Job Search Intensity

over the Business Cycle∗

Gustavo Leyva

University of Minnesota

March 7, 2016

Abstract

The unemployed in the U.S. appear to allocate time to job search activities regardless

of the state of the economy. The evidence I document using data from the American

Time Use Survey between 2003 and 2014 shows that the unemployed increase their search

intensity only slightly if at all during recessions. While their search intensity depends on a

number of factors that change over the business cycle, among other arguments examined

in this paper, I primarily argue that the countercyclicality of the value of a job is the most

promising explanation to reconcile the evidence. This finding has important implications

for understanding business cycles and for the design of policy.

JEL codes : E24, E32, J22, J64

Keywords : search intensity, value of a job, business cycle

∗University of Minnesota, Department of Economics (email: leyva004@umn.edu). I am indebted to José-Víctor Ríos-Rull for all his support, guidance, and insightful feedback. I want to thank Naoki Aizawa, KyleHerkenhoff, and especially Loukas Karabarbounis for their time, encouragement, and invaluable and relentlessadvice. I thank the generous suggestions from Jonathan Heathcote, Ellen McGrattan, Chris Phelan, and DavidRahman and the members of the Labor Workshop at the University of Minnesota. I have also benefited fromstimulating conversations, at different stages of this project, with Job Boerma, Richard Condor, Juan Diaz,Son Dinh, Nicolas Grau, Zhen Huo, Yu Jiang, Bitmaro Kim, Shihui Ma, Zach Mahone, Iacopo Morchio, SergioOcampo, Cloe Ortiz de Mendivil, Alejandro Sevilla, David Strauss, Naoki Takayama, Clay Wagar, Zoe Xie, andBaxter Zaiger. I also want to thank the participants of the Tobin Project’s Prospectus Development Workshop,especially Beth Truesdale for her remarkably helpful comments, and finally, the attendants of the MinnesotaPopulation Center’s Inequality and Methods Workshop. I am solely responsible for the content of this paperand all errors are mine.

1

1 Introduction

Much has been said and written about the unemployed and how the value of their leisure

time is expected to change in response to the booms and busts of the economy. However, little

is known about how workers allocate their time to the job search while unemployed and over

the business cycle.1 Still, this allocation decision has important implications for business cycles.

The decision by the unemployed of investing more or less time according to the state of the

economy may dampen or amplify economic fluctuations. Remaining jobless for a long time or

leaving the pool of unemployment relatively quickly has overt implications for the persistence

and severity of business cycle fluctuations.

By using the American Time Use Survey (ATUS) between 2003 and 2014, I document that

the unemployed in the U.S. appear to allocate their time to job search independent of the state

of the economy. They increase search intensity only slightly if at all during recessions.

It would be odd to interpret this evidence as if the unemployed were unaware of or unaffected

by the changing conditions in the labor market. After all, the unemployed remain attached to

the labor market and their chances of leaving the pool of unemployment vary with the business

cycle. Moreover, their search intensity depends on additional factors that do change over the

business cycle, such as wages, unemployment benefits, and the value of non-working time.

The role of each of these factors could be better grasped with the aid of the following sketch

of the balance of costs and benefits that drives the choice of job search intensity:

(1)current marginalcosts of searching

=(2)

marginal increase inthe job finding probability

×(3)

expectedvalue of a job

The left side of the equation represents the foregone leisure time when exerting an additional

search effort unit. However, this additional effort also brings about benefits. The right side of

the equation highlights two motives. Since looking for work is a risky activity the first motive

is the possibility of boosting their chances of finding a job. The second motive is the ultimate

payoff of having looked for work in the first place: the value of a job.

1 Recent contributions come from Shimer (2004), Mukoyama et al. (2013), Gomme and Lkhagvasuren (2015),and indirectly from Aguiar et al. (2013b).

2

The value of a job is the sum of the benefits minus the opportunity costs of being employed.

Having a job means receiving a wage in exchange for the hours worked. It also implies avoiding

the searching costs that could have been incurred had the unemployed failed to find a job and

kept looking for work. However, working is also costly. The opportunity cost of being employed

consists of the foregone unemployment benefits and the foregone value of non-working time.

The evidence I show implies that (1) does not vary over the business cycle. However, (2)

does vary with the state of the economy and (3) is predicted to do so. On the one hand, it

is well-known that in the U.S., the probability of finding a job tracks closely with the cyclical

shifts of the economy (Shimer, 2005 and Shimer, 2012). On the other hand, the value of a job

is, by construction, strongly procyclical in the Mortensen and Pissarides (1994) search model,

which is the workhorse of the macroeconomics of unemployment.2

Therefore, if the nearly acyclical allocation of time to job search activities by the unemployed

in the U.S. is seen through the lens of the above equation, then we have a puzzle.3

I propose three alternative conjectures aimed to solve this puzzle by addressing (2) and (3)

separately. The first conjecture, which focuses on (2), states that the unemployed view their job

search as a substitute for the prevalent labor market conditions. For instance, during recessions

they will search more intensely to compensate for the decline in the chances of finding work

caused by the limited job opportunities.

The remaining conjectures address (3). The second conjecture maintains that the unem-

ployed will allocate additional time to search activities in times when they foresee a decline in

future consumption. Finally, the third conjecture is that, from the worker’s standpoint, a job

is more desirable during recessions.

Among these, the most promising explanation is that the unemployed place a relatively high

2 This is less so in versions of the model that deviate from the Nash bargaining rule or allow for rigid wages ina rather exogenous way. The canonical search model of Mortensen and Pissarides (1994) will also predict that(2) is less procyclical than what the data suggests. This counterfactual prediction was first shown by Shimer(2005).

3 Of course, the puzzle remains if search intensity is countercyclical. Shimer (2004) documents that the averagenumber of search methods used by the unemployed is countercyclical. Mukoyama et al. (2013) constructintensive and extensive margins for search intensity by linking time-use data and number of search methods.They conclude that search intensity is countercyclical. Finally, Gomme and Lkhagvasuren (2015) argue in theopposite direction.

3

value on a job during recessions. I show this by providing estimates of the cyclicality of the

value of a job in the U.S. To infer the cyclicality of the value of a job, I build on Chodorow-Reich

and Karabarbounis (2015), who construct estimates for the opportunity cost of employment. I

develop a strategy to infer an upper bound for the size of job search costs based on the size of

the value of non-working time. I discipline these estimates by using an expression for the value

of a job that emerges from a search model.

The estimated value of a job is countercyclical for two reasons. First, during recessions the

opportunity cost of employment is relatively low since the employed spend less time working

and their consumption falls. Chodorow-Reich and Karabarbounis (2015) report that the time

series of this cost is as procyclical as the marginal labor productivity. Second, the opportunity

cost of postponing the decision to search for work is relatively high during recessions. The

search costs that accumulate over an expected long period of unemployment deter the worker

from delaying their efforts.

Indeed, I show that the latter costs are countercyclical even if the optimal search intensity

does not vary over the business cycle. In clarifying this apparent contradiction, I contend that

the purpose of the job search activity matters, not its size over the business cycle. By searching

harder during recessions, one is hoping to avoid the cumulative future search costs that are

likely if they remain jobless for a long time. Put simply, the unemployed will reap the marginal

contribution of the current search to the reduction of future search costs as long as they spend

some time in the activity of searching for work.

Therefore, I argue that both the procyclicality of the opportunity cost of employment and

the countercyclicality of future search costs are needed to show that a job is strongly valued

during recessions. Chodorow-Reich and Karabarbounis’s (2015) estimates would imply that,

in a search model with an endogenous search effort, the value of a job is nearly acyclical or

slightly countercyclical in the U.S. I show that the puzzle mentioned above could be solved

when allowing search costs to play a role as well.

The countercyclicality of the value a job to the unemployed has several important implica-

tions for understanding business cycles and for the design of policy.

First, the more persistent the recession is, the higher the incentives to invest time in search-

4

ing for work. One broad interpretation is that fears about the consequences of being jobless for

a long time provide the impetus to look for work.4

The second implication is that wages and unemployment benefits appear to play a relatively

minor role in the allocation of time in the search activities of the unemployed over the business

cycle. This implication contrasts with the decisive role wages play in the allocation of hours

worked in the real business cycle literature. Thus, persistent effects seem to matter more than

intertemporal substitution effects (Clark and Summers, 1982).

Third, given that in a recession the cumulative future search costs, expressed in units of

consumption, are expected to be relatively high, and in response, the unemployed will choose

to give up leisure time to look for work, one may conclude that income effects dominate the

substitution effects. Again, this implication clashes with the primary role assigned to a strong

intertemporal substitution of leisure and procyclical real wages in generating procyclical re-

sponses in the labor supply in the real business cycle literature.5

The fourth implication is that the burden of being unemployed should be assigned a spe-

cific weight in the balance of costs and benefits of providing unemployment insurance during

recessions. The persistence of unemployment by itself also has implications on the design of the

optimal unemployment insurance over the business cycle.

Fifth, if the value of a job varies in a countercyclical way, then the job-to-job turnover in

booms may be more important than what we know. The sixth implication, also pointed out by

Chodorow-Reich and Karabarbounis (2015), is that if the value of a job is countercyclical, then

productivity shocks in the canonical search model will generate still milder fluctuations in the

unemployment rate and number of vacancies.

Finally, Davis and von Wachter (2011) recently conclude that in the canonical search model,

job loss is a rather inconsequential event for the unemployed. In light of the findings of this

paper, the culprit behind such implication of the search model might be the procyclicality of the

4 Davis and von Wachter (2011) show that workers’ anxieties and perceptions about labor market conditionstrack closely with actual conditions, and that prime-age workers’ anxieties are highly correlated to the unem-ployment rate in the U.S. in the period of 1977-2010.

5 Mankiw (1989) provides a critical assessment of this mechanism in the real business cycle model. Ramey andFrancis (2009)) contradict the real business cycle model, showing that leisure time has witnessed a secularincrease over the last century.

5

value of a job. To put it differently, in the canonical search model, unemployment is less costly

in recessions which is something that may sound odd for anyone acquainted with the stakes of

being unemployed for a long time. I would venture that to make the search model conform to

the main findings of this paper, it will require changes that go beyond mere twists on its key

mechanisms.

2 Non-procyclical search intensity: Evidence from ATUS

In this section, I document evidence on how the unemployed in the U.S. allocate their time

in the job search in response to the cyclical shifts of the economy. I use the American Time

Use Survey (ATUS) from 2003 to 2014 to measure the time-use in job search activities in an

average week of a year.

A brief background of the survey seems appropriate. The ATUS is the primary source of

national representative statistics on how people spend their time in a typical day of the year.

The sample is drawn from households that have finished their eighth month of the Current

Population Survey (CPS) interview.

The CPS is the primary source of national representative statistics on unemployment for the

U.S. civilian non-institutional population. It is the basis for the production of reliable monthly

estimates of total unemployment at the national level as well as for regions, states, and large

metropolitan areas. Each month, nearly 60,000 households are selected to be part of the CPS

sample. Members of each participating household aged 15 or over are interviewed once a month

for four consecutive months, dropped from the sample for the next eight months, and inter-

viewed again for the final four consecutive months.

The ATUS respondents are usually interviewed two to five months after they leave the CPS

sample. One respondent in each household is chosen randomly with equal probability. Respon-

dents are asked to provide a detailed account of their activities during the day prior to the

interview, starting at 4 a.m. on that day and ending at 4 a.m. on the interview day. Both the

CPS and the ATUS are conducted by the U.S. Census Bureau and sponsored by the Bureau of

Labor Statistics (BLS).

6

In this paper, I restrict the sample to unemployed people (looking for work) aged 25 and

over. As in Shimer (2004) I focus on people who have already finished school. The unemployed

due to temporary layoff are excluded because they are expected to be called back to work at

previous job. Moreover, unlike previous authors (Shimer, 2004 and Mukoyama et al., 2013),

I exclude the group of searchers who are out of the labor force. Since the timing of looking

for work is important, particularly at the outset of a recession, the sample for my study must

include the typical group of workers who do not have a job but are searching for one, but of

that group, it must only include those who are willing to work. For example, people out of the

labor force may be searching actively for work during recessions but not currently available for

work. Those people are excluded from my study.

A final word on the sample variation embodied in the surveys is worth mentioning. After the

above adjustments, the number of sampled unemployed individuals in the ATUS in an average

year between 2003 and 2014 is 400. In the CPS, approximately 32,000 are sampled in a year.

This striking difference in sample variation of both surveys is well reflected in the confidence

intervals shown in Figure 1.

The number of search methods has been discussed previously in the literature (see Shimer,

2004 and Mukoyama et al., 2013). Although I report additional evidence on the relevance of

this measure of search intensity for the business cycle, I present this discussion in Appendix A.

In the remainder of this section, I focus on the time spent looking for work over the business

cycle.

Table 3 reproduces the list of job search activities contained in the 2014 ATUS survey. Over

the years, the job search activity codes have remained fairly homogeneous.6 Previous authors

have used all activities listed in Table 3 (see Krueger and Mueller, 2010 and Mukoyama et al.,

2013) to construct a measure of job search intensity; however, I proceed differently. First,

the activities coded as 050405, 050499, and 180504 (170504 before 2005) are not consistently

recorded in the survey throughout the years. Second, some of the categories have no bearing on

changes in time-use in job search activities in response to economic conditions. Arguably, only

6 However, there may be concerns about the change in the wording of a couple of activities in 2004. The secondis related to the merging of two previously distinct categories into only one starting in 2005 (categories 050401(active job search) and 050402 (other job search activities) into 050401 (job search activities).

7

the activities coded as 050401, 050402, and 050403 are closely related to job search methods as

defined by the CPS (see Table 1).7

Therefore, I adopt an eclectic and transparent approach. I measure time-use in search activ-

ities using all categories (broad measure) and the restricted set of activities (narrow measure)

with the caveat that I manifest my preference for the latter based on the foregoing reasons.

The short span and low frequency of the ATUS data is a concern. I complement a time series

analysis with evidence that exploits the U.S. state variation. I start by reporting the results

from the time series analysis.

Time series evidence: Figure 7 shows the amount of time, in hours per week, allocated by

the average unemployed to the job search, according to the broad (left panel) and the narrow

(right panel) set of job search activities. It may be argued that most of the job search occurs

during weekdays. To address this concern, I also report the time-use in job search activities by

using all days of the week and weekdays only. In any case, the unemployed in the U.S. spend 4

or 5 hours per week.8

To gain perspective on the magnitude of these estimates, I consider the time-use in a variety

of activities by the employed and unemployed in the U.S., as a benchmark. The average hours

worked per week (including weekends) in the U.S. is a variable of interest for the understanding

of the business cycle. Using the ATUS survey, Aguiar et al. (2013b) document that around 32

hours per week are accrued to market hours worked for a sample of individuals aged between

18 and 65.

Using the same survey in the period of 2003-2013, Chodorow-Reich and Karabarbounis

(2015) report that the unemployed spend 47.6 hours per week on leisure activities (e.g., watch-

ing TV, listening to music, and socializing with friends) and 24.6 hours in home production.

7 Notice that all but one activity (“Submitting applications”) in the category coded as 050402 may be interpretedas passive methods. Although I could have left this category out, it would have been possible only before 2005.After this year, the activities included in this category were combined with the old set of categories listed as“Active job search” into the category “Job search activities”. In addition, there is nothing wrong with usingpassive methods whenever these are complemented with at least one active method. Unfortunately, the use ofactivities is not available with such a degree of detail in the ATUS.

8 These estimates are obtained from the reported time in minutes in the day previous to the ATUS interview.

8

Therefore, the size of the activity of searching for work is small, representing nearly 16%

of the average weekly hours worked and 20% of the time allocated to home production for the

unemployed.

I now turn to the time series variation of the time allocated to job search activities. Al-

though, a priori, there is nothing precluding trends in the time-use in search activities, I do

not perform additional adjustments to this series since there are no discernible increasing or

decreasing patterns throughout the sample period.

Unfortunately, only one recession episode could be examined with the aid of the ATUS data.

In addition, the low frequency of the data makes it difficult to make a clean connection between

search intensity and recessions. Hence, I offer two interpretations of the evidence as seen in

Figure 7. These views differ in the interpretation of the timing of the recession which began

in December 2007 and ended in June 2009, according to the National Bureau of Economic Re-

search (NBER).

If I use the NBER’s timing of the recession as a guide, I would conclude that the typical

unemployed person did not spend more nor less time looking for work during the latest reces-

sion. In this period, the average unemployed person increases his or her search intensity only

slightly, if at all.

Recall that the ATUS sample of unemployed individuals in a typical year is small, so it

is instructive to report confidence intervals. I show these intervals as deviations of one hour

per week around the mean.9 When using the broadest set of time-use categories, the spike in

2008 cannot be distinguished from the estimates in the surrounding periods, 2006-2007 and

2009-2012. Notice that a horizontal line can be traced inside the interval in the period of 2006-

2012. Similarly, the time-use estimate in the narrow set of activities is not distinguished from

the estimates in the period of 2009-2012. Therefore, I conclude that the spike in 2008 is not

statistically different than the time spent during the non-recessionary periods.

