Labor supply with a minimum hours threshold

Carnegie-Rochester North- Holland

Conference Series on Public Policy 33 (19901

137-

168

LABOR SUPPLY WITH A MINIMUM HOURS THRESHOLD DAVID CARD Princeton University*

This paper considers the importance of minimum hours thresholds for An analysis of the interpretation of individual labor supply data. quarterly labor-supply outcomes for prime-age males in the Survey of Income and Program Participation suggests that such thresholds are an important A simple contracting model is presented aspect of weekly hours choices. that incorporates mobility costs and a nonconvexity in the relation between weekly hours and effective labor input. This nonconvexity gives rise to a two-part employment schedule. In periods of low demand, some individuals are temporarily laid off, while others work a minimum threshold level of In periods of higher demand all available workers are employed at hours. The model provides a simple hours in excess of the threshold level. interpretation for the role of demand-side variables in explaining annual It can also explain the weak correlations between labor-supply outcomes. annual hours and average hourly earnings that have emerged in earlier Under suitable assumptions on preferences, the intertemporal studies. labor-supply elasticity can be recovered from the relationship between earnings and hours per week. Estimation results for the SIPP panel yield elasticity estimates that are similar to those in the literature based on annual data. If the model is correct, however, annual labor supply is considerably more sensitive to changes in productivity than these estimates suggest.

Following the lead of Hansen (1985) and Rogerson (1988), real business cycle theorists have recently recognized the importance of distinguishing between changes in the intensity of work effort per period and changes in Although the importance of the partici-

the probability of employment.'

pation decision is widely acknowledged in studies of individual labor supply, most of the literature considers the question of participation at the

l

I also

am grateful

thank

Rochester

‘See

Robert

to

Kristin

Butcher

Miller,

Andrew

Conference

for

comments.

the

survey

recent

0167-2231/90/$03.50

by

01990

Plosser

-

for

Oswald,

assistance and

seminar

in

preparing

participants

the

data

at

Yale

for and

(1989).

Elsevier Science Publishers B.V. (North-Holland)

this the

paper. Carnegie-

I

annual of

level

annual

most

of

with

little

.L

the

or

in

of

12 months.

the

labor

based or

in

with

the

of

in of

with on the

worked,

not

expect

and

changes

data

sets

are

in

these

supply

of

fective

labor

input.

while

others

demand

all

in

mind

the

that

inquire

the

previous

Program

data

Partici-

sets,

the

The SIPP panel

composition

of

labor

the

SIPP

therefore

higher-frequen-

are

in

all

SIPP of

found

suggest

Over

of set.

worked,

be important

hours

that

work

data

weeks

to

90 percent

period

components

the

Although

hours

sample

the

number

supply.

weekly

most of

per

week

jobs

are

individuals

35 hours

contractual

Following

Rosen

between

or more per

workers

are

provides of

employment

is Heckman

a simple labor

wages. in

widely and

any

particular

analyzed

in

studies

for

the

with

the

model,

week

(1986).

excess

vary

to

of

laid

In periods

in

explanation supply

ef-

schedule.

temporarily

hours.

hours

According

Killingsworth

138

of at

labor model

and

hours

are

level

of the

worker

a two-part

employed

annual

for

per

some individuals

a minimum-threshold

model (1985),

hours

generates

demand

controlling

by

a simple

relation

nonconvexity

measures

participation

I present

the

The model

survey

of

men

in

week

threshold.

in

work

of

of

supply.

employed.

This

that

probability

other

adult

per

of

during

available

even

hours

range

employment

threshold.

Ham (1986)

for

individual

the

are

low

and

analysis

changes

threshold.

a nonconvexity

high

the

the

assumes

off,

analyze

a minimum-hours

facts

of

Unlike months.

a descriptive

a minimum-hours

In periods

Income

poorly

labor

per week during

of

four

in

questionnaires

hours

same job

they

See

one might

variation

on annual

Survey

employment,

number

variation

issue

weeks

hours

longitudinal

average

to

labor

and out

with

*The

are

released

begins

tabulations

particular.

in

if

supply.

quarterly

in

indicators,

then

decomposition

Nevertheless,

changes

annual

intra-year

opportunity

in

week whenever

the

sets

and usual

of

a unique

associated

of

components

exception.

of

on the

year.

hours, in

available

every

and changes

minimum

the

an important

of

With

weekly changes

administered

Movements

supply

average

of

recently

paper

observed

of

is

This variance

consists

is

cy changes

sources

data

The

(SIPP)

vary*

most

work

questionnaire provides

per

hours

between

research

and weeks

earnings.

these

weeks

pation

in

little

week

annual

no change

analyzing

Typically, about

per

correlation

hourly

to

surprisingly

hours

Unfortunately, suited

is

into

variation

a systematic average

There

hours

vary

female

of

of the

finding

demand-side changes

with

labor

in

employer-

supply

in

demand conditions. Until all available workers are employed, however, average hourly earnings are constant. Thus, changes in weeks worked are correlated with

demand

indicators, but may

be

independent of average

hourly

earnings. Under some restrictive (but standard) assumptions on preferences, the weekly-earnings elasticity model.

of

function

implied

hours per week

by

the

model

generates

as a conventional

the

same

wage

life-cycle labor supply

Thus, the intertemporal labor-supply elasticity can be estimated by

considering

the

relation of

average

hourly

earnings to hours per week,

although not necessarily to weeks worked. Labor-supply equations for hours per week, weeks worked, and hours per quarter are then estimated on the SIPP data. The estimation methods control for

measurement

generated

by

error

in average

conditioning

on

hourly

employment

earnings status.

and

selection

Perhaps

biases

surprisingly,

however, I obtain estimates of the intertemporal substitution elasticity in the same range as the previous literature.

I. PRELIMINARY DATA ANALYSIS To

investigate

the

characteristics

of

short-term

fluctuations

in

individual hours I have assembled a panel of observations for males age 2262 from the survey of

Income and Program Participation (SIPP).

has two important advantages over other longitudinal data sets. SIPP questionnaire annual

surveys

is administered every four months.3

in

the

Panel

Study

of

Income

The SIPP First, the

Thus, unlike the

Dynamics

(PSID)

and

the

National Longitudinal Survey (NLS), the SIPP interview schedule permits a detailed investigation of within-year variation in labor supply.

Second,

the SIPP is much larger than other longitudinal surveys: 20,000 households versus approximately 5000 in the PSID. the much

shorter

interviewed

8

or

time dimension 9

times

over

of a

These advantages are tempered by

the SIPP period

of

panel.

Each household

36 months.

Despite

is

this

limitation, the size of the panel and frequency of observation make SIPP an attractive data source for analyzing short-run hours determination. The Census Bureau does not yet make available a complete longitudinal

(1987)

?See U.S. Bureau of the Census “Survey of Income and Program Participation for complete details on the SIPP sampling frame and interview schedules.

