and the proportion
of firms hiring in the S-sector (h).
Formally:
subject to
C, = heS[N(1
CD
=
eDIN(l
+
-
0q/h) J" + (1
-
h)e,N"
-
hk, and
0) 1".
Constraint (6) shows that the total amount of the S-good
produced (per consumer) is equal to the proportion produced by
the hiring firms {heS[N(1
+
Oq/h)Ja) and the nonhiring firms [(I-
h) E,N"] less the fixed cost of hiring (hk).
number of firms to be equal to one.
We normalized the
Constraint (7) is simply
total output of firms in the D-sector.
Carrying out this maximization yields the following first
order conditions:
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cDb-l =
es[N(l
I,,
(9)
+ 0q/h) la - eSNa = aeSIN(l + 0q/h) la-l~0q/h+ k,
~,a€,[N(l
+ eq/h) la-'q
C, = heS[N(1
CD = eDIN(l
=
+ 0q/h)Ia +
- 0)laf
I,a[N(l
(1
-
-
0)la-',
(10)
(11)
h)eSNa - hk, and
(12
(13)
where I, and I, are the Lagrange multipliers associated with
constraints (6) and
(7),
respectively.
First order conditions
(8) and (9) are the usual marginal utility conditions.
To understand equations (10) and (ll), consider the following
decentralized version of the social planner's problem in which we
interpret I , to be the price of the S-good, P,, and I, to be the
price of the D-good, PD. Using this convention, first order
condition (11) states that expected real wages (measured in
utility units) are equal across sectors.
Equation (10) is the result of maximizing with respect to the
number of firms hiring in the S-sector, h.
To see the intuition
behind this condition, consider the outcome of the maximization
problem faced by an individual firm in the economy.
Firms that
choose to incur the fixed cost of hiring do so up to the point
where the return from hiring additional workers is equal to the
cost:
The left side of this equation is the difference between
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profits if the firm hires or does not hire.
simply the fixed cost of hiring.
The right side is
Multiplying equation (10) by A,
(P,) and recognizing that W, = A,ar~,[N(l
+
8q/h) la-',
this
condition can be solved to yield first order condition (10).
Equations (10) and (14) state that profits of firms that do hire
must be equal to profits of firms that do not hire, or ash =
nh
T,
.
Although the structure of this model is quite simple, the
first order conditions are highly nonlinear and cannot be solved
for reduced-form expressions.
As an alternative to an analytical
solution, we parameterize this economy and simulate the behavior
of wages, employment, and output for various realizations of the
productivity shocks E, and E,.
111.
Simulations
The purpose of this section is twofold.
First, we briefly
describe the technique used to simulate the model presented in
section 11.
Second, we present the results from several
simulations of the model and the intuition behind them.6
As shown in the appendix, first order conditions (8)-(13) can
be reduced to a system of two equations in two unknowns: 8 and h.
To obtain a measure of the variability of wages, employment, and
output in this economy, we simulate the solutions to 8 and h for
numerous realizations of E, and E, drawn from a random number
generator.
The general forms for E, and E, are as follows:
See the appendix for a discussion of the simulation
technique.
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E, =
m,,
+
B,,ranl, and
=
m,,
+
B,,,ranl
E,
+
B,,,ran2,
where ranl and ran2 are independently distributed uniform random
variables with mean zero and unit variance.
The parameters m,,
and m,, are the means of eS and ED, respectively.
In table 1, we
choose m,, > m,, to generate movements from the D-sector to the Ssector.
The random variable ranl can be interpreted as an
aggregate productivity shock.
The parameters B,, and Be,, measure
the sensitivity of productivity in the S- and D-sectors to
changes in aggregate productivity.
The random variable ran2 is a
sector-specific shock, with Be,, measuring the importance of that
shock to the determination of productivity in the D-sector,
ED
In table 1, under the subheading "aggregate shockstWwe set
B,, < BED,and BED, = 0 to simulate an economy in which productivity
in both sectors is subject to an aggregate productivity shock,
but the variance of the productivity shock is greater in the Dsector than in the S-sector.
Since m,, > m,,, workers continually
relocate from the D-sector to the S-sector; however, the bulk of
this sectoral reallocation occurs during cyclical downturns.
In table 1, under the subheading I1sectoral shocks,11we set BE,
< Be,, and BED,= 0 to simulate an economy in which productivity in
each sector is determined by an independent shock. Since m,, >
m,,,
workers continually relocate from the D-sector to the S-
sector.
When a "badu shock hits the D-sector (or a good shock
11
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hits the S-sector), workers relocate from the D-sector to the Ssector.
