Manufacturing Plants’ Use of Temporary Workers:
An Analysis Using Census Micro Data

Yukako Ono and Daniel Sullivan, Federal Reserve Bank of Chicago1

Abstract
Using plant-level data from the Plant Capacity Utilization (PCU) Survey, we examine
how manufacturing plants’ use of temporary workers is associated with the nature of their
output fluctuations and other plant characteristics. We find that plants tend to hire
temporary workers when their output can be expected to fall, a result consistent with thenotion that firms use temporary workers to reduce costs associated with dismissing
permanent employees. In addition, we find that plants whose future output levels are
subject to greater uncertainty tend to use more temporary workers. We also examine theeffects of wage and benefit levels for permanent workers, unionization rates, turnoverrates, seasonal factors, and plant size and age on the use of temporary workers; based on
our results, we discuss various views of why firms use temporary workers.

Key words: temporary workers, output fluctuations
JEL codes: J2, J3

1

We thank David Autor, Randy Becker and John Steven for insightful advice and helping us to augment
the data sets. All errors are the authors. The research in this paper was conducted while the authors wereSpecial Sworn Status researchers of the U.S. Census Bureau at the Chicago Census Research Data Center.
Views, research results, and conclusions expressed are those of the authors and do not necessarily reflect
the views of the Census Bureau, the Federal Reserve Bank of Chicago, or the Federal Reserve System. This
paper has been screened to insure that no confidential data are revealed. Support for this research at the
Chicago RDC from NSF (awards no. SES-0004335 and ITR-0427889) is also gratefully acknowledged.

11. Introduction
The temporary help industry (THS) has grown rapidly over the last quarter century.
Indeed, the industry’s share of nonfarm employment rose from less than 0.5% in the early
1980s to 2.0% by 2000. The majority of this industry’s employees work under the
direction of managers at client firms, usually alongside the client’s permanent
employees.2
The industry’s rapid growth has attracted substantial attention from researchers(e.g., Segal and Sullivan (1995, 1997), Golden (1996), Polivka (1996), Autor (2003), andHouseman (2001)) who, along with industry analysts, have identified a number ofreasons that temporary workers may be attractive to client firms beyond their traditionalrole of filling in when permanent employees are absent for short periods.
First, it has been suggested that the use of temporary workers may allow client
firms to circumvent nondiscrimination requirements in the provision of benefits. Under
normal circumstances, in order to secure the tax advantages associated with providing
certain benefits, firms need to provide those benefits to all their employees. If the firm
would not otherwise want to provide a certain benefit to a particular segment of its workforce, one strategy might be to staff that segment with employees of a THS agency.
Having such a dual work force may allow it to provide benefits to the remainder of its
workforce without jeopardizing their tax status.3

2

For most legal purposes, temporary workers from THS agencies remain employees of the THS agencies,
which are responsible for their recruitment and hiring as well as for paying their wages and benefits.
3
The legal issues surrounding the employment status of temporary workers are complex. A temporary
worker can under some circumstances be considered an employee of the client firm. In particular, in theMicrosoft case, the U.S. Supreme Court ruled that temporary workers who provided services to Microsoft
for a period of several years were entitled to benefits, including stock options, which Microsoft provided to
all its permanent employees. The Microsoft decision has limited firms’ ability to implement such a strategy
of using the same temporary workers for long periods.

2

The use of temporary workers may also be attractive to firms as a means ofscreening potential permanent employees. Given the sometimes significant costs of
dismissing poorly performing employees, a client firm may want to first observe theirperformance as temps. If that performance is judged inadequate, they can simply request
a new worker from the THS agency. Such a trial period as a temporary worker may be
preferable to a formal probationary period as a permanent employee.
Finally, the use of temporary workers may be attractive when a firm believes
demand for its product may be lower in the future. A firm would want to avoid thepotential costs of dismissing permanent employees should demand turn out to be low.
The firm would also want to avoid the costs of training additional permanent employees
if the workers are going to be needed only for a short period. The firm may be able to
avoid such costs by meeting a portion of its staffing needs with temporary workers.
Avoiding such costs may justify the use of temporary workers even if, in the current
period, the costs of employing temporary workers are greater than those of permanent
workers.
The increased use of temporary workers to accommodate demand fluctuations
may have been particularly important in the manufacturing sector. Temporary services
industry observers report that THS agencies provided very few “light industrial” workers
before the mid-1980s, but by the mid-1990s such workers were a substantial part of theirbusiness. At the same time, the prevalence of temporary layoffs by manufacturing firms
declined significantly.4 This suggests that temporary workers may be playing thebuffering role that firms’ own production workers have historically shouldered. Segal
and Sullivan (1997), Katz and Krueger (1999), and others have conjectured that the3growth of the temporary services industry increased the efficiency of the labor market
search, making it possible for manufacturers and others to vary their output levels without
running into bottlenecks due to difficulties hiring enough qualified workers. This, in turn,
may have played a role in reducing the natural rate of unemployment during the 1980s
and 1990s.
One aim of this paper is to analyze the role of temporary workers inaccommodating fluctuations in production levels, a topic on which there is very little
empirical work. Houseman (2001) surveyed firms about their use of temporary workers
and found that a substantial fraction of firms reported using them to meet fluctuations indemand. Campbell and Fisher (2004) developed a theoretical model describing a firm’s
decision to adjust employment of two groups of workers with some of the characteristics
of temporary and permanent workers and compare their calibration with aggregate level
data. However, there are no empirical studies that examine the relationship between afirm’s use of temporary workers and its own output fluctuations.
One reason for the scarcity of empirical studies has been limited data. Evenamong confidential micro Census data sources such as the Annual Survey of
Manufactures (ASM) and the Census of Manufactures (CM), it is rare that a survey
collects data on the use of temporary workers at the level of the individual businessestablishment. Such data limitations have prevented researchers from learning thecharacteristics of firms that use temporary workers.

4

See, for example, Aaronson, Rissman, and Sullivan (2004).

4

In this paper, we use plant-level data from the Plant Capacity Utilization (PCU)
Survey, which is conducted annually by the Census Bureau.5 In 1998, the survey begancollecting information on the number of temporary workers utilized by plants. For thisstudy, micro-level data for 1998 and 1999 are available.
Taking advantage of these newly available data, we examine how a plant’s
temporary worker share is associated with its output fluctuations. In particular, we focus
on the relationship between a plant’s use of temporary workers and its expected output
growth as well as the magnitude of its typical output fluctuations.
Depending on the primary motive for their use, higher expected output growth
could be associated with greater or lesser use of temporary workers. On the one hand, if
the primary motive for using temporary workers is to reduce the potential costs of
dismissing permanent workers due to the lower expected output, then expectations ofhigher output growth will be associated with less use of temporary workers. In addition,as our stylized model in Section 2 shows, if firing costs are sufficiently high, greater
uncertainty about future output leads the firm to cap the number of permanent workers at
a lower level, and thus hire more temporary workers. On the other hand, if the primary
motive for using temporary workers is to screen future permanent workers, then higher
expected output growth is likely to be associated with a greater use of more temporary
workers. Given a need to significantly increase permanent employment in the near
future, the firm will screen a large number of workers in the current period and may thus
employ a large number of temporary workers.