139

Users’

Guide”

version of the SIPP panel

from

the

data.

available

I have therefore created my own longitudinal cross-sectional

The

samples.4

paper

information

is drawn

from

the

set of men with

for all waves of

the

1984 SIPP panel. To minimize

associated with

imputation errors,

complete

individuals with

of

the

The sample analyzed

merging procedure are described in the Data Appendix. in this

details

longitudinal problems

imputed responses for

earnings, usual hours per week, or weeks worked in any month of the sample have been excluded.5 with

and without

A comparison of the characteristics of individuals

data

imputations suggests

that the biases arising from

this exclusion are small.6 Finally, I have restricted the sample to individuals

who

worked

December 1985.

for pay

at

least one week

between October

1983 and

These combined exclusions generate a usable sample of 4814

men. Although weeks and earnings data are recorded on a monthly basis in the SIPP, hours per week are only recorded once for each employer over the previous four months. observations

It is therefore

on monthly

labor supply,

time

frame

is that each calendar

months

may

contain

independent

I have aggregated the monthly

An additional advantage of the quarterly

information into quarterly data. calendar

impossible to recover and

quarter

either

4

has exactly

or

13 weeks,

5 weeks.

The

whereas

staggering

of

interview dates for the four rotation groups in the SIPP panel implies that complete quarterly observations are only available from 1983-IV to 1985-IV. The

final data set therefore

contains

43,326 observations on the

labor-

supply outcomes of 4814 men in each of 9 quarters. Table

1 presents

information on the demographic

work histories of the sample.

characteristics

and

Data are presented for the sample as a whole

and for the subsample of individuals who were employed

in the first and

last quarter of the sample period and who report no change in their

4l 5

am grateful

L~llard,

“hotdeck” with

Smith

data

imputed

6The survey individuals

to

most

with

and

canmon to and

Butcher

Welch

imputation

earnings

decline

Kristin

for

(1986)

discuss

procedure.

leads

to

without

Their

significant

imputation provide

her

is

earnings imputations

for

assistance

the

limitations

findings

measurement

earnings. information. are

presented

140

with

suggest

this

task.

and

biases

that

in

inclusion

the

Census

of

Bureau

observations

error.

Roughly

15

percent

of

Comparisons

of

the

in

the

Data

Appendix.

individuals characteristics

in

each of

Table 1 Characteristics of SIPP Sample

Overall Sample

One-Employer Subsample

Demographic Characteristics 1.

Average Age

36.9

38.4

(start of panel) 2.

Percent Nonwhite

11.0

3.

Average Education

13.1

9.6 13.1

(start of panel) Employment Data for Main Job 4.

Average Weeks Worked per Quarter

11.2

12.8

5.

Average Hours per Week

41.1

42.6

6.

Average Hours Worked per Quarter

472.1

546.1

7.

Average Probability of Working

85.8

98.2

8.

Average Probability of Working

90.1

99.2

96.1

99.9

(in Quarters Worked)

in a Week (Over 117 Weeks) in a Quarter (Over 9 Quarters) 9.

Average Probability of Working in a Year (Over 2 Years)

10.

Average Hourly Earnings 1984

10.40

11.10

11.

Average Hourly Earnings 1985

10.65

11.32

12.

Sample Size

4814

2864

Note:

Sample consists of males age 22-59 as of Wave

I of the 1984 SIPP

Panel, with no imputations for earnings or hours in any wave and at least one week of paid work between October Appendix.

1983 and December 1985.

See Data

Individuals are followed for 9 quarters (1983-IV to 1985-W).

141

employer during the 9 waves of the SIPP panel.'

Approximately 60 percent

of individuals fall into the latter category. The

demographic

characteristics

of

the

sample

are

similar

very

to

those of a sample of similarly-aged men from the March Current Population Survey (CPS) who report working at some time in the previous year.8 4-11

of

the

table

contain

information

information reported for each

gleaned

from

earnings

individual's main job.

Rows

and

hours

Individuals report

working an average of 11.2 weeks per quarter, and just over 41 hours per week in those weeks in which they work.

Average hourly earnings, reported

in rows 10 and 11 of the table, are again similar to those of men in the same age group in the CPS.' The average employment rate varies

inversely with the length of the

interval used to define employment status.

Over the 27-month sample period

85.8 percent of the sample were employed in any given week, 90.1 percent in any given quarter, and 96.1 percent in either 1983 or 1984.l'

Movements in

and out of employment are clearly a more important source of variation in individual hours at higher frequencies of observation. The

contribution

of

changes

in

employment

var iation in quarterly hours of work is addressed

status

to

the

in Table 2.

total

The total

var iance in quarterly hours around individual-spec ifit means is presented in row 1.

This variance is defined as

&

v = where

Hit

(Hit - Hi)2,

&i~t

represents

the

hours worked

by

individual

i in period

t, Hi

represents the mean hours worked per quarter by i, N represents the number of individuals in the sample, and T (=9) represents the number of time

‘Inspection that

there

of

may

researchers

report

unemployment 8 the

For

(U.S.

example,

average

percent

age

is

the

sequences

both

false

scme

difficulty

Bureau

of

among

men

37.2

of

employer

transitions

and

with

the

Census

age

22-60

years,

the

the

identifiers

coding

(1989).

in

reported

unreported

pp.

the

average

of

changes employer

by in

the

identities

individuals data.

suggests Census

following

a

Bureau spell

of

16-18).

March

1985

years

of

CPS

who

completed

worked

in

the

education

is

previous

year,

13.0,

and

the

worked

in

1984

11.2.

hourly

earnings

in

the

March

1985

CPS

work

some

time

sample

of

men

age

22-60

who

$10.76.

“Recall order

is

nonwhite

‘Average are

be

to

appear

that in

individuals the

had

to

sample.

142

between

October

1983

and

December

1985

in

Table 2 Components of Variance of Quarterly Hours Around Individual-Specific Means (Standard Errors in Parentheses)

Overall Sample 1.

Unconditional Variance of Hours

16586.8 (369.9)

2.

3.

Conditional Variance of Hours

10655.5

Percent of Unconditional Variance

One-Employer Subsample

5766.9 (257.3) 4371.6

(254.1)

(194.7)

48.7

27.0

Due to Probability of Employment 4.

5.

6.

7.

Note:

14.67

Conditional Variance of Log

3.90

Hours (x100)

(-45)

(-27)

Conditional Variance of Log

4.06

1.45

Hours/Week (x100)

(-15)

(*IO)

Conditional Variance of Log

6.44

1.33

Weeks (x100)

(.2I)

(-II)

Conditional Covariance of Log

2.08

Hours/Week and Log Weeks (x100)

(-IO)

See text.

.56 (-06)

All data are deviated from individual-specific means.

143

periods per individual." the

one-employer

deviations

of

In the overall sample v = 15,587, while within

subsample

129 hours

v

and

= 76

5756.

