The transformation of macroeconomic policy and research prize Lecture, December 8, 2004 by

385

monetary factors did not alter Finn’s and my finding that TFP shocks are the

major contributor to business cycle fluctuations in the United States in the

1954–1980 period we consider in our “Time to Build” paper.

But in all cases, to generate business cycles of the magnitude and nature

observed, the aggregate labor supply elasticity must be 3.

8

This attests to the

robustness of the finding and focuses attention on this elasticity parameter. A

variety of evidence that supports the number 3 had to be found before it was

safe to conclude that the neoclassical growth model predicts business cycle

fluctuations of the quantitative nature observed.

5. EVIDENCE THAT THE AGGREGATE ELASTICITY OF LABOR SUPPLY IS 3

A problem with the abstraction that many economists used to incorrectly

conclude that labor supply is inelastic is that it has the prediction that every-

one should make essentially the same percentage adjustment in hours worked.

This is not the case. Over the business cycle, most of the variation in the 

aggregate number of hours worked is in the fraction of people working and

not in the hours worked per worker. Looking at this observation, Rogerson

(1984, 1988) studies a static world in which people either work a standard

workweek or do not work. He shows that in this world, the aggregate elasticity

of labor supply is infinite up to the point that the fraction employed is one.

Rogerson’s aggregation result is every bit as important as the one giving rise

to the aggregate production function.

9

In the case of production technology,

the nature of the aggregate production function in the empirically inter-

esting cases is very different from that of the individual production units

being aggregated. The same is true for the aggregate or a stand-in household’s

utility function in the empirically interesting case.

Aggregate hours of labor supplied to the market per working-age person,

l , equals the product of the fraction employed, e, and hours per employee, h;

that is

(6)

l = eh .

If the principal margin of adjustment in l is the employment rate and not

hours per employee, then aggregate labor supply elasticity will be much bigger

than the elasticity of labor supply of the individuals being aggregated. Given

that the principal margin of adjustment is e and not h, the aggregate labor supply

elasticity is much greater than the individual labor supply elasticity.

8 

For reviews of many more business cycles studies, see Frontiers of Business Cycle Research 

(Cooley 1995).

9

Rogerson uses the Prescott and Townsend (1984a, 1984b) lottery commodity point. This simpli-

fies the analysis, but does not change the results because lottery equilibria are equivalent to Arrow–

Debreu equilibria; see Kehoe, Levine, and Prescott (2002) and Prescott and Shell (2002).

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Multiple margins determine e. Particularly important for males and single

females is the fraction of potential working life that he or she works. This

fraction is smaller if an individual retires earlier. For married females,

Heckman and MaCurdy (1980) find that as the Rogerson theory predicts,

their labor supply is highly elastic, with some estimates being as high as 10.

For all, weeks of vacation and the number of holidays is another important

margin of adjustment in labor supply.

Hansen (1985) derives the consequence of the Rogerson (1988) assump-

tion for business cycle fluctuations and develops a stand-in household for a type.

He finds that in worlds with labor indivisibility, fluctuations induced by TFP

shocks alone give rise to fluctuations 10 percent greater than those observed.

This indicates that aggregate labor supply elasticity is not infinite as in his 

model world.

Hansen’s findings led Finn and me to introduce both margins of labor

supply adjustment. We numerically found the only margin used is e with the

standard production function. The natural question is why? Hornstein and

Prescott (1993) answer this question.

10

We permitted both margins to be ad-

justed. The key modification is that a worker’s output y is

(7)

y = Ah k

␪

,

where h is the workweek length of this individual and k is the capital stock

that this individual uses. A consequence is that payment per hour is an increa-

sing function of h.

A key result is that all the growth facts hold for this modification of the

neoclassical growth model. The important feature of this model is that capital

used by one individual is not used by another in the period.

For the calibrated economy, the finding is that only the e margin is used 

except in extreme cases when all are employed. Only with e = 1 is h >h, where

h is the endogenously determined “standard” week length. A question, then,

is why do we see any variation in h ? My answer is that in worlds with “islands,”

some islands have e = 1 and h

Œh at a point in time. Here island i indicates

occupation as well as location of work activity.

A question is: What is the real wage? The price of each workweek length is

w

it

(h), where i denotes the island. If one naively assumes that an individual

on island i is being paid real wage w

it

(h

it

)/h

it 

and regresses the logarithm of

h

it

on the log of this assumed wage, a small regression coefficient would be

386

10 

Many years prior, Sherwin Rosen (1978) had pointed out that workweeks of different lengths are

different commodities and their price is not, in general, proportional to the length of the work-

week. Introducing this feature of reality into an applied dynamic general equilibrium model of 

business cycles did not occur until Kydland and Prescott (1991). Earlier, Hansen and Sargent

(1988) had two workweek lengths, straight time and overtime.

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