5

These data are used by the Federal Reserve Board to estimate capacity utilization rates for the
manufacturing and publishing industries.

5In addition to testing the above conjectures, we also examine how a plant’s
temporary worker share depends on a number of its other characteristics, such as its size,
age, and industry. Plant size may matter for a number of reasons. One might imagine
that the use of temporary workers to buffer fluctuations in the labor requirement may
require a level of sophistication likely to be found in a large plant. Its larger size may
also increase a plant’s ability to negotiate a lower margin from a temporary services firm.
In addition, a larger plant, with its deeper pockets, may face higher costs in the event ofan unjust dismissal lawsuit. On the other hand, the larger scale of such a plant may allow
the plant to be flexible without relying on temporary workers, by redistributing its
permanent workers across different production processes. Plant age and industry may
also matter for use of temporary workers because of their effect on the level of
uncertainty and other factors.
Moreover, we investigate the relationship between the use of temporary workers
and a plant’s wage and benefit levels. A plant whose permanent workers earn high wage
rates may be more motivated to use temporary workers. However, what should matterfor the choice of temporary worker share is the ratio of temporary worker to permanent
worker wage rates. Industry observers indicate that THS agencies charge client firms ahigher markup over wages in the case of higher skilled workers (Kilcoyne, 2004). Thus,
it is possible that a firm with a high wage rate for permanent workers might use
temporary workers less. A similar argument applies to a firm that provides generous
benefit packages, though the negative effects may be offset because a firm that provides
expensive benefits packages may have more incentive to employ temporary workers tokeep benefit costs down.

6Finally, we analyze how the temporary worker share at the three-digit NAICS
industry level is dependent upon several additional variables. These variables include
unionization, labor turnover rates, and seasonality. We expect unions to resist the use of
temporary workers. Higher turnover rates would likely increase the value of screening
potential employees and thus could lead to greater use of temporary workers. Whenvoluntary turnover is high, the likelihood of a firm needing to fire workers due toinsufficient demand would be lower. So, greater turnover could be associated with lessuse of temporary workers. A stronger seasonal component would also be positively
correlated with the higher use of temporary workers, ceteris paribus.
One can view our study as similar in intent to a number of micro-level studies ofother forms of firm adjustment to demand shocks. For example, using plant-level data,
Copeland and Hall (2005) examine how automakers accommodate shocks to demand by
adjusting price, inventories, and labor inputs through temporary layoffs and overtime.
Such considerations are closely linked to a firm’s decision to adjust temporary worker
share. We intend to examine such interactions in future work.
In Section 2, we outline a simple, stylized model that motivates our empirical
specification. In Section 3, we describe our data in more detail and discuss empirical
implementation. In Section 4, we present our empirical results. Section 5 concludes.

2. Motivational ModelIn this section, we present a stylized model of a plant’s choice on how many permanentand temporary workers to hire. The model is intended to help motivate and guide our

7empirical work and to emphasize the role of temporary workers in accommodating output
fluctuations.
Specifically, we assume that labor is the only factor of production and that, ineach period, the plant manager must hire an appropriate quantity of labor, et , to meet an
exogenously determined level of output, yt = f (et ) , where f is a standard, strictlyincreasing production function. The required labor input can come from a combinationof “permanent employees,” pt , and “agency temporary workers,” at , with the total
quantity of labor given by et = pt + θ at , where θ is a positive constant representing the
productivity of a temporary worker relative to that of a permanent worker. The wage
rates for permanent and temporary workers are wp and wa , respectively. The plant incurs
costs of δ to fire each permanent worker. Thus, the plant’s total costs in a period are

wp pt + wa at + δ max( pt −1 − pt ,0) . We assume that future levels of output are uncertain andthat the firm minimizes the expected present value of total costs given a discountfactor, β = 1/(1 + r ) , where γ is a real interest rate.
Let the unit labor costs for permanent workers be u p ≡ wp and that for temporary
workers ua ≡ wa / θ . We assume that Δu = ua − u p > 0 ; absent firing costs, temporary
workers are more expensive, either because their wage rate is higher ( wa > wp ), they areless productive ( θ < 1 ), or both. We further assume that the cost of firing a permanent
worker is greater than the (discounted) difference in unit labor costs, but less than a fullperiod’s wage; i.e., Δu / β < δ < wp . If Δu > βδ , the plant never hires any temporary
workers; it is cheaper to use permanent workers even if it is certain that they will be fired8

in the next period. The condition that δ < wp is a convenient simplification implying thatthe firm does not keep any idle workers on the payroll; keeping an idle worker on the
payroll costs more than firing the worker in the current period and may also increasefiring costs in the future. With this configuration of costs, the plant faces a tradeoff
between using more permanent workers, which lowers current wage costs, versus using
more temporary workers, which may lower future firing costs.
The Two-Period Case

It is easiest to see the logic of the model when there are only two periods. In this case,the plant is unconcerned about firing costs in the second period. Let y2 represent a
required output level in the second period. The plant meets its entire labor need withpermanent workers, p2 = f −1 ( y2 ) , incurring costs
C2 = wp f −1 ( y2 ) + δ max(0, p1 − f −1 ( y2 )) .

In the first period, given y1 and knowledge of the distribution of y2 , the firmchooses p1 and a1 to minimize total expected discounted costs, TC , which is written as
TC = wp p1 + wa a1 + β E[ wp f −1 ( y2 ) + δ max(0, p1 − f −1 ( y2 ))] . The quantity of labor thatmeets the required level of production is f −1 ( y1 ) = p1 + θ a1 . Thus, we can rewrite TC as afunctionofp1

alone:

TC = u p p1 + ua ( f −1 ( y1 ) − p1 ) + β E[ wp f −1 ( y2 ) + δ max(0, p1 − f −1 ( y2 ))] .

Thus, the derivative of costs with respect to (w.r.t.) permanent labor in the first period isdTCd( p1 ) = −Δu + βδE[max(0, p1 − f −1 ( y2 )] .
dp1
dp1

(1)

9

Assume that y2 follows a continuous distribution with density g ( y2 ) that isstrictly positive over the relevant interval; distribution function is G ( y2 ) . Then, theexpected number of permanent workers fired in the second period given p1 isL( p1 ) = E[max(0, p1 − f −1 ( y2 )] = ∫f ( p1 )0( p1 − f −1 ( y2 )) g ( y2 )dy2 . Thus the derivative of thenumber of permanent workers fired w.r.t. permanent labor in period 1 isL′( p1 ) = ( p1 − f −1 ( f ( p1 )) g ( f ( p1 )) + ∫f ( p1 )0

g ( y2 )dy2 = G ( f ( p1 )) .