Table 2 repeats these experiments with m,, = m,,,
but y > 1.
This causes workers to move from the D-sector to the S-sector
because of an increased demand for services.
Tables 1 and 2 present the results from a subset of the
simulations performed.
Before examining them in detail, we
present a brief overview of the parameter settings for each set
of simulations.
The utility function parameter, 6, is set equal
to .5, the probability of employment, q, is set equal to 1, and
the number of workers per firm, N, is set equal to 1.
We
experimented with several different values of these parameters
and found the results to be qualitatively similar to the results
presented here.
The simulations presented in tables 1 and 2 show the effects
of changing the production function parameter, a, and the fixed
cost of hiring, k.
The simulations are presented in pairs: For
each value of a, we present the simulation results when k = 0 and
k > 0.
To measure the relative variability of wages, employment,
and output, we compute the coefficient of variation for each of
these variables for 50 independent draws of the productivity
shocks
E,
and
E,.
The real wage and real output are measured in utility units.7
The expressions for real wages and output are contained in
the appendix.
12
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Real wages in both sectors (W, and W,) exhibit the same
variability in all simulations.
q
=
1.
This follows from the fact that
As seen in equation (ll), the wages in both sectors are
always equal when the probability of employment (q) is 1. We
therefore present the single measure of wage variability under
the column heading llWage.llReal output is denoted by Y.
In
addition to the coefficients of variation, we also present the
regression coefficients obtained from regressing the real wage in
each sector (deviation from mean) on real output (deviation from
mean).
Again, only one regression coefficient is presented,
since the coefficients for each wage regressed on real output are
identical.
This coefficient is found in the far-right columns of
tables 1 and 2.
It should be clear from the structure of the model presented
in section I1 that sectoral movements in employment (8 > 0) can
be generated either by differences in the preferences for the Sgood and D-good, or by differences in the productivity shocks to
each sector.
The simulations presented in table 1 show the
effects of different mean productivities in each sector.
particular,
In
all of these simulations are for the case where m,,
= 2 and m,, = 1.
In addition, the utility function parameter y
is set equal to 1 to eliminate any effects from preferences.
In
this case, sectoral movement occurs because workers wish to move
from the low-productivity D-sector to the high-productivity Ssector.
The simulations presented in table 2 are for the case in which
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the sectoral movements in employment are caused by differences in
the preferences for the S-good and the D-good.
In particular,
mean productivities m,, and m,, are set equal to 1, and the
utility function parameter y, which measures the weight given to
the consumption of the S-good, is set equal to 1.2.
In table 1, the simulations under "aggregate shocksn are for
the case where B,,,
= 0, so that only the common shock ran1
generates movements in productivity in both sectors.
In
addition, to capture the relative variability of shocks to the Sand D-sectors, we set B,, = .05 and B,,,
= .l. In other words, we
assume that D-sector productivity is twice as variable as Ssector productivity.
The simulations under llsectoralshocks11are
for the case where the D-sector experiences a productivity shock
that is independent of the aggregate shock.
For these
simulations, the productivity shock parameters are as follows:
B,, = .05, B,,,
= 0, and
B,,,
= .l.
The shocks for the simulations
in table 2 are identical in terms of B,,,
B,,,,
and B,,,;
the only
difference is that m,, = mCD = 1.
Results
All of the simulations exhibit both the magnification effect
and dampening of the real wage in the presence of a fixed hiring
cost.
For example, in table 1, the first pair of simulations
under the heading Ifaggregate shocksu shows that increasing the
fixed costs from 0 to .O1 leads to a reduction in the regression
coefficient on real output from 1.00 to .75.
The variability of
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the wage falls from .0075 to .0056 (a 25 percent reduction).
In
addition, the variability of employment, as measured by 8,
increases from .0297 to .0388 (a 31 percent increase).
results are consistent throughout the tables.
These
The presence of a
fixed cost of hiring reduces the regression coefficient and the
variability of the real wage and increases the variability of
employment.
The results for the sector-specific shocks show the same
general pattern; however, the regression coefficients and the
variation in real wages are smaller, while the variation in
employment is larger.
For example, comparing simulations (7) and
(8) to (1) and (2) shows that the regression coefficient fell 47
percent instead of 25 percent when k was increased from 0 to .01.
Simulations (7) and (8) show that increasing the fixed cost from
0 to .O1 causes the coefficient of variation for wages to fall
from .0057 to .0037 (a 37 percent decline), while employment
variability, as measured by 8, rises from .0460 to .0630 (a 37
percent increase).
The regression coefficients in this case
differ from the coefficients of variation because of the
independence of the shocks to both sectors.
