STATE DEPENDENCE IN LABOR MARKET FLUCTUATIONS
| Published date | 01 August 2020 |
| Author | Konstantinos Theodoridis,Carlo Pizzinelli,Francesco Zanetti |
| Date | 01 August 2020 |
| DOI | http://doi.org/10.1111/iere.12448 |
INTERNATIONAL
ECONOMIC
REVIEW
August 2020
Vol. 61, No. 3
DOI: 10.1111/iere.12448
STATE DEPENDENCE IN LABOR MARKET FLUCTUATIONS∗
BYCARLO PIZZINELLI,KONSTANTINOS THEODORIDIS,AND FRANCESCO ZANETTI1
International Monetary Fund, Washington, DC; Cardiff Business School, Cardiff, Wales,
European Stability Mechanism, Luxembourg City, University of Oxford, Oxford, UK
This article documents state dependence in labor market fluctuations. Using a Threshold Vector Autore-
gression (TVAR) model, we establish that the unemployment rate, the job separation rate, and the job-finding
rate (JFR) exhibit a larger response to productivity shocks during periods with low aggregate productivity. A
Diamond–Mortensen–Pissarides model with endogenous job separation and on-the-job search replicates these
empirical regularities well. We calibrate the model to match the standard deviation of the job-transition rates
explained by productivity shocks in the TVAR, and show that the model explains 88% of the state dependence
in the unemployment rate, 76% for the separation rate and 36% for the JFR. The key channel underpinning
state dependence in both job separation and JFRs is the interaction of the firm’s reservation productivity level
and the distribution of match-specific idiosyncratic productivity. Results are robust across several variations to
the baseline model.
1. INTRODUCTION
Numerous studies, starting with Neftci (1984), show that macroeconomic fluctuations differ
across phases of the business cycle. This article builds on this strand of research and identifies
systematic changes in the cyclical properties of labor market variables that are linked to the
state of aggregate productivity. A Threshold Vector Autoregression (TVAR) model, which
identifies the effect of productivity shocks and allows for two distinct regimes based on aggregate
productivity, establishes that the shocks have a significantly larger effect on the unemployment
rate, job separation rate, and job-finding rate (JFR) in periods of low aggregate productivity.
To explain these findings, we develop a Diamond–Mortensen–Pissarides (DMP) search model
with endogenous job separation and on-the-job search (OJS) where workers have different
idiosyncratic productivity. The model embeds two channels that can generate state depen-
dence. The first channel arises from the interaction between the firm’s reservation threshold for
match-specific productivity and the distribution of workers’ individual productivity. The reser-
vation threshold determines whether incumbent workers are dismissed (i.e., job separation)
∗Manuscript received April 2017; revised February 2020.
1This study subsumes previous work circulated under the title: “State Dependence in Labor Market Fluctuations:
Evidence, Theory and Policy Implications.” We would like to thank four anonymous referees and participants at
several seminars and workshops for extremely valuable comments and suggestions. Francesco Zanetti would like to
thank the Bank of Japan and its staff for hospitality and support while some of this work was completed. The present
project was partially supported by the John Fell Fund, and the British Academy and Leverhulme Research Grants.
The views expressed in this article solely represent those of the authors and should not be interpreted as the views of
the International Monetary Fund or its Board, and the European Stability Mechanism. Please address correspondence
to: Francesco Zanetti, Department of Economics, University of Oxford, Manor Road, Oxford, OX1 3UQ, UK. E-mail:
Francesco.Zanetti@economics.ox.ac.uk.
1027
C
(2020) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social
and Economic Research Association
1028 PIZZINELLI,THEODORIDIS,AND ZANETTI
and whether newly matched workers are hired (i.e., job finding). Under standard assumptions,
in states of low aggregate productivity, the threshold lies in a region of the match-specific distri-
bution with a high density of workers. An exogenous movement in aggregate productivity that
changes the threshold generates large adjustments in the separation rate and the JFR and con-
sequently in the unemployment rate. Meanwhile, in a state with high aggregate productivity,
the firm sets a low threshold for efficiency matches that is associated with a low density of
jobs. An equivalent change in aggregate productivity produces limited movements in the job-
transition rates.
The second channel hinges on the nonlinearity in the matching function, which determines
the firm’s hiring intensity. In states of low aggregate productivity, the surplus of new matches
is small and the firm’s vacancy postings become more responsive to shocks, thereby increasing
the volatility in the JFR.
To assess the performance of the theoretical model to replicate the empirical findings and
study the contribution of each channel to the state dependence of labor market variables, we
calibrate the system to match the variance of labor market variables explained by productivity
shocks in the TVAR. The baseline model replicates closely the observed business cycle fluctu-
ations, and the job separation rates and JFRs exhibit larger responses to productivity shocks
in states of low aggregate productivity. The model replicates 88%, 76%, and 36% of the state
dependence in the unemployment rate, job separation rate, and the JFR, respectively. The
response of the job transition probabilities to shocks implies that the volatility of the unemploy-
ment rate is almost twice as large in states of low aggregate productivity. We find that the key
mechanism for the state dependence in the JFR is related to the changes in the productivity
threshold for new matches instead of the nonlinearity in the matching function. Our analysis
shows that the state dependence in labor market variables is primarily related to the interaction
between the firm’s reservation threshold for match-specific productivity and the distribution of
workers’ individual productivity.