(2)

From (2), we can rewrite (1) asdTC( p1 ) = −Δu + βδ G ( f ( p1 )) .
dp1

(3)

Increasing permanent workers by one (and thus lowering the number of temporary
workers by 1/ θ ) in period 1 reduces current costs by the difference in unit costs between
temporary and permanent workers ( Δu ), but raises expected firing costs in the second
period by the product of the cost of firing a worker ( δ ) and the probability that themarginal worker is fired ( G ( f ( p)) ).
Because G ( y ) and f ( p ) are increasing functions,

Moreover,dTC( p1 ) is increasing in p1 .
dp1

dTC
dTC
(0) = −Δu < 0 and lim( p1 ) = −Δu + βδ > 0 . Thus, there exists a
p1 →∞ dpdp1
1unique level of permanent employment, p , such thatdTC( p ) = −Δu + βδ G ( f ( p )) = 0 .
dp1

(4)

See Figure 1 for an illustration of the case in which y2 is uniformly distributed in theinterval from ylow to yhigh and f (e) is linear. If f −1 ( y1 ) < p , as permanent employment

10

increases, TC decreases until permanent employment reaches the level that satisfies theplant’s labor requirements given y1 . Thus, the optimal number of permanent workers is
f −1 ( y1 ) , and that of temporary workers is zero. On the other hand, if f −1 ( y1 ) > p , TC
falls with p1 until p1 = p , and then begins to rise.

Thus the optimal number ofpermanent workers is p , and that of temporary workers is ( f −1 ( y1 ) − p ) / θ , the level
necessary to meet the rest of the labor requirement. We can summarize the solution by
writing the optimal numbers of the first period permanent workers, p1* , and temporary
workers, a1* , as
p1* = min( f −1 ( y1 ), p )(5)

a1* = ( f −1 ( y1 ) − p1* ) / θ ,(6)where p satisfies βδ G ( f ( p )) = Δu . The plant hires permanent workers up to a
maximum level at which the expected discounted costs of firing an additional permanent
worker are equal to the extra current unit labor costs of substituting temporary workers.
In Appendix A, we show that in the case of an infinite horizon with independently andidentically distributed (i.i.d.) random output levels; the plant’s optimal policy isessentially identical to the solution of the first period of the two-period model.
Lognormal Output Levels and Power Production Function

Suppose that the distribution of y2 is lognormal, log y2 ~ N ( μ2 , σ 2 ) and that the
production function takes the power form,f (e) = Aeα .

(7)

11

Then, based on (4), p is such that (s.t.) Δu = βδΦ (log A + α log p − μ2σ

) , where Φ ( x) is

the standard normal distribution function. Alternatively, we can write
log p = α −1[ μ2 − log A + σΦ −1 (

Δu

βδ

)] .

(8)

The impact of σ on p depends on Δu and firing costs δ .6 If firing costs are sufficiently
high so that Δu <1Δuβδ , then Φ −1 ( ) < 0 , and the probability of needing to fire theβδ2marginal worker is less than one half. In this case, greater uncertainty increases theprobability, moving it toward one half. The increased probability of firing causes theplant to use fewer permanent workers and more temporary workers to produce the given
output.7
Implications for Empirical Analysis

The simple model sketched above suggests that expected output growth, g e ≡ μ2 − log y1 ,is an important determinant of a plant’s use of temporary workers. When g e is lower, themodel suggests that firms tend to use more temporary workers in order to avoid futurefiring costs. The model also says that if firing costs are high enough, higher uncertainty,

σ , increases the use of temporary workers. These are two key hypotheses we test in the

Because α and δ are positive constants and Φ (⋅) is an increasing function, a higher value of Δu is
associated with a greater level for p , leading to the use of fewer temporary workers. On the other hand, a6−1higher value of the firing cost, δ , is associated with a lower level of p , leading to the use of more
temporary workers.
7
Note that the opposite is true if firing costs are low so that Δu > (1/ 2) βδ . It is somewhat counterintuitivethat an increase in uncertainty could lead to the use of fewer temporary workers. When firing costs are low,
the plant worries little about firing and thus hires so many permanent workers that the probability of firinga marginal permanent worker in the second period exceeds one half. In such a situation, an increase in theuncertainty in the second period labor requirements lowers the probability of firing to the level closer to
one half. This reduces the marginal expected firing costs and gives the plant the incentive to hire morepermanent workers.

12

empirical section. As noted above, if screening is the primary reason why firms use
temporary workers, then in contrast to the above model, higher expected output growthwould be associated with greater use of temporary workers.

3. Empirical Implementation and Construction of Variables
Empirical Specification

Using (7) and (8) and assuming for simplicity that α and A are one, the condition that aplant hires temporary workers is
f −1 ( y1 ) > p ⇔ Z = − g e − σΦ −1 (

Δu

βδ

) >0.

(9)

Introducing heterogeneity across plants through a normally distributed random
components in log output, ν i , and assuming (9) can be well approximated by a linear
function, we can rewrite the condition that a plant uses temporary workers as
Z i = [ gie , σ i , Xi ]β +ν i > 0 , where Xi contains other control variables. The plant uses notemporary workers when Z i is negative; once Z i is positive, the plant begins using
temporary workers, and its temporary worker share increases as Z i continues to increase.
Both a plant’s likelihood of using temporary workers and its temporary worker share
increases with gie and σ i .
To examine a plant’s discrete choice to use any temporary workers, weestimate the Probit model. We also estimate Tobit models to examine how the temporary
worker share is associated with our key variables. The Tobit model is consistent with ourframework in that plants start using temporary workers once Z i becomes positive andcontinue to increase their use of temporary workers as Z i increases further. Using the13observations on plants with positive numbers of temporary workers, we also fit linear
regression models relating the continuous part of temporary worker share to our key
variables, thus relaxing a restriction imposed by Tobit analysis. Xi includes industry
dummies as well as other plant characteristics such as plant size and age that may proxyfor variation in the level of firing costs and wage differentials between temporary andpermanent workers, which the model says should also influence the use of temporary
workers.
Data

The main data set for this study is the survey of Plant Capacity Utilization (PCU), which
is used by the Federal Reserve Board to estimate capacity utilization rates ofmanufacturing and publishing plants.8 In addition to variables related to a plant’s
operation status and capacity utilization, the survey collects data on workers, including
the number of production workers, their hours of work, and overtime hours. Since 1998,
the survey has collected data on the number of temporary production workers and theirhours of work, which are the key variables in our study. In the PCU questionnaires,
temporary production workers are defined as “production workers not on the payroll(hired through temporary help agencies or as their own agent)”.9 The 1998 and 1999 PCU

8http://www.census.gov/econ/overview/ma0500.html (August 2006)
In the PCU questionnaires, “production workers” are defined as workers (up through the line-supervisor
level) engaged in fabricating, processing, assembling, inspecting, receiving, packing, warehousing,shipping (but not delivering), maintenance, repair, janitorial, guard services, product development,
auxiliary production for plant’s own use (e.g., power plant), record keeping, and other closely associatedservices. They also include truck drivers delivering ready-mixed concrete (U.S Census Bureau, 2000). Notethat while the PCU provides employment and hours data for each shift, examining the allocation of
permanent and temporary workers between different shifts is beyond the scope of this paper. We focus on aplant’s overall use of temporary workers for all shifts in total.
914

micro data are available for this study;10 the surveys collect information for the only
fourth quarter of each year.
In our empirical work, we include only manufacturing plants that are in operationand that provide valid answers to the key employment questions including the number of
temporary production workers. We exclude plants that reported inconsistent responses for
key variables. Among the remaining plants, we further select those for which we cancalculate measures of the expected level and volatility of production. As we describe
below, we calculate such measures using annual shipment data from ASM and CM. The
ASM and CM are available to us for the period from 1976 to 2001. Our sample is limited
to the plants which appeared in the ASM-CM panel for a sufficient number of years for
us to estimate key parameters of their time series process for output. We are also limited
to plants that appear in the ASM for enough consecutive years prior to being in the PCU
to allow us to use lagged variables in the regressions. Appendix B provides more details
about which plants are included in our sample. Combining both years of available PCUsleaves us with about 5,000 plants.
Measure for gie

As our stylized model shows, expected output growth is a key variable in determining aplant’s use of temporary workers.