These

estimates

hours, respectively.

imply

The

standard

corresponding

coefficients of variation are -27 and -14. For a given individual, the variance of hours can be decomposed into a component due to the conditional variance of hours, given employment, and a component

due

to

represent

the

probability

changes

in

employment

that

i

is

status.

employed

in

Specifically,

let

pi

any

let

Ht

quarter,

represent the conditional mean of hours, given that i is employed, and let v$

represent

employed.

the

conditional

Finally,

quarterly hours. vi = p.1

let

variance

represent

Vi

of

i's

hours,

the unconditional

of

that

i

variance of

is i's

Then

vc + p.1 1

(1 - p.) (H")2 1

1

-

The first term can be interpreted as the part of variance

given

hours,

given

employment,

while

Vi

due to the conditional

the second component

can

be

interpreted as the part of Vi due to the variance of employment outcomes. For the entire sample:

V = ~

The

share

of

Ci

the

Vi

1

=

~

=

~

1

average

“i

(pi

Ci

pi

VF + pi

VF

+

variance

(1 - p-) 1

1

(HF) 2),

xi Pi(l - Pi)($)

1J

in hours

due

to the

2variability

of

employment outcomes is then

s _

A Ci

Pi(l - Pi)(HF)2 V

where

Si

over

time

=

variability

“The estimated by

II

pi

(1-pi)(HF)2 /

in

i's

of

hours for

degrees individual

of

Vi

employment

freedom means.

= 4 Ci

of

the

Si,

is the share of Vi status

individual i.

This

ai

estimated

adjustment

would

percent.

144

and

ai

attributable to changes

=

Vi/V

is

the

relative

The value of this share in the

sample reduce

variance the

are

estimated

not

adjusted

variances

for in

Table

the 2

overall sample is just under 50 percent. Thus, quarter-to-quarter movements in

and

out

of

variability

of

employment hours

employment.l*

contribute

as changes

about

in the

as

much

level of

to

hours,

the

average

conditional

on

In the one-employer subsample the share is lower, as could

be expected given the much higher employment probabilities for this group. The conditional variance of hours per quarter can itself be decomposed into a component due to the variation in weeks per quarter, a component due to

the

variation

decomposition

in hours per

is

presented

week, in

and

a covariance

Table

transformation of conditional hours.

2,

based

term.

on

a

One

such

logarithmic

Let nit represent the number of weeks

of employment for individual i in quarter t, let hit represent hours per week

reported

by

i in quarter

t, and observe that Hit = nit hit-

The

conditional variance of log hours for individual i can be written as: var (log HitlHit > 0) = var (log nitlHTt > 0) + var (log nitlHit > 0)

+ 2COV

(log

nit,

log

hit

1 Hit

0).

’

Sample averages of these 4 terms are presented in rows 7-11 of Table 2.13 In both the overall sample and the one-employer subsample the covariance of weeks

worked

attributed

and

hours

per

to

weeks

equally

conditional

variance

quarter

60

is

of

percent

week and

hours in

due

the

is

positive.

hours

per

to changes

overall

If

the

covariance

week,

the

share

in weeks

sample

and

worked

50

of

is the

within

percent

in

a

the

subsample. The data in Table 2 suggest that changes in quarterly labor supply for a

given

individual

arise

from

three

sources:

movements

in and

out

of

employment for an entire quarter; changes in the numbers of weeks worked, conditional

on employment

hours per week.

in the quarter; and changes

in the number of

For individuals who worked at the same job during the

sample period, the contributions of these three components are about equal. For others, the largest share of the unconditional variance is attributable to movements in and out of employment, and the smallest share to changes in

12This attributable

13Again

share

is

to

changes

the

data

roughly in

on

similar

to

employment:

weeks

and

hours

the see

share Hansen

per

week

145

of

the

(1985,

are

variance p.

adjusted

of

311)

and

for

aggregate Coleman

quarterly

hours

(1984).

individual-specific

means.

hours per week.14 Further insight into the nature of hours variation is provided by the cross-tabulations

in Table 3.

Each row of the table gives the percentage

of individuals with a particular range of hours per week during the sample period.

The first 4 rows give the percentages of individuals who report

the same hours per week in all 9 quarters, while the next rows give the percentages

of

individuals with

some variation in weekly hours.

In

the

overall sample 30 percent of individuals report constant weekly hours: the vast majority of these report exactly 40 hours per week.

Among individuals

with some variation in hours per week, two cases are prominent. percent report a minimum of exactly 40 hours.

About 40

Another 40 percent report a

range of hours with a minimum below 35 hours. The distribution of the range of weekly hours is slightly different in the one-employer is the

fact

subsample.

that

An interesting aspect of the table, however,

the distributions

in the overall

sample and the one-

employer subsample are very similar, conditional on the presence or absence of

weeks

of

nonemployment.

Thus

the distribution

in column

4

is very

similar to that in column 1, while the distribution in column 5 is similar to

that

in column

2.

The one-employer

group differs

from the overall

sample mainly in the likelihood of lost weeks. These tabulations suggest that some notion of a minimum threshold in the weekly hours of prime-age males is probably useful.

Three-quarters of

the overall sample and almost 90 percent of the one-employer subsample work at

least

35 hours

per week

whenever

they

Despite

are employed.

these

tendencies, a significant fraction of individuals fall below 35 hours per week

at

some

particularly

point

during

likely among

the

sample

Low

period.

one-half of these fall below 35 hours at some point. weekly-hours

threshold

weekly

hours

are

individuals who suffer weeks of nonemployment:

is

overly

restrictive,

it

Thus although a rigid is

a

useful

first

approximation, at least within jobs.

14These errors

in

calculations

weeks

worked

should and

hours

be per

interpreted week

can

since

carefully, lead

contributions.

146

to

over-

or

differential

understatement

measurement of

the

relative

Table

Individual-Specific

Range in Hours Per Week

Overall

Percent I.

2.

3.

Sample

One-Employer

Subsample

No

Some

No

Some

Weeks

Weeks

Weeks

Weeks

Lost

Lost

Al I

Lost

Lost

All

(1)

(2)

(3)

(4)

(5)

(6)

with:

Constant

Hours Per Week

(a)

40 hours per week

(b)

35-39

(C)

~35 hours per week

.2

Cd)

~40 hours per week

1.4

Variable

35.3

hours per week

14.5

1.2

.5

3.4

.9

26.3

36.520.2

34.4

I .2

.9

1.3.6

1.6

.2

0

.l

1.5

0

1.3

1.1

Hours Per Week

(a)

Minimum 40 hours per week

(b)

Minimum 35-39

(C)

Minimum x35 hours

per

Cd)

Minimum

per

Number

3

of

>40

Individuals

34.2

15.7

26.2

7.8

6.3

7.2

week

5.8

53.6

26.6

week

14.2

5.2

10.3

14.03.6

2719

2095

4014

2502

hours per week

hours

147

33.816.0

7.65.2

5.254.4

31.6

7.3

11.4

12.6

362

2664

II. A SIMPLE CONTRACTING MODEL WITH MINIMUM HOURS This

section

presents

a

simple

contracting

model

of

intertemporal

labor supply that captures some of the features highlighted in the previous section, while

at the same time addressing an important issue raised by Ham's findings, and

Ham's (1986) analysis of intertemporal labor supply. the

results

demand even

presented

below,

suggest

variables

are

important

controlling

for

wages.

that

industry-specific

determinants Ham

of

interprets

individual labor this

against the strict life-cycle labor-supply model. l5 here this

finding

relation between

is

interpreted

as

evidence

of

individual hours and output.

employment-

finding

as

supply, evidence

In the model presented a

nonconvexity

As noted by Rosen (1985),

this nonconvexity gives rise to a two-part employment contract. demand

states,

some

employees

temporarily laid off.

