Job Seekers' Perceptions and Employment Prospects: Heterogeneity, Duration Dependence and Bias

NBER WORKING PAPER SERIES

JOB SEEKERS' PERCEPTIONS AND EMPLOYMENT PROSPECTS:

HETEROGENEITY, DURATION DEPENDENCE AND BIAS

Andreas I. Mueller

Johannes Spinnewijn

Giorgio Topa

Working Paper 25294

http://www.nber.org/papers/w25294

NATIONAL BUREAU OF ECONOMIC RESEARCH

1050 Massachusetts Avenue

Cambridge, MA 02138

November 2018

We thank Ned Augenblick, Raj Chetty, Stefano DellaVigna, Erik Eyster, Manolis Galenianos, Francois

Gerard, Martin Hackman, Nathan Hendren, Greg Kaplan, Peter Kuhn, Atilla Lindner, Brendan Price,

Matthew Rabin, Emmanuel Saez, Dan Silverman, Dmitry Taubinsky and Basit Zafar, and seminar

participants at CalPoly, CEMFI, Harvard, LSE, NYFed, UC Berkeley, UC Davis, UCLA, UC Santa

Barbara, UC San Diego, AEA Meetings San Diego, NBER Summer Institute, the T2M conference,

TEC conference and EM3C conference for helpful comments and suggestions. We also thank Luis

Armona, Jack Fisher, Nicole Gorton, Raymond Lim, Prakash Mishra, Anushka Mitra, Thomas Monk,

Mathilde Muñoz, Will Parker, Ashesh Rambachan and Lauren Thomas for their excellent research

assistance. Johannes Spinnewijn acknowledges financial support from ERC grant 716485. The views

expressed here are our own and do not necessarily reflect those of the Federal Reserve Bank of New

York, the Federal Reserve System, or the National Bureau of Economic Research.

NBER working papers are circulated for discussion and comment purposes. They have not been peer-

reviewed or been subject to the review by the NBER Board of Directors that accompanies official

NBER publications.

sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided

that full credit, including © notice, is given to the source.

Job Seekers' Perceptions and Employment Prospects: Heterogeneity, Duration Dependence

and Bias

Andreas I. Mueller, Johannes Spinnewijn, and Giorgio Topa

NBER Working Paper No. 25294

November 2018, Revised May 2020

JEL No. E24,J6,J64

ABSTRACT

This paper analyses job seekers' perceptions and their relationship to unemployment outcomes to study

heterogeneity and duration dependence in both perceived and actual job finding. Using longitudinal

data from two comprehensive surveys, we document that elicited beliefs are (1) strongly predictive

of actual job finding, (2) subject to an optimistic bias that is larger for the long-term unemployed, and

(3) not revised downward when job seekers remain unemployed. We exploit the joint observation

of beliefs and ex-post realizations, to disentangle heterogeneity and duration dependence in true job

finding rates. To this purpose, we estimate non-parametric bounds as well as a reduced-form statistical

framework that allows for elicitation errors and systematic biases in beliefs. We find a substantial

amount of heterogeneity in true job finding rates, accounting for most of the observed decline in job

finding rates over the spell of unemployment. We also find that job seekers' beliefs systematically

under-react to these differences in job finding rates. We show theoretically and quantify in a calibrated

model of job search how these biased beliefs contribute to the slow exit out of unemployment and

can explain more than 10 percent of the incidence of long-term unemployment.

Andreas I. Mueller

The University of Texas at Austin

Department of Economics

2225 Speedway

Austin, TX 78712

and NBER

[email protected]

Johannes Spinnewijn

Department of Economics

London School of Economics, Houghton Street

London, WC2A 2AE

[email protected]

Giorgio Topa

Federal Reserve Bank of New York

Research & Statistics Group

33 Liberty Street

New York, NY 10045

[email protected]

1 Introduction

A critical challenge for unemployment policy is the high incidence of long-term unemployment. While

long unemployment durations and a large share of long-term unemployed have been a common phe-

nomenon in European countries (see Ljungqvist and Sargent [1998] and Machin and Manning [1999]),

the Great Recession has imported this concern to the US as well (Kroft et al. [2016]).

The consequences

of job loss can be large, but especially so for people who get stuck in longs spells of unemployment (e.g.,

Jacobson et al. [1993], Kolsrud et al. [2018]). Moreover, the high incidence of long-term unemployment

seems indicative of substantial frictions in the search and matching process (e.g., Clark and Summers

[1979]), and can contribute to the persistence of employment shocks (e.g., Pissarides [1992]).

An ubiquitous empirical ﬁnding in the literature is the negative duration dependence of exit rates

out of unemployment. As it is crucial for formulating policy responses, understanding why employment

prospects are worse for the long-term unemployed has been the topic of a long literature.

In theory,

long-term unemployment may reduce a worker’s chances to ﬁnd a job (e.g., due to skill-depreciation

or duration-based employer screening), but less employable workers also select into long-term unem-

ployment. Empirically, separating the role of duration-dependent forces from heterogeneity across job

seekers has been a challenge until today. Since the seminal work by Lancaster [1979] and Heckman

and Singer [1984] among others, several studies have tried to estimate or calibrate the contribution of

diﬀerent forces to the negative duration dependence in exit rates out of unemployment. Direct evidence

on the potential role of heterogeneity has been particularly limited.

This paper takes a novel approach to address this question, using newly available data on unemployed

job seekers’ perceptions about their employment prospects together with actual labor market transitions.

We present a conceptual framework that takes advantage of our ability to jointly observe job seekers’

perceptions and actual job ﬁnding to identify heterogeneity in true job ﬁnding rates and separate

dynamic selection from true duration dependence in explaining the observed decline in job ﬁnding. The

key idea underlying identiﬁcation in this framework is that the covariance between perceptions and

actual job ﬁnding helps uncovering the extent of ex-ante heterogeneity in true job ﬁnding probabilities.

The predictable variation in job ﬁnding provides a lower bound on the ex-ante heterogeneity in job

ﬁnding. Beliefs can also be used in combination with a model that relates job seekers’ elicited beliefs

to their job ﬁnding probability to estimate the heterogeneity in the latter. This builds on recent work

using risk elicitations to estimate heterogeneity in ex-ante risks in Hendren [2013, 2017].

Our analysis goes further in two important dimensions. Both are key to uncover the heterogeneity

in job ﬁnding that contributes to the observed duration dependence and are relevant by themselves.

First, in addition to idiosyncratic error in the beliefs (Hendren [2013]), we allow job seekers’ beliefs to

While the share of long-term unemployed workers (longer than six months) has been consistently above 50% in most

European countries in recent decades, in the US this share rose from 20% to just below 50% in the aftermath of the Great

Recession. In 2019, the share of LT unemployed was 50.4% and 20.3% in the EU and the US respectively (Eurostat; CPS).

See Shimer and Werning [2006], Pavoni [2009] and Kolsrud et al. [2018] for the consequences for the design of the

unemployment beneﬁt proﬁle. See Pavoni and Violante [2007], Spinnewijn [2013] and Wunsch [2013] for the consequences

on the design of workfare, job search assistance and training programs.

For a review of the relevant literature, see Machin and Manning [1999] who write: ‘To conclude, it does not really seem

possible in practice to identify separately the eﬀect of heterogeneity from that of duration dependence without making some

very strong assumptions about functional form which have no foundation in any economic theory.’ See Kroft et al. [2013],

Alvarez et al. [2016], Jarosch and Pilossoph [2018] and Farber et al. [2018] for recent examples in this literature.

systematically over- or under-react to diﬀerences in job ﬁnding, either across job seekers or over the

unemployment spell. This bias aﬀects the covariance between perceptions and job ﬁnding and thus helps

uncovering the heterogeneity in job ﬁnding from that covariance. We identify this bias by leveraging

variation in job ﬁnding rates at diﬀerent unemployment durations. Second, we allow for transitory

diﬀerences in job seekers’ job ﬁnding within a spell (e.g., temporary spells of reduced search, vacancy

supply shocks), which do not contribute to the observed decline in job ﬁnding rates through dynamic

selection. We show that we can separately identify permanent and transitory diﬀerences in job ﬁnding

using the covariances between job ﬁnding and contemporaneous vs. lagged beliefs.

We turn to the data to estimate the relevant moments in our conceptual framework and document

a number of novel facts about job seekers’ perceptions. We use two distinct surveys, which elicited

unemployed job seekers’ beliefs about their chances of re-employment - which we thus refer to as the

job ﬁnding probability. The ﬁrst survey is the Survey of Consumer Expectations (SCE), which started

in December 2012 and is run by the Federal Reserve Bank of New York. The survey has a rotating

panel structure where a representative sample of about 1,300 household heads is interviewed every

month for a period of up to 12 months (see Armantier et al. [2017] for details). The second survey

is the Survey of Unemployed Workers in New Jersey, which surveyed a large sample of unemployment

insurance recipients in NJ every week from October 2009 to March 2010 (see Krueger and Mueller [2011]

for details). A crucial feature of our data is its longitudinal nature, which allows to compare reported

perceptions to ex-post realizations as well as to analyze the evolution of perceptions over the spell of

unemployment for the same individuals. Both surveys also elicited job seekers’ beliefs about job ﬁnding

at diﬀerent horizons and/or in diﬀerent ways, so we can study robustness to the elicitation method and

use multiple measurements to reduce elicitation error (Morrison and Taubinsky [2019]).

The empirical analysis provides three main results. First, the perceived job ﬁnding probabilities

signiﬁcantly and strongly predict actual job ﬁnding at the individual level. This holds even when

we control for a rich set of observable co-variates. In the SCE, the job ﬁnding probability is around

.5 percentage points higher for an individual who reports his or her job ﬁnding probability to be 1

percentage point higher. Moreover, we ﬁnd that the covariances of job ﬁnding with contemporaneous

beliefs vs. with lagged beliefs are of similar size, suggestive of the persistence in job seekers’ prospects.

We use the empirical correlation between beliefs and job ﬁnding to inform our non-parametric bounds,

which indicate substantial heterogeneity in job ﬁnding that can explain at least half of the observed

decline in job ﬁnding.

Second, comparing the perceived and actual job ﬁnding across job seekers, we conﬁrm in our data

Spinnewijn’s (2015) ﬁnding of an overall optimistic bias, but furthermore, we ﬁnd that the bias rises

strongly with unemployment duration. In the SCE, the elicited beliefs are in fact unbiased for job seekers

at the start of the unemployment spell, but the observed decline in perceived job ﬁnding probabilities

is only half of the observed decline in actual job ﬁnding rates. Hence, the long-term unemployed

substantially over-estimate their probability of ﬁnding a job. We use the under-reaction in beliefs to

inform our model of beliefs, and ﬁnd that – combined with the high covariance between beliefs and job

ﬁnding – it suggests that potentially all of the observed declined in job ﬁnding can be explained by

dynamic selection.

Third, when using only within-person variation, we ﬁnd that, if anything, job seekers report slightly

higher job-ﬁnding probabilities the longer they are unemployed. This result is perhaps surprising, given

the large empirical literature trying to identify the true duration dependence in job ﬁnding and often ar-

guing that it is negative. It is consistent, however, with our reduced-form analysis that ﬁnds substantial

heterogeneity in job ﬁnding, thus leaving limited scope for true negative duration dependence.

To jointly estimate the heterogeneity and dynamics of the true and perceived job ﬁnding rates, we

propose a statistical model that allows us to infer the parameters of interest with exact equivalents of

the moments in the data. Our model can allow for a diﬀerential response of beliefs to cross-sectional and

longitudinal variation in job ﬁnding, using both changes in the means of perceived and true job ﬁnding

and their covariances over the spell. We prove the semi-parametric identiﬁcation of a stylized two-period

version of the model and verify that the identiﬁcation arguments hold up in the estimation of the fully-

speciﬁed dynamic model, showing how parameter estimates change with the empirical moments.

The estimates from our statistical model conﬁrm the substantial heterogeneity in true job ﬁnding

rates, accounting for almost all of the observed decline in job ﬁnding rates over the spell of unemployment

(84.7 percent; s.e. 36.4). True duration dependence explains the remainder and thus plays a limited

role, also in comparison to the importance it has been attributed in prior work. In line with the reduced-

form evidence, the pre-dominant role played by dynamic selection proves to be robust to alternative

distributional and functional-form assumptions in the statistical model. The estimation also conﬁrms

the under-response of job seekers’ beliefs to variation in job ﬁnding. Job seekers with a high underlying

job ﬁnding rate tend to be over-pessimistic, whereas job seekers with a low job ﬁnding rate are over-

optimistic. The latter remain unemployed longer, but they do not revise their beliefs downward. In

the absence of signiﬁcant duration dependence in true job ﬁnding, this explains why the long-term

unemployed are over-optimistic. Our statistical framework is parsimoniously speciﬁed but ﬁts the key

moments in our data very well, whereas restricted versions of the model perform radically worse.