In order to create an empirical measure of thisvariable, we have to make three choices. In particular, we have to specify the current
period, the future period, and how the expectation of the future period’s output isestimated. Because information on temporary worker employment from the PCU is thatof the fourth quarter, we take the current period to be the fourth quarter of the survey year

10

Approximately 17,000 plants are surveyed each year.

15

In particular, we use the annualized fourth quarter total value of shipments (TVS)
reported on the PCU survey as the current output; the ASM and the CM, which we use to
estimate time series process for TVS, report annual TVS As a future period, one could
view the length of the horizon considered by the plant as an empirical question to beinvestigated thoroughly. However, given that no monthly or quarterly output series atplant-level are available, we take the entire year following the survey to be the future
period.
Let us define the annualized fourth quarter output for plant i in year t as
ltvsitAQ 4 ≡ ln(4 × tvsitQ 4 ) , where tvsitQ 4 is the TVS of plant i ’s fourth quarter in year t . We

define gite ,Q 4 ≡ Et [ltvsit +1 ] − ltvsitAQ 4 , where Et [ltvsit +1 ] is plant i ’s expected TVS in yeart + 1 . gite,Q 4 reflects the difference between the current quarter’s output and the expected

average quarterly output over the next year. We estimate Et [ltvsit +1 ] using several
specifications for the time series of log annual output levels in the ASM-CM panel.
Specification for the Expected Output Level and the Uncertainty Level

To measure expected future output, Et [ltvsit +1 ] , as well as the uncertainty, σ , for eachplant, we use the time series data of the plant’s TVS from the ASM and the CM. The
combination of ASM and CM, often called the Longitudinal Research Database (LRD),
provides us annual time series data for the U.S. manufacturing plants, and we can matchthese data to PCU by plant identification number. As we previously noted, monthly andquarterly series on plant level TVS are not available in the ASM, CM, or any othersources that can be matched to PCU. Thus we analyze output fluctuations at the annual
frequency.

16

While the CM is a population survey and is conducted every five years, the ASM
is a sample survey in off-census years. Thus, we observe the TVS of all manufacturing
plants in a census year as long as they exist, but in off-census years, we observe only forplants sampled in the ASM. Using a plant identification number, which is given based on
the physical location of the plant, we create an ASM-CM plant-level unbalanced panel
data. To use a consistent plant identifier, we limit ourselves to the ASM and CM
observations from 1976 and after.11 We focus on real TVS by employing the TVS
deflator for each of 4-digit SIC calculated by Bartelsman, Becker, and Gray.12
Note that to measure demand fluctuations, one might also consider using a plant’s
employment given by the Longitudinal Business Database (LBD), which provide annual
employment data for virtually all U.S. business establishments (that have employees).
However, like most other data sources, the employment reported in the LBD includes
only workers on a plant’s payroll and thus excludes temporary workers. To the extent thata plant uses temporary workers to accommodate output fluctuations, permanent
employment fluctuations should be smoother than the fluctuation of all workers including
temporary workers. Thus, any unobserved or uncontrolled factors that increase a plant’s
use of temporary workers may be translated into a smaller fluctuation in permanent11

As a plant identifier, we use the Longitudinal Business Database (LBD) number, which is a revised
version of the Permanent Plant Number (PPN) used for manufacturing plants in the Longitudinal Research
Data. Similar to the PPN, the LBD number does not change in the event of merger and acquisition and isspecific to a plant’s physical location. The LBD number is created as a part of the effort by Census to create
the LBD data set, which reviews and updates the longitudinal linkage as well as the operation status of theestablishments/plants in the Standard Statistical Establishment List. While the Census of Manufactures
goes back to 1963, the LBD begins in 1976.
12
The data sets for the deflators through 1991 are posted at http://www.nber.org/nberces/nbprod96.htm.
We thank Randy Becker for letting us use the preliminary version of the TVS deflators for the later period.

17

employment, which biases our estimation. Thus, in this paper, we use TVS from the
ASM-CM panel to capture output fluctuations.13
If plant production levels were i.i.d. random variables, then expected future output
could simply be taken to be the mean of the log TVS in the ASM-CM data. Moreover,the standard deviation of the residuals (deviation between actual and expected TVS in
logarithm) could be used as a measure of the uncertainty a plant faces. However, there
are several obvious problems with such a procedure. First, for most plants, output levels
have long-term trends, either up or, less frequently, down over time. Second, an issue
arises from the fact that the ASM-CM panel is unbalanced, with plants observed indifferent sets of years. The measure of uncertainty based on a sample mean of log TVS
would depend on the particular set of years in which the plant exists and in which thedata are available for that plant, because of the volatility due to macroeconomic factors
across years. Lastly, the simple mean of log TVS from our sample would also depend on
where in a life cycle the plant is when it is included in the sample.
Given these considerations, we specify a method to estimate the mean andstandard deviation of future output growth. We assume that output growth follows a firstorder autoregressive process. We control for the change in macroeconomic conditions.
Denoting the growth rate of TVS by gtvs , we estimate:gtvsit = β%i + ρi gtvsit −1 + γ dnt + υit ,(12)

where dnt ≡ nt − nt −1 ; nt is a macroeconomic variable that captures the business cycle.
Any linear plant-specific time trend is captured by β%i . In this specification, a plant uses
the past realized output level and growth rate to form its expectation for its future output.
13

Note that labor hours reported in ASM and CM suffer the same problem, as they include only the hours

18

The uncertainty measure σ i is the standard deviation of the residuals of the model, whichis written as gtvsit − Et −1[ gtvsit ] = ltvsit − Et −1[ltvsit ] = υit and represents unforeseeable
events after a plant observes the output or growth rate from the previous year. For nt , weuse the deviation of log real gross domestic products (GDP) from log potential GDP
provided by the Congressional Budget Office. Note that Et [ltvsit +1 ] depends on
expectations of nt +1 . However, because γ nt +1 is common across plants and does not affectrelative variation across plants, we simply use

nt +1 to estimate Et [ltvsit +1 ] , andthus gite,Q 4 .14
Summary Statistics of Key Variables

Applying the above specification to our ASM-CM panel, the distribution of gite,Q 4 forplants in our sample is roughly symmetrical and mostly contained between -2 and 2. We
exclude plants with gite,Q 4 below -2 or above 2, considering to be outliers. Our measure of
uncertainty, σ i , is distributed between 0 and 2 except for a small number of outliers,
which again are removed. After dropping these observations, our sample contains 4,909(plant-period) observations. On average, gite,Q 4 is 0.10 and varies widely across plants.