"standard

work

in the

hours,"

while

In low-

others

are

In high-demand states, all available employees work

"overtime hours," at a premium that depends on the intertemporal elasticity of

labor

prominent

supply.

Such

a

two-part

contract

is useful

spike in the distribution of weekly

to

explain

the

hours at 35-40 hours.

It

also gives a straightforward interpretation of demand-side variables in the labor-supply equation.

These appear as determinants of the probability of

employment in any particular week.

Finally, to the extent that changes in

annual

changes

hours

take

place

through

in

the

number

of

weeks

of

employment at standard hours, the two-part employment contract explains the rather weak correlations between annual hours and average hourly earnings that have emerged in previous studies-l6 The

model

is

a

straightforward

presented by Rosen (1985, Section V). firm-specific

demand

or

re-interpretation

productivity

themselves permanently to firms.

of

the

model

Consider a multi-period economy with shocks

in

which

workers

attach

In each period a firm selects the number

of employed workers, nt, and hours per employed worker, ht.

Revenues of a

particular firm are

15See and

some 16

Card of

See

nonconvexities with

relatively

(1987)

the

and

objections

Altonji

Heckman that

(1986),

can weak

explain

for the

correlations

and

have

MaCurdy

been

example. co-existence between

(1988)

raised

to

Hansen of hours

for their

further

(1985)

and

arbitrarily of

148

work

discussion

of

these

findings

interpretation.

Rogerson

elastic and

average

(1988)

point

intertemporal hourly

earnings.

labor

out

that supply

where ntf(ht) represents effective labor input in t, and et represents a demand or productivity shock.

The correct time period in this context is

the minimum

employment

period over which

naturally to a week.

Assume

decreasing returns to hours.

is fixed, and corresponds most

that f exhibits first

increasing and then

A convenient example of such a function

is

one with "start-up" costs:

f0-Q = 0, =

(ht -

hoI

0<6
ht 2 ho,

Start-up costs, or similar nonconvexities in the relation between hours per worker and effective (see below).

labor input, give rise to a minimum-hours threshold

Fixed costs of travelling to work or nonconvexities in tastes

for leisure could generate the same phenomenon. an

important

component

of

threshold-like

I suspect, however, that

behavior

is

attributable

to

technology. Assume that workers' preferences between hours of work and consumption are additively separable over time.

In addition, assume that the within-

period utility function U is additively separable in consumption, ct. and hours of work:

wt’ where

$1 = u(ct) - +(h&

u and 0 are strictly

+(O)=O.

and

Assume that a pool of workers of size no is initially attached to

the firm. employed

increasing, u is concave, o is convex,

In (nt 5

each period, a random selection nt of these are actually no),

and

the

remainder

are

temporarily

laid off.

The

expected utility earned by a representative worker is therefore

q/no U(ct.

$1 + (1 - nt/nO) U(Q, 01,

where ct denotes consumption in period t if employed, ht represents hours per employed worker in t, and Et represents the consumption of unemployed workers. Suppose that training and recruiting costs per worker are T, and that workers and the firm share a comn

discount rate 6. 149

An optimal contract

is a set of contingent functions ct(et), ct(et), nt(et), and ht(et), and an initial firm size n0 that maximizes

E Et 8t Mntf(ht),

et) - ntct - (“0 - n&l

-

TnO,

subject to

E Et 8t IntU(q,

ht) + (“0 - ntYWt,

011 2 ngV*,

and nt 5 no for all t.

Here, E denotes expectations over the joint distribution of {et, t=O,...m), taken

with

respect

to

information

available

period, and V* represents the equilibrium

in

an

initial

recruiting

value of alternative contracts

available to each worker. Let J, represent the per-worker value of the multiplier associated with the

expected

utility

constraint,

and

let

etu(et)

represent

the

present

value of the multiplier associated with the maximum employment constraint in period

t when

the demand/productivity

shock

is et.

The first-order

conditions for an optimal contract imply that consumption is constant over time and states and independent of employment or unemployment status:

ct(et)

= Q(et)

=

[u’lel (e-l).

The first-order conditions for employment and hours are

f(ht)

f’($)

Rl(ntf(ht).

Rl(ntf(ht),

et) = e+(ht)

+ ut(et),

et) = $-+‘($I.

In periods when nt < no, ut = 0 and these equations can be rewritten as

150

(1)

(2)

f’ ($1

b’(hJ

-f(ht)=xqI’ implying

that

ht

=

h*,

function

is monotonic

independent of

in 9, then

et.

17

If the marginal

there exists a critical

revenue

level of

the

demand/productivity shock, say e*, such that if et < e* then ht = h* and nt < no. while if et > e* then nt = no and ht > hf.

In low-demand states,

hours per worker are fixed and marginal adjustments to the effective labor force are met by changing the level of employment.

In high-demand states,

on the other hand, employment is constrained by the size of the available pool, and marginal changes in the effective labor force are accomplished by varying hours per worker. An

important aspect of this contract is its decentralizability.

On

the demand side, if the firm acts unilaterally to maximize profits, subject to an earnings schedule g(ht) for each employed worker, then the firm will make the jointly optimal employment and hours choices provided that g(ht) = $-+(ht),

where

1,

optimization. '*

is

the

multiplier

from

the

associated

joint

On the supply side, if workers have access to risk-neutral

savings/insurance markets, and face a contractual earnings function g(ht) = then there exists a once-for-all transfer payment from the firm

W(h&

that causes workers to supply the jointly optimal hours choice ht if they are

offered

employment

in period

t,

and

jointly optimal consumption choices."

to unilaterally

implement the

To see this, consider the problem

of choosing consumption if employed ct. hours if offered employment ht, and consumption if unemployed St to maximize

E

“The exhibit and

existence first

of

h”,

‘*This

an

increasing

+(h)=l/E

revenues

6t (nt/nO U(ct,

It

is less

with

E>1>6,

readily wage

hours

and

seen

costs,

ht) + (1 - nt/nO) U(tt,

choice

hl

then

decreasing

then

hf

by

satisfying

= E/(E-6)

the

to

earnings

the

to

and

(2)

scale.

when For

p+

= 0

requires

example,

if

that

f

f(h)=(h-ho)’

ho.

considering

subject

(1)

returns

0))

maximization function

of

the

g(ht)

discounted =

$-+(ht)

present and

value

the

of

constraint

nt
In

some

states

of

randomization

less

than

device)

full to

employment. choose

which

individual workers

151

workers are

employed

must and

still

rely

which

are

on not.

the

firm

subject to E zt at Cnt/ng ct + (1 - nt/ng) St - nt/ng g(ht)l = B,

where 6 is an initial transfer payment from the firm to each worker, and expectations

are

taken

with

respect

to

the

distribution

of

employment

levels induced by the jointly optimal contract.*' Let

x

denote

constraint.

the

multiplier

associated

with

the

lifetime

wealth

The first-order conditions for this problem include

u’(ct)

= u’(Q)

=

A

and +'(ht) = 1 g'(h+

If B is selected to allow the same consumption stream as in the jointly -1 optimal contract, then A=* , the inverse of the multiplier associated with the per-worker utility constraint the

contractual

earnings

in the optimal contract.

