Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter September 10, 2020

The Cyclicality of On-the-Job Search Effort

Hie Joo Ahn and Ling Shao

Abstract

This paper provides new evidence for cyclicality in the job-search effort of employed workers, on-the-job search (OJS) intensity, in the U.S. using American Time Use Survey and various cyclical indicators. We find that the probability of an employed worker to engage in OJS is statistically significantly countercyclical, while time spent on OJS of an employed job seeker is weakly countercyclical. The fear of job loss, employment uncertainty, and workers’ financial situations is crucial in the job search decision of employed individuals. The results imply that the precautionary motive might be the key driver of the countercyclicality in OJS intensity.


Corresponding author: Hie Joo Ahn, Federal Reserve Board, Washington, DC, USA, E-mail:

The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. An earlier version of this paper has been circulated under the title “Precautionary on-the-job search over the business cycle.” We thank Stephanie Aaronson, Leland Crane, Andrew Figura, Shigeru Fujita, Marina Kutyavina, Alison Weingarden, and the anonymous referee for helpful comments on an earlier draft of this paper, and Trevor Dworetz for excellent research assistance.


Appendix: The Cyclicality of On-the-Job Search Effort

1 Alternative Theory

The appendix provides alternative theoretical explanations for the empirical findings. The theory is intended to characterize the countercyclicality in OJS intensity–that is–employed individuals, on average, search harder for a new job as the current labor market condition deteriorates, and they feel more uncertain about the future economic situation and pessimistic about their financial situation. The main feature of the model is that workers who already have a job are likely to look for a new job to insure against possible income or job loss in the future, which is the precautionary motive of job search.[28] This implies that job search activity can be seen as analagous to saving.

1.1 Overview

Consider a two-period consumption model of a worker who already has a job in the first period.[29] The worker is risk averse, and derives utility from consumption. However, she derives disutility from the effort she spends on searching for a new job. Assume that workers do not have access to complete insurance market. Suppose, for simplicity, that saving technology does not exist in this economy.[30] The worker self-insures against possible income loss in the future by raising job-search effort in the first period, when she expects the labor market conditions to deteriorate in the second period or feels uncertain about the labor market situation in the future. By searching hard for a new job, it becomes easier for her to find a job in case she loses her current job, or to switch to a better-paying employer when she experiences a wage cut at her current job. The model is a partial equilibrium model where labor market variables such as the job-arrival rate, job-destruction rate, employment volatility, and wages are determined exogenously.[31]

1.2 Model Timing

  1. First period: In the first period, the worker earns wage, w1, and decides how much of her income she will spend on consumption, c1, and job search, s1.[32]

  2. Second period: In the second period, separation takes place. The worker becomes unemployed with probability δ2. When the worker loses her job, she remains unemployed and receives the unemployment insurance benefit b if the worker did not search for a job in the first period. Or she can find a new job with probability p2 and earn wage w2, if the worker did job-search activities in the first period. When the worker does not lose her job, she can either stay with her current employer, and gets wage w2 if she did not search for a new job. Or she can switch to a new employer with probability p2 and earn wage w2 + μ with μ > 0 if she looked for a new job in the first period.[33][34]

The worker has imperfect knowledge about the labor market condition in the second period. Therefore, her second-period consumption is a random variable that depends on her second-period income.

Let f2 be the aggregate job-finding probability. Then, an employed individual’s probability of finding a new job, p2, is a function of s1 and f2 as follows:

p2=p(s1,f2).

We assume that p(s1,f2)s1>0 and 2p(s1,f2)s12<0.

1.3 Model

In this set-up, the employed worker’s problem is written into the following.

maxs1u(c1,c2)=u(c1)+βE{u(c2)}s.t.c1=w1s1c2=δ2{b+p2(w2b)}+(1δ2)(w2+p2μ)

If we retain the assumption β = 1, for simplicity, the first-order necessary condition for optimal consumption and search effort is obtained from the following Euler equation

(1)u(c1)=E[u(c2){δ2(w2b)+(1δ2)μ}p(s1,f2)s1rateofreturnfromoneunitofjobsearch].

Equation (1) says that the worker should be indifferent between, on the one hand, consuming one more unit in period one and, on the other hand, spending one unit for job search in period one and consuming the units equivalent to the expected outcome of job search in period two. Note that the term in brackets is the rate of return from job search. The key difference from the usual consumption Euler equation is that the rate of return from one unit of job search depends on the expected values of stochastic parameters, δ2, w2, and f2, while the rate of return from saving is a fixed parameter in a usual model of consumption and saving.