σ i is on average 0.189. Large heterogeneity in σ i across plants is observed. An average
plant’s realized annual output deviates from its expectation based on (12) by 18.9%. A
plant with σ i that is one standard deviation (s.d.) larger than the mean experiences
annual output levels that typically deviate from expected values by 30% (=0.189+0.11).
worked by permanent employees. The LBD does not provide any data on labor hours.
14
We also performed our estimation using a simpler specification for output levels:
ltvsit = α i + β iT + γ nt + ε it , where β iT absorbs any linear effect of plant age. We obtain qualitatively thesame results based on both specifications.

19On average in our sample, gite,Q 4 is equivalent to 63% of the volatility ( σ i ) that plants
face. Summary statistics are in Table 1.
In our sample, the fraction of plants employing a positive number of temporary
workers in a particular year is 42%. The remaining 58% of plants operate without using
any temporary workers. Of plants with temporary workers, on average, the temporary
worker share of total production workers is 0.119.
Other Control Variables in Analyses

We also include a number of additional control variables. The most important of these isa variable that controls for the previous level of permanent employees. As we mentioned
above, our two-period model does not address how the previous level of permanent
workers influences a plant’s current use of temporary workers. However, in reality, if aplant’s permanent employment in the previous period is greater than the level required to
produce the current output, then to respond to any positive shock to the current output, aplant would be more likely to rely on already hired permanent workers and less likely torely on temporary workers. Indeed, in a version of our model with more realistic timeseries processes for output, the number of permanent workers from the previous period isa state variable. As a remedy, one might consider controlling for the level of permanent
employment, pt −1 , in the previous period. However, in the cross-section, such a variable
may capture other factors. While the model assumed a homogenous production function,
plants are, in fact, heterogeneous. A high level of pt −1 may simply mean that the plant isunproductive, rather than that it has a binding level of permanent workers on its payroll.

20

As an alternative way to control for variation in the previous number ofpermanent workers relative to current output levels, we include plants’ recent output
growth rates.15 If a plant’s output has been growing, it is unlikely that the number ofpermanent workers in the last period is binding. However, if output has been falling, thenumber of permanent workers inherited from the previous period may constrain the plant;in this case, even when a plant’s current output is greater for a given future expectedlevel, the plant would be unlikely to use temporary workers.
In addition to the control for the previous level of permanent employees, we
control for several other variables that may influence a plant’s use of temporary workers.
Such variables include plant size and age, the wage rate of permanent workers, the ratio
of benefit payments to wages, the unionization rate, and the seasonal factor for the fourth
quarter. The rationales for including these variables were discussed earlier.
For plant size, we use ltvsitAQ 4 . Age is measured based on the first year that aplant’s identifier for its physical location appeared in the LBD. To calculate thepermanent production worker wage rate, witP , for each plant, we use the ASM; the PCU
does not provide any wage information. Note that we cannot distinguish overtime hours
from total production hours in the ASM. Thus the calculation for witP is influenced by
wage premium for overtime; witP would be greater for plants that use more overtime. If aplant’s use of overtime is motivated by a reason similar to why they use temporary
workers, it would induce the positive correlation between witP and temporary worker
share. Thus, we calculate the straight rate permanent worker wage, witSP ≡ witP (1 + .5sitover ) ,15

A dummy variable for a survey year is also included.

21

using the overtime share, sitover ,16from the PCU, and use

this measurein ourregressions. We also use the ASM to calculate supplemental labor costs for each dollar ofwage payments.17
The unionization rate, turnover rate, and seasonal component are all calculated at
the three-digit SIC level, as plant-level information is not available. The data on theunionization rate among production workers are derived from the monthly outgoingrotation files of the Current Population Survey (CPS). We pooled data from 1996
through 2000 to estimate the rate of unionization for each three-digit SIC industry. As aproxy for turnover, we use job-to-job transition rates based on the non-outgoing rotationgroups of CPS.18 Again we pool all data since 1996 for each detailed CPS industry. We
also calculate seasonal components for each 3-digit SIC based on the industrial
production (IP) quarterly series (not seasonally adjusted) for the period between 1987 and2005 from the Federal Reserve Board of Governors. Using IPjtq to denote the IP ofindustry j in q th quarter in year y , we specify the seasonal component of q th quarterfor industry j , f jq , as f jq ≡ ∑ {ln(4 × IPjtq ) − ln( IPjt )} . When we include the above 3-digitt

16

The PCU data provide information on hours for all production workers (including temporary workers),
hours worked by temporary workers (including overtime if any), and total overtime. Assuming that
overtime is performed only by permanent workers, we use the ratio of the overtime to the hours worked bypermanent workers. We also used the ratio of overtime to hours worked by all workers, which did not
qualitatively change our results.
17
Supplemental labor costs are not provided separately for production and non-production workers in the
ASM/CM. We divide such a total number by wage payments to all employees. Note that some years in the
micro data provide the decomposition of supplemental labor costs into voluntary and non-voluntary parts.
Such data are not available for the years relevant to this study.
18
Specifically, we matched each observation in the non-outgoing rotations to the corresponding
observation in the following month using the household ID and line numbers. In addition, we required thatthe sex of respondents match and that the reported ages be within one year of each other. We thendetermined which workers remained employed at the same firm as in the previous month using theemployment status variable and the indicator for whether an employed worker remained at his previous
employer. This latter variable is available starting in 1996 and makes possible the identification of job-tojob transitions. See Fallick and Flieshman (2004).

22

SIC level variables in our models, we report standard errors that account for clustering at
the 3-digit SIC level.
Again, the summary statistics are in Table 1. Plants in our sample are much bigger
and older than that of average manufacturing plants in the CM for 1997. Plant TVS is on
average 59 million based on the 1987 dollar. Sixty-five percent of the plants in our
sample exist in 1975 or before, and among those which are built after 1975, the averageage is 16.

4. Results

In Table 2, we report results with our base specification. The net effects of gite,Q 4 isnegative and significant, and σ i is positive and significant. The data seem to support theview that higher expected growth decreases both a plant’s likelihood of using temporary
workers and, for a plant that uses temporary workers, decreases its temporary worker
share. The model in section 2 illustrated that the expectation of growth reduces theprobability for a marginal permanent worker to be fired, which in turn reduces the
expected future firing costs and motivates a plant to use more permanent workers. Our
results are consistent with such a view, rather than the alternative discussed earlier inwhich a higher expectation of growth might necessitate more screening of futurepermanent workers and thus more current temporary workers.19
Based on the results of the Probit analysis, if gite,Q 4 increases by a one s.d. from its
average, moving from .0977 to .460, the probability of employing temporary workers
decreases from 0.42 to 0.39; about a 7 % decrease. For plants using temporary workers,

23

the Tobit results suggest that a one s.d. increase in gite,Q 4 decreases the temporary worker
share by 1.6 percentage points, which is 13% of the average temporary worker share. The
ordinary leased squares (OLS) results in which we exclude the observations on plants
without any temporary workers suggests a smaller effect than the Tobit. A one s.d.
increase in gite,Q 4 decreases the temporary worker share by 0.8 percentage point based on
OLS.20
Plants that face more uncertainty appear to use more temporary workers. As we
also discussed, when firing costs are large enough, greater uncertainty level increases theprobability of marginal permanent worker to be fired, discouraging plants to hire
permanent employees. For a plant whose uncertainty level is one s.d. greater than average
plant, the plant’s likelihood to use temporary workers is 1.7 percentage points greater,
and for plants using temporary workers, the temporary worker share increases by 1
percentage point, based on Tobit and by 0.8 percentage point based on OLS.21
We also performed quantile regression analysis using the data of plants with any
temporary workers to see whether the magnitude of effects vary between plants indifferent portions of the distribution of the temporary worker share. The quantile
regressions showed that, among plants with temporary workers, the magnitudes of the19