function

is

g(ht)=#.$(ht),

condition for hours is satisfied trivially for any ht.*' optimal

contract

is

supported

by

a

simple

Assuming that

the

first-order

Thus the jointly

earnings

function

that

is

proportional to the disutility of hours function b(h). It is interesting to compare this contractual-earnings function to the earnings

function

generated

by

a

conventional

life-cycle

problem, under a similar specification of preferences. cycle

problem,

earnings

represent

the

product

of

labor

supply

In the usual life-

hours

of

work

and

a

The first-order condition for the optimal choice

parametric wage rate wt. of hours in period t is

“This

formulation

unemployed the

21

The

Unemployed level is

A

foregone

unemployment benefits

benefits

can

be

added

or with

other no

income

change

in

Sources

the

in

the

implications

of

.

model

cho i ces

ignores Unemployment

states.

contract

in

the

leaves sense

individuals

but

more

per

unit.

leisure. Since

individuals

that are

any in

one

However, Xg(h+)

=

who level

of

sense

employed

hours

“better

employed a(h+),

are

the

wi Ii off,”

individuals shadow

leisure.

152

indifferent

because are

value

between

satisfy

of

the they

earning earnings

alternative

first-order have income, just

the

hours

conditions. same

whose offsets

consumption shadow the

value

value

of

+‘($I where

=

A~

wt,

is the marginal utility of wealth

A,

1% is set to give the same consumption stream as the jointly

If

problem.

in the life-cycle allocation

optimal contract, then 0, = JI-~.

Under this assumption the conventional

life-cycle earnings function g,(ht) satisfies

g,($)

since

+(h)

= J, ht +‘(ht)

is convex.

’

a4qJ = g0-Q.

I

However,

if $

exhibits

a

constant

elasticity,

implying that the intertemporal substitution elasticity is constant, then the contractual-earnings function is proportional to the earnings function implied by the usual life-cycle labor-supply model. Specifically, suppose that +(h) = l/~ h", where E = (l+n)/n. and @O. Then the contractual earnings function satisfies log ht= n log (gt/ht) + Constant,

where n is the conventional intertemporal substitution elasticity. the usual

life-cycle model,

however, this equation only

worked in excess of standard hours h*. week,

then

related

changes

to

weekly

labor-supply

in weekly

hours

average hourly

equation.

Monthly

If over

the firm's decision period is a and

earnings or

by

annual

relation to average hourly earnings.

Unlike

holds for hours

above

standard

a conventional

hours

bear

no

hours

are

life-cycle such

For example, if changes

simple

in annual

hours consist of changes in weeks worked at standard hours, then hours will appear to vary at fixed wage rates.

Research by Abowd and Card

(1989)

suggests that much of the measured variation in annual hours for prime-age males actually occurs at constant wages. This model can also explain the role of demand-side variables employment

growth

rates

for

an

annual labor-supply equation.

individual's

industry or

region)

(like in an

According to the model, variation in weeks

worked depends on the realization of demand shocks and is only indirectly related to average hourly earnings while employed. therefore

appear

in an annual

Demand-side variables

labor-supply equation as proxies

determinants of the number of weeks worked. 153

for the

With mobility costs and a non-

convex production technology, it is impossible to specify the labor-supply 22 equation independently of demand-side information. To model

summarize,

with

this

section

a nonconvexity

presents

a

simple

long-term contracting

in the relation between output

and hours

per

worker. This feature gives rise to a two-part contractual-hours function.

In periods of low employment demand, some individuals are temporarily laid off, while the remainder work standard hours. shift

between

earnings. employed

employment periods

In

and

of

at hours greater

unemployment

high

employment

preferences

(including

leisure within periods),

at

constant

demand,

average

all

than standard hours, with

between earnings and hours worked. on

In these states, individuals hours

individuals

a positive

are

relation

Under a set of restrictive assumptions

additive

separability

between

the contractual-earnings

consumption

and

function generates

the

same elasticity between hours and average hourly earnings as a conventional life-cycle

labor-supply

This

model.

relation

only

holds

for

hours

in

excess of standard hours and need not hold for aggregates of hours (such as annual or quarterly totals). It

is worth

preferences

noting

are

that

assumed

to

the model be

is highly

additively

restrictive.

separable

within

First,

and

across

periods, with no allowance for heterogeneity across people or over time. Second, jobs are assumed contractual-earnings

to

schedule

compulsory overtime

Third, the form of the

last indefinitely. ignores

legislation.

institutional

restrictions

I hope to be able to address

such

as

some of

these issues in future work.

III.

MODEL ESTIMATION

This section applies the model of the previous section to quarterly changes

in

According

individual

level employment earnings

labor

to the model, by

a

supply

changes

for

22

A

correlated

similar with

males

the

SIPP.

in which

in

firm-

is fixed should be related to changes in average hourly conventional

intertemporal

interpret this period of fixity as a week. longer periods

prime-age

in hours between periods substitution

elasticity.

I

Changes in labor supply between

(quarters or years) consist of changes in hours per week,

argument reported

shows

annual

how

reported

hours.

154

weeks

of

unemployment

may

be

negatively

which are necessarily correlated with average hourly earnings, and changes Therefore, if the model is correct, one

in weeks worked, which are not.

should expect larger elasticities between average hourly earnings and hours per week than between average hourly earnings and weeks worked. Before proceeding to analyze quarterly data from the SIPP panel, it is worth checking whether annual labor-supply data from the SIPP sample show similar patterns to data from the PSID and NLS. analysis

of

intertemporal

labor

supply

Since much of the previous

has

been

conducted

on

first-

differenced data, I aggregated quarterly information for the SIPP sample into

annual

data

for

1983

and

1984,

and

computed

the

variances

and

covariances of changes in annual hours, annual earnings, and average hourly earnings.

In

the

strongly

SIPP

sample,

changes

in the

logarithm of

negatively correlated with changes

in the

annual

hours

logarithm of

are

average

hourly earnings: the regression coefficient of the change in log hours on the change in log average hourly earnings is -.41, with a standard error of When potential labor market experience

.03.

is used as an instrumental

variable for the change in wages, the estimated elasticity of annual hours with respect to average hourly earnings is .87, with a standard error of -38. These elasticities are not much different from those reported by Abowd and Card (1989) for samples of men drawn from the PSID and NLS. Estimation of the simple model of the previous section is complicated by

three

issues

--

aggregation bias. properties

of

measurement

errors,

sample

selection

bias,

and

The importance of measurement error in the covariance

hours

strong

and

average

negative

hourly

correlations

earnings between

is

well-documented.23

Indeed,

the

changes

in average hourly earnings that appear in virtually every panel

changes

data study are generally attributed to measurement error. agreement on how to handle the problem.

MaCurdy (1981)

in

hours

and

There is less

proposed the use of

polynomials of age and education as instrumental variables for the change in

average

hourly

uncorrelated Even under

with this

earnings. age

and

Provided

education,

assumption,

that

these

the explanatory

are

tastes

for

legitimate

power of

leisure

such variables

extremely weak, often leading to imprecise estimates of the elasticity

23See

Altonji

(1986).

for

examPfe.