Suppose that there is a sufficient statistic of labor market condition in period two, denoted as ξ2, that determines the labor market variables in the second period. Let V(ξ2) be the realized utility from consumption in the second period, then

(2)V(ξ2)=u(c2).

Assume that V(ξ2)ξ2,V2(ξ2)(ξ2)2, and V3(ξ2)(ξ2)3 exist. If we take derivatives of both sides of Equation (2) with respect to s1, then we have

(3)V(ξ2)ξ2ξ2s1=u(c2)[δ2(w2b)+(1δ2)μ]p(s1,f2)s1.

Let ξ¯2 be the value of ξ2 expected in period 1. Then, the optimal level of job search in the first period is also determined by ξ¯2. Suppose that s1=g(ξ¯2) where ξ¯2=h(s1), and ξ¯2s1=h(s1)s1=h. We assume that h = 1 to simplify our analysis, as suppressing the notation h does not influence the key feature of the model. Suppose in addition that ξ2=ξ¯2+e2 where e2IID(0,σ2).

Approximating Equation (3) using Taylor expansion, it follows that

E[V(ξ2)ξ2]=V(ξ2)ξ2|ξ2=ξ¯2+12[V3(ξ2)(ξ2)3|ξ2=ξ¯2]σ2.

Let V(ξ¯2)=V3(ξ2)(ξ2)3|ξ2=ξ¯2 for notational convenience. If we assume that the utility function is a log function, Equation (1) is rearranged into

(4)1c1=1c¯2[δ¯2(w¯2b)+(1δ¯2)μ112V(ξ¯2)σ2(w1s1)p(s1,f¯2)s1],

where E(δ2)=δ¯2, E(w2)=w¯2, and E(f2)=f¯2, and

c¯2=δ¯2{b+(w¯2b)p¯2}+(1δ¯2)(w¯2+p¯2μ).

If we are willing to assume that δ, w, and f are persistent processes, then the expected values of δ2, w2, and f2 are positively correlated with δ1, w1, and f1(δ¯2δ1>0,w¯2w1>0,f¯2f1>0).[35] In addition, note that 112V(ξ¯2)σ2(w1s1) is not zero, as Equation (4) implies that consumption in the first period should be zero, otherwise.

In addition, the rate of return from one unit of job search should be higher when there is uncertainty to compensate for the risk of job search. The following lemma provides the necessary condition for the risk premium associated with job search to be positive.

If 112V(ξ¯2)σ2(w1s1) is between 0 and 1, the rate of return from job search is higher when there is uncertainty.

Proof

Without uncertainty about the labor market condition in the second period, the rate of return from job search implied by the Euler Equation (1) is

[δ¯2(w¯2b)+(1δ¯2)μ]p(s1,f¯2)s1.

The Euler Equation (4) suggests that the rate of return from job search when there is uncertainty is

[δ¯2(w¯2b)+(1δ¯2)μ112V(ξ¯2)σ2(w1s1)]p(s1,f¯2)s1

For the rate of return from job search in the presence of uncertainty to be higher than that without uncertainty, 0<112V(ξ¯2)σ2(w1s1)<1.

Note that 112V(ξ¯2)σ2(w1s1) is the parameter determining the size of risk premium associated with the rate of return from OJS.

Based on the Euler equation (1), now we can analyze how w¯2, δ¯2, f¯2 and σ2 affect the job search effort in the first period.

Proposition

If V(ξ¯2) is positive, job search effort increases as labor market uncertainty, σ2, rises.

Proof

The Euler equation (1) is rearranged into

F=δ¯2b+(1δ¯2)w¯2δ¯2(w¯2b)+(1δ¯2)μ+p¯2(w1s1112V(ξ¯2)σ2(w1s1))p(s1,f¯2)s1=0.

Using the implicit function theorem, the derivative is written into the following,

s1σ2=[Fσ2Fs1],

where Fσ2 and Fs1 are the following:

Fs1=p(s1,f¯2)s1[1+1{112V(ξ¯2)σ2(w1s1)}2]2p(s1,f¯2)s12{w1s1112V(ξ¯2)σ2(w1s1)}>0
Fσ2=[12V(ξ¯2)σ2(w1s1)2{112V(ξ¯2)σ2(w1s1)}2]p(s1,f¯2)s1.

If V(ξ¯2)>0 and Fσ2<0, then s1σ2>0.