We ﬁnally study how the under-reaction in job seekers’ perceptions itself can contribute to the

observed decline in job ﬁnding and the incidence of long-term unemployment. To this purpose, we set

up a job search model `a la McCall [1970], introducing heterogeneity and duration dependence in job

oﬀer rates and allowing for biased beliefs. The key mechanism that we highlight in this structural model

is that job seekers’ behavior mitigates the mechanical eﬀect of diﬀerences in job oﬀer rates on job ﬁnding

rates, but only when these diﬀerences are perceived as such. If perceptions under-respond to diﬀerences

in job oﬀer rates, either across job seekers or over the unemployment spell, the resulting diﬀerences

in job ﬁnding rates will be ampliﬁed. The larger variation in job ﬁnding leads to a stronger decline

in the observed job ﬁnding. To quantify the impact on the incidence of long-term unemployment, we

calibrate the model with moments from our data and the statistical model. Correcting the biases in

beliefs reduces the share of workers who are unemployed for longer than 6 months, by 2 − 3 percentage

points. Deﬁning the incidence of long-term unemployment as the ratio of the LT vs. ST unemployment

rate, we ﬁnd that the biases in beliefs jointly explain 11 − 12% of this incidence.

Our paper aims to contribute to three diﬀerent strands in the literature. As discussed before, we try

to contribute to the large literature studying the diﬀerent sources of duration dependence in job ﬁnding.

We use a novel strategy to separate dynamic selection from true duration dependence, ﬁnding a pre-

dominant role played by dynamic selection. Recent resume audit studies (e.g., Kroft et al. [2013]) have

documented large declines in callback rates over the unemployment the spell, suggesting the importance

of true duration dependence instead. The evidence from audit studies themselves, however, is mixed

(see Farber et al. [2018]) and the duration dependence in callback rates may not translate into duration

dependence in job ﬁnding (e.g., Jarosch and Pilossoph [2018]). Alvarez et al. [2016] use data on multiple

unemployment spells instead and ﬁnd evidence for positive duration dependence.

In general, direct

evidence on the role of heterogeneity has been limited to the dynamic selection in longer unemployment

spells based on observables, which tend to play a moderate role only (e.g., Kroft et al. [2016]).

Second, our analysis of the biases in beliefs relates to a strand in the behavioral labor economics

literature trying to understand the role of information frictions and behavioral biases in the job search

process. The new survey evidence conﬁrms the optimistic bias in job seekers’ beliefs (Spinnewijn [2015],

Arni [2017], Conlon et al. [2018]) and the persistence in beliefs seems consistent with the lack of updating

of reservation wages over the unemployment spell (Krueger and Mueller [2016], Drahs et al. [2018]).

Adding to this evidence, our paper highlights the under-reaction in beliefs to diﬀerences in job ﬁnding,

both across workers and over the unemployment spell, and shows the importance of the optimistic

bias among the long-term unemployed in particular. The biases in beliefs add to other behavioral

frictions distorting job search, like present bias (DellaVigna and Paserman [2005]), reference-dependence

(DellaVigna et al. [2017]) and locus-of-control (Caliendo et al. [2015], Spinnewijn [2015]), and indicate

the potential for information policies in particular.

Third, our work relates to recent papers using survey elicitations to improve the estimation or cali-

bration of structural models of job search. For example, Hall and Mueller [2018] use elicited reservation

and oﬀered wages in the New Jersey survey to identify diﬀerent sources of wage dispersion in a search

model. Conlon et al. [2018] relate expectations to realized wage oﬀers in the SCE and focus on the

updating of beliefs in response to wage oﬀers to estimate a model of on- and oﬀ-the-job search with

learning frictions. Similar to our numerical analysis, they then use the estimated structural model to

assess the quantitative importance of these learning frictions. That job seekers’ beliefs have predictive

value has been documented elsewhere (Spinnewijn [2015], Arni et al. [2016]), but to our knowledge, it

has never been used to bound the heterogeneity in job ﬁnding and its contribution to the observed de-

cline in job ﬁnding. Elicited expectations are increasingly used in other applications, too, for example to

study educational and occupational choices (e.g., Delavande and Zafar [2014], Arcidiacono et al. [2014],

Wiswall and Zafar [2015]) or household ﬁnance (e.g., Fuster et al. [2018] and Crump et al. [2018]).

The paper proceeds as follows. Section 2 discusses the data. Section 3 sets up a conceptual framework

and documents the basic facts in the data. Section 4 sets up the statistical model and estimates hetero-

geneity and duration dependence in perceived and actual job ﬁnding. Section 5 presents a behavioral

model of job search, including numerical results on the impact of biases in beliefs. Section 6 concludes.

See also Honor´e [1993] who proves identiﬁcation with multiple unemployment spells in the context of the mixed

proportional hazard model. The comparative advantage of our approach is that it also captures heterogeneity that is

speciﬁc to a given unemployment spell (e.g., savings, family structure, etc.).

In a related experiment with uncertainty about job search ability, Falk et al. [2006] ﬁnd limited updating in beliefs.

See also the experimental evidence in Belot et al. [2020] who show how tailored information can change job seekers’

scope of search and Altmann et al. [2018] who show how information treatments can improve the re-employment outcomes.

2 Data

As brieﬂy discussed in the introduction, our empirical analysis builds on two distinct surveys. The ﬁrst

survey is the Survey of Consumer Expectations (SCE), which is run by the New York Federal Reserve

Bank and surveys a representative sample of about 1,300 household heads across the US. The sample is a

rotating panel where each individual is surveyed every month for up to 12 months (see Armantier et al.,

2013, for details). Our sample period stretches from December 2012 to June 2019 during which 948 job

seekers have been surveyed while unemployed. The second survey is the Survey of Unemployed Workers

in New Jersey, which was collected by Alan Krueger and Andreas Mueller and surveyed around 6,000

unemployed job seekers (see the appendix of Krueger and Mueller [2011] for details). In what follows, we

refer to the survey as the Krueger-Mueller (KM) survey. The surveyed job seekers were unemployment

insurance recipients in October 2009 and interviewed every week for 12 weeks until January 2010. The

long-term unemployed were surveyed for an additional twelve weeks until March 2012.

Both surveys elicit the beliefs individuals hold when unemployed about their prospects to become

employed again. In the SCE, unemployed job seekers report the probability they expect to be employed

again both within the next 3 and 12 months. In the KM survey, job seekers report the probability that

they expect to be re-employed within the next 4 weeks, as well as how many weeks they expect it will

take before they are employed again.

The beliefs are elicited up to 12 times (5 times) in the SCE

(KM survey) for job seekers who remain unemployed. The KM survey is a weekly survey, but the belief

questions were administered only every four weeks, starting about one month into the survey period.

In addition to the elicited beliefs, both surveys contain information on the individuals’ employment

outcomes, and hence, we can link perceptions to actual outcomes for the same individuals. The SCE

is superior to the KM survey in this respect because it suﬀers less from attrition and skipping. As

reported by Armantier et al. [2017], out of those who completed one interview in the SCE, 74 percent

completed two interviews. Attrition is much lower after the second interview and, in fact, 58 percent

completed all 12 monthly interviews of the SCE panel. In addition, we ﬁnd that nearly half of surveys

where the respondent was unemployed were followed by three consecutive monthly interviews, which is

the sub-sample that we use when comparing elicitations to employment outcomes over the next three

months. Even if there was no attrition, this number would be at most 75 percent, since unemployed

respondents who are rotating out of the panel survey do not have three monthly follow-up surveys

(this aﬀects anyone in interviews 10, 11 and 12).

In the KM survey, out of those 2,384 individuals

who completed the belief questions at least once, 60 percent completed the belief questions twice, but

only 21 percent completed them more than twice. To a large extent, this drop-oﬀ in participation in

the KM survey is simply due to the shorter horizon of the survey. However, we also ﬁnd that the

elicited belief about the probability of ﬁnding a job was negatively related to the number of follow-up

Both are online surveys. The KM survey asked participants to slide a bar between 0 and 100, randomizing the initial

position. The exact questions and response format is shown in Appendix A.

Given that many individuals had already found a job after a month or left the survey for other reasons, and given the

lower interview frequency of the belief questions, the sample of interest for our study is substantially smaller than the full

weekly panel of the KM survey. Note also that for individuals who did not complete a weekly survey exactly four weeks

after the last time the belief questions were administered, the belief questions were administered at the next interview.

Respondents in the SCE who failed to complete three interviews consecutively are not invited back to the survey.

Table 1: Descriptive Statistics for the Survey of Consumer Expectations (SCE) and the

Krueger-Mueller (KM) Survey, and Comparions to the Current Population Survey (CPS)

SCE CPS KM Survey CPS NJ

(in %) 2012-19 2012-19 2009-10 2009-10

High-School Degree or Less 44.5 49.0 32.5 46.6

Some College Education 32.4 29.8 37.4 24.6

College Degree or More 23.1 21.2 30.1 28.7

Ages 20-34 25.4 47.6 38.1 39.4

Ages 35-49 33.5 28.4 35.4 33.4

Ages 50-65 41.1 24.0 26.5 27.2

Female 59.3 45.9 48.6 43.5

Black 19.1 22.2 24.4 21.4

Hispanic 12.5 20.1 27.5 22.1

Monthly job ﬁnding rate

... Full sample 18.7 24.0 10.3 16.4

... Duration 0-6 months 25.8 29.5 13.5 21.6

... Duration 7+ months 12.7 13.4 9.2 10.0

# of respondents 948 — 2,384 —

# of respondents w/ at least 2 surveys 534 — 1,422 —

# of survey responses 2,597 211,129 4,803 2,818

Notes: The SCE and KM survey are restricted to unemployed workers, ages 20-65, with interviews where

the belief questions were administered. The samples for the CPS are restricted to unemployed workers,

ages 20-65. In addition, the fourth column restricts the sample to the state of New Jersey. Survey weights

are used for all statistics shown in the table. The monthly job ﬁnding rate in the SCE and CPS is the

U-to-E transition rate between two consecutive monthly interviews. The monthly job ﬁnding rate in the

KM survey is calculated as the fraction of unemployed workers who accepted a job or started working in

the next four consecutive weekly interviews.

surveys completed.

While the invitations and reminder emails explicitly stated that respondents are

invited back to the survey regardless of their employment status, this suggests that the KM survey still

exhibited some diﬀerential attrition by expected employment outcomes, introducing a potential bias

when relating beliefs to employment outcomes later in the survey. For this reason, we focus mostly on

the SCE when comparing beliefs to employment outcomes.

Table 1 compares some basic survey outcomes and demographics for the unemployed workers in the

two surveys as well as the Current Population Survey (CPS). All samples are restricted to unemployed

workers, ages 20-65. The sample of unemployed in the SCE is relatively small, which is due to the

fact that – unlike the KM survey – the SCE samples the entire population and the sub-sample of

unemployed is only a small fraction of it. Note that while the SCE is representative of the population of

U.S. household heads, the CPS is representative of individuals, which can explain some of the observed

diﬀerences, particularly in age.

The KM survey’s sample is representative of unemployment insurance

We ﬁnd that the elicited probability is 26 percent for those with four weekly surveys within the next four weeks, whereas

it was 34 percent for those with less than four weekly survey within the next four weeks. For linking the employment

outcomes to the elicited beliefs in the KM survey, we ﬁnd that only about 17 percent of survey participants completed

four consecutive weekly interviews following an interview where the 4-week belief question was elicited.

Tables B1 and B2 show how sample characteristics change across the sub-samples used in the analysis.

recipients in New Jersey, see Krueger and Mueller [2011] for details. The KM survey over-sampled long-

term unemployed workers, but the survey includes survey weights, which adjust for both oversampling

and non-response. The diﬀerences in the sampling universe also explain some of the diﬀerences in the

characteristics of the unemployed between the SCE and the KM survey. The monthly job ﬁnding rate in

the SCE is 18.7 percent compared to 10.3 percent in the KM survey, where the lower rate in the latter is

likely due to the lower job ﬁnding rate in the immediate aftermath of the Great Recession, but may also

be driven by diﬀerential attrition. In both datasets the job ﬁnding rates exhibit substantial negative

duration dependence. In the SCE (KM) survey, monthly job ﬁnding rates of long-term unemployed

workers are about one half (two thirds) of the job ﬁnding rates of the short-term unemployed. The job

ﬁnding rate in the CPS is somewhat higher compared to the SCE, but the observed percent decline in

job ﬁnding between the short- and long-term unemployed is similar across the two surveys.

3 Empirical Evidence

This section presents the elicitations of job seekers’ perceptions and how they relate to actual job ﬁnding.

Our central objects of interest are the true and perceived job ﬁnding rate, which we denote by T

i,d

and

i,d

respectively, and how they diﬀer across individuals i and unemployment durations d. We ﬁrst

demonstrate conceptually how the relation between elicited beliefs and actual job ﬁnding can be used

to analyze heterogeneity and duration dependence in both perceived and true job ﬁnding rates. The

conceptual framework guides the reduced-form empirical evidence that we present in this section. We

then add functional and distributional assumptions in the next section to estimate the full distribution

of true and perceived job ﬁnding rates across job seekers and unemployment durations.

3.1 Conceptual Framework

An individual’s job ﬁnding probability T

i,d

cannot be directly observed, nor is it possible to observe

diﬀerences in job ﬁnding across individuals or how individual job ﬁnding evolves over the unemployment

spell. We do, however, observe the realization F

i,d

of the job search of an unemployed individual at

duration d, i.e., whether she ﬁnds a job (F

i,d

= 1) or not (F

i,d

= 0). We can also observe how the average

job ﬁnding rate E

i,d

) = E

i,d

) among the unemployed job seekers changes over the unemployment

spell. This is typically found to be decreasing, as is the case in our data (see Table 1).

