EMPLOYMENT ADJUSTMENT AND LABOR UTILIZATION

• Author: Ija Trapeznikova
• Date: 01 August 2017
• Published date: 01 August 2017
• DOI: http://doi.org/10.1111/iere.12239

INTERNATIONAL ECONOMIC REVIEW

Vol. 58, No. 3, August 2017

EMPLOYMENT ADJUSTMENT AND LABOR UTILIZATION∗

BYIJA TRAPEZNIKOVA1

Royal Holloway University of London, U.K

Standard models of labor adjustment assume that firms can change only the size of their workforce (the

extensive margin) and not the number of hours of their existing employees (the intensive margin) in response

to shocks. I propose a general equilibrium search model that allows for adjustment on both of these margins.

The model includes on-the-job search that generates different vacancy filling and attrition rates across firms.

I calibrate the model to a unique matched employer–employee panel of Danish firms and simulate two labor

market policies aimed at promoting job creation: hiring subsidies and a reduction in the official workweek.

1. INTRODUCTION

The variation in employment depends on the ability of firms to adjust their labor demand in

response to shocks. In the short run, firms can respond to productivity fluctuations by varying the

hours of work of their existing employees. Yet, standard economic models of labor adjustment

allow firms to change only the number of workers they employ (the extensive margin) and not

the amount that each worker works (the intensive margin). The goal of this article is to relax

this assumption and to propose and calibrate a dynamic model that includes both margins of

adjustment.

I start by documenting the importance of hours adjustment for firms’ labor demand policies.

The main reason why many of existing labor adjustment models abstract from changes in labor

utilization is the scarcity of high-frequency microdata on work hours.2This article is using a

unique matched employer–employee panel of Danish administrative firm data that contains

all private firms in the economy for the period of 1999–2006. This data set includes firm-

level information on employment and work hours on a quarterly basis. Based on these data,

I show that firms use variation in hours to economize on changes in the number of workers.

In particular, the growth rate of hours per worker and employment growth are negatively

correlated at the firm level; whereas lagged changes in hours are positively correlated with

changes in employment.3An adjustment cost model provides a natural framework for explaining

these empirical facts.

∗Manuscript received April 2014; revised October 2015.

1I am grateful to my late Ph.D. advisor, Dale Mortensen, for his extensive help and guidance throughout this project. I

thank the editor, Guido Menzio, and three anonymous referees for very helpful comments and suggestions. I also thank

Rasmus Lentz, Christopher Taber, Eva Nagypal, Gadi Barlevy, Eric French, Pieter Gautier, and seminar participants

at Chicago Fed, Northwestern University, Pennsylvania State University, Purdue University, Einaudi Institute for

Economics and Finance, Uppsala University, Tinbergen Institute, Aarhus University, University of Bristol, Essex

University, Oxford University, and NBER Summer Institute. This research was supported by the Labour Market

Dynamics and Growth (LMDG) project at Aarhus University. Finally, I want to express my special thanks to Henning

Bunzel for sharing his expertise on the data—this project would not exist without his invaluable help.

Please address correspondence to: Ija Trapeznikova, Department of Economics, Royal Holloway University of

London, Egham Hill, Egham, Surrey, TW20 0EX, UK. E-mail: ija.trapeznikova@rhul.ac.uk.

2The existing empirical studies are either limited to industry-level data (see, for instance, Hamermesh and Pfann,

1996) or firm-level data that are more than three decades old (for example, Cooper et al., 2007, use Longitudinal

Research Database 1972–80).

3These facts have been documented also for the U.S. labor market by Cooper et al. (2007).

889

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(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

890 TRAPEZNIKOVA

In this article, I develop a general equilibrium model of joint dynamics of the number of

workers and hours per worker. I extend a standard random search framework (see Mortensen

and Pissarides, 1994) to include multiworker firms with a decreasing returns to scale revenue

function. The driving force of the model is idiosyncratic profitability shocks, which firms can

accommodate by changing the work hours of their existing employees, instead of (or jointly

with) varying the size of their labor force. Hours of work and compensation in the model are

determined as an outcome of a cooperative game according to the firm’s and workers’ Shapley

values. The presence of frictions in the labor market means that matching workers with vacant

jobs takes time and uses resources. On the other hand, raising hours can be done immediately,

although at a cost of higher wages. Hence, the firm faces a trade-off between these two channels

of adjustment.

An important feature of the model is on-the-job (OTJ) search. First, job-to-job transitions

have important implications for firm-level employment dynamics: In this setup, not only does a

firm post more vacancies in the event of a positive shock, it also finds it easier to fill vacancies and

to retain its current employees, which increases the speed of employment adjustment. Second,

OTJ search is a necessary component that explains why there exists a negative correlation

between hours and employment growth rates at contracting firms. That is, firms that are hit by

a negative profitability shock face an increase in the quit rate of their existing workers. As the

number of workers keeps falling due to higher attrition, the average work hours start rising.

Finally, I find that OTJ search enables the model to capture most of the features of the data

regarding worker flows.