It is possible that screening matters for short-run growth prospects. Our data, however, do not allow us tocapture plant-level growth rates at the monthly or quarterly levels.
20
We also perform the analysis, controlling for a variable representing a current year shock,ltvsit − Et −1[ltvsit ] , to see if our data identify any effect of current shock separate from that of gite ,Q 4 . We
find that the measure of current shock obtains a positive and significant coefficient, while the coefficiente ,Q 4for the expected growth rate remains negative and significant. The size of the effect of git

remains

almost the same. Note that, in this regression, we exclude gtvsit as it is highly correlated with the current
year shock measure.
We also performed Probit and Tobit analyses replacing expected annual output level in t + 1 with its
realized value. For this exercise, out of 4,909 plants used in Table 3, we used the data of 4,617 plants,

21

24

effects of our key variables are much greater for plants with higher temporary worker
shares. Our OLS result was similar to that for plants with high temporary worker shares.
Once we replace our dependent variable with log of the temporary worker share,
however, the quantile regressions obtain almost the same coefficients across all quantiles.
It seems that the effects of our key variables are constant in terms of the percentage bywhich they increase the share.
The results generally suggest that bigger plants are more likely to use temporary
workers, and if they do, the temporary worker share is greater than smaller plants. It is
possible that fixed costs are involved in using temporary workers for, perhaps,
negotiating with temporary help agencies. The results may also be reflecting that larger
plants are more likely to face greater penalty in the event of an unjust dismissal lawsuit.
Such effect seems to offset possible negative effect, if any, from the larger plants’ ability
to redistribute workers within itself. A one s.d. increase in ltvsitAQ 4 raises a plant’s
likelihood to use temporary workers by 2.0 percentage points. Note that the ability tonegotiate or allocate workers should be better captured at firm level rather than plantlevel. Thus we also performed our analyses, adding a dummy indicating whether theplant is affiliated with multi-plant firm and, if so, its firm’s size.22 Neither variableobtains a significant coefficient, and the qualitative results of other variables remained
the same.
We found that older plants tend to use temporary workers less. The likelihood forplants built pre-1975 to use temporary workers is 9.3 percentage points smaller thanwhich appear in ASM sample in the year following their PCU survey. The results remain qualitatively thesame.
22
We use the log of total employments of all plants affiliated with a firm; TVS is not available for all
plants.

25

newer plants. For plants using temporary workers, the temporary worker share for older
plants is 4.1 percentage points lower than newer plants based on Tobit, and 2.1
percentage points lower based on OLS. Plant age may reflect an uncertainty level that is
not captured by σ . While σ is an average measure of uncertainty over the lifecycle of aplant, the degree of uncertainty may change over time.
Next we explore the effect of other variables, including wage, unionization rate,
job-to-job transition rates, and seasonality. The results are summarized in Table 3. First,
we include two variables that summarize the compensation paid to permanent workers.
As discussed earlier, one might expect that plants that pay high wages or high benefits
would have an incentive to use temporary workers to reduce labor costs. In contrast,
industry analysts report that the markup that staffing agencies charge over wages for
temporary workers tends to be higher for high wage occupations. Thus, higher wage
plants may use fewer temporary workers. The latter story seems to hold, as shown inColumns 1, 2, 3 in Table 3. Based on our sample, the straight rate wage for permanent
production workers and the supplemental labor costs per dollar of permanent worker
wages are both negatively correlated with plants’ use of temporary workers. Note thatwhen we control for these two variables, the significance of the positive coefficientobtained for plant size increases. Since bigger plants tend to pay higher wages, once weseparate the negative effect of wage, the scale effect seems to be more pronounced.
Next we add the unionization rate, the turnover rate, and the fourth-quarterseasonal component, which we measure at the three-digit SIC level. Columns 4, 5, 6 inTable 3 show the results where we replace three-digit SIC dummies with these threecontinuous variables. Based on Probit and Tobit analyses, we find that the unionization

26

rate is negatively correlated with a plant’s use of temporary workers. This is counter tothe idea that unions might increase the use of temporary workers through their effect inincreasing wages as well as firing costs relative to productivity. Similar results are foundin the study by Houseman (2001). Analogous to what she argues, it is possible that our
results reflect the fact that unions oppose the use of non-standard employment
relationships to secure regular employment positions. Note that the coefficient forunionization rate is not significant in OLS result. The unionization rate may not influence
temporary worker share once plants decide to use temporary workers.
Using Probit analysis, we also examined whether the unionization rate has any
interaction effect with gite,Q 4 . The coefficient for the interaction term seems to suggest that
greater union pressures against the use of temporary work arrangements also enhance thenegative effect of gite,Q 4 on a plants’ likelihood to use temporary workers.
Coefficients for the job-to-job transition rate are not significant in any
specification. This is different from our original conjecture that higher turnover reduces
the probability of needing to fire permanent workers in the future and thus increases thepermanent worker share. Note that our measure of the job-to-job transition rate may not
be a good proxy for the turnover rate. In the CPS, we cannot distinguish a voluntary quitfrom a transition motivated by layoff among people who have different jobs between two
periods. The Bureau of Labor Statistics (BLS) produces a voluntary quit rate, but only at
the level of broad industry category, which does not provide us enough detail for ourstudy. Our result may alternatively be explained by the role of temporary employment inscreening. It is possible that greater turnover increases the on-going need to recruit

27

workers through temporary employment, and this might have offset the effect of thedecreased probability of needing to fire permanent workers.
The coefficients for the fourth-quarter seasonal component are not significant in
Probit but are significant in the Tobit and OLS. We consider the coefficient of theseasonal component to capture the effect of time-invariant fourth quarter component on
the share of temporary workers.23
Note that in the specifications with the above additional controls, the coefficientsfor our key variables, gite,Q 4 and σ , are still consistent with our conjectures. It would be,
however, instructive to note that the variations of our control variables such as plants’size, wage, benefit, and unionization rate seem to have large contribution to the overallvariation of the plants’ use of temporary workers. Based on the Probit analysis in Column
4 in Table 3, one s.d. increases of wage, benefit, and unionization rate respectively
decrease the probability for a plant to use some temporary workers by 7.1, 2.6, and 4.2
percentage points, and that of plant size increases the probability by 7.7 percentage
points, where one s.d. increases in gite,Q 4 and σ increase the probability by 2.6 and 1.2
percentage points, respectively. In terms of the variation of temporary worker sharesacross plants, based on the Tobit analysis in Column 5 in Table 3, one s.d. increases inwage, benefit, and unionization rate respectively decrease the share by 2.8, 1.1, and 1.4
percentage points, and that of plant size increases the share by 2.7 percentage points,
where one s.d. increases in gite,Q 4 and σ increase the share by 1.1 and 0.9 percentage