The alternative view recognizes that even though the recession as defined by the NBER

ended in June 2009, the ensuing slow recovery did not greatly alter the expectations of the

9 Estimates of the standard deviation are computed by using the ATUS replication weights. For the broad(narrow) set of categories, one hour amounts to 1.2 standard deviations (1.4), when using weekdays andweekends, and 1.3 standard deviations (1.5), when using weekdays only.

9

unemployed concerning their possibilities of finding work which, in turn, provided a reason for

them to keep looking for work even after June 2009. This argument follows when search inten-

sity is measured as the time-use in the narrow set of job search activities. In fact, by 2010 the

unemployment rate had reached its peak of 8.6% and receded only slowly afterwards. By 2012,

the unemployment rate was 6.8%, almost double the level in 2007 (3.6%).

In any case, it is reassuring to note that the unemployed in the U.S. did not spend less time

in search activities during the recent recession. This finding contrasts with the prediction of the

Mortensen and Pissarides (1994) search model when the choice of search intensity is endogenous.

Evidence from U.S. state variation: The measure of time-use in search activities in state j

with j = 1, . . . , 51 (including the District of Columbia) in period t is calculated as follows:

sjt =∑

i

(

wulookijt

∑

iwulookijt

)

sijt, (1)

where sijt denotes the time-use of an unemployed person looking for work who resides in state

j in period t and wijt denotes the number of people that such unemployed individual represents

in the U.S. unemployment population aged 25 and over. Likewise, the unemployment rate is

calculated as

urulookjt =

∑

iwulookijt

∑

iwulookijt +

∑

iwnijt

, (2)

where wuijt is the weight assigned to the unemployed individual (looking for work) i in state j

in period t, and wnijt is the weight assigned to the employed worker.

I construct these two variables along a maximum of T periods. There is a trade-off on the

choice of T . The larger T is, the more observations I have per U.S. state over time, at the

expense of estimating sijt and urjt with a small sample size in each period t = 1, . . . T . I group

observations along equally sized time periods. Below I report results using T = 2, 3, 4. When

T = 2 the periods are 2003-2007 and 2008-2014, when T = 3 the periods are 2003-2006, 2007-

2010, and 2011-2014. Finally, when T = 4 I group observations over the periods 2003-2005,

10

2006-2008, 2009-2011, and 2012-2014.

The U.S. state variation analysis is justified provided that sjt and urjt vary enough. As a

natural benchmark, consider the time series variation of these variables. According to Figure

7, along the entire sample period, the average unemployed individual looking for work spends

between 2 and 9 hours per week looking for work.

The unemployment rate also varies considerably in the period of 2003-2014. I use the

ATUS survey to compute two national rates of unemployment, the first one, based on the

unemployed looking for work only, following equation (2), and the second, based on the total

number of unemployed workers, including those on temporary layoff. Mean estimates of these

rates fluctuate between 3.2 and 7.6, and 3.9 and 8.4, respectively, with the peaks corresponding

to 2010 in both cases. The amplitude of these fluctuations compares successfully with its BLS

counterpart. According to the BLS, the annual unemployment rate of people aged 25 and over

in the U.S. varies between 3.6 and 8.2 in the same sample period, with the maximum value

observed, again, in 2010.

Figure 8 displays measures of sjt and urjt by U.S. state by assembling observations in two

periods: 2003-2008 and 2009-2014. Interestingly, the range of values in which both the time-use

and the unemployment rate fluctuate across U.S. states without considering outliers mimics

that of their time series counterparts.

To uncover the cyclicality of search intensity, if any, I perform the following regression:

sjt = α + βurulookjt + εjt (3)

where εjt is the error term. Coefficient β is the parameter of interest. sjt is measured as the

number of minutes per week.

Before jumping to the estimation results, I pause to comment on three issues: simultaneous

causality, compositional bias, and measurement issues.

Simultaneous causality is potentially an issue in equation (3). Suppose β is negative. This is

consistent with two alternative views on the direction of causality. First, a high unemployment

rate reflects higher competition among the unemployed which may discourage search intensity

11

individually. At the same time, a higher unemployment rate is the consequence of not searching

enough for work.

There are also two competing views in case β > 0. On the one hand, even if the unem-

ployment rate is high, the combination of low consumption and a limited ability to self-insure

against unemployment shocks could encourage the unemployed to search more intensely. On

the other hand, everyone searching more intensely at the same time may end up in congestion

and to the detriment of the individual prospects of finding a job. Later, I discuss a partial

remedy for this issue.

In equation (3), the linkage between search intensity and labor market conditions over the

business cycle may be affected by compositional changes in the population of unemployed work-

ers. To address this issue, I include some demographic variables such as age, marital status,

sex, race, and education. The rationale of including these variables is in order.

Aguiar et al. (2013a) report that the job search profile of the typical unemployed in the U.S.

is hump-shaped over the life-cycle. The unemployed aged 21 to 25 spend roughly 2.2 hours per

week and ages 46 to 50 spend spend a maximum of 6.6 hours per week.

The job search behavior may also depend on the presence of a partner in the household. In

recessionary periods, the pooling of income may help the unemployed insure themselves against

unemployment shocks. In addition, women and men may allocate time to search activities dif-

ferently as part of a specialization of tasks within the household. Race may also account for

non-market considerations in the availability of jobs and difficulty of finding a job. Finally,

education may affect the job search behavior in two different ways. On the one hand, the most

educated unemployed individuals have more to lose in times when job opportunities are scarce,

so they may be willing to search more intensely. On the other hand, the most educated may

have additional means to self-insure during the state of unemployment. The less educated may

be more desperate and, therefore, more willing to search intensely.

I discuss alternative measures of both sjt and urjt. The measure of search intensity is re-

stricted to the narrow set of activities displayed in Table 3. It may be argued that most of the

job search activities occur during weekdays. To address this concern, I also report the time-use

in job search activities by using all days of the week and weekdays only. One caveat is pertinent

12

here. By dropping weekends, 50% percent of the sample is lost as a result of the sampling design

of the ATUS.10

For the unemployment rate, I consider both the rate of unemployed people looking for work,

using (2), and the rate of unemployed people that also includes the unemployed who are tem-

porarily laid off. The latter unemployment rate may be estimated with fewer measurement

errors. In addition, I consider a third measure of the unemployment rate as a corrective pro-

cedure to the presence of measurement errors. I follow Aguiar et al. (2013b) who suggest

rescaling the ATUS weights such that the ATUS unemployment rate is exactly the same as its

CPS counterpart. This procedure, however, is innocuous for sjt since the measure of time-use

pertains only to unemployed people.

Now, I return to equation (3). I report estimates for β in Table 5 and Table 6, depending

on whether I use weekdays and weekends or weekdays only. In all of the regressions, estimates

on β were obtained by clustering the variance estimation by state. In column 1, I report the

full unweighted sample estimates, also pictured in Figure 9 and Figure 10. From column 2

onwards, I begin reporting estimates obtained by dropping outliers (state-time observations

with time-use exceeding three times the average time spent looking for work (around 5 hours,

see Figure 7). This is the only difference between columns 1 and 2. I then report results in

column 3 by weighting observations by the size of the population in each state, as a way to deal

with measurement errors. Finally, in column 4, besides weighting observations, I include the

demographic variables discussed above.

I start with Table 5, which shows the results for the narrow set of activities and when using

all days of the week. I prefer the last two columns since they are obtained by weighting states

according to their size and controlling for demographic variables.

Interestingly, all estimates obtained under different measures of unemployment, different

time periods, and across alternative estimation procedures, reveal a positive association be-

tween search intensity and the unemployment rate. This suggests that workers living in U.S.

states where the unemployment rate is higher spend more minutes per week searching for work.

For the alternative measures of unemployment rate, the rate based on the unemployed look-

10See U.S. Bureau of Labor Statistics (2015).

13

ing for work is the most favorable to the positive association between search intensity and the

unemployment rate. The least favorable is the CPS unemployment rate, possibly due to the

presence of measurement errors. Moreover, as expected, estimates on β become less reliable as

we move from the top to the bottom of the table, reflecting possibly the role of measurement

errors.

When significant, the estimates of β range from 15 to 20 additional minutes per week spent

in search activities as the unemployment rate increases by 1 percentage point. To gain insight on

these values, consider the increase in the unemployment rate in the latest recession. According

to BLS estimates, the annual unemployment rate increased from 3.6 in 2007 to 8.2 in 2010, an

increase of almost 5 percentage points. This would mean the unemployed worker spent roughly

an additional 75 to 100 minutes in a typical week during that period.

Table 6 reproduces virtually the same patterns displayed in Table 5. However, all estimates

are smaller in magnitude and more uncertain than in Table 5. When significant, however, the

estimates range from 8 to 11 additional minutes per week spent in search activities as the un-

employment rate increases by 1 percentage point.

One additional concern is that the ATUS time-use estimates are not meant to be represen-

tative at the state level. Unfortunately, the small sample size makes this problem more acute.

The rescaling of the ATUS weights, which in this case amounts to running regression (3) against

the CPS unemployment rate, is one way to partially deal with the presence of measurement

errors. The second approach is discussed next.

Consider the following decomposition of the total hours spent in job search activities by the

unemployed looking for work:

sjt ≡ (h/u)jt = (h/su)jt (su/u)jt

where su denotes the measure of unemployed person who report some minutes spent in search

activities during the day prior to the ATUS interview. Since the ATUS is a survey based on a

time diary not all unemployed people report some minutes spent in search activities.

I construct two measures of the hours per unemployed people by keeping constant (su/u)jt

14

in two different ways. First, I compute

swjt = (h/su)jt1

51

51∑

j=1

(su/u)jt (4)

and then

sbjt = (h/su)jt1

T

T∑

t=1

(su/u)jt (5)

where the first measure calculates the hypothetical series of hours per unemployed individual

under the assumption that the measure of searchers does not vary across states (exploits only

the within variance in the measure of searchers). The hypothetical series in the second equation

is calculated by holding the measure of searchers fixed over time (exploits only the between

variance in the measure of searchers). This exercise not only is intended to shed some light

on the drivers behind the changes in sjt ≡ (h/u)jt. I am interested in the changes in (h/su)jt

driving the total hours per unemployed individual. It also addresses measurement errors. By

calculating averages, either across states or over years, measurement bias is expected to be

mitigated.

I report the results of this exercise in Tables 7-8 when using weekdays and weekends and in

Tables 9-10 when using weekdays only. Most the of the above patterns along different T , across

columns, and over several measures of the unemployment rate also apply here.

What is revealing, however, are that the estimates reported in Tables 7-8, when significant,

remain even after holding the measure of searchers su constant, either across states or over

time. These results lend support to the finding that, in general, the number of hours per

searcher accounts for more than half of the state variation in hours spent by the unemployed.

When using weekdays and weekends, the estimates range from 8 to 20 minutes per week and,

when using weekdays only, the range shrinks to 5 to 12 minutes per week.

Even when T = 2, the significance of parameter β does not survive when regressing time-use

against the CPS unemployment rate and when holding the measure of searchers constant.

To conclude, the results reported in this section echo those presented in the time series

15

analysis. In any case, the time spent in search activities does not seem to decline in response to

adverse aggregate conditions as measured by the unemployment rate. Search intensity appears

to be either slightly countercyclical or acyclical. With the return of searching for work strongly

procyclical, it is puzzling why search efforts do not seem to be as responsive to changes in the

state of the economy as the job finding probability.

3 Model Economy

In this section, I lay out a model to discipline the conjectures aimed to solve the puzzle that

motivates this paper. I focus exclusively on the problem of a big representative household that

faces a problem of allocation of income and time. I deliberately restrict the set of choices of the

household since my interest is in the characterization of the optimal search intensity in response

to changes in the aggregate labor market conditions. I follow the Mortensen and Pissarides

(1994) canonical search model in some respects but depart from it in others.

In the canonical search model, the source of aggregate fluctuations is productivity shocks.

According to this model, the number of unemployed people increases in recessions because they

face limited job opportunities as firms are reluctant to open new job vacancies, let alone closing

the ones currently filled, as a result of an exogenous decline in productivity. The problem is

aggravated when there is more competition among the ever-increasing number of unemployed

people.

As in the canonical search model, I assume that workers and jobs meet according to a

matching technology that captures the role of trading frictions in the labor market. Searching

for work is a risky and costly activity. I depart from the canonical search model in that I

ignore the role of firms in the creation of job vacancies. The source of fluctuations is then the

availability of jobs.

The representative household is composed of a unit measure of ex-ante identical workers. At

any discrete period, each member of the household is either employed or unemployed. When

employed, she receives a stochastic endowment yn(θ), where θ captures the tightness of the

labor market. The employed values consumption cn and dislikes working, the degree of dislike

16

given by γ > 0 as in Shimer (2010). Later, I allow γ to vary in response to θ.

When unemployed the worker receives the endowment yu(θ), with yu(θ) < yn(θ) for fixed θ.

In this state, she values consumption cu as well. However, being unemployed is also costly: it

involves spending time s searching for work. This is the only means she has to leave the pool

of unemployed workers, which in turn, could expand when employed workers lose their jobs at

exogenous rate λ ∈ (0, 1).11

The preferences of the household in any arbitrary period t are represented by the following

instantaneous utility function

U(cut , cnt , st) = ut

(U(cut )− V (st)

)+(1− ut)

((U(cnt )− γ

)

where ut denotes the measure of unemployed workers in period t, U is the utility function over

consumption, and V is the disutility over time spent in search activities.

At any time, the measure of unemployed workers within the household is constantly changing,

expanding or shrinking, as employed workers lose their jobs and unemployed workers find jobs.

This measure then evolves according to

ut+1 = ut + (1− ut)λ− utf(st, st, θt) ≡ λ+ α(st, st, θt, λ)ut (6)

where α(s, s, θ, λ) = 1 − λ − f(s, s, θ) and f(s, s, θ) is the probability of finding a job that

depends on the individual search intensity s, the average search intensity s, and the tightness

of the labor market θ = v/u, where v stands for the number of unfilled job vacancies.

In this model, θ is the aggregate shock in the economy. I will assume an implicit linkage

between θ and a measure of aggregate productivity in the economy p, reflecting the creation

of jobs that will show up naturally in a general equilibrium setup when firms face a positive

productivity shock.

11Instead of laying out the problem of the individual worker (see for example, Pissarides (2000), Mortensen andPissarides (1994), and Shimer (2004)) I adopt the big household interpretation pioneered by Andolfatto (1996)and Merz (1995), and subsequently used by Shimer (2010), Christiano et al. (2013), and Chodorow-Reich andKarabarbounis (2015). There are only gains by proceeding in this way. The preferred framework would allowme to discuss two alternative setups that differ in the possibility of pooling income within the household. Inaddition, no intuition is lost.

17

Before proceeding, I stress that the aggregate productivity shock will have, through its effect

on θ, two consequences in the model economy. First, it will determine the endowment processes

for both employed and unemployed. Second, current productivity shocks will affect the future

employment status of the worker.

I make two comments on α(s, s, θ, λ). First, labor market flow estimates reported in the

literature imply that α > 0 (Shimer, 2005). Second, α may be regarded as a persistence

coefficient of the law of motion of unemployment. It could be said that if both λ and f are

small then the process of destruction and creation of jobs is weak, in which case the worker

would expect to remain in the unemployment pool for a longer time. This is more eloquently

shown in the decomposition of the unemployment rate in the steady state

uss =λ

λ+ f(sss, θss)= λ

1

1− α(sss, θss, λ)≡ incidence of

unemployment ×duration of

unemployment

where λ is the incidence of new spells of unemployment and 1/(1 − α) is the average duration

of those out of work.

I now turn to the household problem. The representative household maximizes

max{cu

t(θt), cn

t(θt), st(θt)}t≥0

∞∑

t=0

∑

θt

π(θt)βt[

ut(θt)(U(cut (θ

t)− V (st(θt)))+(1− ut(θ

t))(U(cnt (θ

t))− γ)]

subject to

ut+1(θt+1) = λ+ α(st(θ

t), st(θt), θt), λ)ut(θ

t) ∀t ≥ 0

θt follows a Markov chain

and subject to equation (6) in every period t ≥ 0, and by taking st for any t, γ, λ, (u0, θ0) and

processes for ynt (θ) and yut (θ) as given. Additional technical constraints guarantee that st ∈ [0, 1]

and ut+1 ∈ [0, 1] ∀t ≥ 0.

I accommodate two alternative setups that depend on whether pooling of income is possible.

18

The additional constraint that the household faces is then

cj(θt) =

yj(θt) j ∈ {u, n} (no full insurance)

uyu(θt) + (1− u)yn(θt) j ∈ {u, n} (full insurance).