Corollary 1

Job search effort increases, as the job loss rate rises (s1δ1>0)

Proof

The implicit function theorem gives

s1δ¯2=[Fδ¯2Fs1],

of which the sign is determined by

Fδ¯2=(w¯2b)[δ¯2(w¯2b)+(1δ¯2)μ][δ¯2b+(1δ¯2)w¯2](w¯2bμ)[δ¯2(w¯2b)+(1δ¯2)μ]2<0.

Therefore, s1δ¯2>0, and thus s1δ1>0.

Corollary 2

Job search effort increases to a fall in future wages, if the wage gain associated with switching to a new job is sufficiently large. Job search effort decreases to a fall in future wages, otherwise.

Proof

The implicit function theorem gives

s1w¯2=[Fw¯2Fs1],

of which the sign is determined by

Fw¯2=δ¯2b+(1δ¯2)2μ.

s1w¯2<0 if μ>[δ¯2(1δ¯2)2]b, and s1w¯2>0 if μ<[δ¯2(1δ¯2)2]b.

The corollary implies the following. When workers expect the wage from current job to fall in the future, then they will search harder for a new job, if they can get a much higher wage at a new job. Otherwise, when wages fall, it is more beneficial for a worker to reduce job-search effort and to stay unemployed receiving the unemployment insurance benefit when losing the current job.

References

Acemoglu, D., and R. Shimer. 1999. “Efficient Unemployment Insurance.” Journal of Political Economy 107 (5): 893–928, https://doi.org/10.1086/250084.Search in Google Scholar

Aguiar, M., E. Hurst, and L. Karabarbounis. 2013. “The Life-Cycle Profile of Time Spent on Job Search.” The American Economic Review 103 (3): 111–6, https://doi.org/10.1257/aer.103.3.111.Search in Google Scholar

Aiyagari, S. R 1994. “Uninsured Idiosyncratic Risk and Aggregate Saving.” The Quarterly Journal of Economics 109 (3): 659–84.10.2307/2118417Search in Google Scholar

Bell, B., and J. Smith. 2002. “On Gross Worker Flows in the United Kingdom: Evidence from the Labour Force Survey”, Bank of England working papers 160. Bank of England.10.2139/ssrn.340500Search in Google Scholar

Bloemen, H. G. 2005. “Job Search, Search Intensity, and Labor Market Transitions an Empirical Analysis.” The Journal of Human Resources 40 (1): 231–69. https://doi.org/10.3368/jhr.XL.1.232.Search in Google Scholar

Cragg, J. G. 1971. “Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods.” Econometrica 39 (5): 829–44, https://doi.org/10.2307/1909582.Search in Google Scholar

DeLoach, S., and M. Kurt. 2013. “Discouraging Workers: Estimating the Impacts of Macroeconomic Shocks on the Search Intensity of the Unemployed.” Journal of Labor Research 34 (4): 433–54, https://doi.org/10.1007/s12122-013-9166-0.Search in Google Scholar

Eeckhout, J., and I. Lindenlaub. 2019. “Unemployment Cycles.” American Economic Journal: Macroeconomics 11 (4): 175–234, https://doi.org/10.1257/mac.20180105.Search in Google Scholar

Engen, E. M., and J. Gruber. 2001. “Unemployment Insurance and Precautionary Saving.” Journal of Monetary Economics 47 (3): 545–79, https://doi.org/10.1016/s0304-3932(01)00051-4.Search in Google Scholar

Faberman, R. J., and M. Kudlyak. 2019. “The Intensity of Job Search and Search Duration.” American Economic Journal: Macroeconomics 11 (3): 327–57, https://doi.org/10.1257/mac.20170315.Search in Google Scholar

Fallick, B. C., and C. A. Fleischman. 2004. “Employer-to-employer Flows in the U.S. Labor Market: The Complete Picture of Gross Worker Flows”, Finance and Economics Discussion Series 2004-34, Board of Governors of the Federal Reserve System (U.S.).10.2139/ssrn.594824Search in Google Scholar

Fujita, S. 2012. “An Empirical Analysis of On-the-Job Search and Job-to-Job Transitions.” Working Papers 10–34, Federal Reserve Bank of Philadelphia, https://doi.org/10.21799/frbp.wp.2010.34.Search in Google Scholar

Gertler, M., C. Huckfeldt, and A. Trigari. 2016. “Unemployment Fluctuations, Match Quality, and the Wage Cyclicality of New Hires”, NBER Working Papers 22341, National Bureau of Economic Research, Inc, https://doi.org/10.3386/w22341.Search in Google Scholar