The observed duration dependence in job ﬁnding can be decomposed as follows:

i,d

) − E

d+1

i,d+1

) = E

i,d

− T

i,d+1

) +

cov

i,d

, T

i,d+1

)

1 − E

i,d

)

, (1)

where the subindex denotes the duration at which the job seekers are sampled to evaluate the corre-

sponding moment. This decomposition clearly demonstrates how any negative duration dependence in

job ﬁnding can be driven by true duration dependence in job ﬁnding, E

i,d

− T

i,d+1

) > 0, or by the

The comparison sample for the KM survey in the CPS includes both recipients and non-recipients, which likely explains

their higher job ﬁnding rate. Krueger and Mueller [2011] show in administrative data that UI weekly exit hazard in the

sample frame is 2.6% per week, or 10.0% per month, which is close to the 10.3% job ﬁnding rate in the survey.

We provide the derivations underlying the equations in this section in Appendix C.

dynamic selection of job seekers with worse re-employment prospects into prolonged unemployment,

cov

i,d

, T

i,d+1

) > 0. The dynamic selection itself depends on how much heterogeneity there is in

individuals’ job ﬁnding and whether individuals’ job ﬁnding probabilities are persistent,

cov

i,d

, T

i,d+1

) = var

i,d

) − cov

i,d

, T

i,d

− T

i,d+1

) . (2)

When all heterogeneity in job ﬁnding probabilities is permanent, the contribution of dynamic selection

to the observed decline in job ﬁnding is fully determined by the variance in job ﬁnding var

i,d

). In

the other extreme, where all heterogeneity in job ﬁnding probabilities is transitory, dynamic selection

does not contribute to the observed decline in job ﬁnding.

The challenge is to separate the role of these forces empirically as individual job ﬁnding rates

cannot be observed. Through surveys, however, we can elicit an individual’s perceived job ﬁnding

probability Z

i,d

and how it evolves over the unemployment spell. Importantly, when ex-ante elicitations

are predictive of ex-post realizations, their relationship can be leveraged to learn about the ex-ante

heterogeneity in true job ﬁnding itself. The elicited beliefs can also be compared to job seekers’ average

job ﬁnding to learn about biases in beliefs and their evolution over the unemployment spell.

Lower Bound on Heterogeneity If individuals had perfect information about their employment

prospects, the heterogeneity in job ﬁnding chances would be fully captured by the variance in elicited

beliefs. Beliefs, however, may be subject to bias and elicited with error. Still, the predictive value

of individuals’ elicitations can help uncovering the heterogeneity in true job ﬁnding probabilities. For

binary risks the covariances of beliefs with ex-post job ﬁnding realizations and with ex-ante job ﬁnding

probabilities simply coincide, cov

i,d

, F

i,d

) = cov

i,d

, T

i,d

). So, when elicited beliefs are an unbiased

- but potentially noisy - measure of job ﬁnding, the covariance between beliefs and ex-post job ﬁnding

exactly identiﬁes the variance in ex-ante job ﬁnding probabilities var

i,d

) (see Hendren [2013]).

More generally, even when beliefs are biased, we can bound this variance using the Cauchy-Schwarz

inequality (see Morrison and Taubinsky [2019]),

var

i,d

) ≥

cov

i,d

, F

i,d

)

var

i,d

)

. (3)

For a given variance in elicitations, a larger covariance between elicitations and realizations indicates

less noise in the elicited beliefs, and thus a larger variance in the job ﬁnding probabilities. When the

elicited beliefs are subject to noise, we can further tighten this bound by using multiple elicitations in

job seekers’ beliefs, Z

i,d

(which are available in both surveys). Following a similar argument as Morrison

and Taubinsky [2019], we ﬁnd that the variance in job ﬁnding probabilities is bounded by

var

i,d

) ≥

cov



i,d

, F

i,d



cov



i,d

, F

i,d



cov



i,d

, Z

i,d



. (4)

This bound relies on the elicitations not being negatively correlated, conditional on job ﬁnding chances,

and their conditional expectation (and thus the bias) being the same.

The bounds in (3) and (4) use only beliefs to predict the variation in job ﬁnding probabilities. More

generally, from the variance decomposition, we know that any predictable variance, var

i,d

)),

provides a non-parametric lower bound on the variance in true job ﬁnding probabilities, var

i,d

While this holds for any set of observables, we ﬁnd that job seekers’ beliefs are particularly predictive.

Model of Beliefs While the non-parametric bounds are robust to biases in beliefs, we can go

beyond partial identiﬁcation by specifying how beliefs relate to observable variation in job ﬁnding.

Consider the following model of beliefs where job seekers’ elicited beliefs are an aﬃne transformation of

true job ﬁnding,

i,d

= b

+ b

i,d

+ ε

i,d

, (5)

with ε

i,d

capturing random error in the elicited beliefs (E(ε

i,d

) = 0). The intercept b

captures a

bias in perceptions that is common to all individuals. The slope parameter b

captures the extent to

which the variation in job ﬁnding rates is perceived. The covariance between perceived and actual job

ﬁnding scales the variance in true job ﬁnding rates with the slope parameter b

cov

i,d

, F

i,d

) = b

var

i,d

). (6)

If job seekers’ elicitations under-react to variation in job ﬁnding (b

< 1), the covariance between

perceived and actual job ﬁnding underestimates the variance in true job ﬁnding, and vice versa.

Now we can leverage the variation in job ﬁnding rates across durations to learn about the slope

parameter. Intuitively, this parameter is revealed by the compression of the diﬀerences in Z’s relative

to the distribution of T ’s across durations. For the linear model, this becomes

d+1

i,d+1

) − E

i,d

)

d+1

i,d+1

) − E

i,d

)

. (7)

E.g., with b

< 1, the low-T

i,d

types are more optimistic and thus over-optimism is predominant among

those who fail to ﬁnd a job and remain unemployed for longer.

Note that our identiﬁcation argument for var

i,d

) continues to hold in the presence of non-classical

measurement error with E(ε

i,d

) linear in T

i,d

. While it changes the interpretation of b

, capturing

both biases and non-classical measurement error, it does not change any of the equations above.

use the statistical model further below to probe the sensitivity of our results to the type of measurement

Note that the lower bound in equation (3) can also be expressed as β

OLS

cov

i,d

, F

i,d

) where β

OLS

is the coeﬃcient

in the linear regression of F

i,d

on Z

i,d

. Similarly, the lower bound in equation (4) can be expressed as β

cov

i,d

, F

i,d

)

where β

is the coeﬃcient in the linear regression of F

i,d

on Z

i,d

, but where Z

i,d

is instrumented for by Z

i,d

In principle, we could use other observable variation in job ﬁnding rates to estimate how perceived and true job ﬁnding

relate, for example between more and less educated job seekers. However, in that case we would need to assume that the

average bias remains constant across workers with diﬀerent education (or any other observable used). Using time spent

unemployed to obtain variation in job ﬁnding rates gives the advantage that we can actually observe how job seekers’

beliefs change over the spell, allowing us to relax the assumption that perceptions respond in the same way to variation in

job ﬁnding across and within job seekers. We show this in the statistical model in Section 4.

To be precise, the covariance between elicitations and job ﬁnding in (6) still pins down the variance of job ﬁnding

probabilities, subject to the attenuation factor b

, which is still identiﬁed by the compression of the diﬀerences in Z’s

relative to the diﬀerences in T ’s across durations in (7).

error, and ﬁnd that our results are generally robust.

Persistence in Job Finding The decomposition in equations (1) and (2) highlights that tran-

sitory heterogeneity in job ﬁnding does not contribute to dynamic selection. Only if diﬀerences in job

ﬁnding probabilities are persistent, does the lower bound on heterogeneity translate to an upper bound

on the role of true duration dependence. We can again use the relationship between actual job ﬁnding

and elicited beliefs, but now using the lagged rather than contemporaneous beliefs, to shed light on the

persistence in job ﬁnding probabilities. For the linear beliefs model, we have

cov

d+1

i,d

, F

i,d+1

) = b

cov

d+1

i,d

, T

i,d+1

) , (8)

which relates to the dynamic selection term in equation (1). When the heterogeneity in job ﬁnding can

be represented by permanent diﬀerences and random transitory shocks, T

i,d

= T

+ τ

i,d

, their respective

role is fully captured by the diﬀerence in predictive value of lagged and contemporaneous beliefs.

In what follows, we describe the elicited beliefs, how they relate to actual job ﬁnding, and how

they change over the spell of unemployment. We use this evidence to gauge the importance of the

diﬀerent forces underlying the observed duration dependence in job ﬁnding, following the decomposition

arguments above. We then develop these arguments in full in the context of a statistical model in Section

4. It is important again to note that our identiﬁcation of the distribution of actual job ﬁnding does not

rely on separating the role of biases vs. elicitation errors, nor does it depend on how job seekers’ search

strategy relates to the elicited beliefs. We do, however, take a stance on both issues when we study the

impact of beliefs on search in Section 5.

3.2 Elicited Beliefs about Job Finding

The two surveys ask unemployed job seekers to report their chances of ﬁnding a job that they will accept,

which we refer to as the job ﬁnding probability (see Appendix A for the wording of the questions asked

in both surveys). Figure 1 shows the histograms of these perceived job ﬁnding probabilities at the three-

month horizon in the SCE and the one-month horizon in the KM survey.

For both surveys there is

substantial dispersion over the entire range of potential probabilities. The perceived probabilities over

the one-month horizon in the KM survey are more skewed to the left than the perceived probabilities

over the three-month horizon in the SCE and the former are relatively high compared to the latter.

While the elicitation horizon may be relevant, this comparison is diﬃcult because it is across diﬀerent

samples. A common issue when eliciting probabilities is that subjects may bunch at round numbers.

We do observe signiﬁcant bunching for both measures, in particular at 50%, as apparent in Figure 1.

In Appendix C, we show indeed that, in this case,

cov

d+1

i,d+1

, F

i,d+1

) − cov

d+1

i,d

, F

i,d+1

) = b

var

(τ

i,d

)



1 −

var

)

[1 − E

i,d

)]



. (9)

The question in the KM survey was for a 4-week period, but for simplicity we refer to it as a 1-month period.

Manski [2004] discusses other surveys where respondents use the entire range of probabilities from 0 to 100, as well as

additional evidence that respondents are willing and able to provide meaningful probabilistic responses.

Figure 1: Histogram of Elicitations of the 3-Month Job Finding Probability in the SCE (left panel) and

the 1-Month Probability in the KM survey (right panel)

0 .5 1 1.5 2

Density

0 .2 .4 .6 .8 1

Prob(Employed in 3 Months)

0 .5 1 1.5 2

Density

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1

Prob(Employed in 1 Month)

To assess the validity of our elicitations and the robustness to bunching, we compare the elicited

beliefs about job ﬁnding at diﬀerent horizons in the same sample of job seekers. In the SCE, job seekers

report the perceived job ﬁnding probability at a three-month horizon as well as at a twelve-month

horizon. We compare the distribution of the twelve-month job ﬁnding probabilities to the imputed

job ﬁnding probability over twelve months based on the elicitation over a three-month horizon (see

Appendix Figure D3). We ﬁnd a high correlation of 0.76 between the two measures at the individual

level. We also ﬁnd that the distribution of the ratio of the two statistics has a mode of 1 (see Appendix

Figure D4). This suggests that many survey respondents submit responses that are fully consistent

with each other, at least if they believe that they live in a stationary world where the unemployment

probability does not change over the spell of unemployment.

In the KM survey, job seekers report not only the perceived probability of ﬁnding employment,

but also how many weeks they expect it will take to be employed again. The inverse of the expected

unemployment duration equals the perceived job ﬁnding rate averaged over the remaining unemployment

spell. Hence, the elicited average job ﬁnding rate and the job ﬁnding rate for next month should be

related, again depending on whether an individual expects the job ﬁnding rate to change over the

unemployment spell.

Importantly, the alternative elicitation has the advantage that it avoids the

sharp bunching at 0, 50 and 100, but except for the diﬀerence in bunching, the distribution looks very

similar to the distribution of the perceived job ﬁnding rates for the next month. The individual-level

correlation between the two measures equals 0.65 (see Appendix Figure D3).

The similarity between

the diﬀerent measures is also conﬁrmed by Figure D4 in the Appendix, which plots the distribution

of the ratio of the two measures, indicating that for most peoples the two measures indeed coincide.

To be precise, given that the question was phrased in weeks, we impute the implied 1-month re-employment probability

as 1 − (1 −

)

, where x is the elicited remaining weeks unemployed.

Note that throughout the paper we trim extreme outlier observations: In the KM survey, we eliminate 51 responses

where the elicited and imputed probability are more than 75 percentage points apart and thus clearly inconsistent with each

other. In the SCE, we eliminate 316 observations, where the 3-month probability is larger than the 12-month probability.

We report robustness checks in the Appendix for not imposing these restrictions. If we do not impose this restriction, the

correlation coeﬃcient between the two measures remains high at 0.56 in the KM survey and 0.72 in the SCE.

Figure 2: Averages of Actual Job Finding Probabilities, by Bins of Elicited Probabilities (SCE)

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1

Realized 3−Month U−E Transition Rate

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1

Elicited Prob(Find Job in 3 Months)

Mean of Realized 3−Month U−E Transition Rate

95% Confidence Interval

Overall, the similarity between the alternative elicitations is re-assuring. Our empirical analysis using

the KM survey will focus on the elicited probability, but we will show that our results are similar for

the expected duration measure and robust to the observed bunching at 0, 50 or 100.

3.3 Job Finding Beliefs and Outcomes

We now study how job seekers’ beliefs about job ﬁnding probabilities compare to actual job ﬁnding

outcomes.