Next, I characterize the optimal search intensity choice. The Lagrangian function could be

written as follows

L({st(θ

t), ut+1(θt+1)}∞t≥0

)=

∞∑

t=0

∑

θt

π(θt)βt{[

ut(θt)(U(cut (θ

t)− V (st(θt)))+(1− ut(θ

t))(U(cnt (θ

t))− γ)]

+µt(θt)

[

λ+ α(st(θt), st(θ

t), θt), λ)ut(θt)− ut+1(θ

t+1)

]}

The first-order conditions imply that

Vs(s⋆t (θ

t)) = fs(s⋆t (θ

t), θt)µ⋆t (θ

t) (7)

µ⋆t (θt)π(θt) =

∑

θt+1

[

π(θt+1)β∆n(s⋆t+1(θ

t+1); ynt+1(θt+1), yut+1(θ

t+1), γ)

+ π(θt+1)βα(s⋆t+1(θ

t+1), θt+1, λ)µ⋆t+1(θ

t+1)

]

(8)

where

∆n(s, u, yn, yu, γ) =

U(yn(θ))− U(yu(θ))− γ + V (s) (no full insurance)

(yn(θ)− yu(θ))Uc[uyu + (1− u)yn]− γ + V (s) (full insurance).

and the star symbol denotes the solution of the household problem. It is understood that ∆n is

independent of u when there is no full insurance within the household. Notice that in symmetric

equilibrium, st = st for every t.

Equation (7) characterizes the optimal search intensity. The left side denotes the marginal

19

cost of searching, which reflects the foregone leisure time. The right side highlights two motives.

The first is increasing the odds of finding a job. The marginal probability per unit of search

intensity is denoted by fs(s, s, θ). The second motive is denoted by the multiplier µ. In the

subsequent discussion, I construct a case in favor of the relevance of understanding the role

played by the multiplier in shaping the choice of search intensity.

The Lagrange multiplier µ⋆t represents the marginal utility of an infinitesimal decrease in

the current measure of unemployed workers ut. Precisely, the constraint of the household reads

ut+1 ≥ λ+ α(st, st, θt, λ)ut

The direction of the inequality is not arbitrary. To see this, consider the following useful

rearrangement

ut+1 − λ

α(st, st, θt, λ)≥ ut

The latter inequality can be viewed as a budget constraint. Suppose the current measure of

unemployed workers shrinks by a small amount. The worker faces the following dilemma. She

could either substitute leisure time for time spent searching for work or she may even search

more intensely, thereby boosting her chances of finding work in the next period. A reduction in

ut then loosens the constraint.

How much is the worker willing to pay to start with a smaller ut? The answer is given by

the multiplier µt. Working out equation (8) up to T periods ahead gives12

µ⋆t (θt) =

∞∑

i=t+1

∑

θt+1

π(θi)

π(θt)βi−t

( i−1∏

j=t+1

α(s⋆j(θj); sj(θ

j), λ, θj)

)

∆n(u⋆i (θ

i), s⋆i (θi); yni (θ

i), yui (θi), γ

)(9)

12I rule out bubbles in µ, that is

limT→∞

∑

θt+1

π(θs+T

)t+T∏

j=t+1

βα(s⋆j , sj , θj , λ)µ⋆t+T = 0

which establishes that µ does not grow faster than the discount gross rate given by(∏

∞

j=t+1βα(s⋆j , sj , θj , λ)

)−1

as the future becomes more distant.

20

The variable µ allows a useful interpretation that will be invoked repeatedly in the remainder

of this paper. It is the marginal utility of a decline in ut. Thus, µ is the price, in units of

leisure time, the unemployed worker is willing to pay for such a reduction. I distinguish three

components in equation (9): the discount factor β, the fruits of search effort ∆n(s, u, yn, yu, γ),

and the persistence of the unemployment process α(s, s, θ, λ).

First, clearly, µ is simply the present value of the stream of future search benefits. As β

increases, the future fruit of their efforts becomes more meaningful. Second, the higher the

future fruit of effort ∆n(s, u, yn, yu, γ), the higher the incentive to search and the more willing

they are to give up leisure. If yn is regarded as the reemployment wage, then this component

resembles the usual opportunity cost of leisure, highlighted in the real business cycle literature.

In addition, notice that although an increase in yu — say, the unemployment insurance benefit

— would make the unemployed exert less effort, the generosity of the benefit is counterbalanced

by the associated costs of being unemployed (the future effort costs denoted by V (si) with i

starting in t + 1). Think of the unemployed person who has to provide proof of an active job

search in order to remain eligible to claim the unemployment benefit. That is, even collecting

benefits is costly. Third, the higher the persistence of the process of unemployment α(s, s, θ, λ)

or the longer the duration — caused, for instance, by a reduction in θ — the higher µ. Intu-

itively, this component is associated with the costs during the period of unemployment, that is,

the costs associated with unsuccessfully keep looking for work.

In a nutshell, µ is the present value of the future marginal benefits (∆n(s, u, yn, yu, γ)) and

the marginal contribution of searching today to the reduction of future effort costs.

The recursive representation of the household problem will prove to be useful in the subse-

quent discussion. Let

B (u0, θ0; yn, yu, s, γ, λ) = E0

∞∑

t=0

βtU(cu⋆t , cn⋆t , s

⋆t ) (10)

be the indirect utility of a household, upon following an optimal strategy for cu, cn, and s, that

starts with the measure of unemployed workers u0 and shock θ0, and takes s, γ, λ, and processes

for yn(θ) and yu(θ) as given.

21

I write the problem of the representative household in recursive form. The problem of the

household is to solve

B(u; yn, yu, s, γ, θ) = maxs,u′

{

U(cu, cn, s) + β

∫

Θ

B(u′; yn, yu, s, γ, θ′)Q(θ, dθ′)

}

(11)

subject to

u′ = λ+ α(s, s, θ, λ)u (12)

given yn(θ), yu(θ), s, γ, λ, u0 and θ0, and the transition function Q.

The optimal condition is

Vs(h(u, θ) = βfs(h(u, θ), s, θ)

∫

Θ

−Bu(u′, θ′)Q(θ, dθ′) (13)

and the envelope condition

Bu(u, θ) = −∆n(h(u, θ), u, yn, yu, γ) + βα(h(u, θ); θ, s, λ)

∫

Θ

Bu(u′, θ′)Q(θ, dθ′) (14)

where h(u, θ) is the optimal search intensity as a function of the state of the economy.

From the comparison between the sequential problem and the recursive form problem, it can

be seen that

µ⋆ = β

∫

Θ

−Bu(u′, θ′)Q(θ, dθ′) (15)

That is, as stated above, µ⋆ represents the willingness to pay in units of leisure time for a

reduction in the measure of unemployed workers. This has to be equal to the expected value of

a job(∫

Θ−Bu(u

′, θ′)Q(θ, dθ′)), discounted by β.

22

Three rewards of searching

Combining the optimal condition and the envelope condition yields:

Vs(s⋆) = fs(s

⋆, θ) β

∫

Θ

{

∆′n(s′⋆, u′, y′n, y′u, γ) + α(s′⋆, θ′, λ

) Vs(s′⋆)

fs(s′⋆, θ′)

}

Q(θ, dθ′)

︸ ︷︷ ︸

expected value of a job ≡ µ⋆t

(16)

According to this equation there are three rewards the unemployed expect to gain from searching.

The first is the contribution of the additional search effort in boosting their chances of finding

a job in the future fs(s⋆, θ). Second, upon finding a job, the worker will receive the difference

in utility of moving from unemployment to employment ∆′n(s′⋆, u′, y′n, y′u, γ), part of which is

the marginal utility of consumption. In recessions, the unemployed will search more intensely

as they look forward to smoothing consumption. Third, the current effort may contribute to

the reduction of future effort costs, which is the gain that will be realized in case the job search

is successful. This gain is

α(s′⋆, θ′, λ

) Vs(s′⋆)

fs(s′⋆, θ′)

Some comments on each component of the above expression seem pertinent here. The contri-

bution of the current job search is measured in terms of the foregone leisure time, as reflected

by the need to increase the search intensity in the future as long as the worker stays in the

pool of unemployment. These costs must be deflated by the marginal contribution of the search

effort in increasing the likelihood of leaving the unemployment pool in the future. Thus, the

expression Vs/fs.

If the state of unemployment is persistent enough, this will add up to how much the future

is valued because one is expected to be jobless for a longer time. In this sense, α in equation

(16) is a type of discount factor. The higher the persistence α, the more weight is placed on the

future search costs. There is, then, a smoothing motive in the allocation of efforts over time.13

13The presence of this smoothing motive is also recognized by Merz (1995).

23

4 Evaluating the conjectures

I use the model laid out in the previous section to evaluate the following conjectures. The

first conjecture, which has received some attention in the literature, addresses the role of the

complementarity between search intensity and the labor market conditions in the matching

function. The second conjecture suggests that the unemployed search more intensely during

recessions motivated by their aversion over fluctuations in consumption. Finally, the third

establishes that to reconcile the evidence, the unemployed must value a job relatively high

during recessions.

These conjectures focus on different aspects of the problem of a representative worker. The

first one focuses on a property of the matching function. The other two share a common feature:

they rely on the preferences of a representative worker over fluctuations in the unemployment

rate. Next, I elaborate on these conjectures. I start by invoking the model with no full insurance

within the household to study the role of complementarities in the matching function in the

cyclicality of search intensity.

Complementarities in the matching function

Broadly speaking, this complementarity may be interpreted in at least two ways. First,

it could mean simply that the unemployed view searching time as a substitute for the preva-

lent labor market conditions in the economy. In recessions, they will search more intensely to

compensate for the decline in their chances to find work since there are less job opportunities.

Conversely, in booms, the unemployed will minimize the hassle and enjoy additional leisure time

instead of intensely searching for work.

The alternative interpretation rests upon complementarities in the creation of jobs. Reces-

sions are times when firms create a limited numbers of jobs and the unemployed are desperately

looking for open job vacancies, so these jobs become easier to fill.

In any case, one would observe the unemployed allocating more time to search activities in

recessions despite the limited availability of jobs.

For simplicity, I omit the underlying mechanisms that may lead to these complementarities.

24

Both stories may be reinterpreted as a property of a black box technology (i.e., matching func-

tion) that makes finding a job more or less successful depending on the unemployed individual’s

effort and the labor market tightness.

To be consistent with the previous observation, such a technology must have the property

that the value of posting an additional job vacancy decreases as the unemployed search more

intensely for work. Such a property is the substitutability, as opposed to complementarity, be-

tween search intensity and labor market tightness, that is, fsθ < 0.

Shimer (2004) and Mukoyama et al. (2013) entertain this possibility in different ways. In

Shimer (2004), who builds on Stigler (1961) to allow for a countercyclical search intensity in

a general equilibrium search model, the negative correlation between search intensity and the

tightness of the labor market arises as a natural consequence of the discrete time setting. In his

model, search intensity, which is approximated by the number of search methods, depends on

the job finding probability in a nonlinear fashion. Search intensity is countercyclical for values

of the job finding rate exceeding 80%, a lower bound that does not seem to bind in light of the

evidence on transition probabilities in the U.S. (see Shimer, 2005 and Shimer, 2012).

In Mukoyama et al. (2013), the substitutability between search intensity and the tightness

of the labor market is allowed by assuming a flexible constant elasticity of substitution (CES)

matching function. They find that this property of the matching function implies that search

intensity is not procyclical when shocks to the labor market tightness are temporary.

To gain insight on how s and θ are combined, consider the following definition.

Definition: Let the individual probability of finding a job be defined as

f(s, s, θ) = sm(su, θ)

su,

where

m(su, θ) =(

(su)σ−1

σ + θσ−1

σ

) σ

σ−1

25

is the matching function proposed by den Haan et al. (2000). Finally,

f(s, s, θ) =s

s

(

sσ−1

σ + θσ−1

σ

) σ

σ−1

. (17)

Parameter σ ∈ (0, 1) is the constant elasticity of substitution between the average search inten-

sity and the labor market tightness. If σ < 1, it is guaranteed that the job finding probability

will be well defined (i.e., f(s, s, θ) ≤ 1). For a proof of this, see Appendix B.

In symmetric equilibrium, s = s, so the probability function reduces to

f(s, θ) =(

sσ−1

σ + θσ−1

σ

) σ

σ−1

(18)

In the remainder of this section, I argue that the procyclicality of search intensity will rely

exclusively on complementarities in the probability function under two assumptions. First, I

assume hand-to-mouth workers. They consume the endowment that corresponds to their cur-

rent employment status. Second, I assume that the value of a job is procyclical. I begin by

making sure that the value of a job is well defined. The next proposition ensures that this value

is positive.

Proposition 1: B(u, θ) is strictly decreasing in u for fixed θ.

Proof: See Appendix B.

In the absence of full insurance within the household, the worker will be risk neutral over

fluctuations in the unemployment rate. The next proposition states this formally.

Proposition 2: B(u, θ) is linear in u for fixed θ.

Proof: See Appendix B.

Recall that one consequence of the absence of full insurance within the household is that the

26

difference in utility of moving from unemployment to employment is

∆n(s⋆, u, yn, yu, γ) = U(yn)− U(yu) + V (s)− γ

which is independent of the measure of unemployed workers u. So far, I have been silent on

the dependency of the optimal search intensity to movements in u. Recall the dilemma that

the worker faces when u shrinks. She could either substitute leisure time for time spent looking

for work or she may even search more intensely, thereby boosting her chances of finding a job

in the next period. It is not clear what the net effect is. The following proposition establishes

that the net effect is zero.

Proposition 3: The optimal search intensity h(u, θ) is independent of u for fixed θ.

Proof: See Appendix B.

The main result of this section also rests upon the procyclicality of the value of a job. Other

things equal, sufficiently strong procycical wages would be sufficient to prove that the value of

moving from unemployment to employment is procyclical. This intuition is captured by the

next proposition. In preparation, I need the following definition:

Definition: A function f(x, y) is supermodular in x and y if and only if

∂2f(x, y)

∂x∂y> 0

The interpretation of this complementarity in f(x, y) is that the (marginal) value of either

x or y increases as the use of the other argument increases. In the canonical search model, the

value of being employed increases when labor market conditions tighten. In the partial equilib-

rium model discussed in the previous section, this will also happen under some conditions.

27

Proposition 4: −B(u, θ) is supermodular in u and θ.

Proof: See Appendix B.

To show that the unemployed will search more intensely in recessions, it will suffice to as-

sume a type of substitutability in the matching technology. The purpose of the next proposition

is to show that this statement does not depend on the stochastic nature of θ.

Proposition 5: If fsθ > 0 then h(u, θ) is strictly increasing in θ regardless of the nature of θ.

Proof: See Appendix B.

Remark: When θ is I.I.D. fsθ > 0 is also a necessary condition.

If the shock is either I.I.D. or correlated, the previous proposition states that a sufficient

condition for the optimal search intensity to be procyclical is the presence of complementarities

in the probability of finding a job. The latter result resembles Proposition 1 in Mukoyama

et al. (2013) when θ is I.I.D. Hence Proposition 5 extends their results by finding that the latter

property remains sufficient for recessions of any type of persistence. This is a pertinent finding

given that recessions are typically followed by slow recoveries.

However, I argue that the sufficient condition fsθ > 0 cannot be disciplined from the data

for two reasons. First, as suggested by the latter proposition, the procyclicality of the optimal

search intensity relies exclusively on the complementarity between search intensity and labor

market conditions. Second, there is no independent data to judge the complementarity in the

matching function. Not surprisingly, if data on time spent in search activities are used along

with indicators on the availability of jobs in the estimation of a matching function, the substi-

tutability between their arguments will only be verified, giving the conjecture little room to be

rejected. A hypothesis of that type could not be subject to criticism.

I conclude that entertaining the presence or absence of complementarities in the matching

function is not a promising candidate to account for the cyclicality of search intensity. This

conclusion does not rule out arguments that rest upon microfoundations of the matching func-

tion. These efforts would represent important avenues for future research.

28

This pessimistic conclusion is not definitive if we consider alternative and perhaps more

interesting explanations on why the representative unemployed worker may search harder in re-

cessions. Intuitively, in recessions, consumption is expected to be low. In the absence of assets,

it will not be possible to smooth consumption over time. Thus, recessions will be regarded as

periods in which consumption is highly valued and desperately needed. As a rational response,

searching more intensely would be warranted. How hard will the unemployed worker search for

work depends on her preferences toward risk. The key question is: What is the degree of risk

aversion necessary for the optimal search intensity to be countercyclical? I elaborate on this

next.

The role of risk aversion

The second conjecture maintains that recessions are times when the unemployed foresee a

decline in their future consumption. Although they can consume the same regardless of their

employment status within a period, they cannot do so over time in the absence of assets. This

story stresses the possible role of searching for work in contributing to consumption smoothing.

As a result, this conjecture will give the degree of risk aversion of the representative worker a

role in shaping her decision on the allocation of time to the job search time over the business

cycle.