23

As a robustness check, we also use a different method to estimate the coefficients for three-digit SIClevel variables. We first estimate three-digit SIC dummies based on the specification in Columns 1, 2, 3 inTable 3, and then run weighted least square to relate the coefficients for dummies with these three-digit SIC
level variables. The results show the negative coefficients for unionization and positive coefficients for28

points, respectively. The effects of our key variables are larger than that of seasonal
factor; a one s.d. increase in fourth-quarter seasonal factor increases the share by 0.7
percentage point.
Finally, we examine whether our key results hold when we control for the effects
of geographical variables. In Columns 1, 2, 3 in Table 4, we show the results based on
our base specification, adding a dummy indicating urban plants (plants in metropolitan
areas). We then limit our sample to urban plants and control for metropolitan fixed
effects in addition to three-digit industry effects. We find that in both cases, the effect ofour key variables stay qualitatively the same. We also found that plants in urban area are
more likely to use temporary workers. To the extent that markets for temporary worker
are local, there are many geographic variables such as the unemployment rate and thedegree of local concentration of temporary agencies, which would be associated with aplant’s use of temporary workers. Examining the effect of these variables requires athorough consideration of local labor markets. We leave it to our future research to
explore the influence of local demand and supply of the temporary workers on a plant’s
use of temporary workers.

5. Conclusion

We have provided some evidence in support of the proposition that temporary work
arrangements facilitate flexibility in a firm’s use of labor and allow it to accommodate
output fluctuations at lower cost. Our stylized model identifies the expected output
growth rate and the uncertainty in that expectation as two key variables in a firm’s

fourth-quarter seasonal component. R-squared from these regressions are, however, not very high, showingthat much of the industry-specific effects are left unexplained.

29

decision to use temporary workers. We approximated both of these variables using the
ASM and the CM. We used Probit, Tobit, and OLS analyses to examine the relationshipbetween these two variables and plants’ actual use of temporary workers.
First, we found that plants make greater use of temporary workers when their
expected output growth is lower. This suggests that a plant chooses temporary workers
over permanent workers when it expects its output to fall and thus wants to avoid costs
associated with dismissing permanent employees. This effect remains identified after
netting out the effect of a seasonal factor in a plant’s output, which itself had a positive
relationship with a plant’s use of temporary workers, as well as other variables.
Second, we found that a plant with greater uncertainty over its future output level
uses more temporary workers. Firing costs appear to be large enough to induce a morevolatile plant to make greater attempts to minimize the costs of firing permanent workers;
this might have made the plant rely more on temporary workers even though the current
unit costs of using temporary workers is greater than those for permanent workers.
In addition to output fluctuations, we also examined the effect of several othermotivations that are thought to play an important role in a plant’s decision to use temps.
First, we found evidence that a plant’s that requires high-skill workers are less likely to
use temporary workers, likely because the wage premium or the margin paid to agencies
for high-skill temporary workers may be higher than that for low-skill temporary
workers. Second, a plant in an industry that is highly unionized seems to use fewer
temporary workers, possibly because unions are successful in resisting the use of
nonmembers’ labor.

30

Table 1. Summary StatisticsgPlant characteristics (4,909 observations)
Mean(S.d.)

0.0977(0.362)0.189(0.111)11.0(1.26)

0.00710(0.203)0.02022.66
0.275(0.224)(0.348)(0.104)e ,Q 4
it

σi
AQ 4
it

ltvs
gtvsit : growth rate of annual real output in survey years
gtvsit −1 : growth rate of annual real output in previous years
ln. straight wage of perm production worker†
Benefit per $1 perm wage†
Fraction of plants that existed from 1975 or before: 0.646
Fraction of plants from 1999 PCU: 0.476

Three-digit SIC level variables included in the study (3,716 observations)†
Unionization rates
0.236(0.117)
Job-to-job transition rates
0.0197(0.00559)
Fourth quarter seasonal factor
0.00608(0.0398)†: The sample is restricted due to the missing observations of overtime used to calculate straightwage. It is used in Table 3.

31

Table 2. Base specification
Probit
dF/dX

Tobit

OLS

-0.097***[4.42]-0.044***[5.56]-0.023***[3.11]

0.152**[2.16]

0.087***[3.61]

0.072***[3.42]

0.016**[2.15]

0.004[1.54]-0.0008[0.33]

0.218***[5.68]

0.089***[6.45]

0.036***[2.68]

0.106***[3.10]

0.045***[3.71]

0.017[1.52]

D=1 for plants born pre 1975

-0.093***[-5.92]-0.041***[-7.27]-0.021***[4.21]

D=1: Survey Year 1999

0.027*[1.83]

0.011**[2.08]

0.005[1.14]

3-digit SIC dummies

Yes

Yes

Yes

gite,Q 4 := Et [ltvsit +1 ] − ltvsitAQ 4σi
ltvsitAQ 4
gtvsit := ltvsit − ltvsit −1
gtvsit −1 := ltvsit −1 − ltvsit − 2

Observations
4,909
4,909
2,067
[ ]: Robust z-statistics for Probit, t-statistics for Tobit, and robust t-statistics for OLS;
* significant at 10%; ** significant at 5%; *** significant at 1%

32

Table 3. Specification with wage and other variables(1)(2)
ProbitTobit
dF/dX

gite,Q 4 := Et [ltvsit +1 ] − ltvsitAQ 4

(3)
OLS

(4)
Probit
dF/dX

(5)
Tobit

(6)
OLS

-0.095***[3.59]-0.036***[4.17]-0.016**[1.98]-0.073***[2.58]-0.029***[3.36]-0.0101[1.25]

0.140*[1.68]

0.077***[2.96]

0.070***[2.99]

0.117[1.30]

0.081***[3.13]

0.0779***[3.13]

0.042***[4.50]

0.014***[4.40]

0.0035[1.17]

0.060***[4.62]

0.021***[7.92]

0.0049[1.52]

0.218***[4.73]

0.081***[5.36]

0.032**[2.11]

0.209***[3.89]

0.083***[5.41]

0.034*[1.96]

0.077*[1.85]

0.034**[2.55]

0.014[1.16]

0.083*[1.91]

0.036***[2.61]

0.017[1.39]

D=1 for plants built pre-1975-0.084***[-4.53]-0.035***[-5.71]-0.019***[3.52]-0.087***[-3.76]-0.039*** -0.022***[-6.45][4.04]

D=1: Survey year 1999

0.034*[1.96]

0.011*[1.87]

0.002[0.46]

0.038**[2.28]

0.012**[2.11]-0.222***[-7.26]-0.094***[-9.62]-0.053***[5.38]-0.205***[-4.74]-0.081*** -0.032***[-8.68][3.20]-0.220**[-2.43]-0.083***[-2.82]-0.0375[1.36]-0.254**[-1.99]-0.104***[-3.53]-0.0503*[1.79]

Unionization rate

-0.361**[-2.01]-0.121***[-4.21]-0.023[0.69]

Job-to-job transition rate

-2.161[-0.82]-0.359[-0.67]0.523[0.84]

Fourth-quarter seasonal factor

0.331[1.27]

0.181**[2.45]

0.140*[1.95]

No

No

No

σi
ltvsitAQ 4
gtvsit := ltvsit − ltvsit −1
gtvsit −1 := ltvsit −1 − ltvsit − 2

ln. straight rate wage rate forperm workers
Supplemental labor costs per $1
perm wage