Predictive Power of Beliefs We can assess the predictive power of job seekers’ beliefs by relating

the elicited beliefs about job ﬁnding to actual job ﬁnding. Figure 2 shows the average job ﬁnding

probability within the next three months by the perceived three-month job ﬁnding probability in the

SCE. The positive gradient clearly reveals the strong predictive nature of the elicited beliefs - on

average, people who report a higher job ﬁnding probability are more likely to ﬁnd a job. Still, job

seekers reporting the lowest probabilities tend to be too pessimistic (on average), while job seekers

reporting higher probabilities tend to be too optimistic. The average job ﬁnding probability ranges

from 18 percent to 72 percent for job seekers reporting probabilities in the ﬁrst to the last decile.

Panel A of Table 2 reports the corresponding regression estimates, regressing a binary indicator for

We focus here on the SCE’s 3-month elicitation as it suﬀers less from attrition and gaps in survey completion, but

we replicate all results in this Section for the KM survey in the Appendix. In the SCE, we restrict the sample to those

interviews where we have 3 monthly consecutive follow-up interviews, to make sure that we do not miss any employment

spells. Similarly, for the KM survey, we restrict the sample to those with four weekly consecutive interviews to avoid

under-counting of job ﬁnding due to attrition and gaps in the weekly survey.

Table 2: Linear Regressions of Realized Job Finding Rates on Elicitations (SCE)

Panel A. Dependent Variable:

3-Month U-E Transition Rate (1) (2) (3) (4)

Prob(Find Job in 3 Months) 0.586*** 0.464*** 0.501***

(0.073) (0.069) (0.092)

Prob(Find Job in 3 Months) x LT Unemployed -0.258*

(0.142)

LT Unemployed -0.078

(0.094)

Controls x x x

Observations 1,201 1,201 1,201 1,201

0.131 0.148 0.218 0.259

Panel B. Dependent Variable:

3-Month U-E Transition Rate (1) (2) (3) (4)

Prob(Find Job in 3 Months) 0.346**

(0.136)

3-Month Lag of Prob(Find Job in 3 Months) 0.366*** 0.301***

(0.105) (0.101)

Controls x x

Observations 474 474 474 474

0.063 0.123 0.063 0.159

Notes: Survey weights are used in all regressions. All samples are restricted to unemployed workers in the SCE, ages

20-65. Controls include dummies for gender, race, ethnicity, household income, educational attainment, and age and

age squared (see Appendix Table D1 for results showing the control variables). Robust standard errors (clustered at

the individual level) are in parentheses. Asteriks indicate statistical signiﬁcance at the *0.1, **0.05 and ***0.01 level.

whether a job seeker has found a job within the next three months on the elicited probability. The

results conﬁrm the predictive nature of the elicited beliefs. On average, the job ﬁnding probability

is 0.59 percentage points higher for an individual who reports his or her job ﬁnding probability to

be 1 percentage point higher. The coeﬃcient is only slightly lower when adding various controls,

including gender, age, income, educational attainment, race and ethnicity, in column 3 of the table. This

demonstrates that individuals’ beliefs contain relevant information about future employment prospects

above and beyond these demographic controls. The coeﬃcient on the elicited job ﬁnding probability

is high, but still signiﬁcantly smaller than 1. This attenuation could be driven both by random errors

in perceptions or elicitations, which increase the variance in elicited beliefs, or by systematic biases in

beliefs reﬂected by the parameter b

in the linear beliefs model.

In similar regressions carried out in the KM survey, we ﬁnd a coeﬃcient of 0.260 (s.e. 0.109) for

the 1-month probability question (see Table D3 in the Appendix). The smaller coeﬃcient in the KM

survey compared to the SCE could be driven by the diﬀerent horizon used for the elicitation. Indeed,

we ﬁnd a larger coeﬃcient (0.402; s.e. 0.178) when we run the same regression but with the inverse of

the expected duration as the independent variable. Similar to the SCE, the perception questions retain

signiﬁcant predictive value when adding controls, and the predictive power is higher for the short-term

unemployed with a coeﬃcient of 0.382 for the 1-month probability and 0.513 for the inverse of the

expected duration, compared to a coeﬃcient of 0.501 in the SCE, as reported in column 4 of Table 2.

Robustness We probe the robustness of our estimates by running diﬀerent versions of the re-

gression reported in column 1 of Table 2. Appendix Table D2 shows that our results are robust (1) to

instrumenting the 3-month eliciation with the 12-month elicitation (coeﬃcient of 0.71), (2) to excluding

answers equal to 50% (coeﬃcient of 0.59), (3) to not trimming the sample for inconsistent answers

between the 3- and 12-month elicitation (coeﬃcient of 0.55), (4) to including only one unemployment

spell for each person (coeﬃcient of 0.62), (5) to including only the ﬁrst observation for each person (co-

eﬃcient of 0.44), (6) to including only those individuals who entered the SCE survey as employed and

separate into unemployment during the survey period (coeﬃcient of 0.65), (7) to controlling for cohort

and time ﬁxed eﬀects (coeﬃcient of 0.57), (8) to including only answers for those unemployed 3 months

or less (coeﬃcient of 0.57). In line with column 4 in Table 2, we also ﬁnd that the coeﬃcient declines

with unemployment duration, with a value of 0.50 for those unemployed 4-6 months and a value of 0.35

for those unemployed 7 months or more, though the coeﬃcient remains highly statistically signiﬁcant in

all samples. Note also that we cannot reject the hypothesis of the equality of coeﬃcients with the one

in the baseline speciﬁcation for all sub-samples except for the long-term unemployed. Overall, we ﬁnd

that our results are robust and conﬁrm the substantial predictive power of reported beliefs for realized

job ﬁnding. We also report the same robustness checks for the regression with controls, as in column 3

of Table 2. Again, the results for all robustness checks are similar to the baseline results.

Lower Bound on Heterogeneity The explanatory power of the beliefs in the SCE is large

= 0.13) and almost the same as for all other observables together (R

= 0.15).

Moreover, the

results in column 2 and 3, where the R

increases from 0.15 to 0.22 when adding the elicited beliefs

to the regression model with controls, conﬁrm that the elicited beliefs have predictive power above

and beyond observable characteristics. To formally assess the amount of heterogeneity in job ﬁnding,

we calculate the non-parametric lower bounds on the variance in job ﬁnding probabilities derived in

Section 3.1. The ﬁrst row in Table 3 reports the lower-bound using the 3-month elicitation only, which

is computed as

cov(F

i,d

)

var(Z

i,d

)

and equals 0.032. This lower bound can be tightened by including the

12-month elicitation in the SCE data as a second elicitation,

cov(F

i,d

)cov(F

i,d

)

cov(Z

i,d

)

. This increases the

lower bound to 0.038.

As discussed, we can also tighten the bound further by including observable

characteristics. The variance of the predicted job ﬁnding, using both beliefs and demographics (column

Note that even if the perceived and actual job ﬁnding probabilities were to coincide, we would not expect an R

of 1 as

we are not using the actual job ﬁnding probability but a dummy variable for the realization of the probability. The inherent

randomness associated with the realization of the job ﬁnding probability thus implies an R

that is substantially lower

than 1 even if beliefs were unbiased and measured without error. In the case where job seekers had perfect information

about their types, the R

of the regression of actual job ﬁnding on beliefs would be equal to

var(Z

i,d

)

E(Z

i,d

)(1−E(Z

i,d

))

for large

N. Using these moments from the SCE data, we obtain a value of 0.36, suggesting that the R

of 0.13 for the actual job

ﬁnding realizations is substantial and that the elicited job ﬁnding probabilities have substantial predictive power.

As discussed, the lower bound argument requires the conditional expectations of the respective elicitations to be equal

and the elicitations, conditional on job ﬁnding, not to be negatively correlated. Hence, we converted the elicited 12-

month probability (

i,d

) into a 3-month probability (Z

i,d

), assuming the latter is constant over the spell of unemployment:

i,d

= 1 − (1 −

i,d

)

Table 3: Non-parametric Lower Bounds for the Variance

of 3-Month Job Finding Probabilities (SCE)

Lower bound based on: Value S.e.

... 3-month elicitations only 0.032 (0.009)

... 3- and 12-month elicitations 0.038 (0.010)

... controls only 0.036 (0.009)

... controls and both elicitations 0.054 (0.010)

Notes: Standard errors are bootstrapped with 2,000 replications.

3 in Table 2), equals 0.054. To interpret the magnitude of these variances, we compute how much the

implied dynamic selection could contribute to the observed negative duration dependence in job ﬁnding

(see equations (1) and (2)). The decline in the 3-month job ﬁnding rate between months 0-3 and months

4-6 equals 17.0 percentage points. A variance in 3-month job ﬁnding of 0.032 could account for a decline

in the job ﬁnding rate of 8.9 percentage points through selection, which is 52% of the observed decline

of 17.0 percentage points. The higher variance of 0.054 could explain a decline of 15.1 percentage points

through selection or 89% of the total observed decline.

A ﬁrst caveat with these calculations is that we use the full sample to compute the lower bounds in

Table 3, while it is the variance in job ﬁnding conditional on unemployment duration that is relevant for

determining the contribution of selection to the observed negative duration dependence in job ﬁnding.

We fully address this in our statistical model in the next section that parametrizes the relevant hetero-

geneity and dynamics and uses the reduced-form empirical moments for estimation by simulating exact

equivalents in the model. Our reduced-form evidence already indicates that beliefs become somewhat

less predictive when controlling for unemployment duration, though it remains highly predictive for the

short-term unemployed (see columns 4 in Table 2 for the SCE). Indeed, in the SCE, when residualizing

the beliefs, taking out the variation across durations, the lower bound variance becomes smaller (0.03),

but could still account for half of the decline in the observed job ﬁnding rate at the beginning of the

unemployment spell. When restricting instead to the short-term unemployed (see Appendix Table D4),

the lower bound variance becomes larger again (0.06) and could in fact account for all of the decline,

leaving no role for true duration dependence.

A second caveat is that some of the heterogeneity in job ﬁnding identiﬁed by our approach may

be transitory and thus does not contribute to selection over the unemployment spell. To assess this

further, we use the elicited beliefs in the SCE to infer the persistence in individual job ﬁnding rates,

by restricting the sample to those who remained unemployed for at least 4 months and relating actual

job ﬁnding to beliefs lagged by 3 months. The results in Panel B of Table 2 show that in this sample

Appendix Table D5 reports the non-parametric bounds in the KM survey, which are substantially lower than in the

SCE, but refer to the 1-month probability rather than to the 3-month probability. The lower bound on the variance

based on the 1-month elicitation in the KM survey can account for an observed decline in the monthly job ﬁnding rate of

0.45 percentage points per month, or 3.3 percent per month, when expressed as a percent of the job ﬁnding rate for the

short-term unemployed. Computed over a period of 3 months, this is about two thirds of the relative decline estimated

based on the 3-month elicitation in the SCE.

As illustrated in Figure 5a in the statistical model, the variance of job ﬁnding probabilities is likely to be declining

with unemployment duration, which is consistent with the observation in both datasets that the covariance between beliefs

and job ﬁnding is lower for the long-term unemployed.

the coeﬃcient on the reported beliefs are generally smaller, but the reported beliefs retain a strong

predictive power beyond the horizon of the 3-month question administered in the SCE. We ﬁnd that

for this sample of job seekers the relative diﬀerence in the covariance between the job ﬁnding and the

contemporaneous and lagged beliefs, is only 11%. This suggests that most of the variation in job seekers’

job ﬁnding prospects, captured by the 3-month horizon question, is driven by persistent diﬀerences.

Again, the statistical model in the next section is used to properly account for this issue.

Overall, our reduced-form results suggest that heterogeneity in job ﬁnding is important for explaining

the observed duration dependence in job ﬁnding.

3.4 Biases in Beliefs

We now document how beliefs and actual job ﬁnding diﬀer along the unemployment spell. In contrast

with job seekers’ true job ﬁnding, we can also study the within-individual change in their beliefs over the

unemployment spell. As discussed above, it is possible to identify a lower bound on the heterogeneity

in job ﬁnding from elicitations in beliefs without reference to potential biases in beliefs. However, if one

wants to go beyond the lower bound and identify the level of the variance in job ﬁnding, one needs to

identify the nature of these biases in the ﬁrst place.

Average Bias by Duration While we cannot compare the actual and perceived job ﬁnding

probabilities at the individual level, we can compare averages at the group level. Overall, the results

indicate an average optimistic bias that is largely driven by the long-term unemployed. At the three-

month horizon in the SCE, we ﬁnd an average optimistic bias (8 pp) indicating that job seekers perceive

their chances to be 20 percent higher than they are. Figure 3 compares the averages in the SCE by

unemployment duration. The ﬁgure conﬁrms that the observed duration dependence in actual job

ﬁnding rates is strongly negative. The perceived job ﬁnding rates are also decreasing, but at a slower

rate. As a result, the bias is increasing with unemployment duration, resulting in a clear bias towards

over-optimism for the long-term unemployed. In the KM survey, the overall bias is substantially larger

in the KM survey, but we ﬁnd similar results by duration of unemployment.