I find a clean sufficient condition for the procyclicality of search intensity. This condition

balances out a measure of complementarity between search intensity and the labor market tight-

ness and a measure of risk aversion over unemployment fluctuations. Interestingly, this result

holds regardless of the nature of the recession, whether it is temporary or persistent.

To put emphasis on the role of risk aversion, I will assume that fsθ > 0 holds and the

value of a job is procyclical in the framework where the worker can consume the same regard-

less of the employment status. In the context of full insurance within the household, the next

proposition shows that the worker will be risk averse over fluctuations in the unemployment rate.

Proposition 2’: B(u, θ) is strictly concave in u for fixed θ.

29

Proof: See Appendix B.

Changes in θ will have two effects with different implications on the choice of search intensity.

If the complementarity between s and θ in the probability of finding a job is sufficiently high,

then a reduction in θ would bring the marginal return of search downwards and would call for

a reduction in s as well. That is, s would be procyclical. However, if the worker is sufficiently

risk averse, she will, in anticipation, consider the effect of the current drop in θ in the decline in

future consumption. When the marginal utility of consumption is sufficiently elastic, a minimal

decline in consumption will make the worker increase her search intensity. The next proposition

illustrates this tension.

Proposition 6: h(u, θ) is strictly increasing in θ if fsθ > 0 and

fsθfsfθ

>u∫

ΘBuu(u

′, θ′)Q(θ, dθ′)∫

ΘBu(u′, θ′)Q(θ, dθ′)

(19)

Proof: See Appendix B.

Remark: When θ is I.I.D. the latter condition is also necessary.

The latter proposition offers a condition that could be judged even when fsθ > 0. The above

inequality is sufficient regardless of the stochastic nature of the shock.14 The left side of the

inequality depends entirely on the matching function. The right side looks more complicated but

familiar as well. At first sight, it is a degree of risk aversion over fluctuations in the employment

status of the members of the household. Below, I show that this degree of aversion could be

readily linked to the more familiar degree of risk aversion over consumption.

In working against this hypothesis, I treat the left side of the inequality (19) as a lower

bound for the degree of risk aversion. Thus, the degree of risk aversion would need to be at

least equal to this bound to be suspicious about the strong procyclicality of s. Next, I describe

14Interestingly, this condition mimics the condition that guarantees optimal investment is procyclical in theone-sector growth model when the shock is correlated. See Hopenhayn and Prescott (1992).

30

the procedure to make this test operational.

Computation of the bound: Under equation (18) the bound adopts the form:

fsθfsfθ

=1

f

The size of this bound depends exclusively on the probability of finding a job. To compute this

bound in the steady state, I construct a series of the probability of finding a job following Shimer

(2012) for the period of 1967.II-2012.IV based on the calculation of transition probabilities by

using linked data from the CPS. I find that:

f = 0.31 so 1f= 3.23

Degree of risk aversion over u: I turn now to the right side of the inequality (19). I show

that in the steady state the risk aversion of adding an (un)employed worker to the household

has a direct bearing on the degree of risk aversion over consumption. To see this, I start by

defining

σu =uBuu(u, θ)

Bu(u, θ)

as the relative risk aversion over fluctuations in the employment status of the members of the

household. Next, I invoke the envelope condition to derive

Buu(u, θ) = (yu(θ)− yn(θ))Ucc(c⋆)∂c⋆

∂u,

which, under some convenient rearrangements, could be alternatively expressed as

uBuu(u, θ)

Bu(u, θ)=∂c⋆

∂u

u

c⋆(yn(θ)− yu(θ))σc

Uc(c⋆)

Bu(u, θ),

where

σc = −cUcc(c)

Uc(c)

31

is the relative risk aversion over consumption. Finally,

σuσc

= −εc,u

(yu(θ)− yn(θ)

Bu(u, θ)/Uc(c⋆)

)

(20)

According to this expression, the relative risk aversion over fluctuations in unemployment could

be amplified or dampened with respect to σc, depending on the magnitude of two things:

the elasticity of consumption to unemployment εc,u and the size of the foregone wage net of

unemployment benefits (yn − yu) relative to the total marginal costs of being unemployed

−Bu(u, θ)/Uc(c⋆), expressed in units of consumption.

The intuition behind equation (20) is as follows. Fluctuations in u are meaningful insofar as

these fluctuations are ultimately reflected in the changes in consumption. Perhaps the elasticity

of consumption to unemployment shows this more clearly. This dependency is regulated by the

importance of the foregone consumption when unemployed in the total cost of being jobless.

Degree of risk aversion over u: elasticity. I compute the elasticity of consumption to

unemployment by calculating

εc,u = ρc,usd(c)

sd(u)

where x denotes the deviation of x from its steady state, ρ is the correlation coefficient, and

sd(x) stands for the standard deviation of x. I find that

εc,u = −0.780.87

12.47= −0.05

by using a series for real private consumption — non-durables plus services — constructed

based on nominal private consumption (NIPA Table 1.1.5) deflated by price indexes (NIPA

Table 1.1.4) and for the unemployment rate for people aged 16 and over, from the BLS. To

compute the cyclical components of these two series, I use the Hodrick-Prescott filter with

smoothing parameter 1600. The sample period is 1967.II-2012.IV.15

Degree of risk aversion over u: foregone wage. The remaining component of equation

15The NIPA tables correspond to the BEA’s date of revision of May 30, 2013.

32

(20) requires more intermediate results and further explanation. I begin by again invoking the

envelope condition

Bu(u, θ) = (yu(θ)− yn(θ))Uc(c⋆) + γ − V (s⋆) + α(s⋆, θ, λ)

∫

Θ

Bu(u′, θ′)Q(θ, dθ′)

which could also be written as

Bu(u, θ) = (yu(θ)− yn(θ))Uc(c⋆) + γ − V (s⋆)− α(s⋆, θ, λ)

Vs(s⋆)

fs(s⋆, θ)

in light of the optimal condition for search intensity. As in Chodorow-Reich and Karabarbounis

(2015), I express this value in units of consumption:

Bu(u, θ)

Uc(c⋆)= yu(θ)︸ ︷︷ ︸

b

−yn(θ) +γ

Uc(c⋆)︸ ︷︷ ︸

ξ

−V (s⋆)

Uc(c⋆)− α(s⋆, θ, λ)

Vs(s⋆)

fs(s⋆, θ)Uc(c⋆)

I use this equation together with evidence gleaned for the U.S. to infer the size of each of the

components of Bu/Uc(c⋆). Since size is a relative notion, I need a benchmark to make precise

statements on what big or small means. Chodorow-Reich and Karabarbounis (2015) work out

an expression akin to the one above. They express some of the components relative to the

after-tax marginal productivity of employment (MPN) and provide evidence that, for instance,

the size of ξ and b are

ξ ∈ (0.41, 0.9) and b = 0.06

Next, I discuss how we can infer the magnitudes of the remaining components. I start by

assuming that the wage is equal to the MPN and thus its size is simply

yn = 1

There could be many reasons to surmise that the wage would not entirely reflect the gains in

labor productivity. One of them has a particular bearing on the context of the search model:

the presence of hiring costs.16 Nevertheless, notice that this assumption, in light of the size of

16See, for example, Pissarides (2000).

33

ξ, does not seem untenable.

My main interest, however, is to provide an estimate for the size of

αVsfsUc

Three elements give rise to this measure of marginal search costs. The presence of Vs is obvious.

The marginal return of searching fs appears to deflate these costs. That is, a complete picture

of how costly searching for work is must also account for the benefits of that effort. Finally, the

greater the persistence of unemployment, denoted by α, the greater the chance of remaining

jobless for a longer time in combination with all the implied associated future search costs.

To put it differently, even though the forgone leisure time when searching for work may be

small, one has to also consider the purpose that the activity of searching entails, and not only

its size.17 The purpose of the activity of searching is well captured by the terms fs and α above.

That is, even spending a small fraction of time searching for work could boost the chances of

finding a job. Moreover, by exerting a little effort in the current period the individual may end

up entirely avoiding the need to exert effort in the future, upon finding a job.

In the subsequent discussion, I make an educated guess on the size of αV/Uc(c⋆). I suggest

the following upper bound based on the assumption V (s) < γ. I note that

αVsfs

1

Uc

could be written as

αVsfs

1

Uc=

(

αεV,sV

s

1

Uc

)(s

f |s=s

)

,

where

εV,s =∂V

∂s

s

V

17Above, I document that unemployed workers aged 25 and over — looking for work, as opposed to those ontemporary layoff — spend, on average, roughly 4 or 5 hours per week on searching activities.

34

is the ratio of marginal to average search costs and

fs|s=s =

(f |s=ss

)

By exploiting the assumption that the costs of this leisure time are greater for the employed

than for the unemployed, I have

αεV,sf−1 V

Uc< αεV,sf

−1 γ

Uc

I add the remaining component V/Uc to the previous expression to obtain:

V

Uc+ αεV,sf

−1 V

Uc<

γ

Uc+ αεV,sf

−1 γ

Uc

To compute this bound, I assume conservatively that

V (s) = χs, χ > 0

This assumption is innocuous for the above results as shown in Appendix B. With this specifi-

cation, εV,s = 1. I parameterize α, the persistence of the unemployment process, by using the

average values of the series for λ and f constructed following Shimer (2012) for the period of

1967.II-2012.IV.18 I find that

α = 0.67 and f−1 = 0.31−1 = 3.23

Finally, I find that the marginal costs of searching cannot exceed

(1 + αεV,sf

−1) V

Uc< 1.30

where I have used the more conservative value for γ/Uc(c⋆), 0.41, as estimated by Chodorow-

Reich and Karabarbounis (2015).

18The values λ = 0.02 and f = 0.31 imply an unemployment rate in the steady state of 6.1%.

35

Degree of risk aversion over u: summary. I now return to the equation of interest:

σuσc

= −εc,u

(yu(θ)− yn(θ)

Bu(u, θ)/Uc(c⋆)

)

I can now provide rough upper and lower bounds for

yu(θ)− yn(θ)

Bu(u, θ)/Uc(c⋆)

The lower bound is obtained by using the upper bound for the marginal search costs I just

obtained. The upper bound is obtained by assuming the absence of search frictions on the part

of the unemployed (i.e., s = 0). In sum,

yu − yn

Bu/Uc∈ (0.51, 1.77)

By bringing this latter estimate and that of the elasticity together, I conclude that

σuσc

∈ (3%, 9%)

The ratio of σu/σc then is much lower than the bound 1/f = 3.23. Based on the range

of values that the ratio σu/σc could take, σc would need to be between 34 and 117, which

implies values that are even larger than the ones contemplated in Mehra and Prescott (1985).

Therefore, risk aversion, although a natural candidate, is not enough to make search intensity

countercyclical.

Countercyclical value of a job

In the previous sections, I entertained two hypotheses on why the optimal search intensity may

not be procyclical. The first one, I claimed, cannot be disciplined with independent data. The

second provided a condition that compares the degree of complementarities in the matching

function with the curvature of the worker’s value function. Using this condition, I concluded

that in order for the optimal search intensity to be countercyclical or acyclical, the representa-

36

tive household must exhibit a huge risk aversion over consumption, which is much greater than

the values emerged from empirical studies and pervasively used in the literature of business

cycles (see Kydland and Prescott, 1982, for a starting point).19

Both hypotheses rely on the proposition that the value of a job is procyclical, and this

proposition, in turn, rests upon a key assumption that lies at the core of old and heated debates

in macroeconomics: whether wages are strongly or mildly procyclical.

While the strong procyclicality of wages is an assumption in a partial equilibrium setup,

that cyclicality would be a result in a framework that incorporates firms’ decisions as well. In

particular, it is well-known that in the canonical search model, wages absorb most of the pro-

ductivity shocks when the former is settled using the Nash bargaining rule (see Shimer, 2005).

As stated before, the procyclicality of wages would be a reason to expect the unemployed to

search less intensely during recessions. Shimer (2004), for instance, asserts that the value of a

job is almost, by definition, procyclical in the canonical search model as a direct consequence of

assuming the Nash bargaining rule. He also notes that in accounting for the countercyclicality

of search intensity, which he documents by using the number of search methods used by the

unemployed in the U.S., wages would need to be strongly countercyclical to offset the procycli-

cality of fs.

In this section, I show that this claim does not necessarily hold through when search inten-

sity is an endogenous variable and the opportunity cost of delaying search efforts plays a role

in shaping the value of a job.

It is time then to spell out the last conjecture. Recessions are times when the opportunity

cost of postponing the decision to search for work increases. When the recession is persistent

enough, the unemployed would expect to remain jobless for a long time. Since being unemployed

is costly in any period, the allocation of time in search activities becomes an intertemporal de-

cision: the marginal contribution of the current search is the reduction of future search costs.

Other things equal, this smoothing of search costs implies that a job would be more desirable

in a recession. Using data for the U.S. and estimates on the value of non-working time from

Chodorow-Reich and Karabarbounis (2015), I find that the opportunity cost of postponing the

19See also Mehra and Prescott (1985) and Mehra and Prescott (2003), and references therein.

37

decision to search for work are strongly countercyclical. Next, I describe the procedure.

I start by rewriting the envelope condition implied by the household problem as follows,

Bu(u, θ)

Uc(c⋆)= − yn(θ)

︸ ︷︷ ︸

wage

−

(V (s⋆)

Uc(c⋆)+ α(s⋆, θ)

Vs(s⋆)

fs(s⋆, θ)Uc(c⋆)

)

︸ ︷︷ ︸

searchingcosts

+ yu(θ)︸ ︷︷ ︸

unemploymentbenefits

+γ

Uc(c⋆)︸ ︷︷ ︸

value ofnon-working

time

where the value of moving to unemployment Bu is expressed in units of consumption. The

negative −Bu/Uc will be called the value of a job which, in turn, denotes the marginal cost

of unemployment. This value is the sum of the benefits minus the opportunity costs of being

employed. Having a job means receiving a wage in exchange for the hours worked. It also

implies avoiding the searching costs that could have been incurred had the unemployed failed

to find a job and kept looking for work. However, working is also costly. The opportunity cost

of being employed consists of the foregone unemployment benefits and the foregone value of

non-working time.

For simplicity, define

Bcu ≡

Bu

Uc(c⋆)

as the value of unemployment in units of consumption, and

εBcu,θ =

∂Bcu

∂θ

θ

Bcu

as the elasticity of this value with respect to θ. Notice that the sign of this elasticity may be

confusing. Keep in mind that if εBcu,θ > 0 then Bc

uθ < 0; that is, the value of a job is procyclical,

since Bcu < 0.

The elasticity of Bcu with respect to θ may be written as follows:

εBcu,θ =

(−yn

Bcu

)

︸ ︷︷ ︸

+

εyn,θ︸︷︷︸

+

+

(z

Bcu

)

︸ ︷︷ ︸

−

εz,θ︸︷︷︸

+

+

(−V/UcBcu

)

︸ ︷︷ ︸

+

εV/Uc,θ︸ ︷︷ ︸

+

+

(

−αVs/(fsUc)

Bcu

)

︸ ︷︷ ︸

+

εαVs/(fsUc),θ︸ ︷︷ ︸

−

38

where z = ξ + b as in Chodorow-Reich and Karabarbounis (2015). Thus, the value of un-

employment is a weighted average of the elasticities of its components. The weight assigned

to each of these components will be determined by the fraction they represent in the value of

unemployment.

Results presented in the previous subsection imply that

Bcu = − yn

︸︷︷︸

1

+ z︸︷︷︸

0.47

−V

Uc︸︷︷︸

0.41

−αVsfsUc︸ ︷︷ ︸

0.89

= −1.83

This means that the value of unemployment is twice the value, in units of consumption, of a unit

of marginal labor productivity. Alternatively, a job is valued twice the marginal productivity

of labor. The primary reason a job is valued by the unemployed more than the marginal

productivity of an employed worker is because of the future search costs. Having a job means

the unemployed person does not have to worry about looking for work today or in the future.

To gauge estimates for the elasticity of wages to θ εyn,θ and the elasticity of the foregone

value of non-working time εz,θ, I rely on estimates from previous authors. I leave this discussion

for later. Next, I focus on the remaining two elasticities. I start by simplifying the expression

for the total search costs

εV/Uc,θ =

{VsUchθ +

V

Uc

σcεc,θθ

}

︸ ︷︷ ︸

∂[V/Uc]/∂θ

θ

V/Uc

and

εαVs/(fsUc),θ =

{1

Uc

[αhθfs

(

Vss −Vsfssfs

)

− αVsfsθf 2s

− Vs

(

hθ +fθfs

)]

︸ ︷︷ ︸

∂[αVs/(fsUc)]/∂θ

+αVsfsUc

σcεc,θθ

}θ

αVs/(fsUc)

where hθ denotes the optimal response of search intensity to changes in the labor market con-

ditions. In section 2, I argue that this response is nearly acyclical, which implies hθ = 0.