As seen in table 1, simulations (5) and (6), the real wage and
variability of employment effects are not sensitive to our choice
of k.
In fact, the coefficient of variation for the real wage in
the case of k
=
.001 is actually smaller than in the case where k
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= .01.8
Throughout the simulations, we find that arbitrarily
small values of k generate the dampened real wage and
magnification of employment effects.
The impact of increasing the production function parameter (a)
can be seen by examining the difference between simulations (2)
and (4).
It is clear that the dampening of the real wage and the
magnification of employment are lessened by increasing a.
This
result makes sense, since it is the existence of a positive
producer's surplus, due to the decreasing returns-to-scale
technology, that gives firms the incentive to pay the fixed cost
in order to hire additional workers.
Notice that with fixed
costs (positive k), a competitive equilibrium does not exist when
a = 1.'
The simulations in table 2, where preferences drive the
sectoral dispersion, show the same general results.
Simulations
(11) and (12) demonstrate that increasing the fixed cost from 0
to .O1 leads to a reduction in the regression coefficient on real
output from 1.0 to .91.
The variability of the real wage then
falls from .0099 to .0091 (an 8 percent reduction) and the
variability of 8 increases from .0386 to 0.1819 (a 471 percent
increase).
In general, we find that the magnification effects
and the dampening of the real wage are present whether we
generate sectoral dispersion through differences in the average
Wage variability increases with k once k is positive
because the marginal utility of consumption of the S-good is
increasing with k.
' This
can be seen from equation (14) when a = 1 and k = 0.
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productivities in each sector or through differences in
preferences for the two goods.
The latter mechanism, however,
consistently produces dramatic employment magnification effects.
IV. Conclusion
We attempt to show the effects of a small, fixed hiring cost
on the relative variability of output, employment, and real wages
in the face of productivity shocks.
The model presented in
section 11, although very basic, illustrates that if firms face a
fixed cost of hiring, then for a given size shock the real wage
response will be smaller and the employment response will be
larger than if there were no fixed cost.
The intuition behind this result is clear.
When a recession
begins, workers leave the sector most affected by the recession
(durable goods) for the service sector.
As more workers relocate
(0 increases), the return to hiring an additional worker rises.
As the number of firms hiring increases, the tendency for the
real wage to fall in the high-demand sector (services) is
dampened (increasing h decreases 0/h, which leads to an increase
in the real wage).
This leads to a further rise in the number of
workers moving from the low-demand sector to the high-demand
sector, which leads to a further dampening of the real wage.
At
the same time, the outflow of workers from the low-demand sector
mitigates the wage decline in that sector.
As stated in the introduction, the results of this analysis
suggest a possible mechanism for generating increased employment
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variability and decreased real wage variability within an RBC
framework.
In order to do this, the model must be extended to
incorporate some dynamic elements.
Although we are still in the
process of formulating this extension, we anticipate that a
dynamic version of this model will yield similar results.
In
addition, a dynamic version will yield different implications for
the adjustment of employment and wages to permanent versus
transitory productivity shocks.
The firm is most likely to incur
the fixed cost of hiring (and the worker is most likely to move)
if the shock is perceived to be permanent.
In that case, we
expect to observe the dampened real wage and the magnification of
employment effects.
This would make sense, since the model
presented here considers only permanent shocks.
Thus, a possible
way to test for this effect would be to examine the differential
response of real wages to permanent versus transitory changes in
productivity.
Our model predicts that the real wage response to
a permanent productivity shock will be less than the real wage
response to a temporary productivity shock.
In addition to adding dynamics, any extension of this
framework should also consider adding leisure to the utility
function.
This would reinforce the effects illustrated above,
because there would then be two sources of adjustment to a given
shock: movements in and out of the labor force and movements from
one sector of the economy to the other.
Our model generates the dampening real wage and magnification
of employment effects within a sectoral-shifts framework. The
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basic results, however, could easily be generated in a more
general framework in which individuals face the choice of not
working (producing in the household sector) or working in the
production sector.
In such a framework, a positive productivity
shock to the production sector will cause individuals to leave
the household sector.
As individuals flow into the labor force,
more firms will find it worthwhile to hire workers, leading to an
increase in the real wage and thereby inducing additional workers
to relocate.
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Appendix
Solution Technique
Normalizing
6,
= 1, the first order conditions (8)-(13) can
be solved to yield two equations and two unknowns Z and h, where
z
= 0/h:
Given values for N, a, y, 6, e,,
and q, equation (Al) is
solved using Newton's method (see Press [1988]).
The value of Z
that solves equation (Al) is then plugged into equation (A2).