Using the patterns of perceived and realized job ﬁnding, one can inform the model of beliefs in

section 3.1. Based on equation (7), we compute an estimate of b

for two diﬀerent duration intervals

in the SCE. We ﬁnd estimates of b

of 0.512 (0-3 vs. 4-6 months) and 0.556 (4-6 vs. 7+ months),

suggesting that jobseekers’ perceptions under-respond to their true job ﬁnding probability. Using an

average of 0.534 of the two estimates and an estimate of 0.054 of the covariance between the 3-month

eliciation and realized job ﬁnding, cov(Z

i,d

, F

i,d

), we can leverage equation (6), to obtain an estimate for

the variance in job ﬁnding probabilities of var(T

i,d

) = 0.101. Benchmarking this as before, such variance

Combining equations (6) and (9), one can solve for var(τ) as a function of b

and data moments. Using our estimate

of b

= 0.534 from further below and the values for the moments cov

d+1

i,d+1

, F

i,d+1

) = 0.0308, cov

d+1

i,d

, F

i,d+1

) =

0.0289 and E

i,d

) = 0.491, we get an estimate of var(τ ) = 0.0045, which corresponds to 8% of the total variance. The

covariance moments are computed in the sample used for the regressions in Panel B of Table 2. Note that this derivation is

done for a stylized model that ignores true duration dependence in job ﬁnding. Moreover, we compute again all moments

over all durations, whereas the equations are exact only for a given duration d.

Table D6 in the Appendix contains underlying numbers for both the SCE and the KM survey. Note that we restrict

the sample for this comparison to interviews that were followed by 3 consecutive monthly interviews (SCE) or 4 consecutive

weekly interviews (KM survey).

Figure 3: Perceived vs. Realized Job Finding by Duration of Unemployment (SCE)

.2 .3 .4 .5 .6 .7

Prob(Find Job in 3 Months)

0−3 Months 4−6 Months 7−12 Months 13 Months +

Length of Unemployment Spell

Perceived Job Finding Rate Realized Job Finding Rate

would account for a decline of 28 percentage points over the ﬁrst three months of the unemployment

spell through selection, which more than fully accounts for the observed decline. However, the relevant

moments in the decomposition equation (1) condition on duration and account for the persistence in

job ﬁnding, which reduces the contribution of dynamic selection to the decline in job ﬁnding.

Job Finding Beliefs by Duration The panel dimension of the surveys provides a unique oppor-

tunity to assess the duration dependence in perceived job ﬁnding. Table 4 shows the results of linear

regressions of the elicited beliefs on duration of unemployment, measured in months. The ﬁrst column

shows the results for the sample restricted to the ﬁrst observation for each unemployment spell, the sec-

ond and third column shows the results for the pooled cross-section of all observations available during

an unemployment spell. The results of all three columns conﬁrm the negative eﬀect of unemployment

duration on the elicited beliefs in the cross-section. However, it is again unclear whether these patterns

are due to selection – those with high perceived probabilities ﬁnd jobs faster and leave the sample – or

due to changes in the beliefs at the individual level.

To adjust for selection, we exploit the repeated survey questions answered by the same job seekers

over the unemployment spell. Column 4 in Table 4 includes in the regression spell or person ﬁxed

eﬀects. Note that in the SCE, some individuals have multiple unemployment spells and thus we control

for each spell separately, whereas in the KM survey we only observe one spell per person.

In the SCE,

the estimated eﬀect of duration turns from negative to positive when including spell ﬁxed eﬀects with

the job ﬁnding probability at the 3-month horizon increasing by 0.2 (0.6) percentage points per month,

though the coeﬃcient is not statistically signiﬁcantly diﬀerent from zero. Panel B in Table 4 shows

Using the residualized covariance, which takes out all variation across durations, we obtain an estimate for the variance

of 0.067 (see Appendix Table D4). The implied decline in job ﬁnding is just above the observed decline (18.6 p.p.).

Consistent with Elsby et al. [2015], we treat transitions from unemployment to out of the labor force and back to

unemployment as part of the same unemployment spell.

Table 4: Linear Regressions of Elicitations on Unemployment Duration (SCE and KM)

Panel A. SCE, Dependent Variable:

Elicited 3-Month Probability (1) (2) (3) (4)

Unemployment Duration, in Months -0.0057*** -0.0050*** -0.0043*** 0.0022

(0.0007) (0.0007) (0.0006) (0.0064)

Demographic Controls x

Spell Fixed Eﬀects x

Observations 882 2,281 2,281 2,281

0.110 0.090 0.155 0.824

Panel B. KM Survey, Dependent Variable:

Elicited 1-Month Probability (1) (2) (3) (4)

Unemployment Duration, in Months -0.0012 -0.0020 -0.0025* 0.0216**

(0.0020) (0.0021) (0.0014) (0.0077)

Demographic Controls x

Individual Fixed Eﬀects x

Observations 2,278 4,435 4,318 4,435

0.001 0.003 0.119 0.902

Notes: Survey weights are used in all regressions. All samples are restricted to unemployed workers, ages

20-65. The demographic controls are the same as in Table 2. Column 1 shows the results for a sample that

is for each individual restricted to the ﬁrst observation in the survey; column 2 shows the results for the full

sample; column 3 shows the results for the full sample with demographic controls; and column 4 shows the

results for the full sample with spell or individual ﬁxed eﬀects. Robust standard errors are in parentheses

and are clustered at the individual level except for column 4 in Panel A, where they are clustered at the

spell level. Asteriks indicate statistical signiﬁcance at the *0.1, **0.05 and ***0.01 level.

that this pattern is much stronger for the KM survey, where an additional month spent unemployed

signiﬁcantly increases the perceived job ﬁnding probability by 2.2 (0.8) percentage points per month.

Figure 4 illustrates the diﬀerence between the observed (cross-sectional) duration dependence and

the true (individual-level) duration dependence in the reported beliefs graphically. To increase power

and control for potential cohort eﬀects, the ﬁgure aggregates by time unemployed in survey rather than

showing results by duration of unemployment. The left panel shows how the average of the perceived

job ﬁnding probability is decreasing in time spent unemployed since the ﬁrst interview observed in a

given spell, conditional on still being unemployed.

The right panel in Figure 4 shows the change in

the perceived job ﬁnding probability within individual unemployment spells, again as a function of time

spent unemployed since the ﬁrst interview. The ﬁgures conﬁrm the ﬁndings from the regression. In

the cross-section, the perceived job ﬁnding probability is decreasing in time spent unemployed, but this

decline disappears once we control for selection and look at the within-spell changes only.

In the KM

Note that in an environment where the 1-month horizon probability is increasing, the 3-month horizon probability

may increase by less or more, depending on the initial level of the job ﬁnding probability.

Figure D7 also shows results by unemployment duration for each cohort in the KM survey. There is no evidence of

see-saw patterns or systematic cohort eﬀects in beliefs, as there is for search eﬀort in Krueger and Mueller [2011].

In principle, the patterns of the within-spell changes could be driven by dynamic selection, since the observations later

in the spell require the job seeker to be unemployed for longer. The relationship in column 4 of Table 4, however, remains

positive in both surveys even when we restrict the sample to those with relatively short spells of 6 months or less.

Figure 4: Perceived Job Finding Probabilities by Time since First Interview (SCE and KM)

A. SCE Survey

−.2 −.15 −.1 −.05 0 .05 .1 .15

Prob(Find Job in 3 Months)

0 1 2 3 4 5 6

Time Since First Interview (in Months)

Within and Across Spell Changes

−.2 −.15 −.1 −.05 0 .05 .1 .15

Prob(Find Job in 3 Months)

0 1 2 3 4 5 6

Time Since First Interview (in Months)

Within Spell Changes Only

B. KM Survey

−.15 −.1 −.05 0 .05 .1 .15

Prob(Find Job in 1 Month)

0 1 2 3 4

Time Since First Interview (in Months)

Within and Across Spell Changes

−.15 −.1 −.05 0 .05 .1 .15

Prob(Find Job in 1 Month)

0 1 2 3 4

Time Since First Interview (in Months)

Within Spell Changes Only

survey, job seekers even report higher job ﬁnding rates as they remain unemployed for longer.

Robustness We extensively probe the robustness of the ﬁnding that beliefs are not revised down-

ward and also evaluate potential forces that may underlie the (weakly) increasing beliefs about job

ﬁnding probabilities. We report here only a brief summary and refer to the Appendix D.3 for details.

First, we ﬁnd that the results in column 4 of Table 4 are similar for other measures of perceived job

ﬁnding, such as expected remaining duration in the KM survey and the 12-month probability in the

SCE survey. The results are also robust to excluding answers of 50 or 100 percent, or to excluding

individuals who ﬁnd a job within the next month. Moreover, we ﬁnd that our results are robust to

controlling for changes in aggregate labor market conditions or aggregate time ﬁxed eﬀects during our

sample period. Finally, we ﬁnd that our estimates are unlikely to be biased due to sample selection

based on individuals dropping out of the labor force: In the SCE, those unemployment spells with a

transition into out of the labor force do not exhibit any signiﬁcant decline of beliefs over the spell of

unemployment. Moreover, in the KM survey, the belief questions were administered independent of

search eﬀort and thus including those dropping out of the labor force. We conclude that our ﬁnding

that beliefs are not revised downward is very robust.

Discussion Our analysis of job seekers’ beliefs corroborates earlier evidence that job seekers’ are

too optimistic about their re-employment prospects (Spinnewijn [2015], Arni [2017], Conlon et al. [2018],

Drahs et al. [2018]). Importantly, we ﬁnd that the over-optimistic bias is particularly strong among

long-term unemployed workers, implying that beliefs are under-responsive to diﬀerences in job ﬁnding,

across job seekers and/or along the unemployment spell. As discussed, this under-reaction is important

for inferring the heterogeneity and duration dependence in true job ﬁnding using job seekers’ beliefs.

We develop this insight further in Section 4. The under-reaction in beliefs is also important if it entails

that job seekers do not adjust their search strategy to the speciﬁc employment prospects they face. We

will study this issue further in Section 5.

The empirical ﬁnding that job seekers, if anything, update their perceived job ﬁnding probability

upward over the unemployment spell is surprising. However, our reduced-form evidence already suggests

that there is limited scope for negative true duration dependence in the actual job ﬁnding probabilities.

This suggests that various mechanisms underlying true duration dependence like human capital depre-

ciation (see Acemoglu [1995] and Ljungqvist and Sargent [1998]), stock-ﬂow sampling (see Coles and

Smith [1998]) and employer-screening based on unemployment duration (see Lockwood [1991]) are em-

pirically not important or, at least, not perceived as such. However, even with substantial variation in

employment prospects across job seekers (rather than over the spell), we would expect that job seekers

learn from the lack of success and update their beliefs downwards the longer they are unemployed. The

lack of updating that we ﬁnd thus remains surprising, but seems consistent with Krueger and Mueller

[2016] who show – using data from the KM survey – that reservation wages are nearly constant over the

spell. Their ﬁnding, however, is not suﬃcient to infer a lack of updating in beliefs about job ﬁnding, as

other inputs into the probability of job ﬁnding such as search eﬀort, the oﬀer probability or the wage

oﬀer distribution may change over the unemployment spell, too.

While we do not attempt to micro-found these biases, it is worth noting that a number of behavioral

models can explain the observed optimistic biases in beliefs, why biases become more important or

why there may be lack of learning over the spell. For example, regarding the dynamics, job seekers

may be subject to the gambler’s fallacy. This is an application of the law of small numbers with

unsuccessful job seekers inferring from a series of bad draws (as their unemployment spell lasts) that

the probability of a good draw increases (Rabin and Vayanos [2010]).

Job seekers may also have

motivated beliefs, managing their expectations to maintain a positive self-image or to get positive

Providing direct evidence that biases in beliefs distort behavior is challenging. In Section 5, we study this through the

lens of a model that we calibrate to match true and perceived job ﬁnding in our data. In Appendix D.3.3, we discuss some

further evidence on how perceptions correlate with reported search eﬀorts and reservations wages.

In fact, if job seekers learned about the wage oﬀer distribution and revised their reservation wage downward as in

Burdett and Vishwanath [1988], this type of learning would provide a reason for positive true duration dependence in

job ﬁnding. However, the perceived wage oﬀer probabilities and (expected) search eﬀort may change as well. We study

the relation between wage oﬀer probability, reservation wages and job ﬁnding in a McCall model of job search in Section

5. Regarding search eﬀorts, the evidence in Krueger and Mueller [2011], which documents patterns of search behavior in

the KM survey, suggests a decline in search activity over the unemployment spell at the individual level, but two recent

papers ﬁnd that search activity is constant or even increasing, at least prior to the exhaustion of unemployment beneﬁts

(see Marinescu and Skandalis [2019] and DellaVigna et al. [2020]).

Note that the same application of the law of small numbers may induce job seekers to become overly discouraged as

they over-infer from a series of bad draws how employable they are (Rabin and Vayanos [2010]).

value from optimistic expectation, potentially accounting for the implied distortions in their search

behavior (e.g., Brunnermeier and Parker [2005] and Koszegi [2006]). The argument would be that

lasting unemployment causes hardship and increases the demand for optimistic expectations. We cannot

provide directs test of either theory, but the ﬁndings that the perceptions of long-term unemployed are

more biased and less predictive can be consistent with these behavioral models.

In a similar spirit,

we provide further evidence in Appendix D.3.3 that the perceptions of unemployed individuals are not

responsive to macro-economic indicators (while the perceptions of employed workers are).