We perform robustness analysis that considers alternative calibrations and specifications of
the baseline model that exclude OJS and assumes exogenous job separation, which shows that
the calibration of the idiosyncratic productivity distribution is critical to generate plausible
aggregate fluctuations and replicate the observed state dependence in labor market variables.
Under our baseline calibration, OJS is important to generate significant state dependence in
the JFR. When OJS is possible, low-productivity workers search for alternative posts that yield
higher wages and hence have a high probability of leaving the current firm. Thus, hiring these
workers is more costly in presence of OJS since the worker is more likely to separate from
the job and the firm must rehire another worker. Therefore, the firm sets a high reservation
productivity threshold to compensate for the increase in expected costs. The higher threshold is
located in a region of the match-specific productivity distribution with a high density of workers.
Therefore, movements in aggregate productivity have a larger impact on the JFR. If OJS is not
possible, however, the firm’s threshold of reservation productivity is low and the degree of
state dependence is substantially weakened. In this case, the firm hires workers with lower
productivity who remain in the same job and are likely to acquire a higher level of productivity
in subsequent periods, which increases the joint surplus of the match.
Our analysis relates to empirical and theoretical studies on the asymmetry of labor market
fluctuations over the business cycle. On the empirical side, the works by Neftci (1984), Altissimo
and Violante (2001), Panagiotidis and Pelloni (2007), Barnichon (2012), Abbritti and Fahr
(2013), Barattieri et al. (2014), Caggiano et al. (2014), and Benigno et al. (2015) show that
unemployment and wages fluctuate differently across phases of the business cycles. Compared
to these studies, we show that state dependence in labor market fluctuations is linked to the level
of aggregate productivity, and we extend the analysis to job transition rates. A large body of
research has identified specific historical periods in which business cycle volatility has changed
(e.g., the Great Moderation), attributing those changes to the conduct of monetary policy in
the Volcker era or the Zero Lower Bound period (e.g., Liu et al., 2018), or the magnitude of
exogenous shocks (e.g., Justiniano and Primiceri, 2008). While focusing on the labor market
alone, our empirical analysis uncovers changes in the responses of macroeconomic variables to
STATE DEPENDENCE IN LABOR MARKET FLUCTUATIONS 1029
shocks that occur systematically throughout the business cycle since the post-WWII era instead
of specific periods.
On the theoretical side, our work is related to studies that develop structural models to
investigate asymmetric dynamics of the labor market. Sedl´
aˇ
cek (2014) and Kohlbrecher and
Merkl (2016) consider the importance of the reservation productivity threshold for the dynam-
ics of the JFR. Unlike these studies, we investigate how this mechanism contributes to state
dependence in both the job finding and job separation rates, and the TVAR model identifies
as important empirical sources of state dependence for the unemployment rate. Ferraro (2018)
shows that employment cycles are characterized by large skewness and develops a search model
with permanent worker heterogeneity in productivity to explain the finding. Our version of the
DMP model hinges on heterogeneity in match-specific productivity, which allows for job-to-job
transitions, building on the work of Fujita and Ramey (2012), who show that OJS is critical
for the standard DMP model to deliver a realistic performance and generate the Beveridge
Curve. Petrosky-Nadeau and Zhang (2017) show that a standard DMP model with exogenous
job separation generates state dependence via the inherent nonlinearities of the policy function
for market tightness. Although our version allows for this channel, we find it to be less quan-
titatively important, under our calibration, to explain the state dependence of labor market
variables at business cycle frequency identified by the TVAR model.
The remainder of the article is structured as follows. Section 2 presents the empirical findings.
Sections 3 and 4 outline the benchmark model and discuss the main mechanisms generating
state dependence in labor market fluctuations, respectively. Section 5 describes the calibration
and presents the main results. Section 6 performs a series of robustness checks on the calibration
and alternative specifications of the model. Section 7 concludes.
2. EMPIRICAL EVIDENCE
This section isolates systematic differences in fluctuations of labor market variables linked
to the state of aggregate productivity. Comovements of unemployment and job-transition rates
with average labor productivity are stronger in periods of low aggregate productivity, resulting
in a larger volatility of labor market variables. Before studying these dynamics with a structural
TVAR model, we use a simple scatter plot to show the changes in the comovements of these
variables over the business cycle.
We use quarterly series for the unemployment rate, the JFR, the job separation rate, output,
hours, and labor productivity over the period 1950:I–2014:IV. To extract the cyclical component
of variables, we use the filtering method in Hamilton (2018).2Figure 1 plots quarterly first
differences for the unemployment rate, job separation rate, and JFR against the quarterly
growth rate of labor productivity for periods in which the level of productivity is above (left
panels) and below (right panels) the median value. The elasticity coefficients are larger in periods
of low productivity, suggesting that the comovement between changes in labor market variables
and changes in productivity is stronger in periods of low productivity. In the next subsection, we
assess this finding more formally through a TVAR model that isolates the response of variables
to shocks across different regimes of productivity.
2.1. The TVAR Model. The TVAR model, based on the original study by Chen and Lee
(1995), allows the VAR parameters to vary across an aggregate state of the economy. The
switching mechanism is based on the value of one of the endogenous variables being above or
below a threshold, and unlike Markov-Switching models, the parameter change is endogenous
to the dynamics of the VAR process. The reduced-form model can be expressed as follows:
Zt=ξtc1+
K
k=1
Bk,1Zt−k+1/2
1vt+(1−ξt)c2+
K
k=1
Bk,2Zt−k+1/2
2vt,(1)
2Appendix A.1 provides details on the data sources.
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