3-digit SIC dummies

Yes

Yes

Yes

0.00096[0.23]

Observations
3,716
3,716
1,727
3,716
3,716
1,727
[ ]: Robust z-statistics for Probit, t-statistics for Tobit, and robust t-statistics for OLS (errors are clustered forplants in the same three-digit SIC for Columns 4 and 6); * significant at 10%; ** significant at 5%; ***significant at 1%

33

Table 4. Analyses with MSA fixed effects
All plants with urban dummy
Probit
Tobit
OLS
dF/dX

gite,Q 4 := Et [ltvsit +1 ] − ltvsitAQ 4σi
ltvsitAQ 4
gtvsit := ltvsit − ltvsit −1
gtvsit −1 := ltvsit −1 − ltvsit − 2

Urban plants with MSA fixed effects
Probit
Tobit
OLS
dF/dX

-0.0979*** -0.0438*** -0.0229*** -0.128*** -0.0528*** -0.0274***[4.44][5.59][3.14][4.37][5.65][2.77]
0.149**[2.14]

0.0861***[3.56]

0.0704***[3.35]

0.141[1.52]

0.0851***[2.92]

0.0643**[2.17]

0.0157**[2.11]

0.00399[1.49]-0.00088[0.35]

0.00996[0.99]

0.00207[0.62]

0.000275[0.08]

0.219***[5.70]

0.0893***[6.48]

0.0369***[2.73]

0.208***[4.04]

0.0787***[4.75]

0.0347*[1.94]

0.106***[3.12]

0.0449***[3.73]

0.0166[1.53]

0.120***[2.59]

0.0393***[2.74]

0.00869[0.63]

D=1 for plants born pre-1975-0.0942*** -0.0411*** -0.0211*** -0.0781*** -0.0317*** -0.0186**[5.96][7.35][4.30][3.55][4.47][2.52]

D=1: Survey year 1999

0.0280*[1.88]

0.0116**[2.18]

0.00547[1.22]

D=1 for urban plants

0.0306*[1.78]

0.0179***[2.91]

0.0137***[2.76]

3-digit SIC dummies
MSA dummies

Yes
No

Yes
No

Yes
No

0.0291[1.50]

0.0100[1.57]

0.00139[0.23]

Yes
Yes

Yes
Yes

Yes
Yes

3,275

1,431

Observations
4,909
4,909
2,067
3,275
[ ]: Robust z-statistics for Probit, t-statistics for Tobit, and robust t-statistics for OLS;
* significant at 10%; ** significant at 5%; *** significant at 1%

34

Figure 1. The determination of the cap on permanent workers: Two-period modeldTC( p1 )
dp1−Δu + βδ0−Δuf −1 ( ylow )pf −1 ( yhigh )p1

35

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Perspectives, Federal Reserve Bank of Chicago, April 1995, pp. 2-19.
Lewis M. Segal and Daniel G. Sullivan, “Wage differentials for temporary service work:
Evidence from administrative data”, Federal Reserve Bank of Chicago, working paper,
No. 9823, 1998.
U.S. Census Bureau, Form MQ-C1; Survey of Plant Capacity Utilization, Current
Industrial Reports

37

Appendix
A. A More General Model

Here, we consider the case in which the plant’s horizon is infinite and the exogenouslevels of required outputs over time are i.i.d. random variables. The plant’s optimal
policy is essentially identical to the solution of the first period of the two period model.24
The intuition is that given future optimal behavior, the choice of pτ at time τ
determines the number of permanent workers fired at time τ + 1 . However, subsequentlayoffs depend on the independent choice of pτ +1 , pτ + 2 , etc. and not pτ . Thus inconsidering the optimal choice of permanent employment level at τ , future firing costconsiderations are identical to those in the first period of the two-period model. That is,
the marginal expected discounted firing cost associated with an increase in pτ isβδ G ( f ( pτ )) . Given that a plant starts with a level of permanent workers in the previous
period such that pτ −1 < p , the marginal change in expected costs from employing an
additional permanent worker differs only slightly from the two-period case. This isbecause, if pτ < pτ −1 , then increasing pτ saves on firing costs in the current period.25
Thus,

in

the

i.i.d.

case,dTC( pτ ) = −Δu − δ I [ pτ < pτ −1 ] + βδ G ( f ( pτ )) ,
dpτ

where

I [ pτ < pτ −1 ] is an indicator function for pτ < pτ −1 . This function has a discrete jump

24

The only qualification is that the plant must start with a level of permanent workers that is less than orequal to, the cap derived in the two-period model Section 2. As long as this is the case, it is optimal to−1

follow the rule that pτ = min( f ( yτ ), p ) . If this were not the case (i.e., the plant started with pτ −1 > p ), it*

is possible that the optimal level is such that pτ > p . However, once a realization of the yτ comes in−1

below f ( p ) , the rule pτ = min( f ( yτ ), p ) becomes optimal for the rest of time.
*25

In the two-period case, we implicitly assumed that the plant started the first period with no perms. Thus,
we did not have to consider the effect of its decision on the number of permanent workers laid off in thefirst period.

38

at pτ = pτ −1 . However, it is still strictly increasing and given that pτ −1 < p , it still is equal
to zero at pτ = p (See Appendix Figure 1).
Appendix Figure 1: Determination of the Cap on Permanent Workers: Infinite Horizon
i.i.d.

dTC( pτ )dpτ

−Δu + βδ0−Δu−Δu − δf −1 ( ylow )

pτ −1

p

f −1 ( yhigh )pτ

B. Our sample based on the PCU data

In the questionnaire, plants are asked to report, for each shift, the total number of
production workers, temporary production workers, total hours worked by production
workers, hours worked by temporary workers, and overtime hours. We consider that aplant operates a given shift if it reports positive total production workers for the shift,which are defined to include temporary workers in the instructions for the questionnaire
given to the plant. Among plants operating a particular shift, however, many left the
information for temporary production workers unfilled, and often, such plants do notprovide a temporary worker number for any shifts. In such a case, it is not clear whether

39the plant did not use temporary workers or did not fill out the item. We consider that they
did not fill out the item, since the instructions for the PCU survey explicitly instructs
them both in words and with visual examples of the tables to write zero when plants
operate a given shift but do not use temporary workers. We exclude such plants withmissing temporary employment data for any of their active shifts (i.e., shifts for which
the plant reports positive total number of production workers).
In addition, by the definition given in the instructions, when a given shift exists,
the total number of production workers should be greater than or equal to the number of
temporary workers. We exclude plants with any inconsistency regarding these figures.
We also exclude a few plants reporting the same number for both total and temporary
workers for some shifts. It is possible that these shifts are actually supported by only
temporary workers. However, such incidents are rare and we cannot tell whether theseare miss data entry.
Once we clean the PCU data, we limit the sample to those for which we canestimate our key variables based on the ASM and the CM as discussed in the main text.
Based on the method discussed in Section 3, for a plant to be included in estimation, theplant has to appear in consecutive three years more than once in ASM-CM panel. We
limit our sample to plants that appear in three years consecutively at least three times toavoid outliers. Some further outliers based on other variables are excluded.

40