39

Hence,

εV/Uc,θ = σcεc,θ

= σcρc,θsd(c)

sd(θ)

≈ 2

(

0.7970.870

24.432

)

≈ 2 (0.03) = 0.06

and

εαVs/(fsUc),θ = −εf,θ

(α + f

α

)

+ σcεc,θ

≈ −

(

0.8948.746

24.432

)(0.67 + 0.31

0.67

)

+ 2(0.03)

≈ −0.47 + 0.06 = −0.41

where I use σc = 2 as in most studies of the business cycle.

Now, I invoke the expression of the elasticity of Bcu with respect to θ:

εBcu,θ =

(−yn

Bcu

)

︸ ︷︷ ︸

0.55

εyn,θ︸︷︷︸

+

(z

Bcu

)

︸ ︷︷ ︸

−0.26

εz,θ︸︷︷︸

+

(−V/UcBcu

)

︸ ︷︷ ︸

0.22

εV/Uc,θ︸ ︷︷ ︸

0.10

+

(

−αVs/(fsUc)

Bcu

)

︸ ︷︷ ︸

0.49

εαVs/(fsUc),θ︸ ︷︷ ︸

−0.41

To make these elasticity values comparable to those in Hagedorn and Manovskii (2008) and

Chodorow-Reich and Karabarbounis (2015) — who provide estimates on the elasticity of wages

and z with respect to a measure of marginal productivity, respectively — I need to express

this with respect to the marginal labor productivity p. Using data on the unemployment rate,

the number of unfilled job vacancies from Barnichon (2010), and the after tax-marginal labor

productivity taken from Chodorow-Reich and Karabarbounis (2015), I show that

εBcu,θ εθ,p︸︷︷︸

3.74

=

(−yn

Bcu

)

︸ ︷︷ ︸

0.55

εyn,p︸︷︷︸

0.449

+

(z

Bcu

)

︸ ︷︷ ︸

−0.26

εz,p︸︷︷︸

1

+

(−V/UcBcu

)

︸ ︷︷ ︸

0.22

εV/Uc,p︸ ︷︷ ︸

0.37

+

(

−αVs/(fsUc)

Bcu

)

︸ ︷︷ ︸

0.49

εαVs/(fsUc),p︸ ︷︷ ︸

−1.54

40

I conclude that

εBcu,θεθ,p = −0.67

which means that for every 1% increase in the marginal productivity of labor, the value of a job

decreases by 0.67%. Admittedly, this is an upper bound for the countercyclicality of the value

of a job. I compute a lower bound. In the absence of search costs

εBcu,θεθ,p =

(−yn

Bcu

)

︸ ︷︷ ︸

1.89

εyn,p︸︷︷︸

0.449

+

(z

Bcu

)

︸ ︷︷ ︸

−0.89

εz,p︸︷︷︸

1

= −0.04

Thus, Chodorow-Reich and Karabarbounis (2015) estimates would imply that in a search model

with an endogenous search effort, the value of a job is nearly acyclical or slightly countercyclical

in the U.S. Taken together, these bounds imply that the value of a job is countercyclical, that

is

εBcu,p ∈ (−0.67,−0.04)

In the extreme case, the elasticity of the value of a job to changes in the marginal labor pro-

ductivity compares satisfactorily with the elasticity of the marginal probability of finding a job.

Precisely, this elasticity is

εfs,p = εfsθεθ,p

εfs,p = (0.32)(3.74) = 1.20

5 Conclusion

I document that the unemployed in the U.S. appear to allocate their time to job search activities

regardless of the business cycle. This finding, when seen through the lens of the Mortensen

and Pissarides (1994) search model, represents a puzzle. Among the arguments examined in

41

this paper, I conclude that the countercyclicality of the value of a job is the most promising

explanation to reconcile the evidence.

42

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46

6 Appendix A

6.1 Measuring search intensity

In this paper, searching for work means searching actively, that is, using at least one search

method that could result in a job offer (e.g. submitting a job market paper, answering job ads,

submitting a resume) without any further action by the job seeker,20 as opposed to using only

passive methods. Examples of passive methods, which offer little or no likelihood of finding work

are looking at ads in newspapers or through the Internet, and attending job training courses.

Accordingly, time-use for job search activities would be the amount of time spent using at least

one active search method. Moreover, the search process does not need to be related to the

previous occupation or industry of the worker.

Measuring search intensity or even approximating it is not free from difficulties and chal-

lenges. I start by presenting evidence on the number of search methods, not job applications,

used by unemployed people in the U.S. For these estimates, I use the CPS. The advantages of

using this survey are: (1) the CPS sample is representative for the nation as well as for regions,

states, and large metropolitan areas; (2) the detailed data per household member has been

public since 1976 allowing me to study 5 recession periods; and (3) the data are available on a

monthly basis so the connection between search intensity and recession periods is expected to

be neat.

Although the use of a higher number of methods in a recession suggests greater searching

intensely, as a means of diversifying search outcomes, the connection between this variable and

search time is not as tidy as I would desire. Unfortunately, there is no information in the CPS

about the time spent in each method. The other drawback of this variable is that arguably a

more informative variable would be the number of total job applications.

Information on the time-use in job search activities is available and is the second measure of

search intensity I rely on in this paper. I use the ATUS to measure this variable, which would

seemingly be the ideal measure of search intensity. However, these data have some drawbacks

that compare one-to-one with the benefits of the CPS. First, although the ATUS is a national

20This is the definition of an active search method adopted by the BLS.

47

representative sample, it is not so at the state level. Second, it has a short time span, from 2003

to 2014. Third, the data are annual.21

I make a difference between searchers and non-searchers. Unlike previous authors (Shimer,

2004 and Mukoyama et al., 2013), I exclude people who are out of the labor force from the

group of searchers. The timing of those who look for work is important, particularly at the

outset of a recession. Besides the typical requirements to treat a worker as unemployed, such

as not having a job and searching for work, I include searchers who are also willing to work.

People out of the labor force may be searching actively for work during recessions but may not

be currently available for work. In this paper only the unemployed people looking for work are

considered searchers. This and other adjustments to the raw available sample of unemployed

people are discussed next.

6.2 Sample

I focus on a specific group of people. First, I intend to restrict the sample to people who have

already finished school by excluding very young people as in Shimer (2004). Specifically, I

confine my attention to unemployed people aged 25 and over. Second, I rely on information

provided by the unemployed people looking for work. In general, an unemployed individual is

someone out of work who is seeking a job during a particular period. Although this definition

may suffice in other circumstances, it is necessary to make it more precise.

According to the most recent CPS definitions, an unemployed individual is either looking

for work or waiting to be recalled as a result of a temporary layoff. A person is considered

unemployed if she meets three criteria during the survey week which includes the nineteenth

of every month: (1) she has not worked during the previous week, (2) she has been willing to

accept a job if it had been offered within the same period, except for temporary illness, and

either (3a) she has searched for work actively during the four weeks prior to the survey week or

(3b) she is waiting to be called back to a job from which she had been laid off.22 Requirement

21It is possible to measure this variable on a monthly and quarterly basis at the expense of reliability on theestimates as a result of the reduced sample size.

22Requirement (3b) has changed over the years. Before 1994 requirement (3b) referred to waiting to be calledback to a job from which she had been laid off and waiting to report to a new wage or salary job within 30

48

(3) distinguishes the two groups of unemployed people. In the CPS survey, unemployed people

on temporary layoff are asked whether they have looked for job in the last 4 weeks but are not

asked about their specific job search activities. On average, unemployed people looking for work

represent 81% and 85% of the total unemployed population aged 25 and over in the periods of

1976-1993 and 1994-2013. This split sample is not a whim. The reason is spelled out in the

next section.

In the remainder of this paper, I use these two sources of data separately.23 In this paper, I

can at least make sure that the CPS and ATUS samples represent the same number of people

in the U.S., which is another reason I focus on people aged 25 and over.

Even though the ATUS sample is based on a subset of people interviewed in the CPS,

there is a crucial difference between the two surveys. The CPS is a household survey while the

ATUS survey collects information on a single member of the household, usually referred to as the

designated person (who later becomes, upon agreement on participating in the survey, the ATUS

respondent). The ATUS designated person is chosen following a simple random sampling so

that each household member faces the same chance of being selected. This apparently innocuous

difference has overt implications in the calculation of the number of unemployed people in the

U.S. Indeed, the labor force status of the ATUS respondent may differ from her labor force

status recorded in the CPS in case the latter was reported by a different person (the CPS

household respondent).24 It may be argued that this situation is more pertinent to young

ATUS respondents since the CPS respondent is expected to be one of the parents.25

In practice, the consequence is that young people are overrepresented in the ATUS sample.

To see this, the left panel of Figure 1 compares the number of unemployed people looking for

days. There was a further distinction among the laid off: those who were given a date to be called back within30 days and those whose waiting period was either 30 days or more or indefinite. Thus, the CPS questionnairewas not useful to verify whether laid off individuals on layoff expected to be recalled. The CPS redesign in1994 introduced two questions to overcome that shortcoming. Individuals who report being laid off are firstasked whether they were given a date to return to work. If they were not, then they are asked whether theywere given any indication that they would be recalled to work within the next 6 months.

23Mukoyama et al. (2013) combine the data from the ATUS and the CPS to construct measures of searchintensity at the extensive and intensive margins.

24According to U.S. Census Bureau (2006) the household respondent is a household member 15 years of age orolder who is knowledgeable about the household.

25I note, however, that the ATUS respondents are interviewed 2 to 5 months after leaving the CPS sample. Thisreasoning would apply to people who have not changed their labor force status in this time span.

49

work using the CPS and the ATUS for the population aged 16 and over. Restricting the sample

to workers aged 25 and over seems to bring both surveys into agreement as suggested by the

right panel of Figure 1.

6.3 Number of job search methods

The third requirement to classify a jobless person as unemployed is probed in the CPS. After

answering that she has been doing something to find work in the last 4 weeks, the CPS respon-

dent is asked to detail the specific efforts undertaken to find a job. She is allowed to describe

them freely, and CPS interviewer needs to fit her answers into the categories listed in Table 1.26

The search methods and their classification displayed in the right panel of Table 1 represent

a major improvement over the list of methods that were prevalent in the CPS questionnaire

before 1994 (left panel),27 the year the CPS underwent a major redesign. The narrow scope

of the list (the interviewers were instructed to classify non-listed active methods in the “other”

category) and the lack of distinction between active and passive methods (the interviewers were

instructed to classify passive methods as “nothing”) made the CPS survey, before 1994, partic-

ularly sensitive to mistakes in the classification of people according to their labor force status

and in the recording of the methods used by the unemployed people.28

Besides refining the list of job search methods, another key difference is that a comprehen-

sive series of questions were added to the questionnaire in 1994 with the intention of depicting

the job search effort more accurately. An introductory and general question about the things

done to find work in the last four weeks was complemented by a couple of clarifying questions

that were conditional on reporting no active search.29 For the question “What are all of the

26See U.S. Census Bureau (2013), pages C4-18 to C4-20, for a thorough description of each method.27Including of the use of search methods as a further requirement to categorize a jobless person as unemployed

dates back to 1962 when a president-appointed committee recommended refining the unemployment definition(Bortnick and Harrison, 1992).

28Polivka and Rothgeb (1993) discuss the redesign of the CPS questionnaire thoroughly.29According to the CPS Interviewing Manual, an active method could result in a job offer without any further

action by the jobseeker. A passive method precludes that possibility. Other things equal, only people who useat least one active method are counted as unemployed looking for work.

50

things you have done to find work during the last 4 weeks?”30 answers such as “do not know”

or “nothing” would sound inconsistent with having reported looking for work in the first place.

For such answers, the CPS interviewer responds: “You said you have been trying to find work.

How did you go about looking?” CPS respondents who have reported doing something to find

work, expressed willingness to work but whose answers to the introductory question are only

interpreted as passive job searching are classified as out of the labor force. To make sure these

respondents are not classified incorrectly, the CPS interviewer presses for more detail: “Can you

tell me more about what you did to search for work?”

Let sit be the number of job search methods that an unemployed person, identified by i,

is ascribed in quarter t when interviewed in the CPS. Let wit be the number of people that

person i represents in the unemployed population aged 25 and over. Let Nt be the number

of unemployed people interviewed in quarter t. The arithmetic average number of job search

methods is then calculated as follows:

st =N∑

i=1

(

wit∑N

i=1wit

)

sit

I construct a quarterly series of st using the CPS monthly public microfiles.31 I do not take

the average of the monthly estimates of s. Instead, I append the monthly files of a given quarter

following U.S. Census Bureau (2006), which results in more reliable figures. Figure 2 shows this

series before and after the 1994 redesign.

A final adjustment of the raw series is worth mentioning. I discard unemployed people who

use only passive methods. This adjustment is rather corrective. Although necessary, it is small

or inessential in practice. It represents nearly 2% of the number of unemployed people looking

for work aged 25 years and over in the period of 1976-1993. In the period of 1994-2014, the

adjustment is minuscule.

The average number of search methods is meaningful in its own right. However, in addition,

30Before the redesign, a version of this question was “What have you been doing in the last 4 weeks to findwork?”

31Available here: http://www.nber.org/data/cps_basic.html. I thank Robert Shimer for his generous helpin dealing with an error found in the CPS microfiles.

51

it is important when linked to the time spent in search activities as Mukoyama et al. (2013)

show. In this section, I present facts that shed light on the relevance of the average number of

methods as a measure of search intensity.

The raw series for the average number of search methods is displayed in Figure 2 for the

period of 1976-2014. First, the average unemployed person has used an ever-increasing number

of methods since 1976, although it is rather slight, as shown in the figure. It is interesting to

note, however, that this has occurred while the job finding probability, as measured by Shimer

(2012), has witnessed an ever-decreasing trend in the period of 1967-2010. One interpretation

is that the worsening job market opportunities has led the unemployed to resort to a far more

diversified job search process.

Second, I note differences in the volatility in the average number of methods between peri-

ods 1976-1993 and 1994-2014. I attribute this to the design of the list of methods prior to the

1994 CPS overhaul. The higher volatility in the latter period is a consequence of the redesign

that intends to capture the job search attempts more accurately. Finally, although Figure 2 is

still a raw measure to warrant conclusions about the cyclicality of search intensity, it can be

already seen that the unemployed seem to respond to the deterioration of economic conditions,

as reflected by the surge in the average number of methods in every recession since 1976.

Next, I construct a case in favor of the strong cyclicality of the average number of search

methods. This adds value to the view that such behavior is pervasive and persistent rather than

merely accidental.

Average number of methods is highly countercyclical: Unemployed people, on average,

use a higher number of search methods during recessions, while in expansions, they seem to

eliminate part of their portfolio of methods. Although Figure 2 already hints at this, I next un-

dertake a more careful analysis using the gross domestic product (GDP) to measure the stance

of the economic activity in the U.S.

First, I report that the choice of the number of search methods is highly sensitive to the

stance of the economy. Figure 3 displays the cyclical components of both the average number

of methods and the GDP, calculated using the Hodrick-Prescott filter. The negative correlation

between these two series is of the order of 0.85 and 0.92 in the periods of 1976-1993 and 1994 to

52

2014.32 Thus, the cyclicality of this measure of search intensity stands out against the cyclical-

ity of other aggregate variables, such as private consumption, hours worked, labor productivity,

and probably, only resembles that of well-known volatile variables such as investment and un-

employment.

Second, I identify the peaks and troughs of the cyclical component of both series and com-

pare the timing of those turning points. To my surprise, these coincide remarkably. The timing

is intriguing given the well-known fact that the unemployment rate (or the number of unem-

ployed people) follows the stance of the economy with some lags. This is clear from Figure 6

which plots the cross correlation patterns of the average number of methods and the number of

unemployed people looking for work with respect to the GDP. This outstanding synchronization

of turning points implies a strong self-awareness of the prevalent economic conditions. Watching

the news may not be the only reason. If everyone is losing their jobs, a person may ascribe this

to aggregate conditions. Similarly, if the people are already unemployed, they may feel that it

is harder to find jobs when the recession hits. After all, the “business” of the unemployed is

looking for work and more than anyone else, allegedly, they perceive when job opportunities

become scarce as the recession develops.

This synchronization, however, is also congruent with a less subtle point. It may be that

the spike in the average number of search methods observed at the outset of every recession

since 1976 is driven by the linkage between a job search and eligibility to claim unemployment

benefits. In most U.S. states, it is required to prove that the unemployed person is engaging in

an active job search in order to remain eligible for unemployment benefits.33 Thus, the spike

could be driven by job losers who rush to file for unemployment benefits and by those who were

already unemployed and, although reluctant to file for benefits before the recession begins —

motivated, for example, by a negative attitude toward unemployment insurance — they may

32The response of the unemployed seems to differ in recessions and expansions. As noted before, the use ofa higher number of methods tends to follow suit quickly as the economy enters into the recession. Duringthe recovery, however, the average number of methods recedes slowly. This phenomenon occurs during everyrecession.