Next we apply Newton's method to (A2) to obtain solutions for Z
and h, which are then used to calculate wages, employment, and
output.
Expressions for Real Wages and Real Output
S-sector wage
D-sector wage
Real output
S-sector output
D-sector output
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References
Barro, R., !!New Classicals and Keynesians, or the Good Guys and
the Bad Guys,If National Bureau of Economic Research, Working
Paper 2982, May 1989.
Chatterjee, S., and R. Cooper, llMultiplicityof Equilibria and
Fluctuations in an Imperfectly Competitive Economy with
Entry and Exit,I1 The Hoover Institute, Working Paper E-88-25,
June 1988.
, tlMultiplicityof Equilibria and Fluctuations in
University of
Dynamic Imperfectly Competitive Econornie~,~
Iowa, Working Paper 89-01, January 1989.
Cho, J., and R. Rogerson, I1Family Labor Supply and Aggregate
FluctuationsIflJournal of Monetary Economics, vol. 21,
March/May 1988.
Cooper, R., and A. John, ffCoordinatingCoordination Failures in
Keynesian ModelsI1lguarterlv Journal of Economics, August
1988.
Diamond, P., "Aggregate Demand Management in Search EquilibriumIn
Journal of Political Economv, October 1988.
Lilien, D., "Sectoral Shifts and Cyclical UnemploymentlW Journal
of Political Economv, vol. 90, August 1982.
Loungani, P., and R. Rogerson, ffCyclicalFluctuations and Sectoral
Reallocation: Evidence from the PSIDIM Journal of Monetary
Economics, March 1988.
, ffUnemploymentand Sectoral Shifts: Evidence from
the PSID,ll University of ~lorida,Working Paper, December
1989.
Press, W., Numerical Reci~es: The Art of Scientific Computinq.
Cambridge, Mass.:
Cambridge University Press, 1988.
Rogerson, R., "Sectoral Shifts and Cyclical Fluctuations,~~
University of Rochester, Working Paper, 1986.
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Table 1: Productivity
( Y = 1)
I. Aggregate Shocks
E, = 2
ED = 1
+
+
.05.ranl
0. leranl
Coefficient of Variation
k
(1)
0
a!
Wage
Y
0.5
0.0075
0.0075
8
0.0297
0.0056
0.0075
.O1 0.5 (2) - 0.0388
Regression
Coefficient on Y
Wage/Y
1.0
0.75
0
0.9
0.0071
0.0071
0.0289
1.0
1.0
(4)
.01
0.9
0.0067
0.0071
0.0312
0.94
0.94
(51
0
0.5
0.0075
0.0075
0.0297
1.0
1.0
0.5
0.0053
0.0074
0.0298
0.72
0.72
. (3)
(6)
.001
11. Sectoral Shocks
E, = 2 + .05-ran1
ED = 1 + 0.l.ranl
Coefficient of Variation
k
a!
Wage
Y
8
Regression
Coefficient on Y
Wage/Y
Wage
(71
0
0.5
0.0057
0.0057
0.0460
1.0
1.0
(8)
.O1
0.5
0.0037
0.0057
0.0630
0.65
0.53
(9)
0
0.9
0.0052
0.0052
0.0450
1.0
1.0
.01
0.9
0.0047
0.0052
0.0490
0.90
0.89
(10)
Source: Authors1 simulations.
www.clevelandfed.org/research/workpaper/index.cfm
Table 2: Preferences
(y = 1.2)
I. Aggregate Shocks
= 2
= 1
E,
E,
+
+
.05-ran1
O2.l.ranl
Coefficient of Variation
k
a
Wage
Y
8
Regression
Coefficient on Y
Wage/Y
Wage
(11)
0
0.5
0.0099
0.0099
0.0386
1.0
1.0
(12)
.01
0.5
0.0091
0.0099
0.1819
0.91
0.91
(13)
0
0.9
0.0098
0.0098
0.0384
1.0
1.0
(14)
.01
0.9
0.0097
0.0098
0.0492
0.98
0.98
11. Sectoral Shocks
E , = 1 + .O5.ranl
E , = 1 + 0.l.ranl
Coefficient of Variation
k
a
Wage
Y
8
Regression
Coefficient on Y
Wage/Y
Wage
(15)
0
0.5
0.0068
0.0068
0.100
1.0
1.0
(16)
.01
0.5
0.0064
0.0069
0.5965
0.92
0.71
(17)
0
0.9
0.0066
0.0066
0.1008
1.0
1.0
(18)
.O1
0.9
0.0064
0.0066
0.1365
0.95
0.94
Source: Authorsf simulations.
@FedFRASER