4 Statistical Framework

This section describes a statistical model that allows us to use the reduced-form moments from our

empirical analysis to jointly identify (1) the extent of heterogeneity in job ﬁnding rates, (2) the dynamics

of job ﬁnding rates over the spell of unemployment and (3) the biases in perceived job ﬁnding rates

as well as their evolution over the spell of unemployment. The model draws heavily on the conceptual

framework developed in Section 3.1, but fully speciﬁes the heterogeneity across job seekers and the

dynamics over the unemployment spell, which allows to infer the parameters of interest with exact

equivalents of the moments in the data.

4.1 Model Setup

We introduce notation T

i,d

to denote the probability of ﬁnding a job in the next x months for individual

i with unemployment duration d. The monthly job ﬁnding probability equals T

i,d

= T

i,d

and T

i,d

+(1−T

i,d

i,d+1

+(1 − T

i,d

)(1− T

i,d+1

i,d+2

is the probability of ﬁnding a job in the next 3 months.

i,d

is the elicitation of the corresponding perceived probability. F

i,d

describes the actual job ﬁnding.

We assume that the monthly job ﬁnding rate of individual i at duration d satisﬁes

i,d

= (1 − θ)

+ τ

i,d

) ∈ [0, 1], (10)

where θ is a scalar that determines the depreciation in job ﬁnding over the spell of unemployment (or

appreciation when negative), T

is the persistent component of the job ﬁnding rate that is common

across durations and τ

i,d

is a transitory change in job ﬁnding rate at duration d with E(τ

i,d

) = 0.

and τ

i,d

are distributed according to some distributions g

and g

respectively.

We continue to impose the same linear structure on the relationship between job ﬁnding rates and

elicited beliefs at the 3-month horizon:

i,d

= b

+ b

i,d

+ ε

i,d

∈ [0, 1]. (11)

As stated before, we cannot separate the role of biases in perceptions vs. elicitations underlying the

bias parameters and error terms. The variable ε

i,d

captures random error in the elicited perceptions,

which can be driven by either noise in the beliefs themselves or by noise in the elicitation of the beliefs.

This ﬁnding is also supported by the recent experimental evidence in Altmann et al. [2018] showing the diﬀerential

impact of information on workers by predicted time spent unemployed.

In our baseline model, we assume that the conditional mean of the error term is independent of T

i,d

E(ε

i,d

) = 0, but non-classical measurement could still be captured through the slope parameter

. While this separation is not needed to identify the heterogeneity in job ﬁnding, we do gauge the

robustness of our estimates to diﬀerent distributional assumptions on the error term, including the

mean-independence assumption.

4.2 Identiﬁcation

A key advantage of the statistical model is that the parameters of interest are estimated using exact

equivalents of the moments in data. To be more precise, in the conceptual framework, we derived

relationships between data moments and parameters for a given duration d, but due to limited sample

size, it is not possible to compute these moments in our data for each month of the unemployment spell.

Instead, the data moments are computed over intervals of duration (or the entire unemployment spell)

and thus subject to selection and duration dependence within these intervals. The statistical model

develops an account of the data that fully addresses these issues in an internally consistent manner.

For the identiﬁcation of the parameters in the statistical model, we build on the identiﬁcation

arguments presented in Section 4 and develop them formally in a stylized two-period version in Appendix

Section E.3. To further validate the identiﬁcation arguments in the full model, we show how the

estimated parameters change with the values of the targeted moments and how the model’s ﬁt changes

when restricting the key features of the model, in particular regarding the heterogeneity and duration

dependence of both actual and perceived job ﬁnding rates. We also show extensively how the model

estimates are robust to diﬀerent functional forms, distributional assumptions and incidental parameters.

As discussed in Section 3, we face two interdependent identiﬁcation challenges. The ﬁrst is to

disentangle the heterogeneity and true duration dependence in job ﬁnding rates that underlies the

observed duration dependence. The second is to identify how beliefs change with variation in job

ﬁnding rates. Given our assumptions on the geometric depreciation and the permanent vs. transitory

shocks, we can rewrite the earlier decomposition of the observed job ﬁnding in equation (1) as

d+1

i,d+1

)

i,d

)

= (1 − θ)



1 −

var

)

i,d

)(1 − E

i,d

))



, (12)

where the subindex again denotes the duration at which the job seekers are sampled to evaluate the

corresponding moment. The evolution of the observed job ﬁnding depends on the depreciation in job

ﬁnding and the variance in the persistent component only.

In the absence of transitory shocks and biases in beliefs, we could simply identify the relevant

variance in job ﬁnding through the covariance between perceived and actual job ﬁnding, and equation

(12) would give the depreciation of job ﬁnding. In the presence of transitory shocks, the covariance

between perceived and actual job ﬁnding is no longer suﬃcient. As discussed before in Section 3.1,

transitory shocks generate more contemporaneous covariance of elicitations and job ﬁnding rates, but

do not generate more covariance between elicitations and the job ﬁnding one period ahead. Hence, we

can separately identify the variance in transitory shocks through the diﬀerence in covariances, since the

contemporaneous covariance depends on both persistent and temporary components of T

i,d

, whereas the

one period ahead covariance only depends on the persistent component. We develop this identiﬁcation

argument formally in Appendix Section E.3 and show that the ahead covariance is a monotone function

of the dispersion in transitory shocks.

Finally, the presence of systematic biases in beliefs also changes the covariance between perceived

and actual job ﬁnding relative to the variance in true job ﬁnding. If job seekers under-react to variation

in job ﬁnding (b

< 1), the covariance between perceived and actual job ﬁnding underestimates the

variance in true job ﬁnding. As already discussed in Section 3.1, we identify this potential compression

by leveraging the variation in job ﬁnding rates across durations.

By jointly exploiting the elicited beliefs and the structure on the relationship between elicited beliefs

and job ﬁnding embedded in a dynamic framework, the statistical model goes beyond earlier work

identifying the role of heterogeneity through the dynamic selection on observables only. Other prior

work has tried instead to use indirect evidence on true duration dependence in job ﬁnding (e.g., Kroft

et al. [2013]) or to infer heterogeneity in multiple-spell data. Compared to the approach that uses

data on multiple unemployment spells as a source of identiﬁcation (see, e.g., Honor´e [1993] and Alvarez

et al. [2016]), our approach is made possible by the availability of elicitations and realizations for the

same individual in the same unemployment spell and thus does not rely on multiple spells for the same

individual.

As mentioned before, our identiﬁcation strategy abstracts from search decisions underlying

the job ﬁnding rates and how they are aﬀected by job seekers’ beliefs, which we study in Section 5.

4.3 Distributional and Functional Form Assumptions

We propose to parametrize our model relatively parsimoniously. Baseline job ﬁnding rates, T

, follow the

Beta distribution with shape parameters α and β. The Beta distribution is deﬁned over the interval [0, 1]

and is quite ﬂexible in terms of its shape.

The transitory component of the job ﬁnding rate, τ

i,d

, follows

a uniform distribution subject to the bounds [−T

(1−θ)

− T

], and with masspoint(s) at the bounds of

this interval such that E(τ

i,d

) = 0 for all T

Random error in perceptions or elicitations, ε

i,d

, follows

a uniform distribution on the interval [−σ

, σ

] subject to the bounds [−b

− b

i,d

, 1 − b

− b

i,d

], and

with masspoint(s) at the bounds of this interval such that E(ε

i,d

) = 0 for all T

i,d

As discussed

In particular, Appendix Section E.3 starts with a formal proof of identiﬁcation, showing that in a two-period version of

the statistical model, where σ

= 0, all other parameters are an explicit function of moments with an empirical counterpart

in the data. We then develop the identiﬁcation arguments in a two-period model with σ

> 0. While we cannot solve

explicitly the model for these parameters, we complement the argument by showing that a monotone relationship exists

between σ

and the one period ahead covariance. We then also prove the identiﬁcation of an extra longitudinal belief

parameter

θ 6= θ discussed in Section 4.5.

Relying on multiple unemployment spells may skew the estimation results since a sample of individuals with multiple

(frequent) spells may not be entirely representative of the population. In addition, identiﬁcation through multiple un-

employment spells only identiﬁes the extent of heterogeneity that is ﬁxed between unemployment spells, which may be

years apart, whereas our approach also identiﬁes the heterogeneity that is ﬁxed within a spell but varies across spells (e.g.,

changes in marital status, savings or unemployment insurance eligibility may aﬀect the job ﬁnding probability).

Note that for our exercise here it is important that there is a continuum of job ﬁnding probabilities or at least a large

number. Assuming two types for the job ﬁnding probabilities and estimating their relative mass is not an attractive option,

because our observed elicitations are reported on the interval between 0 and 1. A model with only two underlying job

ﬁnding rates thus would not perform well in matching the distribution of these elicitations.

More precisely, τ|T

follows a uniform distribution on the interval [max(−σ

, −T

), min(σ

(1−θ)

− T

)], with a mass-

point at the bound of this interval if a bound is binding, such that E(τ

i,d

) = 0 for all T

More precisely, ε|

i,d

follows a uniform distribution on the interval [max(−σ

, −b

− b

i,d

), min(σ

, 1 − b

− b

i,d

)],

with a masspoint at the bound of this interval if a bound is binding, such that E(ε

i,d

) = 0 for all T

i,d

before, the identiﬁcation of heterogeneity does not rely on particular distribution functions for T

, τ

i,d

and ε

i,d

, and we test the sensitivity of our results to alternative distributional assumptions. Finally, job

ﬁnding rates depreciate at a geometric rate over the unemployment spell in our baseline speciﬁcation,

with θ

= (1 − θ)

. In an alternative speciﬁcation, we assume a piece-wise linear speciﬁcation for the

depreciation where θ

= 1 − dθ if d ≤ 12 and θ

= 1 − 12θ otherwise.

4.4 Targeted Moments and Estimated Parameters

In our data, we observe the means of realized and perceived job ﬁnding rates at diﬀerent durations,

as well as their covariance and the variance in perceived job ﬁnding rates. As already noted above,

we focus on the moments from the SCE data, because due to attrition we have less conﬁdence in the

moments in the KM data that relate to the co-variance of perceptions and actual job ﬁnding. In the

estimation of our model, we target the following moments in the SCE data:

1. The mean of the 3-month job ﬁnding rate at durations 0-3 months, 4-6 months and 7+ months:

= 0.642, m

= 0.472 and m

= 0.256.

2. The mean of elicitations of the percent chance of ﬁnding a job in the next 3 months at durations

0-3 months, 4-6 months and 7+ months: m

= 0.616, m

= 0.529 and m

= 0.409.

3. The variance of elicitations of the percent chance of ﬁnding a job in the next 3 months: s

= 0.093.

4. The covariance of the 3-month job ﬁnding rate and elicitations: c

F,Z

= 0.054.

5. The covariance of the 3-month job ﬁnding rate (3-month ahead) and elicitations: c

= 0.025.

6. The monthly change in 3-month elicitations as measured by the coeﬃcient on duration in the

regressions of perceived job ﬁnding rates on unemployment duration, controlling for individual

ﬁxed eﬀects: m

= 0.008.

This implies that we have a total of 10 moments that we try to match. With two parameter

distributions, there are 7 parameters to estimate (α, β, σ

, θ, b

, b

, σ

) and thus the model is over-

identiﬁed. Following our earlier discussion, the parameters α and β and θ are mainly identiﬁed through

the mean of job ﬁnding rates at durations 0-3, 4-6 and 7 and higher, and the covariance of elicitations

and job ﬁnding rates, whereas the parameter σ

is mainly identiﬁed through the diﬀerences in the

covariances c

and c

d+3

. The parameters b

and b

are mainly identiﬁed through the mean of

the deviations of elicitations from actual job ﬁnding rates at durations 0-3, 4-6 and 7 and higher. While

is mainly identiﬁed by the average bias between elicitations and job ﬁnding, b

is identiﬁed by the

gradient of this bias by duration.

The parameter σ

is identiﬁed through the variance of elicitations.

Note that we assume that the maximum duration for each job seeker is two years, but we relax this assumptions in a

set of robustness checks, where we allow for a maximum duration of up to ﬁve years.

Note that this is slightly higher than the value reported earlier in the paper, because the sample here is restricted to

the sample where we have at least 3 consecutive interviews.

Note that the gradient of the perceived job ﬁnding depends on the covariance of elicitations and job ﬁnding rates,

determining the dynamic selection, and on the mean of monthly innovations in elicitations, determining the true-duration

dependence in beliefs. As shown in Appendix Section E.3, in a stylized two-period model, the mean of monthly innovations

provides no additional identifying variation.

Table 5: Estimation Results

A. Parameter Estimates

Parameter/Moment Explanation Estimate (S.e.)

E(T

) Mean of distribution of permanent component, T

0.403 (0.057)

V ar(T

) Variance of distribution of permanent component, T

0.045 (0.022)

Dispersion in transitory component of job ﬁnding rate, τ

i,d

0.334 (0.213)

θ Depreciation in job ﬁnding 0.017 (0.047)

Intercept bias 0.265 (0.045)

Slope bias 0.550 (0.101)

Dispersion in elicitation errors, ε

i,d

0.453 (0.020)

B. Additional Moments

Moment Explanation Estimate (S.e.)