33I note, however, that the quite recent requirement of proving that a person is engaged in an active job searchstarted to be binding by law, in 2012. The observation of the law is left to the states and, therefore, we expect tofind differences in its application. See http://workforcesecurity.doleta.gov/unemploy/comparison2013.asp, section “Nonmonetary Eligibility”.

53

understand that they can no longer dispense with the benefits.34 An alternative explanation

would be consistent with an ever-expanding mass of unemployed people who would have stopped

claiming UI benefits as a result of finding a job had the economic conditions not become worse.35

I offer another suggestive piece of evidence on the countercyclicality of search intensity as

measured by the number of search methods. I examine the sources of the fluctuations in the

average number of search methods. The peculiar design of the CPS survey allows me to identify

three types of unemployed people currently looking for work. I exploit the rotation scheme of

the CPS instrument to link individuals in two consecutive months and compute the average

number of methods for three types of unemployed people, depending on their previous month’s

labor force status.

I ask the following question: Which type is the most responsible for fluctuations in the

average number of methods? Next, I evaluate my answer in light of what we know about the

drivers of the unemployment rate in the U.S. over the business cycle. Fortunately, there is an

easily accessible benchmark with which to compare my answer. Based on a novel analysis of

U.S. labor market flows, Shimer (2012) finds that the job finding probability (the transition

from unemployment to employment) has accounted for three-quarters of the fluctuations of the

unemployment rate in the period of 1967-2010. My findings echo the importance of the unem-

ployment to employment transition in cyclical fluctuations uncovered by Shimer (2012).

More specifically, let j ∈ {eu, iu, uu} denote the previous labor force status of the currently

unemployed. I write the average number of search methods as follows:

st =∑

j∈{eu,iu,uu}

µjtsjt

34Vroman (2009) finds, however, in the 2005 CPS supplement that asks unemployed people for reasons of non-filing for UI benefits, that only 5 percent of the unemployed people do not file for benefits for related reasons.

35This is not to utterly debunk the role of self-reporting bias: CPS unemployed respondents may associateinquiries about their active job search activities with their eligibility to claim benefits. However, I note thatthe CPS as well as the ATUS respondents are informed of the confidentiality and the voluntary aspects ofthe survey before answering the questionnaires. See U.S. Census Bureau (2006) and U.S. Bureau of LaborStatistics (2015). In addition, the CPS, except for the March Supplement, and the ATUS do not containquestions about participation programs.

54

where µjt and sjt denote the measure of type j unemployed people and their (average) search

intensity in period t. I gauge the importance of the search intensity of each unemployed type

in the fluctuations of the aggregate measure of search intensity st by allowing only the search

intensity of the type of interest to vary. For instance, I denote by suu the analogue of st in which

the only intensity that is allowed to vary is that of the continuing unemployed people:

suut = µeut seut + µuut s

uut + µiut s

iut

where the rest of the variables are imputed their average values in the corresponding period

(denoted by the bar above the variable). To measure the variance contribution of the search

intensity of this type of unemployed I compute the regression coefficient

βuu =cov (st, s

uut )

var(st)

With the probability of leaving the labor force, conditional on being currently unemployed, con-

tributing little to the dynamics of the unemployment rate, Shimer’s (2012) findings are easily

interpreted as reporting that the main driver behind these fluctuations is the persistence of the

state of being unemployed. Interestingly, suut accounts for 60% of the fluctuations in st. A very

high proportion of the variability of st is then accounted for by the job search behavior of the

continuing unemployed.

Compositional bias due to some observable characteristics is quite small: One con-

cern is the possibility that the typical unemployed person is a different individual depending on

whether the economy is in a bust or boom. The characteristics responsible for this difference

may or may not be observable, like education, work experience or age. I give credit to this hy-

pothesis by computing the average search methods holding the distribution of people constant

— according to a specific observable characteristic such as education and age.

I use the unemployed person’s age, sex, marital status, education, previous occupation and

industry, (interrupted) length of unemployment, primary reason for being unemployed, state res-

idence, and unemployment insurance eligibility (approximated following Krueger and Mueller

55

(2010)) to assess the extent of this compositional bias.36

In Figures 4 and 5, I report two series: sreal and scomp. The former is the average number of

methods computed by holding the measure of unemployed workers constant. The latter measure

is obtained by allowing only the measure of unemployed workers to vary.

I conclude that the compositional bias is very small. This conclusion, however, is not defini-

tive. Evidently, behind the interviewee’s choice of using more or less job search methods, there

are personal considerations that I do not observe. In addition, even if I had nearly objective

measures of other characteristics such as education and duration of unemployment, those may

interact in an intricate manner.

36Krueger and Mueller (2010) approximate UI eligibility by using two variables: the worker’s full/part timestatus on the previous job and the reason for unemployment. The rationale is that a worker who has losta full/part time job is highly probable to be UI eligible. Exceptions occur at the state level. Mine is acrude version of Krueger and Mueller’s (2010) measure because I do not exploit U.S. state variations in therequirements to be UI eligible. I note, however, an assumption overlooked by Krueger and Mueller (2010).The variable full/part time status refers to the type of job the unemployed person is looking for and not thestatus of her previous job. Like them, I am also making this strong assumption.

56

Figure 1: Number of unemployed people looking for work (in thousands), 2003-2014ATUS (blue, solid) and CPS (red, dashed)

Confidence intervals around one standard deviation

16 years and over 25 years and over

........03.

04.

05.

06.

07.

08.

09.

10.

11.

12.

13.

14.0 .

4,000

.

8,000

.

12,000

.

16,000

.

20,000

........03.

04.

05.

06.

07.

08.

09.

10.

11.

12.

13.

14.0 .

2,000

.

4,000

.

6,000

.

8,000

.

10,000

.

12,000

Notes: My own calculations based on the ATUS annual microfiles and the basic CPS monthly microfiles. ATUS

weighted estimates are calculated using the variable TU06FWGT from 2003 and 2005 and TUFINLWGT, thereafter (see

http://www.bls.gov/tus/changes.pdf). CPS weighted estimates are calculated using the Composited Final Weight (lines 846-

855 in the CPS record layout). Confidence intervals are shown as 1 standard deviation around the mean estimate. The standard

deviation is calculated using the ATUS replication weights as described in http://www.bls.gov/tus/atususersguide.pdf,

p. 40 and the parameters in Table 14-1, p. 14-5 in http://www.census.gov/prod/2002pubs/tp63rv.pdf for the number of

unemployed people in the CPS. The standard deviation estimates for unemployed people aged 16 and over are 0.61 and 0.14 (in

thousands), using ATUS and CPS, and for unemployed people aged 25 and over are 0.42 and 0.12 (in thousands), respectively.

Shaded areas denote NBER recession periods.

Figure 1 highlights discrepancies in the number of unemployed people looking for work in the U.S. when calculated by using

ATUS and CPS. There are sizable differences when the sample includes people aged 16-24. These people are overrepresented

in the ATUS sample, apparently, as a consequence of self-reporting. See section 6.2 of this paper for further details.

57

Table 1: Job Search Methods in the Current Population Survey

Before the 1994 CPS Redesign After the 1994 CPS Redesign

Active Methods

checked with employer directly contacted employer directly/interview

checked with private employment agency contacted public employment agency

checked with public employment agency contacted private employment agency

checked with friends or relatives contacted friends or relatives

placed or answered ads contacted school/university employment center

other sent out resumes/filled out application

checked union/professional registers

placed or answered ads

other active

Passive Methods

looked at ads

attended job training programs/courses

other passive

Source: CPS Interview Record Layout, several issues before 1994 (see http://www.nber.org/data/cps_

basic.html.) and U.S. Census Bureau (2013).

Notes: The “nothing” category appears in both layouts.

58

Figure 2: Average number of job search methodsUnemployed people looking for work, aged 25 and over

1976.I-1993.IV 1994.I-2014.IV

......

....

76

........

78

........

80

........

82

........

84

........

86

........

88

........

90

........

92

......

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

......

....

94

........

96

........

98

........

00

........

02

........

04

........

06

........

08

........

10

........

12

........

14

..

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

Notes: My own calculations based on the basic CPS monthly microfiles. Shaded areas denote NBER recession periods.

Figure 2 shows the quarterly series of the average number of search methods used by the unemployed people looking for work,

aged 25 and over. This series is based on the number of search methods being used during the 4 weeks previous to the CPS

survey week. The survey week contains the 19th day of each month. Figures are not seasonally adjusted.

59

Figure 3: Average number of job search methods (blue, solid) and GDP (red, dashed)Cyclical components relative to trend (in %)

1976.I-1993.IV 1994.I-2014.IV

..........76........

78........

80........

82........

84........

86........

88........

90........

92......−6 .

−4

.

−2

.

0

.

2

.

4

.

6

..........94........

96........

98........

00........

02........

04........

06........

08........

10........

12........

14..−6 .

−4

.

−2

.

0

.

2

.

4

.

6

Notes: My own calculations based on the basic CPS monthly public microfiles. Shaded areas denote NBER recession

periods.

Figure 3 shows the cyclical components of both the quarterly series for the average number of search methods used by

the unemployed people looking for work, aged 25 and over and the gross domestic product. The cyclical components were

calculated as described in the appendix.

60

Figure 4: Average number of job search methods, 1976-1993srealt (blue, solid) and scompt (red, dashed)

age race sex

......

....

76

........

78

........

80

........

82

........

84

........

86

........

88

........

90

........

92

......

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

......

....

76

........

78

........

80

........

82

........

84

........

86

........

88

........

90

........

92

......

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

......

....

76

........

78

........

80

........

82

........

84

........

86

........

88

........

90

........

92

......

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

marital status education looking for full or part time

......

....

76

........

78

........

80

........

82

........

84

........

86

........

88

........

90

........

92

......

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

......

....

76

........

78

........

80

........

82

........

84

........

86

........

88

........

90

........

92

......

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

......

....

76

........

78

........

80

........

82

........

84

........

86

........

88

........

90

........

92

......

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

industry occupation region

......

....

76

........

78

........

80

........

82

........

84

........

86

........

88

........

90

........

92

......

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

(interrupted) spell of unemployment reason for unemployment UI eligibility

......

....

76

........

78

........

80

........

82

........

84

........

86

........

88

........

90

........

92

......

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

......

....

76

........

78

........

80

........

82

........

84

........

86

........

88

........

90

........

92

......

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

......

....

76

........

78

........

80

........

82

........

84

........

86

........

88

........

90

........

92

......

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

Notes: My own calculations based on the basic CPS monthly public microfiles. Shaded areas denote NBER recession

periods. Figure 4 shows the quarterly series for the average number of search methods used by the unemployed people

looking for work, aged 25 and over. This series is based on the number of search methods being used during the 4 weeks

previous to the CPS survey week. The survey week contains the 19th day of each month. Figures are not seasonally

adjusted.

61

Figure 5: Average number of job search methods, 1994-2014srealt (blue, solid) and scompt (red, dashed)

age race sex

......

....

94

........

96

........

98

........

00

........

02

........

04

........

06

........

08

........

10

........

12

........

14

..

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

......

....

94

........

96

........

98

........

00

........

02

........

04

........

06

........

08

........

10

........

12

........

14

..

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

......

....

94

........

96

........

98

........

00

........

02

........

04

........

06

........

08

........

10

........

12

........

14

..

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

marital status education looking for full or part time

......

....

94

........

96

........

98

........

00

........

02

........

04

........

06

........

08

........

10

........

12

........

14

..

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

......

....

94

........

96

........

98

........

00

........

02

........

04

........

06

........

08

........

10

........

12

........

14

..

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

......

....

94

........

96

........

98

........

00

........

02

........

04

........

06

........

08

........

10

........

12

........

14

..

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

industry occupation state

......

....

94

........

96

........

98

........

00

........

02

........

04

........

06

........

08

........

10

........

12

........

14

..

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

......

....

94

........

96

........

98

........

00

........

02

........

04

........

06

........

08

........

10

........

12

........

14

..

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

......

....

94

........

96

........

98

........

00

........

02

........

04

........

06

........

08

........

10

........

12

........

14

..

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

(interrupted) spell of unemployment reason for unemployment UI eligibility

......

....

94

........

96

........

98

........

00

........

02

........

04

........

06

........

08

........

10

........

12

........

14

..

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

......

....

94

........

96

........

98

........

00

........

02

........

04

........

06

........

08

........

10

........

12

........

14

..

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

......

....

94

........

96

........

98

........

00

........

02

........

04

........

06

........

08

........

10

........

12

........

14

..

1.0

.

1.3

.

1.7

.

2.0

.

2.3

.

2.7

.

3.0

Notes: My own calculations based on the basic CPS monthly public microfiles. Shaded areas denote NBER recession

periods. Figure 5 shows the quarterly series for the average number of search methods used by the unemployed people

looking for work, aged 25 and over. This series is based on the number of search methods being used during the 4 weeks

previous to the CPS survey week. The survey week contains the 19th day of each month. Figures are not seasonally

adjusted.

62

Figure 6: Cross correlation patterns of number of unemployed people looking for work andaverage number of search methods with respect to GDP, 1976.I-2014.IV

1976.I-1993.IV 1994.I-2014.IV

.....-4.

-3.

-2.

-1.

0.

1.

2.

3.

4.−1 .

−0.8

.

−0.6

.

−0.4

.

−0.2

.

0

.

order of (auto)correlation

.

corr

elat

ion

.

. ..st

. ..yt(sign inverted)

. ..Nut

.....-4.

-3.

-2.

-1.

0.

1.

2.

3.

4.−1 .

−0.8

.

−0.6

.

−0.4

.

−0.2

.

0

.

order of (auto)correlation

.co

rrel

atio

n.

. ..st

. ..yt(sign inverted)

. ..Nut

Notes: My own calculations based on the basic CPS monthly public microfiles and BEA (for GDP). Figure 6 shows the

cross correlation pattern of the number of unemployed people looking for work Nut

(who use at least one active search

method), and the average number of search methods st with respect to GDP yt. All are quarterly figures. The cyclical

components were calculated as described in the appendix.

63

Table 2: Covariance analysis

1976-1993 1994-2014

sk βk βk

seu 0.13

siu 0.12

suu 0.60

sum 0.85

Notes: Based on linked monthly CPS data.

64

Table 3: 2014 ATUS job search activities list

Job search activities (050401)

Formerly called “Active job search (050401)” before 2005

Contacting employer

Sending out resumes

Sending resumes to employers

Placing/answering ads

Researching details about a job

Asking about job openings

Researching an employer

Making phone calls to prospective employer

Asking former employers to provide references

Auditioning for acting role (non-volunteer)

Auditioning for band/symphony (non-volunteer)

Filling out job application

Meeting with headhunter/temp agency

Formerly called “Other job search activities (050402)” before 2005

Reading ads in paper/on Internet

Checking vacancies

Writing/updating resume

Picking up job application

Submitting applications

Job interviewing (050403)

Interviewing by phone or in person

Scheduling/canceling interview (for self)

Preparing for interview

Waiting associated with job search or interview (050404)

Waiting to go in for an interview

Security procedures rel. to job search/interviewing (050405)

Opening bags for security search (job search)

Being searched at security checkpoint (job search)

Passing through metal detector (job search)

Job search and interviewing, n.e.c. (050499)

Travel related to job search & interviewing (180504)

Notes: n.e.c means not elsewhere classified.

65

Figure 7: Average time use in hours per week, 2003-2014Unemployed people looking for work, aged 25 and over

Confidence intervals shown as deviations of 1 hour per week around the mean

all job search related activities job search and interviewing activities only

(weekdays and weekends) (weekdays and weekends)

..........03

....04

....05

....06

....07

....08

....09

....10

....11

....12

....13

....14

..0 .1

.

2

.

3

.

4

.

5

.

6

.

7

.

8

.

9

..........03

....04

....05

....06

....07

....08

....09

....10

....11

....12

....13

....14

..0 .1

.

2

.

3

.

4

.

5

.

6

.

7

.

8

.

9

all job search related activities job search and interviewing activities only

(weekdays only) (weekdays only)

..........03

....04

....05

....06

....07

....08

....09

....10

....11

....12

....13

....14

..0 .1

.

2

.

3

.

4

.

5

.

6

.

7

.

8

.

9

..........03

....04

....05

....06

....07

....08

....09

....10

....11

....12

....13

....14

..0 .1

.

2

.

3

.

4

.

5

.

6

.

7

.

8

.

9

Notes: My own calculations based on the ATUS microfiles. To compute weighted estimates, I use the variable

TU06FWGT from 2003 and 2005 and TUFINLWGT, thereafter (see http://www.bls.gov/tus/changes.pdf). Time

diary values include weekdays and weekend days (top panel) and only weekdays (bottom panel). Minutes in the previ-

ous day are converted to hours per week (÷60×7 or ÷60×5). The figures in the left panel includes all job search codes

from Table 3 and the figures in the right panel includes only activity codes 050401, 050402, and 050403. Confidence

intervals are shown as deviations around 1 hour per week, which amounts to 1.2 and 1.4 standard deviations (top panel),

and 1.3 and 1.5 (bottom panel), respectively. The standard deviation is calculated using the ATUS replication weights

as described in http://www.bls.gov/tus/atususersguide.pdf, p. 40. The standard deviation is 0.81 and 0.70 (hours

per week) for the series at the top, right and left, respectively, and 0.80 and 0.69 at the bottom. Shaded areas denote

the NBER recession.