155

are

instruments. is

between hours and average hourly earnings.24 The

use

of

quarterly

alternative instrument. characterized changes

in

changes

that

future).

observations

hourly

occurred

an

opportunity

for

an

Suppose that individual employment situations are

by a match-specific

average

provides

4

seasonal productivity

earnings

quarters

will

ago

be

component.

positively

(or that occur

Then

correlated

4 quarters

with

in the

Among men in the one-employer subsample this individual-specific

seasonal

correlation

is small, but highly statistically

significant.

A

regression of the change in log average hourly earnings on the change 4 quarters yields

in the past and a set of unrestricted quarterly dummy variables

a

coefficient

important

limitation

of

-035, with

of

this

a

standard

instrument

error

is that

it

of

.007.25

An

is unavailable

individuals who did not work 4 and 5 quarters in the past.

for

In the one-

employer subsample the fraction of quarterly observations affected by this problem is small (1.4 percent). Compared to the

issue of measurement

bias has received relatively labor

s~pply.~~

With

error, the issue of selection

little attention

quarterly

data,

in the literature on male

however,

selection

bias

is

a

potentially serious problem, since many more individuals spend at least a full quarter unemployed than spend a whole year unemployed.

To see the

likely nature of the biases, consider the following equation for log hours per week of individual i in quarter t:

log hit = oi + rl log Wit + Vit'

Here, ai

refers

to

a person-

and

(3)

job-specific

constant,

Wit

refers

to

average hourly earnings in the quarter, rl is the intertemporal substitution and vit is a stochastic disturbance

elasticity,

24This variables average 25

is

hourly

26 Heckman

Note

Sample and

of

by the

the

rather

elasticity

large of

standard

changes

in

error annual

associated hours

with

with

the

respect

instrumental to

changes

in

earnings.

that

since

leisure,

evidenced

estimates

incorporating measurement

this

selection Killingsworth

correlation

seasonal

unrestricted

quarterly

is

routinely (1986)

dummies

addressed for

a recent

does are

not

in survey.

156

simply

reflect

seasonal

tastes

for

included.

the

literature

on

female

labor

supply.

See

error.

According

to the model

in Section II,

the probability that i is

employed in t, and therefore observed in the sample, depends only on the

If i is employed, hours and earnings are

state of demand at i's employer.

related by a deterministic earnings function. On this strict interpretation Uit consists solely of measurement error, and there is no selection bias (i.e., E(uitlHit>O) does not depend on

If

Wit).

hours per week and the

probability of employment share any discretionary components, however, one would expect vit to be positively correlated with the likelihood that i is In this case, the sample-selection process

employed in t.27

leads to a

negative bias in estimates of rl. Suppose that i is employed in period t if a latent random variable yit is positive, where

Yit

=

Yi

+ ZitH

-

(4)

Sit_

Here ri has the interpretation of a person- and job-specific fixed effect, Zit consists of measured covariates, and Sit is a transitory component. According to the model developed above, Zit should contain proxies for the strength

of

employment

demand

in

i's

industry

in

period

t.

In

the

application below, Zit consists of the level of employment in quarter t in i's l-digit industry. To the best of my knowledge there is no completely satisfactory method for handling the selection biases implied by (4) in the estimation of (3). The following strategy is based on a suggestion of Olsen (1980). that Sit is uniformly distributed on the interval [O,l].

Suppose

Then pit' the

probability that i is employed in t, is given by

Pit = Yi

The

parameter(s)

l

Zit”

II can

be

estimated

by

a

first-differenced

linear-

probability model applied to the actual sequence of employment indicators

*‘For individuals

example, to

reduce

sickness their

or hours

other when

soucces employed

of

taste and

157

to

variation reduce

ignored the

probability

in

the of

model

may

employment.

lead

for individual i.

Suppose in addition that

i.e., that the conditional expectation of the error component vit is linear in Sit*

Then

E(lOg hitIHit’0)

=

ai

+

n

log

=

“i

+

II

log Wit

=

where c2 = cI/2. consistently

Wit

+

CO

+

CO + Cl

(Co + ai + C2.Yi) +

+

rl

Cl

E(Fitltit

-

5

Yi

+

(Yi + ZitH)/Z

log Wit

+ c2

(Zit*)9

Given an estimate of II, say a, the parameter

estimated

by

taking

Zit”)

first-differences

of

n can be

observed

hours

choices (conditional on positive hours in t and t-l):

AIOg

hit = n AlOg Wit + C2 (AZiti)

The assumptions underlying this procedure very

least,

however,

estimates

of

c2

(5)

+ eit-

are quite restrictive.

provide

simple

evidence

At the on

the

importance of sample-selection biases in the estimation of quarterly hours equations. The

final

issue

in

estimation

of

the

model

is

the

fact

that

observations on the critical "hours per week" variable are only available quarterly.

If

hours

per week are constant within a quarter, then the model

applies directly and there is no aggregation bias. within a quarter, however, two problems arise.

If

hours

per week vary

First, recall biases and

the wording of the SIPP question on hours per week make it conceivable that some individuals report an answer like "40 hours per week" rather than a

158

Second, even if individuals correctly

precise average of weekly hours.**

an average of weekly hours, the convexity of the weekly earnings

report

function

implies

that

averages

of

hours

per

week

related to average hourly earnings by (3).*' reporting

biases

in

the

SIPP,

not

necessarily

Whatever the magnitude

these problems is more important than the second. of

are

I suspect that the first of

however,

they

are

presumably

less

troublesome than the biases in an annual survey. Estimation

results

various

for

first-differenced

labor-supply

equations fit to observations for the one-employer subsample of the SIPP data set are presented in Table 4.

Each column of the table corresponds to

a particular choice of estimation method, sample, and instrumental variable For each choice, estimation

for the change in average hourly earnings.

results are presented for three measures of labor supply: the logarithm of total quarterly hours, the logarithm of hours per week, and the logarithm Because the logarithm of quarterly hours is the sum of

of weeks worked.

the logarithms of hours per week and weeks worked, the coefficients in rows 4(i) and 5(i) sum to the coefficients in row 3(i). Two samples are constructed from the quarterly

labor-supply data of

the one-employer SIPP sample: the set of all available quarterly changes in labor supply (denoted by the column heading "All"); and the subsample of changes

for

which

in

quarters

the

a

corresponding

future

is

change

available

4 quarters

(denoted

in the

by

the

past

column

or

4

heading

Use of Alog Wit-4 or AlOg Wit+4 as an instrumental variable

"Subsample").

for Alog Wit is restricted to the subsample. Ordinary

least

squares

columns (1) and (2).

(OLS)

estimation

results

are

presented

in

The estimates are very similar in the two samples,

and suggest that changes in hours per week and changes in weeks worked are both

strongly

earnings. to

negatively

correlated

average

20In than

an

hourly

parameters

the

fact, with

average

2gThis suPPlY

is

changes

in

average

hourly

The estimated elasticity of total quarterly hours with respect is -.39,

earnings

literature based on annual data.

individuals

with

of

interviewer hours

hours

problem shorter will

SIPP

varying

arises than

differ

per

per

week

quite the

from

manual week

over

the

the

to

(U.S. report

true

similar

If of

Bureau their

preceding

generally.

periodicity

very

to

estimates

in the

It is interesting to note that the

the

parameters.