The model is calibrated to fit Danish firm data and is successful in capturing the overall

features of the data. Given the calibrated parameter values, I find that the average cost of

hiring a new worker is equal to about two weeks of wages. This value is low compared to the

estimates found for other European countries (see, among others, Rota, 2004; Goux et al.,

2001; and Kramarz and Michaud, 2004), reflecting the fact that the Danish labor market is very

mobile, with worker flow rates averaging around 8% per month. In the next step, I simulate

two types of policy experiments aimed at fostering job creation: (i) introducing a hiring subsidy

and (ii) imposing an upper limit on the work hours. Using this model, I can assess which of the

two policies is more effective in reducing the unemployment rate and at what cost. I find that

a hiring subsidy reduces unemployment, whereas a shorter workweek increases it, although

the effects are quantitatively small in both cases. I find considerably larger effects (or even

qualitatively different) in a “partial equilibrium” version of the model, in which the vacancy

filling rates and the quit rates are kept unchanged. These results suggest that a partial equilibrium

model significantly overestimates the effect of the adjustment costs on aggregate employment.

Moreover, I show that excluding OTJ search from the model generates counterintuitive results

in the above policy experiments, thus implying that endogenous offer acceptance and quit rates

are key not only for matching main features of the data, but also for predicting a negative effect

of hiring subsidies on unemployment.

There are two strands of literature that this work is based on. First, there is an extensive body

of research that examines the effect of adjustment costs on employment within a neoclassical

framework (see Hamermesh and Pfann, 1996, for a comprehensive survey).4Previous work that

accounts for labor utilization in adjustment cost models includes Caballero et al. (1997) and

Cooper and Willis (2009). Most of these papers are set within a partial equilibrium framework

where firms optimize their labor demand in isolation from decisions of other firms or workers.

The predictions of these models are often very different from those derived from a general

equilibrium analysis.5In contrast, my model accounts for equilibrium interactions between

4The literature on labor adjustment costs is also closely related to the investment literature (see, for example,

Caballero and Engel, 1991). Bond and Van Reenen (2007) survey econometric research on adjustment processes for

both capital and labor using microdata.

5For example, Bentolila and Bertola (1990) show that higher dismissal costs increase aggregate employment in a

partial equilibrium framework, whereas Hopenhayn and Rogerson (1993) find that this prediction is actually reversed

in their general equilibrium model of heterogeneous firms with endogenous entry and exit.

EMPLOYMENT ADJUSTMENT AND LABOR UTILIZATION 891

firms and workers through a matching function and shows that hiring externalities across firms

are quantitatively very important.

Second, this article is linked to standard random search models (see, for instance, Mortensen

and Pissarides, 1994) and more recent work that introduces a theory of multiworker firms into

search models (see, for instance, Coles and Mortensen, 2016; Acemoglu and Hawkins, 2014;

and Moscarini and Postel-Vinay, 2013).6This article is most closely related to Cooper et al.

(2007), which examines the variation in hours, employment, and vacancies using U.S. data.

Given that the focus of their paper is primarily to examine the differences in labor dynamics

at the firm level and in the macrodata, they simplify labor adjustment and wage determination

processes.7Instead, I allow for richer and more realistic worker and hours dynamics across firms

by extending their model to introduce endogenous quits and joint determination of hours and

compensation.

The article proceeds as follows: Section 2 presents empirical evidence on employment and

hours adjustment using Danish firm data. Section 3 introduces and describes the model. Section

4 shows the calibration of the model and its fit to the data. Section 5 proceeds to demonstrate the

impact of policy experiments on aggregate employment and output. Section 6 summarizes the

findings. The Appendix provides details on the data sources used in this article, on the Shapley

Values, as well as on the numerical simulation procedure.

2. DATA

The Danish labor market is known for its so-called “flexicurity” (flexibility +security) model

featuring a minimum set of regulations and a generous unemployment insurance scheme. De-

spite a high level of unionization in Denmark, recent trends toward decentralization allow for

more flexibility in determining both wages and working time because many conditions can now

be negotiated at the firm level. The empirical analysis in this article is based on administrative

Danish data that contain all private firms in the economy for the period of 1999–2006 (a detailed

description of the data sources and the Danish labor market is provided in the Appendix). Em-

ployment information is drawn from a monthly matched employer–employee panel, whereas

hours data come from two sources.

The first data set is based on the Earnings survey that collects individual-level hours infor-

mation on an annual basis.8The trade-off between the number of workers and hours exists

primarily in the short run as firms eventually adjust their employment to its optimal level.

Therefore, to investigate the firm-level hours dynamics, we need to observe changes in hours

on a more frequent basis. To this end, I use the second data set drawn from firms’ mandatory

pension contributions. In Denmark, the amount of pension contributions that a firm pays for

each of its employees depends on which of the four intervals her weekly work hours fall into:

0–9, 9–18, 18–27, or more than 27 hours a week. Each firm reports the total amount of its

contributions paid for all employees over a quarter. Based on this information and the number

of workers for each firm, I compute a quarterly measure of the average hours per worker to

capture the short-term variation in the intensive margin of employment.9

6Kaas and Kircher (2015) develop a multiworker firms model within a competitive search framework that has many

similar implications for employment growth at the firm level.

7Cooper et al. (2007) simplify the wage setting mechanism by assuming that firms are paying workers their outside

option so that workers are indifferent between being employed or unemployed. In that case, job-to-job transitions

become irrelevant as workers get the same wage at all firms. Moreover, their setup implies that firms cannot adjust

wages in the case of a negative profitability shock.

8This survey covers all private firms with more than 10 full-time employees, with the exception of agriculture and

fishery.

9In particular, I use the left boundary of each nine-hour interval to obtain the lower bound (LB) measure of hours.

Alternatively, I construct an upper bound measure using the right boundary of each nine-hour interval. These two

measures behave very similarly; hence, I only report the results based on the LB measure. Appendix A.2 provides a

detailed discussion on the construction of both of these variables.