66

Table 4: Decomposition of total hours per unemployed person, aged 25 and over

all search activitiesactive job search

and interviewing

only suu

only hsu

only suu

only hsu

varies varies varies varies

weekdays and weekends

2003-2014 50% 44% 47% 47%

2007-2009 42% 19% 28% 36%

weekdays only

2003-2014 46% 46% 42% 51%

2007-2009 32% 27% 23% 40%

Notes: Total hours per unemployed are decomposed as h

u= h

su×

su

u.

67

Figure 8: Cross U.S. state variation in hours per unemployed looking for work (T = 2),2003-2014: narrow set of activities (weekdays and weekends)

Maine

Rhode Island

D.C.

slope = +19.55

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate ATUS (only looking)

Notes:

68

Table 5: Baseline results for 2003-2014: narrow set of activities(weekdays and weekends)

6-year periodsβ β β β

full unweighted weighted demo

Unemployment rate29.08 28.69 19.55 23.51

(ATUS, only looking)

Standard error (8.01) (6.98) (5.96) (9.35)

Unemployment rate24.87 27.01 16.38 18.24

(ATUS)

Standard error (7.70) (6.82) (6.02) (9.19)

Unemployment rate38.26 23.83 13.27 13.97

(rescaled-CPS)

Standard error (14.03) (8.38) (6.87) (9.97)

Observations 102 100 100 100

4-year periods

Unemployment rate26.45 30.48 20.82 19.49

(ATUS, only looking)

Standard error (7.38) (6.33) (6.16) (8.20)

Unemployment rate21.98 27.45 16.86 13.63

(ATUS)

Standard error (7.16) (6.10) (6.00) (7.83)

Unemployment rate48.42 36.71 19.45 15.79

(rescaled-CPS)

Standard error (16.29) (8.96) (8.24) (11.32)

Observations 152 150 150 150

3-year periods

Unemployment rate24.83 25.13 12.63 7.66

(ATUS, only looking)

Standard error (5.94) (5.99) (5.85) (6.82)

Unemployment rate19.69 22.65 10.40 5.37

(ATUS)

Standard error (5.84) (5.60) (5.62) (6.51)

Unemployment rate38.94 21.88 7.61 2.27

(rescaled-CPS)

Standard error (16.12) (7.61) (6.74) (7.83)

Observations 199 197 197 197

Notes: All parameter estimates are expressed in number of minutes per week.

Includes states with zero time in search activities. Observations for Maine

and Rhode Island in the periods 2009-2014 (6), 2007-2010 (4), and 2009-2011

(3) are dropped.

69

Figure 9: Cross U.S. state variation in hours searched per unemployed looking for work,2003-2014: narrow set of activities (weekdays and weekends)

Maine

Rhode Island

D.C.

slope = +19.55

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate ATUS (only looking)

Maine

Rhode Island

D.C.

slope = +16.38

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate ATUS

Maine

Rhode Island

D.C.

slope = +13.27

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate CPS

Notes: Time-use in search activities and unemployment rate calculated by U.S. state and for T = 2. The slope number is

expressed in weakly minutes searched per 1 percentage point of increase in the unemployment rate.

70

Table 6: Baseline results for 2003-2014: narrow set of activities(weekdays only)

6-year periodsβ β β β

full unweighted weighted demo

Unemployment rate18.39 18.42 10.71 8.96

(ATUS, only looking)

Standard error (9.60) (9.62) (5.39) (6.70)

Unemployment rate15.65 16.06 8.04 4.97

(ATUS)

Standard error (8.49) (8.52) (5.08) (6.32)

Unemployment rate30.84 23.90 8.89 7.99

(rescaled-CPS)

Standard error (13.29) (11.37) (5.92) (7.67)

Observations 100 99 99 99

4-year periods

Unemployment rate16.73 17.82 10.49 9.77

(ATUS, only looking)

Standard error (7.90) (7.18) (5.27) (6.61)

Unemployment rate14.64 16.06 7.28 5.15

(ATUS)

Standard error (6.78) (6.42) (5.23) (6.67)

Unemployment rate37.67 21.97 9.54 8.54

(rescaled-CPS)

Standard error (14.62) (7.55) (6.64) (8.22)

Observations 148 145 145 145

3-year periods

Unemployment rate11.77 12.69 5.29 1.02

(ATUS, only looking)

Standard error (6.36) (5.54) (4.49) (5.11)

Unemployment rate9.13 11.39 4.23 -0.09

(ATUS)

Standard error (5.20) (4.80) (4.39) (4.98)

Unemployment rate26.47 13.01 2.91 -0.48

(rescaled-CPS)

Standard error (12.48) (6.34) (5.48) (6.13)

Observations 190 186 186 186

Notes: All parameter estimates are expressed in number of minutes per week.

Includes states with zero time in search activities. Observations for Maine

and Rhode Island in the periods 2009-2014 (6), 2007-2010 (4), and 2009-2011

(3) are dropped.

71

Figure 10: Cross U.S. state variation in hours searched per unemployed looking for work,2003-2014: narrow set of activities (only weekdays)

slope = +10.71

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate ATUS (only looking)

Maine

Rhode Island

D.C.

slope = +8.04

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate ATUS

Maine

Rhode Island

D.C.

slope = +8.89

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate CPS

Notes: Time-use in search activities and unemployment rate calculated by U.S. state and for T = 2. The slope number is

expressed in weakly minutes searched per 1 percentage point of increase in the unemployment rate.

72

Table 7: Baseline results for 2003-2014: narrow set of activities(weekdays and weekends, allows only for between variance in su/u)

6-year periodsβ β β β

full unweighted weighted demo

Unemployment rate23.41 23.41 11.83 14.52

(ATUS, only looking)

Standard error (5.26) (5.26) (4.26) (5.96)

Unemployment rate18.93 18.93 8.79 8.99

(ATUS)

Standard error (5.15) (5.15) (4.13) (5.59)

Unemployment rate26.39 26.39 9.00 9.91

(rescaled-CPS)

Standard error (8.23) (8.23) (4.76) (5.87)

Observations 102 102 102 102

4-year periods

Unemployment rate19.48 21.13 14.17 15.97

(ATUS, only looking)

Standard error (5.50) (5.45) (4.32) (5.08)

Unemployment rate16.05 17.58 11.24 11.25

(ATUS)

Standard error (5.10) (5.00) (4.17) (4.82)

Unemployment rate33.68 33.56 15.23 15.95

(rescaled-CPS)

Standard error (8.67) (8.59) (5.69) (6.67)

Observations 152 151 151 151

3-year periods

Unemployment rate19.18 21.07 12.86 10.52

(ATUS, only looking)

Standard error (4.30) (3.84) (3.81) (4.41)

Unemployment rate15.16 17.78 11.34 8.89

(ATUS)

Standard error (4.13) (3.53) (3.58) (4.17)

Unemployment rate28.08 28.72 14.19 11.80

(rescaled-CPS)

Standard error (6.90) (6.07) (4.36) (4.97)

Observations 199 197 197 197

Notes: All parameter estimates are expressed in number of minutes per week.

Includes states with zero time in search activities.

73

Table 8: Baseline results for 2003-2014: narrow set of activities(weekdays and weekends, allows only for within variance in su/u

6-year periodsβ β β β

full unweighted weighted demo

Unemployment rate31.34 33.51 17.02 19.20

(ATUS, only looking)

Standard error (6.62) (6.21) (5.24) (8.57)

Unemployment rate26.11 29.02 13.22 12.74

(ATUS)

Standard error (7.10) (6.43) (5.14) (8.12)

Unemployment rate30.21 26.69 9.02 7.94

(rescaled-CPS)

Standard error (9.40) (8.45) (5.32) (8.44)

Observations 102 101 101 101

4-year periods

Unemployment rate26.12 28.60 17.48 14.79

(ATUS, only looking)

Standard error (5.53) (5.00) (5.63) (7.03)

Unemployment rate21.34 23.62 13.18 8.63

(ATUS)

Standard error (5.24) (4.74) (5.33) (6.42)

Unemployment rate39.22 39.03 12.92 7.50

(rescaled-CPS)

Standard error (11.46) (11.39) (7.60) (9.60)

Observations 152 151 151 151

3-year periods

Unemployment rate23.64 23.95 9.42 3.94

(ATUS, only looking)

Standard error (5.90) (5.92) (4.71) (5.27)

Unemployment rate18.58 19.77 7.15 1.60

(ATUS)

Standard error (5.73) (5.59) (4.35) (4.91)

Unemployment rate28.34 25.41 5.76 0.48

(rescaled-CPS)

Standard error (8.39) (7.78) (4.78) (5.48)

Observations 199 198 198 198

Notes: All parameter estimates are expressed in number of minutes per week.

Includes states with zero time in search activities.

74

Figure 11: Cross U.S. state variation, 2003-2014: narrow set of activities (weekdays andweekends)

Hours per searcher(

hsu

)Measure of searchers

(suu

)

010

2030

4050

6070

Hou

rs p

er w

eek

per

sear

cher

0 5 10 15

Unemployment rate ATUS (only looking)

0.1

.2.3

.4.5

.6.7

.8.9

1

Mea

sure

of s

earc

hers

0 5 10 15

Unemployment rate ATUS (only looking)

010

2030

4050

6070

Hou

rs p

er w

eek

per

sear

cher

0 5 10 15

Unemployment rate ATUS

0.1

.2.3

.4.5

.6.7

.8.9

1

Mea

sure

of s

earc

hers

0 5 10 15

Unemployment rate ATUS

010

2030

4050

6070

Hou

rs p

er w

eek

per

sear

cher

0 5 10 15

Unemployment rate CPS

0.1

.2.3

.4.5

.6.7

.8.9

1

Mea

sure

of s

earc

hers

0 5 10 15

Unemployment rate CPS

Notes:

75

Figure 12: Cross U.S. state variation, 2003-2014 in hours per unemployed looking for work:narrow set of activities (weekdays and weekends)

allows only for within variance allows only for between variance

in measure of searchers in measure of searchers

slope = +17.02

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate ATUS (only looking)

slope = +11.83

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate ATUS (only looking)

slope = +13.22

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate ATUS

slope = +8.790

1020

30

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate ATUS

slope = +9.02

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate CPS

slope = +9.00

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate CPS

Notes:

76

Table 9: Baseline results for 2003-2014: narrow set of activities(weekdays only, allows only for between variance in su/u

6-year periodsβ β β β

full unweighted weighted demo

Unemployment rate15.41 15.43 7.47 8.23

(ATUS, only looking)

Standard error (5.53) (5.44) (4.06) (4.92)

Unemployment rate11.69 11.95 4.83 3.96

(ATUS)

Standard error (5.17) (5.13) (3.95) (4.75)

Unemployment rate21.68 17.17 3.56 3.67

(rescaled-CPS)

Standard error (8.27) (6.65) (4.76) (5.40)

Observations 100 99 99 99

4-year periods

Unemployment rate11.37 11.71 7.31 7.67

(ATUS, only looking)

Standard error (4.44) (4.44) (3.80) (4.37)

Unemployment rate9.40 9.56 5.32 4.68

(ATUS)

Standard error (4.34) (4.29) (3.75) (4.30)

Unemployment rate21.93 19.57 6.07 5.61

(rescaled-CPS)

Standard error (7.81) (7.68) (5.40) (5.85)

Observations 148 147 147 147

3-year periods

Unemployment rate8.93 9.82 5.58 3.36

(ATUS, only looking)

Standard error (3.80) (3.35) (3.19) (3.40)

Unemployment rate6.50 7.94 4.70 2.39

(ATUS)Standard error (3.43) (2.96) (3.02) (3.28)

Unemployment rate17.25 16.66 6.90 5.13

(rescaled-CPS)

Standard error (5.86) (4.68) (3.74) (4.01)

Observations 190 188 188 188

Notes: All parameter estimates are expressed in number of minutes per week.

Includes states with zero time in search activities.

77

Table 10: Baseline results for 2003-2014: narrow set of activities(weekdays only, allows only for within variance in su/u

6-year periodsβ β β β

full unweighted weighted demo

Unemployment rate23.03 23.07 12.04 9.56

(ATUS, only looking)

Standard error (8.36) (8.43) (4.59) (6.05)

Unemployment rate18.39 18.83 8.32 3.89

(ATUS)

Standard error (7.86) (7.94) (4.48) (5.76)

Unemployment rate27.49 19.95 5.45 1.92

(rescaled-CPS)

Standard error (11.06) (7.76) (5.11) (6.39)

Observations 100 99 99 99

4-year periods

Unemployment rate18.70 19.12 11.91 9.12

(ATUS, only looking)

Standard error (5.80) (5.82) (4.92) (5.72)

Unemployment rate15.82 16.01 8.73 4.78

(ATUS)

Standard error (5.34) (5.36) (4.70) (5.42)

Unemployment rate29.52 26.62 8.82 4.55

(rescaled-CPS)

Standard error (8.64) (8.54) (6.72) (7.48)

Observations 148 147 147 147

3-year periods

Unemployment rate13.48 12.88 3.91 -0.38

(ATUS, only looking)

Standard error (6.62) (6.66) (4.35) (4.26)

Unemployment rate10.37 10.33 2.44 -2.04

(ATUS)

Standard error (5.97) (6.01) (3.95) (3.92)

Unemployment rate18.45 15.11 2.44 -1.07

(rescaled-CPS)

Standard error (7.16) (6.45) (4.52) (4.61)

Observations 190 189 189 189

Notes: All parameter estimates are expressed in number of minutes per week.

Includes states with zero time in search activities.

78

Figure 13: Cross U.S. state variation, 2003-2014: narrow set of activities (weekdays only)

Hours per searcher(

hsu

)Measure of searchers

(suu

)

010

2030

4050

6070

Hou

rs p

er w

eek

per

sear

cher

0 5 10 15

Unemployment rate ATUS (only looking)

0.1

.2.3

.4.5

.6.7

.8.9

1

Mea

sure

of s

earc

hers

0 5 10 15

Unemployment rate ATUS (only looking)

010

2030

4050

6070

Hou

rs p

er w

eek

per

sear

cher

0 5 10 15

Unemployment rate ATUS

0.1

.2.3

.4.5

.6.7

.8.9

1

Mea

sure

of s

earc

hers

0 5 10 15

Unemployment rate ATUS

010

2030

4050

6070

Hou

rs p

er w

eek

per

sear

cher

0 5 10 15

Unemployment rate CPS

0.1

.2.3

.4.5

.6.7

.8.9

1

Mea

sure

of s

earc

hers

0 5 10 15

Unemployment rate CPS

Notes:

79

Figure 14: Cross U.S. state variation, 2003-2014 in hours per unemployed looking for work:narrow set of activities (weekdays only)

allows only for within variance allows only for between variance

in measure of searchers in measure of searchers

slope = +12.04

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate ATUS (only looking)

slope = +7.47

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate ATUS (only looking)

slope = +8.32

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate ATUS

slope = +4.830

1020

30

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate ATUS

slope = +5.45

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate CPS

slope = +3.56

010

2030

Hou

rs p

er w

eek

per

unem

ploy

ed lo

okin

g fo

r w

ork

0 5 10 15

Unemployment rate CPS

Notes:

80

Figure 15: Unemployment rate by U.S. state in the ATUS and the CPS, 2003-2014

45°

02

46

810

1214

16

Une

mpl

oym

ent r

ate

AT

US

0 2 4 6 8 10 12 14 16

Unemployment rate CPS

Notes:

81

7 Appendix B

7.1 Main Propositions

In this section I provide proofs of the propositions stated in the paper. These proofs correspond

to the case in which there is full insurance within the household. When pertinent, I provide

remarks that specialize these results to the case in which every type of worker consumes their

respective endowment. These latter proofs are omitted here since they can be easily inferred

from the case of full insurance.

Let the unit interval [0, 1] be the set of possible values for the state u. Let

Γ(u, θ; s, λ) =[λ+ α(1, s, θ, λ)u, 1

]

be the feasibility set, which comprises all the possible values that the measure of unemployed

workers could take in the next period given that the current state is given by u and θ, and given

values for s and λ.

Consider the following assumptions:

Assumption 1: Γ(u, θ; s, λ) is monotone decreasing in u for fixed θ and given s and λ; that is,

u2 > u1 implies Γ(u2, θ; s, λ) ⊆ Γ(u1, θ; s, λ).

Assumption 2: U(c), V (s), and f(s, s, θ) are once-differentiable functions with respect to the

first argument. Further U(c) is strictly increasing, V (s) is strictly increasing, and f(s, s, θ) is

strictly increasing in s for fixed s and θ. Also, β ∈ (0, 1).