V ar

i,0

) Variance in 3-month job ﬁnding rates at d = 0 0.076 (0.014)

V ar

) Variance in permanent component of T

i,0

at d = 0 0.057 (0.023)

V ar

i,0

) Variance in 3-month elicitations at d = 0 0.081 (0.005)

TD 12-month decline in job ﬁnding rates (total) 0.459 (0.061)

LD 12-month decline in job ﬁnding rates (longitudinal) 0.070 (0.171)

1 −

T D

Share explained by selection (in %) 84.71 (36.37)

Notes: The total decline (TD) in 3-month job ﬁnding is deﬁned as E

i,0

) − E

i,12

). The longitudinal decline (LD) in

3-month job ﬁnding is deﬁned as E

i,0

− T

i,12

) .

4.5 Estimation and Results

We use the method of simulated moments to estimate the model parameters and minimize the sum of

squares of the deviation of the empirical moments from the moments simulated from the model. We use

the inverse of the bootstrapped covariance matrix of the empirical moments as weighting matrix, where

the bootstrapped variances were computed with 2,000 repetitions. Standard errors were obtained by

estimating the model on 200 bootstrap samples and taking the standard deviation of estimates across the

200 samples. As shown in the Appendix Table E1, our model matches the 10 moments very well, even

though it is over-identiﬁed. There is almost no discernible diﬀerence for the monthly innovations and the

variance and co-variance moments, which all carry a large weight in the estimation. The weighted sum

of squared residuals is 0.47. Table 5 shows the parameter estimates and selected moments of interest.

The estimation delivers two important sets of results, which conﬁrm the reduced-form ﬁndings.

Heterogeneity vs. Depreciation The estimation reveals substantial heterogeneity in the job

ﬁnding rates and conﬁrms that the negative duration dependence in job ﬁnding rates is predominantly

driven through dynamic selection. Figure 5a shows that the model estimates imply a large dispersion

of persistent types, T

, at the start of the unemployment spells. The estimated Beta distribution

is unimodal and slightly skewed to the left. As the high-T

types ﬁnd jobs, the distribution of the

persistent component T

among survivors becomes more skewed to the left with a substantially lower

average overall. These changes are more extreme one year into the unemployment spell. Figure 5b

Figure 5: Heterogeneity and Duration Dependence in the Estimated Model

(a) Distribution of T

among Survivors

0 0.2 0.4 0.6 0.8 1

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Density

At duration d=0

At duration d=6

At duration d=12

(b) Duration Dependence in Job Finding

0 2 4 6 8 10 12

Duration of Unemployment, in Months

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

3-Month Job Finding Probability

Observed Duration Dependence in Job Finding Rates

True Duration Dependence in Job Finding Rates

shows that the large amount of heterogeneity in job ﬁnding rates accounts for most of the observed

duration dependence in job ﬁnding rates. The ﬁgure compares simulations of the baseline model (solid

line), with a model where all heterogeneity is eliminated and the only source of duration dependence

in job ﬁnding rates is θ 6= 0 (dashed line). Our model attributes 84.7% (s.e. 36.4%) of the decline in

3-month job ﬁnding rates, which is from 0.70 to 0.24 over the ﬁrst year of unemployment, to selection.

The remainder – a decline of only 7 percentage points – is due to the depreciation of the job ﬁnding

probability over the spell of unemployment. This corresponds to a modest monthly depreciation rate

of 1.7 percent for the 1-month job ﬁnding rate.

To assess the amount of heterogeneity predicted by our model, we can compare it to our reduced-

form estimates in Section 3. The variance of 3-month job ﬁnding probabilities in our model for all

durations is 0.102, which exactly coincides with our earlier calculation using reduced-form estimates for

cov(Z

i,d

, F

i,d

)/b

. The importance of adding structure on the beliefs can be gauged by comparing this

value to our non-parametric lower bound estimates in Section 3.3. We found that the non-parametric

lower bound on the variance in job ﬁnding using the 3-month elicitation alone was 0.032. This corre-

sponds to 31 percent of the estimated variance in 3-month job ﬁnding probabilities in our model. We

tightened this bound further by including both the 3-month and the 12-month elicitation as well as the

observables used before to obtain a variance of predicted values of 0.054, which now corresponds to 53

percent of the estimated variance. The total variance of 3-month job ﬁnding probabilities in our model

is somewhat larger than the variance of 0.076 that is reported in Table 5, where we restrict the sample

to newly unemployed workers. Finally, a signiﬁcant share of this variation (25%) is driven by transitory

shocks, which do not contribute to dynamic selection. Overall, the diﬀerences in job ﬁnding are thus

We note that this relative role is relatively imprecisely estimated, but this is not too surprising, given its residual

nature and thus dependence on all other parameters in the estimation. Nevertheless, we strongly reject the case that

attributes all of the observed duration dependence to depreciation at the individual level.

estimated to be highly persistent, but somewhat less than suggested by the reduced-form evidence.

Biases in Beliefs The estimation also conﬁrms the importance of biases in beliefs. Perceptions

substantially under-react to the variation in job ﬁnding across workers. On average, workers who face a

10 percent higher job ﬁnding probability on average perceive their chances as only 5.50 percent higher

(s.e. 1.01). The slope bias is thus large and signiﬁcant. Since the average wedge between actual and

perceived job ﬁnding is small, low-T

types are estimated to be over-optimistic and conversely high-T

types are over-pessimistic. Our baseline model does not allow for the variation in job ﬁnding rates to

be perceived diﬀerently across and within job seekers. This implies that job seekers perceive only about

half of the 7 percentage point decline of job ﬁnding over the ﬁrst 12 months of their spell.

We probe the robustness of our results to the latter assumption, and extend our model to allow for

beliefs to be perceived diﬀerently across and within job seekers. Speciﬁcally, we assume a linear model

for the elicitations of the perceived 3-month job ﬁnding rate:

i,d

= b

+ b

i,d

+ ε

i,d

∈ [0, 1], (13)

where we deﬁne the variable

i,d

, in analogy to equation (10) above,

i,d

= (1 −

θ)

+ τ

i,d

) ∈ [0, 1]. (14)

The variable

i,d

captures the duration dependence in perceptions through the parameter

θ.

This

dynamic parameter depends on the perceived depreciation, but also any learning from unsuccessful job

search and is expressed at the monthly frequency so that it directly corresponds to the parameter that

controls the true duration dependence, θ. For example, while b

< 1 implies that perceptions under-

react to variation in job ﬁnding across individuals,

θ < θ implies that perceptions change even less with

variation in job ﬁnding over the spell.

We can identify any additional duration dependence in beliefs that is separate from duration de-

pendence in job ﬁnding (i.e.,

θ 6= θ) using the variances of perceived job ﬁnding and the covariances

of actual and perceived job ﬁnding over the spell of unemployment. Intuitively, more depreciation in

perceived job ﬁnding (higher

θ) implies a lower variance of perceived job ﬁnding and a lower covariance

between actual and perceived job ﬁnding at higher durations of unemployment. We again develop this

identiﬁcation argument formally in Appendix Section E.3.

We add the variance of perceived job ﬁnding and the covariance with actual job ﬁnding at diﬀerent

duration intervals as additional moments to estimate the new parameter

θ. Column 14 of Appendix

Table E4 shows the estimation results, which are very similar to the baseline model. The slope coeﬃcient

is almost identical (b

= 0.52) and the duration dependence parameter θ is 0.022, which is small and

This is higher than in our back-of-the-envelope calculation in footnote 3.3, which did not condition on a given duration

d and ignored any potential true duration dependence in job ﬁnding.

Note that

i,d

+ (1 −

i,d

)

i,d+1

+ (1 −

i,d

)(1 −

i,d+1

)

i,d+2

Appendix Section E.3 starts with a formal proof of identiﬁcation, showing that in a two-period version of the statistical

model, where σ

= 0 and

θ 6= θ, all parameters are an explicit function of moments with an empirical counterpart in the

data. We then develop the identiﬁcation arguments in the full model. While we can no longer solve explicitly for these

parameters, we show that a monotone relationship exists between

θ and both the variance of perceived job ﬁnding for the

long-term unemployed as well as the covariance with actual job ﬁnding for the long-term unemployed.

very close to the 0.017 in the baseline model. The corresponding beliefs parameter

θ is slightly larger

at 0.037, but note that the change in perceptions over the unemployment spell depends on both the

parameter

θ as well as b

. More precisely, while

θ is slightly larger than θ and thus

i,d

declines more

over the spell than T

i,d

, to get to the change in Z

i,d

, the change in

i,d

is multiplied by b

= 0.52. As

shown in Table E4, the extended model predicts a decline of actual job ﬁnding at the individual level

of 8.9 percentage points over the ﬁrst 12 months of the unemployment spell, whereas the decline in

perceived job ﬁnding equals 8.2 percentage points. The fact that the perceived and actual job ﬁnding

decline at similar and modest rates over the spell, indicates that there is limited scope for learning

from remaining unemployed.

We note that the fact that perceptions decline slightly at the individual

level is still consistent with our positive within-spell estimates in the empirical section because of the

presence of mean reversion in transitory job ﬁnding. We also note, not surprisingly, that the ﬁt of the

restricted model in column 15 where

θ = θ is close to the ﬁt of the unrestricted version in column 14.

4.6 Robustness

We study the robustness of our results when using alternative speciﬁcations, alternative moments, and

alternative functional forms and distributions.

We have aimed to parametrize our model as parsimoniously as possible. To illustrate this, we

estimate a number of versions of the model where we restrict parameter choices as reported in Table

6 (see also the Appendix Table E2, which reports all the estimated parameters). Regarding the actual

job ﬁnding rates, we ﬁrst estimate a version of the model where we do not allow for any depreciation

in job ﬁnding rates, θ = 0 (column 2). Unsurprisingly, this model version ﬁts the data nearly as well

as the baseline. In contrast, when we estimate a version of the model where we do not allow for any

heterogeneity in T

i,d

, the model ﬁts the data very poorly (column 3). The two versions jointly underline

the relative importance of heterogeneity relative to true duration dependence to explain the empirical

moments. We also estimate a version of the model, where we set only σ

= 0, i.e., we do not allow for

any transitory changes in job ﬁnding. As shown in column (4) of Appendix Table E2, this speciﬁcation

has diﬃculty in matching both c

and c

d+3

. The version without transitory shocks implies a

much larger extent of heterogeneity in T

and, as a result, an appreciation of the job ﬁnding rates over

the unemployment spell (θ < 0). Given our estimation procedure leveraging elicitations to learn about

heterogeneity in types, it proves to be important to allow for transitory heterogeneity.

Regarding the perceived job ﬁnding rates, we estimate a version of the model where we do not allow

for any under-response to diﬀerences in job ﬁnding (column 5 with b

= 1). The ﬁt gets substantially

worse, indicating the importance of allowing for the slope bias. Very similar results are obtained when

adding also the restriction that the intercept bias equals zero (column 6 in Table E2 with b

= 0).

We also assess the estimated heterogeneity in our statistical model using the variation in job ﬁnding

that is not predictable based on observable characteristics. To this purpose, we estimate the model on

a set of moments obtained from the residuals of regressions of the 3-month belief question and of the

This is also illustrated in Appendix Figure E2, which shows the diﬀerence in actual and perceived job ﬁnding by duration

of unemployment in the estimated extended model. It shows that at the individual level, there is almost no change in the

bias by duration of unemployment. The ﬁgure also implies that the optimistic bias of the long term unemployed is almost

entirely driven by the dynamic selection of over-optimistic individuals into long-term unemployment.

Table 6: Selected Moments and Model Fit for Restricted Versions of the Model

(1) (2) (3) (4) (5) (6)

Moments Baseline θ = 0

No heterog.

= 0 b

= 1

= 0

in T

i,d

= 1

V ar

i,0

) 0.076 0.079 0.000 0.085 0.051 0.047

V ar

) 0.057 0.065 0.000 0.085 0.040 0.033

LD 0.070 0.000 0.430 -0.116 0.054 0.071

1 − LD/T D (in %) 84.71 100.00 0.000 125.67 82.20 77.53

Weighted SSR 0.470 0.695 49.198 2.514 12.251 21.613

Notes: TD stands for total decline in 3-month job ﬁnding, whereas LD stands for longitudinal decline

in 3-month job ﬁnding over the ﬁrst 12 months of the unemployment spell. See Table 5 for details.

3-month job ﬁnding rate on demographic controls (the same set of controls as used for the regressions

reported in Table 2). The estimation results are similar to the baseline, with the role played by true

duration dependence being close to zero.

Of course, the extent of heterogeneity is smaller, as the

eﬀects of observables are parsed out from all moments. We also obtain a comparable estimate for b

(0.559), which suggests that the relationship between observed heterogeneity in job ﬁnding and beliefs

is similar as the relationship between unobserved heterogeneity in job ﬁnding and beliefs.

We ﬁnally probe the robustness of our ﬁndings to alternative assumptions about functional form and

distributions as well as extensions of the model, as reported in Appendix Tables E3 and E4. Without

discussing these estimates in detail, the table shows that the parameter estimates are very stable across

all of the results reported in the table. In particular, our results are robust to assuming that T

follows

the Gamma distribution, and to assuming that ε follows a truncated normal distribution, which no

longer satisﬁes mean-independence of the error term. Our results are also robust to assuming piecewise

linear duration dependence instead of geometric depreciation and extending the horizon of the model to

5 years. We also ﬁnd that our results are robust to fully persistent elicitation errors (i.e., ε

i,d

= ε

) and

bunching at 0, 0.5 and 1 of the elicited beliefs. Furthermore, we report the results for a model, where

a share α of individuals has random elicitations (Z

i,d

= b

+ ε) and a share 1 − α correctly perceives

their job ﬁnding prospects (Z

i,d

= T

i,d

). The model results are very similar to our baseline, and the

value of 1 − α is close to the value of b

, suggesting that b

in our baseline may instead capture the

share of individuals who perceive their job ﬁnding prospects correctly. Finally, our results are very

similar when excluding individuals with recall expectations when generating the data moments, when

restricting the set of moments by using only 0-6 and 7+ months for the time intervals and dropping the

mean of monthly innovations, so that the model is exactly identiﬁed, or when using the inverse of the

bootstrapped variances as weights instead of the full variance-covariance matrix.