159

of “most

the

Census

frequent”

(1989)) weekly

instructs hours

rather

months.

the available

correct

“period” data,

the

for estimated

analyzing

labor

labor-supply

Table

Estimated

Hours

Equations: Fit

to

4

First

Differenced

One-Employer

(Standard

Errors

Specifications

Subsample in

Parentheses)

Estimation

Method

and

Sample

OLS

IV Sub-

I

Al

Sample:

(1)

I.

Instrumental for

Sub-

sample

Al I

Al I

(2)

(3)

(4)

EXP

EXP

--

Variable

Correction

3.

Log

Equation

Hours

Wage

(i)

(ii)

Coefficient

Selection

No

No

No

.oo

-.39

-.X3

(.Ol)

C.01)

C.50)

--

Co-

efficient

Log

Hours/Week

(i)

Wage

(ii)

Coefficient

Selection

Weeks

(ii)

.I8

-.29

-.28

C.01)

C.01)

C.36)

--

Co-

Coefficient

(7)

(8)

EWP

EWP

Awt_4 9

Selection

:

All

which Selection

log

earnings

A?+4

Yes

No

Yes

-.Ol

-.Ol

-.02

.16

.I4

(.50)

C.52)

C.52)

C.22)

C.22)

7.26

6.37

--

(1.45)

(1.58)

No

Yes

6.02 (1.27)

.I8

.22

.21

.10

.lO

t.36)

C.38)

C.38)

C.14)

C.14)

2.78

2.55

--

2.80

(1.02)

(1.16)

(.79)

-.09

-.I8

-.19

-.23

-.24

.05

.05

C.01)

C.32)

C.32)

C-33)

C.33)

(.13)

C.13)

--

-_

4.48

3.03

--

3.21

( .91)

contains in

row

average four

I,

19842

average

correction In

t-4,

C.01) Co-

sample

change

text.

tt4

AW

-.I0

efficient

in

(6)

Equation

Wage

(i)

Notes

(5)

Education

efficient

Log

Subsample

AW

Selection

5.

Subsample

Awt

2.

4.

Subsample

samp I e

is Exp hourly

quarters

observations.

hourly based

refers

earnings

on to

earnings, in

estimated

potential and

(I .02)

Subsample four

contains

quarters

in

first-differenced labor-market

Aw~_~/Aw~+~ refer

past/future.

160

19566

observations

past/future linear

experience, to

C.76)

changes

is

probability Awt

refers in

log

model: to

for

available.

the

average

see change hourly

elasticity

of

hours

per

week

is more

negative

than

the

elasticity

of

One simple explanation for this finding is that measurement errors

weeks.

are proportionally

smaller in the weeks measure

hours per week.30

Given the nature of the SIPP

than

in the measure

of

questionnaire, this seems

plausible. Instrumental variables

estimates that potentially eliminate the

(IV)

biases caused by measurement errors in hours are presented in columns (3) The estimates in columns (3)-(6) use potential labor-market

through (8).

experience (age minus education minus 5) as an instrument for the change in average hourly earnings.

The use of this instrumental variable leads to

similar results on the total sample and subsample.

In both cases the IV

estimate of the elasticity of hours per week with respect to average hourly earnings

is positive but relatively imprecise.

The

IV estimates of the

elasticity of weeks with respect to average hourly earnings are negative, but again relatively imprecise.

The elasticities of hours per week and

weeks tend to offset each other,

leading to a wage elasticity of total

quarterly hours that is close to zero. Columns

(4) and (6) combine

IV estimation with the linear selection

correction proposed in equation (3).

The first-stage equation uses changes

in the log of aggregate employment in the individual's one-digit industry as well as an unrestricted set of quarterly dummy variables to predict the change in the probability of employment. are

reasonably

strong

predictors

of

Industry-level employment changes

the

change

in

the

probability

of

employment: the t-statistic associated with the measured change in industry employment is 2.7.

Again, estimation results are similar in the complete

sample and the subsample: in all cases the estimated coefficient associated with the selection term is positive and statistically significant, although the addition of the selection term has little impact on the estimated wage elasticities.

As expected, the selection term has a larger coefficient in

the equation for the number of weeks worked than the number of hours per week, although one can reject the hypothesis that the number of hours per week

is

independent

of

average hourly earnings.

30Any error the hourly

in more

measurement log

average

negative

is

error hourly the

OLS

in

industry

demand,

controlling

for

the

level

of

The large and statistically significant estimates

log

hours

earnings. estimate

or The

of

the

weeks greater elasticity

earnings.

161

induces the

a perfectly

variance between

in the

negatively such hours

correlated

measurement

errors,

measure

average

and

of

the

selection

changes

coefficients

in demand-side

confirm

variables

the

influence

finding

of

Ham

(1986)

that

individual labor supply, even

controlling for individual wages. The earnings

last two 4

columns

quarters

in

of

table

the

past

4 use

or

instrumental variable for the change

4

the change

quarters

leading

to

a

substantial

in

the

hourly

future as an 31 This

in average hourly earnings.

instrument is more strongly correlated with earnings,

in average

the change in average hourly

reduction

in the

estimated

standard

errors associated with the wage elasticities, although little change in the point estimates.

Again, the estimated coefficients of the selection terms

are positive and statistically significant,

but their inclusion

leads to

little change in the estimated wage elasticities. Irrespective of the choice of instrumental variable, the estimates of the wage elasticity of hours per week, which can

be

interpreted

as

estimates

of

in the context of the model

the

intertemporal

substitution

elasticity, are in the same range as those obtained by MaCurdy (1981) and Altonji (1986) using annual hours data from the PSID.

There is no evidence

to suggest that analysis of quarterly observations on hours per week will lead to a new assessment elasticity.

of the

size of

the

intertemporal

substitution

Either the intertemporal labor-supply elasticity is relatively

small (on the order of estimates already in the literature), or, contrary to

the model

curvature

in Section

of

weekly

II, one cannot

earnings

recover

schedules.

its magnitude

Since

there

is

from

the

considerable

variation in weekly earnings and hours in the SIPP sample, it remains an interesting

question

how

this

variation

is

determined,

if

not

by

preferences over intertemporal labor supply.

IV. SUMMARY This

paper

begins with

a descriptive

analysis

of

short-term

hours

variation among males in the Survey of Income and Program Participation. unique

feature

of

the

SIPP

is

its

4-month

interview

schedule.

A

This

schedule permits a detailed investigation of the components of variance in individual labor supply over time.

31 the

past

I

tested or

whether

4 quarters

changes in

the

in future

wages but

are found

A simple decomposition

correlated no

162

significant

differently

with

difference.

suggests that

changes

4

quarters

in

quarter-to-quarter movements number

variation

in hours worked

arises

from three

sources:

in and out of employment for an entire quarter; changes in the

of

weeks

conditional

worked,

on

employment;

and

changes

in the

For individuals with the same employer over the

number of hours per week.

sample period, these three components contribute about equal shares to the overall variation in hours around individual-specific means. movements

For others,

in and out of employment for the entire quarter contribute the

largest share of variance, whereas changes in hours per week contribute the smallest share. Motivated

by the observation that weekly

labor supply exhibits some

minimum hours threshold, the second part of the paper constructs a simple contracting model with mobility costs and a nonconvexity in the relation between hours per worker and output.