Assumption 3: yn(θ) > yu(θ) for fixed θ and (yn(θ)− yu(θ))Uc(c)− γ + V (s) > 0 for fixed u

and θ.

Assumption 4: α(s, θ; s, λ) ≡ 1− λ− f(s, s, θ) > 0 for every λ, s, s, and θ.

This assumption ensures that the persistence of the measure of unemployed workers, over

time, is positive as in the data.

The following Lemma will be useful to prove the subsequent proposition:

82

Lemma 1: Let U , V , f , yn, yu, γ, and λ satisfy Assumptions 2-4. Then U(u, u′, θ) is strictly

decreasing in u for fixed u′ and θ.

Proposition 1 (Strict decreasing monotonicity of B(u, θ) with respect to u): Let Γ, U , V , f ,

yn, yu, γ, λ and β satisfy Assumptions 1-4. Then B(u, θ) is strictly decreasing in u for fixed θ.

Proof: I rely on the theory developed by Lucas et al. (1989), Chapter 4. In particular, I

invoke Theorem 4.7 (Lucas et al., 1989, p. 80). First, I note that since the set [0, 1] is compact

then the boundedness assumption on the return function U could be easily disregarded for the

application of Theorem 4.7.

Continuity of U is implied by Assumption 2. Lemma 1 establishes that U is strictly decreasing

in u for fixed u′ and θ. Indeed, notice that

∂U

∂u= (yu(θ)− yn(θ))Uc + γ − V (s)− α(s, s, θ, λ)

Vs(s)

fs(s, s, θ)< 0

under Assumptions 2-4. In the previous expression, I have benefited from an intermediate result,

∂s

∂u=α(s, s, θ, λ)

ufs(s, s, θ)> 0

which is obtained by applying the Implicit Function Theorem to the law of motion of unem-

ployment and holding u fixed.

Assumption 1 requires that the feasibility set satisfies a monotonicity condition with respect

to u. It is straightforward to verify, from the law of motion of unemployment, that u2 ≥ u1

implies Γ(u2, θ; s, λ) ⊆ Γ(u1, θ; s, λ). That is, Γ(u, θ; s, λ) is in this sense monotone decreasing

in u.

Using Theorem 4.7 in Lucas et al. (1989) I conclude that B(u, θ) is strictly decreasing in u.

Remark: In the absence of full insurance within the household, B(u, θ) is also strictly decreas-

ing in u for fixed θ.

Assumption 5: U(c), V (s), and f(s, s, θ) are twice-differentiable functions with respect to the

83

first argument. U(c) is strictly concave, V (s) is weakly convex and f(s, s, θ) is strictly concave

in s for fixed s and θ.

The following Lemma and Assumption will be useful to prove the subsequent proposition:

Lemma 2: Let V and f satisfy Assumptions 2 and 5. Then U(u, u′, θ) is strictly concave in u

and u′ for fixed θ.

Remark: In the absence of full insurance within the household, U is weakly concave.

Assumption 6: Γ(u, θ; s, λ) is convex in u for fixed θ and given s and λ.

Proposition 2 (Strict concavity of B(u, θ) with respect to u): Let Γ, U , V , f , yn, yu, γ, λ and

β satisfy Assumptions 1-6. Then B(u, θ) is strictly concave in u for fixed θ.

Proof: I invoke Theorem 4.8 from Lucas et al. (1989), Chapter 4, p. 81. I need to verify two

assumptions. Lemma 2 guarantees that U(u, u′, θ) is strictly concave with respect to u and u′

for fixed θ. I show this by constructing the Hessian matrix. I first compute

∂U

∂u= −(yn − yu)Uc + γ − V −

αVsfs

∂U

∂u′=

Vsfs,

from which I calculate the entries of the Hessian matrix

∂2U

∂u2= (yn − yu)2Ucc +

α2

uf 2s

[Vsfssfs

− Vss

]

∂2U

∂u′2=

1

uf 2s

[Vsfssfs

− Vss

]

∂2U

∂u′∂u=

−α

uf 2s

[Vsfssfs

− Vss

]

Assumptions 2 and 5 ensure that ∂2U∂u2

< 0. In addition, notice that ∂2U∂u2

∂2U∂u′2

−(∂2U∂u′∂u

)2=

(yn−yu)2Uccψuf2s

> 0, where ψ = Vsfssfs

− Vss < 0, under those assumptions. Thus, the Hessian

84

matrix is negative definite. I conclude that U(u, u′, θ) is strictly concave in u and u′ for fixed θ.

Finally, Γ(u, θ; s, λ) is convex in the sense that if u′ ∈ Γ(u, θ; s, λ) and w′ ∈ Γ(w, θ; s, λ) then

φu′ + (1− φ)w′ ∈ Γ(φu+ (1− φ)w, θ; s, λ) for any φ ∈ (0, 1). Hence Assumption 6 is verified.

Using Theorem 4.8 in Lucas et al. (1989), I conclude that B(u, θ) is strictly concave in u for

fixed θ.

Remark: In the absence of full insurance within the household, B(u, θ) is linear in u for fixed

θ. I use the equivalence (15) highlighted earlier in the paper. By using equations (9) and (15),

it is easy to see that Bu is a constant. Therefore, I conclude that B(u) is linear in u.

Next, I make an assumption that will ensure the interiority and uniqueness of the optimal

search intensity even under the linearity of the value function.

Assumption 7: f(s, s, θ) satisfies the Inada’s conditions with respect to s.

Note: Two of the conditions are already implied by Assumption 2 and 5. In addition, I assume

that

lims→0

fs(s, s, θ) = ∞

Note: Even if B(·, θ) and V (s) are linear, Assumption 7 guarantees that the optimal search

intensity is a unique interior solution. To see this recall equation (13). The intuition is simply

that a little bit of effort is highly valuable. That is, the unemployed worker would be better-off

if exerting a minimal positive level of effort.

The following assumption is crucial to prove the subsequent proposition:

Assumption 8: Let the value function B(u, θ) be a smooth function with respect to u and θ.

Let l(u, θ) denote the next period’s optimal measure of unemployed workers as a function of

the state (u, θ). The policy function l(u, θ) is, of course, linked to the optimal search intensity

85

h(u, θ) through the law of motion of unemployment:

l(u, θ) = λ+ α (h(u, θ), s, θ, λ)u

Proposition 3 (Strict monotonicity of h(u, θ) with respect to u): Let B, Γ, U , V , f , yn, yu,

γ, λ and β satisfy Assumptions 1-8. Then the optimal search intensity is a strictly increasing

function of u for fixed θ.

Proof: I use the optimal condition for search intensity and apply the Implicit Function The-

orem to obtain:

hu(u, θ)

[

Vss(h(u, θ))︸ ︷︷ ︸

≥0

+ β︸︷︷︸

+

fss(h(u, θ), s, θ)︸ ︷︷ ︸

−

Bu(u′, θ′)

︸ ︷︷ ︸

−

− β︸︷︷︸

+

u︸︷︷︸

+

fs(h(u, θ), s, θ)2

︸ ︷︷ ︸

+

Buu(u′, θ′)

︸ ︷︷ ︸

−

]

=

− β︸︷︷︸

+

fs(h(u, θ), s, θ)︸ ︷︷ ︸

+

Buu(u′, θ′)

︸ ︷︷ ︸

−

α(h(u, θ), s, θ, λ)︸ ︷︷ ︸

+

The assumptions made on the primitive functions U , V , and f lead to the conclusion that

h(u, θ) is strictly increasing in u for fixed θ.

Remark: In the absence of full insurance within the household, h(u, θ) is linear in u for fixed

θ. The reason why the optimal search intensity does not depend on u is twofold. Neither do

the marginal costs nor the marginal benefits of searching depend on the state. The latter is a

direct consequence of the absence of full insurance within the household.

Two of the conjectures entertained in the paper use the procyclicality of the value of a

job as an assumption. Next, I provide conditions that guarantee this to happen. I rely on

supermodularity techniques developed by Topkis’s (1998). To use his theorems, I express the

objective function as dependent of n′, n, and θ, where n = 1 − u is the measure of employed

workers. Let

H(n, n′, θ) = U(n, n′, θ) +

∫

Θ

B(n′, θ′)Q(θ, dθ′)

be the objective function (the right side of the Bellman equation), where the tilde denotes that

86

the problem is restated in terms of the measure of employed workers.

Consider the following assumptions:

Assumption 9: f is strictly increasing in θ.

Assumption 10: The transition probability Q is monotone increasing.

Assumption 11: f(s, θ) has strictly increasing differences in s and θ, i.e., fsθ > 0.

Assumption 12: f(s, θ) has strictly decreasing differences in s and θ, i.e., fsθ < 0.

Assumption 13:

∂U(n, n′, θ)

∂n∂θ=yn(θ)

∂θ−yu(θ)

∂θ−∂γ

∂θ+∂V

∂θ+∂(αVs/fs)

∂θ> 0

where

∂V

∂θ+∂(αVs/fs)

∂θ= −

Vsfθfs

+ α

(fθf 2s

[Vsfssfs

− Vss

]

−Vsfsθf 2s

)

Then under Assumption 13 wages, net of unemployment benefits, are more procyclical than

the value of non-working time when moving from unemployment to employment. The next

proposition asserts than under this assumption the value of a job is procyclical, as in the canon-

ical general equilibrium search model.

Proposition 4 (Strict increasing monotonicity of Bn(n, θ)): Let Q, U , V , f , and λ satisfy

Assumptions 2, 4, 5, 9, 10, and 11. Then B(n, θ) is supermodular in n and θ, i.e., Bn,θ > 0.

Proof: First I prove that U(n, n′, θ) is strictly supermodular in (n, θ) and has strictly increasing

differences in (n′, n) and (n′, θ). Notice that

∂2U

∂n′∂n= −

α

uf 2s

[Vsfssfs

− Vss

]

> 0

∂2U

∂n′∂θ= −

fθf 2s

[Vsfssfs

− Vss

]

+Vsfsθf 2s

> 0

87

establishes that U has strict increasing differences in (n′, n) and (n′, θ), respectively. The sign

of the following expression

∂2U

∂n∂θ=

∂∆U(θ)

∂θ− α

(

−fθf 2s

[Vsfssfs

− Vss

]

+Vsfsθf 2s

)

−Vsfθfs

,

where ∆n(θ) ≡ (yn − yu)Uc + V (s(θ)) − γ or ∆n(θ) ≡ U(yn(θ)) − U(yu(θ)) + V (s(θ)) − γ

(depending on whether full insurance within the household is possible), is not clear. Under

Assumption 13, the first term in the above equation outweighs the remaining term so that U is

supermodular in (n, θ). Finally, by Proposition 2 in Hopenhayn and Prescott (1992), it follows

that B(n, θ) is supermodular in (n, θ).

Now, I am ready to state the main propositions regarding the choice of search intensity in

response to changes in θ.

Proposition 5 (Strict increasing monotonicity of h(u, θ) with respect to θ): Let Q,B,Γ, U ,

V , f , λ, γ, and β satisfy Assumptions 1-10. Further let θ be either I.I.D. or correlated. Then

h(u, θ) is strictly increasing in θ if fsθ > 0 in the absence of full-insurance within the household.

Proof: The optimal condition reads as follows

Vs(h(u, θ)) = −βfs(h(u, θ), θ)

∫

Θ

Bu(u′, θ′)Q(θ, dθ′)

where u′ = λ+ α(s, s, θ, λ)u.

Taking derivatives with respect to θ gives:

Vsshθ = −β(fsshθ + fsθ)

∫

Θ

Bu(u′, θ′)Q(θ, dθ′)− βfs

∂∫

ΘBu(u

′, θ′)Q(θ, dθ′)

∂θ

88

or

hθ

Vss︸︷︷︸

≥0

+ β︸︷︷︸

+

fss︸︷︷︸

−

∫

Θ

Bu(u′, θ′)Q(θ, dθ′)

︸ ︷︷ ︸

−

− β︸︷︷︸

+

u︸︷︷︸

+

f 2s

︸︷︷︸

+

∫

Θ

Buu(u′, θ′)Q(θ, dθ′)

︸ ︷︷ ︸

0

=

− β︸︷︷︸

+

fsθ︸︷︷︸

+

∫

Θ

Bu(u′, θ′)Q(θ, dθ′)

︸ ︷︷ ︸

−

− u︸︷︷︸

+

fs︸︷︷︸

+

fθ︸︷︷︸

+

∫

Θ

Buu(u′, θ′)Q(θ, dθ′)

︸ ︷︷ ︸

0

+ fs︸︷︷︸

+

Q′(θ)︸ ︷︷ ︸

+

∂∫

ΘBu(u

′, θ′)Q(θ, dθ′)

∂θ′︸ ︷︷ ︸

−

where the signs are added in light of the assumptions previously made and the results proved

so far. Recall that, in the absence of full insurance within the household, B(u, θ) is linear in

u for fixed θ. With the value of moving from unemployment to employment procyclical (i.e.,

Bnθ(n, θ) > 0 or Buθ(u, θ) < 0), the procyclicality of search intensity depends almost exclusively

on the procyclicality of the marginal return of searching fs.

Remark: When θ is I.I.D. fsθ > 0 is also a necessary condition.

Note: The sufficiency and necessity of fsθ > 0 for the deterministic case is shown by Mukoyama

et al. (2013) in their Proposition 1.

Proposition 6 (Strict increasing monotonicity of h(u, θ) with respect to θ): Let Q,B,Γ, U ,

V , f , λ, γ, and β satisfy Assumptions 1-10. Further let θ be either I.I.D. or correlated. Then

h(u, θ) is strictly increasing in θ if fsθ > 0 and

fsθfsfθ

>u∫

ΘBuu(u

′, θ′)Q(θ, dθ′)∫

ΘBu(u′, θ′)Q(θ, dθ′)

in the presence of full insurance within the household.

89

Proof: The optimal condition reads as follows

Vs(h(u, θ)) = −βfs(h(u, θ), θ)

∫

Θ

Bu(u′, θ′)Q(θ, dθ′)

where u′ = λ+ α(s, s, θ, λ)u.

Taking derivatives with respect to θ gives:

Vsshθ = −β(fsshθ + fsθ)

∫

Θ

Bu(u′, θ′)Q(θ, dθ′)− βfs

∂∫

ΘBu(u

′, θ′)Q(θ, dθ′)

∂θ

or

hθ

Vss︸︷︷︸

≥0

+ β︸︷︷︸

+

fss︸︷︷︸

−

∫

Θ

Bu(u′, θ′)Q(θ, dθ′)

︸ ︷︷ ︸

−

− β︸︷︷︸

+

u︸︷︷︸

+

f 2s

︸︷︷︸

+

∫

Θ

Buu(u′, θ′)Q(θ, dθ′)

︸ ︷︷ ︸

−

=

− β︸︷︷︸

+

fsθ︸︷︷︸

+

∫

Θ

Bu(u′, θ′)Q(θ, dθ′)

︸ ︷︷ ︸

−

− u︸︷︷︸

+

fs︸︷︷︸

+

fθ︸︷︷︸

+

∫

Θ

Buu(u′, θ′)Q(θ, dθ′)

︸ ︷︷ ︸

−

+ fs︸︷︷︸

+

Q′(θ)︸ ︷︷ ︸

+

∂∫

ΘBu(u

′, θ′)Q(θ, dθ′)

∂θ′︸ ︷︷ ︸

−

where the signs are added in light of the assumptions previously made and the results proved

so far and just discussed.

Remark: When θ is I.I.D. the latter condition is also a necessary condition.

90

7.2 Additional Proofs

Proposition 7: Consider the following expression for the probability of finding a job of an

individual unemployed worker under symmetric equilibrium (s = s):

f(s, s, θ)|s=s =(

sσ−1

σ + θσ−1

σ

) σ

σ−1

If σ < 1 then f ≤ 1.

Proof: First, I note that f can be alternatively expressed as follows:

f(s, s, θ) =sθ

s1−σ

σ + θ1−σ

σ

,

which is the matching function proposed by den Haan et al. (2000). With this function the

proof of this proposition is straightforward. Suppose, by using an argument by contradiction,

that f > 1. This implies that

sθ >(

s1−σ

σ + θ1−σ

σ

) σ

1−σ

.

Now define s = s1−σ

σ and θ = θ1−σ

σ and notice that the right side of the inequality could be

written as

sθ = (sθ)σ

1−σ .

Take logarithms to the right side of the inequality and invoke the Jensen inequality to conclude

that

σ

1− σ(ln s+ ln θ) ≤

σ

1− σln (s+ θ)

where I have used σ < 1. By taking exponentials to both sides of the latter inequality

(sθ)σ

1−σ ≤(

s+ θ) σ

1−σ

91

we reach a contradiction.

Note: It can be verified that this function is of the constant returns to scale type and increasing

in both arguments as noted by den Haan et al. (2000). It also exhibits decreasing returns to

both arguments. Desirable properties of the CES function have also been pointed out by Menzio

and Shi (2010).

92