Gomme, P., and D. Lkhagvasuren. 2015. “Worker Search Effort as an Amplification Mechanism.” Journal of Monetary Economics 75 (C): 106–22, https://doi.org/10.1016/j.jmoneco.2015.02.002.Search in Google Scholar

Jaimovich, S., and H. Siu. 2012. “The Trend is the Cycle: Job Polarization and Jobless Recoveries.” The Review of Economics and Statistics. https://doi.org/10.3386/w18334.Search in Google Scholar

Kahn, L. M. 2012. “Temporary Jobs and Job Search Effort in Europe.” Labour Economics 19 (1): 113–28, https://doi.org/10.1016/j.labeco.2011.09.001.Search in Google Scholar

Kimball, M. 1990. “Precautionary Saving in the Small and in the Large.” Econometrica 58 (1): 53–73.10.3386/w2848Search in Google Scholar

Krause, M. U., and T. A. Lubik. 2010. “On-the-job Search and the Cyclical Dynamics of the Labor Market.” Working Paper 10-12, Federal Reserve Bank of Richmond.10.2139/ssrn.2189550Search in Google Scholar

Krueger, A. B., and A. Mueller. 2010. “Job Search and Unemployment Insurance: New Evidence from Time Use Data.” Journal of Public Economics 94 (3): 298–307, https://doi.org/10.1016/j.jpubeco.2009.12.001.Search in Google Scholar

Lilien, D. M. 1982. “Sectoral Shifts and Cyclical Unemployment.” Journal of Political Economy 90 (4): 777–93, https://doi.org/10.1086/261088.Search in Google Scholar

Lise, J. 2013. “On-the-Job Search and Precautionary Savings.” The Review of Economic Studies 80 (3): 1086–113, https://doi.org/10.1093/restud/rds042.Search in Google Scholar

Mortensen, D., and É. Nagypál. 2007. “More on Unemployment and Vacancy Fluctuations.” Review of Economic Dynamics 10 (3): 327–47, https://doi.org/10.1016/j.red.2007.01.004.Search in Google Scholar

Mukoyama, T., C. Patterson, and A. Şahin. 2018. “Job Search Behavior over the Business Cycle.” American Economic Journal: Macroeconomics 10 (1): 190–215, https://doi.org/10.1257/mac.20160202.Search in Google Scholar

Nagypál, É. 2006. “On the Extent of Job-to-Job Transitions.” 2006 Meeting Papers 10, Society for Economic Dynamics.Search in Google Scholar

Nakamura, L. I., and M. E. Trebing. 2008. “What Does the Philadelphia Fed’s Business Outlook Survey Say about Local Activity?” Research Rap Special Report. RePEc:fip:fedprr:y:2008:i:dec.Search in Google Scholar

Orlik, A., and L. Veldkamp. 2014. “Understanding Uncertainty Shocks and the Role of Black Swans”, Working Paper 20445, National Bureau of Economic Research, https://doi.org/10.3386/w20445.Search in Google Scholar

Pissarides, C. A. 1994. “Search Unemployment with On-the-Job Search.” The Review of Economic Studies 61 (3): 457–75, https://doi.org/10.2307/2297899.Search in Google Scholar

Pissarides, C. A. 2000. Equilibrium Unemployment Theory, Vol. 1, 2nd ed. Cambridge, MA: The MIT Press.Search in Google Scholar

Regis, S. F. B., and Y. Zylberberg. 2016. “Access to Jobs and Duration Dependence.” Unpublished manuscript.Search in Google Scholar

Schwartz, J. 2014. “The Job Search Intensity Supply Curve: How Labor Market Conditions Affect Job Search Effort.” In Upjohn Working Papers and Journal Articles, 14–215. Kalamazoo, MI: W.E. Upjohn Institute for Employment Research.10.17848/wp14-215Search in Google Scholar

Shimer, R. 2004. “Search Intensity.” Unpublished manuscript, https://doi.org/10.3386/w10326.Search in Google Scholar

Stewart, J. 2013. “Tobit or Not Tobit.” Journal of Economic and Social Measurement 38 (3): 263–90.10.3233/JEM-130376Search in Google Scholar

Tumen, S. 2014. “Is Search Intensity Countercyclical?” Unpublished manuscript.Search in Google Scholar

Received: 2019-12-09
Accepted: 2020-06-17
Published Online: 2020-09-10

© 2020 Walter de Gruyter GmbH, Berlin/Boston