In states

schedule.

This model generates a two-part hours

of low demand, some individuals are temporarily laid

off, while others are employed at a minimum weekly hours level. of

high

demand

all

individuals

work

hours

in

excess

of

In states

the

minimum

threshold. The contract is supported by a simple schedule relating earnings per worker to

hours per worker.

separability

additive

between

Under the assumption of within-period leisure

and

consumption,

elasticity between hours and average hourly earnings

the

implied

is the conventional

intertemporal labor supply. The model

offers

a simple

explanation

for the role of demand-side

variables in an individual labor-supply function.

According to the model,

changes in weeks worked occur at fixed average hourly earnings, reflecting the realization of employment demand.

Changes in annual measures of labor

supply, which consist in part of changes in weeks worked, will therefore be correlated

with

measures

of

employment

demand

faced

by

an

individual's

employer, even after controlling for average hourly earnings. The model

implies that estimates

of

the

intertemporal

labor-supply

elasticity can be obtained from estimates of the wage elasticity of hours per

week

for

individuals

observed

in

the

same

contract

over

time.

Estimates are constructed from quarter-to-quarter changes in labor supply for

men

with

the

same

employer

during

the

SIPP

sample

period.

The

estimation procedures take account of measurement error in average hourly earnings and possible selection biases associated with movements in and out of

employment

for an entire quarter.

Even with

these adjustments,

the

estimates of the wage elasticity of hours per week are relatively small, ranging from -10 to -22.

If the basic point of the model is correct, however, it is important 163

to realize that variation changes

in productivity

in labor supply may be much more sensitive to

than

these

estimates

suggest.

This

is because

changes in productivity have a direct effect on the fraction of individuals employed

at a given firm and on the number of weeks worked

individual.

by a given

The evidence in this paper shows that changes in weeks are a

major source of variation in individual labor supply and that these changes are highly correlated with industry-demand conditions. little

indication

that

these

changes

supply schedule.

164

occur

along

However, there is

a conventional

labor-

DATA APPENDIX The

data

from

cross-sectional

consecutive

data

sets.

A

interviews of panel

can

information from the 9 interview "waves."

be

the SIPP

are

constructed

released

by merging

as the

Individuals are identified in

each wave by a combination of three variables: the sample unit identifier, the entry address identifier, and the person number.

I merged information

for men whose age is between 22 and 62 in all waves of the 1984 panel by these

three

Department

identifiers.

of

Commerce

As

(1987),

noted

individuals

are

occasionally

assign the same series of

incorrectly

in

chapter merged,

the 6),

SIPP it

since

is the

User's

Guide

possible SIPP

(U.S.

that

interviewers

identifiers to different

people.

This is most likely to happen in the event of a marital dissolution. the other hand,

individuals who move cannot

be merged

sampling frame is based on residential location. members

to the sample as they move

some

On

because the SIPP

The SIPP also adds new

into existing sample households.

I

found 8280 individuals who reported information in 8 consecutive interviews in the 1984 SIPP panel and another 8458 individuals for whom information was missing in at least one interview.

The following table compares the

characteristics of those with complete longitudinal data and those without:

165

Comparisons of Individuals with Complete and Incomplete Data

Characteristic (at first interview)

Mean In Sample With: Complete Data

Incomplete Data

1.

Age (years)

2.

Education (years)

16.9

16.2

3.

Percent worked 4 weeks

83.9

75.5

1388.3

1208.9

8.4

10.8

38.1

40.1

in previous month 4.

Monthly earnings ($) (including zeros)

5.

Percent Black

A second significant reduction in the size of the sample occurs when individuals with imputed data on earnings, weeks worked, and hours per week Of the 8280 individuals in the sample with complete are excluded. longitudinal data, 1965 have an imputed value for one of these variables at some point in the sample. The following table compares the characteristics of those with imputed data and those without:

Comparisons of Individuals With and Without Imputed Data

Mean In Sample With: Characteristic

Imputed Data

No Imputations

40.4

40.3

1.

Age in 1986 (years)

2.

Monthly earnings (lb)excluding nonworkers:

3.

5.

September 1983

1758.8

1791.4

December 1986

1955.3

1983.6

Usual hours per week excluding nonworkers: September 1983

42.8

42.4

December 1986

43.0

42.4

Percent Black

9.7

8.1

166

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On the Covariance Structure of Earnings and Hours Changes. Econometrica,

57: 411-45.

Altonji, J. (1986)

Intertemporal Micro Data.

Substitution

in

of Political

Journal

Labor

Supply:

Economy,

Evidence

from

S176-S215.

94:

Card, 0. (1987)

Supply and Demand in the Labor Market. Princeton University Industrial Relations Section Working Paper 228.

Coleman, 1. (1984)

Essays on Aggregate Labor Market Business Cycle Fluctuations. Unpublished Ph.D. Thesis, University of Chicago.

Ham, J. (1986)

Testing Whether Unemployment Represents Inter-temporal Labour Supply Behavior.

Review of Economic Studies,

53: 559-78.

Hansen, 6. (1985)

Indivisible Labor and the Business Cycle. Economics,

Journal of Monetary

16: 309-327.

Heckman, J. and MaCurdy, T. (1988)

Empirical Tests Carne-gieRochester

of Labor-Market Equilibrium: An Evaluation. Conference

Series on Public Policy,

28: 231-5.

Heckman, J. and Killingsworth, M. (1986)

Female Labor Supply: A Survey.

Orley Ashenfelter and Richard

Layard, (eds.), Handbook of Labor Economics.

New York: North

Holland. Lillard, L, Smith, J., and Welch, F. (1986)

What

Do

We

Nonreporting Economy,

Really and

Know

Census

94: 489-506.

167

About

Wages?

Imputation.

The Journal

Importance of

of

Political

MaCurdy, T. (1981)

An Empirical Model of Labor Supply in a Life-Cycle Setting. Journal of Political Economy,

1059-85.

89:

Olsen, R. (1980)

A

Least

Squares

Econometrica,

Correction

for

Selectivity

Bias.

48: 1815-20.

Plosser, C. (1989)

Understanding

Real

Business

Perspectives,

3: 51-77.

Indivisible

Labor,

Cycles.

Journal of

Economic

Rogerson, R (1988)

Monetary Economics,

Lotteries,

and

Equilibrium.

Journal of

21: 3-16.

Rosen, S. (1985)

Implicit Contracts: A Survey.

Jownal of Economic

Literature,

23: 1144-75. United States Oepartment of Commerce Bureau of the Census (1987)

Survey

of

Income

and

Program

Participation

Users'

Guide.

Washington, D.C.

(19@4

SIPP 5010 Interviewer's Manual.

(1989)

The 1984 SIPP Full-Panel Research File.

168

Washington, O.C.

Washington, D.C.