5 Structural Model of Job Search with Biased Beliefs

In the statistical model we have estimated the heterogeneity and duration dependence in perceived

and true job ﬁnding, but we have abstracted from the underlying behavior of job seekers and how it

The estimation results and targeted moments are shown in Tables E4 and E5 in the Appendix.

depends on their beliefs. Using our estimates from the statistical model, in this section, we calibrate a

McCall type model, which explicitly relates workers’ job search to their perceived and true job ﬁnding

prospects. We use the calibrated model to quantify the impact of biases in beliefs on unemployment

duration and the incidence of long-term unemployment. We refer to Appendix F for further details on

the model and its calibration.

5.1 Model

We consider a stylized version of McCall’s search model in which agents decide how to set their reserva-

tion wage. We allow for heterogeneity and duration dependence in both the true and perceived arrival

rates of wage oﬀers, denoted by λ

i,d

and

i,d

respectively.

Wage oﬀers are drawn from a known

distribution w ∼ F



, σ



. The perceived value of unemployment for agent i at duration d equals

i,d

= u(b

) +

1 + δ

max

i,d+1

i,d

(w) − U

i,d+1

)] dF (w)},

where δ is the discount rate, u(b

) is the per-period utility ﬂow when unemployed and V

(w) is the

value of being employed at wage w.

A job seeker sets her reservation wage R

i,d

to maximize her

perceived continuation value at any time of the unemployment spell. At this reservation wage, the

agent is indiﬀerent between accepting a job and remaining unemployed, U

i,d

= V (R

i,d

). The resulting

actual and perceived job ﬁnding rate for agent i at time t equal

i,d

= λ

i,d

(1 − F (R

i,d

)) and Z

i,d

(1 − F (R

i,d

)) (15)

respectively, corresponding to the actual and perceived job ﬁnding rates in our statistical model.

We assume two types of job seekers: a high type h and a low type l, with λ

> λ

, and φ denoting the

share of job seekers with a high arrival rate. For both types of job seekers, the arrival rate depreciates

at geometric rate θ. As in the statistical model, we allow for three types of biases in job seekers’ beliefs,

but now applied to the arrival rates. First, job seekers may be subject to a uniform bias B

. That is,

any type’s arrival rate is perceived as

= λ

+ B

. Second, job seekers misperceive their employability

type with probability 1 − B

. That is, P rob(

i,0

|λ

i,0

= λ

) = B

. This is a parsimonious way to

capture that job seekers’ beliefs under-react to their diﬀerences in risk. Finally, job seekers perceive a

depreciation rate of their arrival rates of B

θ.

In order to provide tractable characterizations of the impact on job ﬁnding and on duration dependence, all the action

in terms of heterogeneity, dynamics and biases is introduced through the arrival rates. As we assume that the wage oﬀer

distribution is known, optimal search behavior is represented by a simple reservation price rule (see Rothschild [1974] and

Bikhchandani and Sharma [1996]) and this is not aﬀected by the dynamics we introduce in the perceived arrival rate.

We abstract away from other potential biases. See Dubra [2004] and Conlon et al. [2018] for models with varying priors

regarding the wage oﬀer distribution and learning based on the received wage oﬀers. See Spinnewijn [2015] for a model of

search eﬀorts with biased beliefs, distinguishing between baseline beliefs - regarding the baseline probability of job ﬁnding

- and control beliefs - regarding the increase in the job ﬁnding probability when searching more.

The value of employment follows a similar structure, given an arrival rate of oﬀers, λ

, and accounting for an exogenous

job separation rate, σ. For our analytical derivations, we set λ

= σ = 0, but we relax this in the numerical analysis.

The arrival rate of worker i of type j after d periods of unemployment equals λ

i,d

= (1 − θ)

, while the perceived

arrival rate equals

i,d

= (1 − B

θ)

+ B

with probability B

and

i,d

= (1 − B

θ)

−j

+ B

otherwise. Note that our

model ignores additional random errors in the beliefs, which we cannot credibly separate from noise in the elicitations.

Biased Beliefs The setup allows us to illustrate a key behavioral mechanism in the presence of

biased beliefs. When a job seeker’s employment prospects change, she adapts her job search strategy

to mitigate the impact on her employment chances. This response, however, only comes into play when

the change in employment prospects is perceived. In our model, when the arrival rate of oﬀers increases

for a job seeker, this mechanically increases the job ﬁnding rate. However, the job seeker becomes more

selective and increases her reservation wage (and thus decreases the job ﬁnding rate), but only to the

extent that the increase in the arrival rate is perceived. The mechanical and behavioral eﬀect thus work

in opposite directions:

dT = [1 − F (R)]dλ

| {z }

Mechanical Eﬀect

− [λf (R)

∂R

∂

| {z }

Behavioral Eﬀect

. (16)

For constant arrival rates, we show that the pass-through elasticity of the arrival rate to the job

ﬁnding rate simpliﬁes to

T,λ

= 1 −

dλ

, (17)

for κ

1+δ

f(R

)

1−F (R

)



u(w)−u(R

)

|w ≥ R



≥ 0. Importantly, the mitigating behavioral eﬀect is pro-

portional to d

/dλ

, highlighting the impact biased beliefs have on actual unemployment outcomes.

For the same true arrival rates, job seekers who are more optimistic about their employment prospects

take actions that cause them to exit unemployment more slowly.

Heterogeneity vs. Duration-Dependence The wedge between the true and perceived arrival

rates, either across agents or over the unemployment spell, changes the observed duration dependence

in job ﬁnding rates. Giving the mitigating impact of job seekers’ behavior, any diﬀerence across job

seekers’ or over the unemployment spell that is not perceived leads to larger diﬀerences in actual job

ﬁnding. This implies stronger negative duration dependence in job ﬁnding and thus a higher incidence

of long-term unemployment. In our model, we can state:

Proposition 1. Starting from a stationary, single-agent model (θ = 0, λ

= λ

λ) and assuming

κ < min{1/B

, λ

i. A mean-preserving spread in the true arrival rates (λ

> λ

for φ = 1/2) introduces negative

duration dependence in the job ﬁnding,

i,1

)

i,0

)

< 1, and at a higher rate when B

< 1.

While we introduce variation in job ﬁnding through the arrival rates, it is important to note that the mechanical and

behavioral eﬀect would continue to have opposite signs when changing the mean of the wage oﬀer distribution instead,

like in Conlon et al. [2018]. A more favorable wage oﬀer distribution increases job ﬁnding for a given reservation wage,

but workers would increase their reservation wage if this is perceived. See Dubra [2004] for general conditions under which

optimistic job seekers remain unemployed for longer. The mechanical and behavioral eﬀect have also opposite signs in a

model with endogenous search, like in Spinnewijn [2015], when varying the baseline probability of ﬁnding employment,

keeping the returns to search ﬁxed. The two eﬀects would have the same sign, however, when varying the returns to search

instead; job seekers with higher returns to search ﬁnd jobs at a higher rate and search more if they perceive the higher

returns. In contrast with the other three sources of heterogeneity, this ﬁnal source of heterogeneity would give rise to a

positive correlation between job ﬁnding and the optimistic bias, which is opposite to what we ﬁnd in the data.

ii. Geometric depreciation in the true arrival rates (θ > 0) introduces negative duration dependence

in the job ﬁnding rates,

d+1

(

i,d+1

)

(

i,d

)

< 1, and at a higher rate when B

< 1.

See Appendix F.1.1 for the proof. First, when arrival rates are heterogeneous across job seekers,

those with lower resulting job ﬁnding rates are more likely to remain unemployed. Following equations

(1) and (2), the dynamic selection is stronger the larger the variance in job ﬁnding rates. We can

approximate this variance at the start of the spell for limited heterogeneity (λ

λ + dλ

) by

var

(T )

∼

var



[1 − F (R)]dλ −

λf (R)

∂R

∂



(18)

∝



1 + κ

− 2κ(2B

− 1)



var

(dλ) . (19)

The approximation shows that the variance in job ﬁnding rates is increasing in the heterogeneity in true

arrival rates, but less so the more this heterogeneity is perceived.

Second, the evolution of job ﬁnding rates over the spell depends on how the arrival rates evolves

and how the reservation wage responds,

d+1

i,d+1

)

i,d

)

(λ

d+1

[1 − F (R

d+1

)])

(λ

[1 − F (R

)])

Any depreciation of the arrival rates translates mechanically into negative duration dependence in the

job ﬁnding rates. However, when job seekers perceive the depreciation in arrival rates, they will adjust

their reservation wages and thus the acceptance rates. Starting from a stationary setting, the eﬀect on

the relative job ﬁnding rate equals



d+1

(

i,d+1

)

(

i,d

)



dθ

∼

− 1,

where the behavioral eﬀect is again scaled by the perception of the depreciation B

. As the perceived

depreciation lowers the arrival rates more later in the spell, it induces workers to lower the reservation

wage more later in the spell, translating into a larger increase in the acceptance rate later on. This

behavioral response thus works in the opposite direction as the mechanical eﬀect.

In sum, both heterogeneity and true duration dependence cause the observed duration dependence in

job ﬁnding rates to be magniﬁed when the respective force is under-estimated. Making job seekers’ beliefs

more accurate would thus reduce duration dependence and the incidence of long-term unemployment.

5.2 Numerical Analysis

We calibrate our structural model with heterogeneity and duration dependence in the actual and per-

ceived arrival rates, targeting a subset of moments from our empirical and statistical analysis.

Ap-

The argument regarding the variance holds at any duration d, but its impact on duration dependence is normalized

by E

i,d

) (1 − E

i,d

)). Hence, changes in the average job ﬁnding rate E

i,d

) can lead to oﬀsetting eﬀects for d > 0,

while the job ﬁnding rate at d = 0 remains constant for a mean-preserving spread.

While in theory it is possible, to perform the same estimation exercise in the structural model as in the reduced form

statistical model, ﬁtting our cross-sectional data moments requires a large number of types, which is computationally

pendix Tables F1 and F2 show the targeted moments and calibrated parameters. As in the statistical

model, the targeted moments include the empirical true and perceived job ﬁnding rates for the short,

medium and long-term unemployed. But rather than targeting the covariances between true and per-

ceived job ﬁnding rates, we directly target the true duration dependence in job ﬁnding as estimated

in the statistical model. In particular, we target the ratio of the sample average of job ﬁnding when

long-term unemployed (> 6 months) vs. the sample average of job ﬁnding when short-term unemployed

(≤ 6 months). This ratio is estimated to be 0.90 in the statistical model. We gauge the sensitivity of

our results to setting this target ratio at 0.75, which is below any estimate from the statistical model.

The estimated parameters minimize the sum of squared diﬀerences between data moments and

simulated moments from the model. We closely match our targeted moments and obtain plausible

values for standard labor market statistics. We provide details on the calibration in Appendix F.2.

Comparative Statics We use the calibrated model to illustrate the opposing mechanical and

behavioral eﬀects on job ﬁnding (see Appendix Figure F1). Starting from our baseline model, decreasing

the arrival rate of job oﬀers by 10 percent increases the unemployment duration by 10 percent in the

absence of behavioral responses, but this increase is mitigated to only 6.8 percent when the worse

employment prospects are accurately perceived. In line with Proposition 1, we also ﬁnd that a 10

percent increase in the spread of arrival rates increases the share of unemployed workers who are

unemployed for longer than 6 months by 28 percent. A 10 percent increase in the correlation between

the actual and perceived arrival rates, however, reduces that share of LT unemployed by 3.7 percent.

Similarly, increasing the depreciation rate from its baseline level to the high level, corresponding to our

two calibration models respectively, the share of LT unemployed increases by 16 percent, but the impact

would be mitigated to an increase of 13 percent if the change in depreciation were perceived as such.

Counterfactual Analysis We also use the calibrated model to quantify the impact of eliminating

the biases in beliefs on job seekers’ employment and the incidence of long-term unemployment in partic-

ular (see Appendix Table F3). While eliminating all three biases jointly (B

= 0, B

= B

= 1) lowers

the average unemployment duration slightly, the impact on the share of LT unemployed is signiﬁcant as

it decreases by 8.2 percent (2.4 pp). Interestingly, the results are qualitatively similar for the calibrated

model with a high depreciation rate. While the eﬀect on the average unemployment duration is slightly

larger, the eﬀect on the share of LT unemployed is basically the same at 8.9 percent. The model’s

prediction that biased beliefs contribute substantially to the high incidence of LT unemployment seems

robust to the relative importance of heterogeneity vs. depreciation in the true arrival rates. This is

not too surprising as job seekers’ perceptions under-react to the overall variation in job ﬁnding in both

calibrations. In line with Proposition 1, both under-reacting to the cross-sectional and to the longi-

tudinal variation increases the incidence of LT unemployment.

Expressed as the ratio of the LT vs.

ST unemployment rate, we conclude that 11 − 12 percent of the high incidence of LT unemployment

challenging, given that we need to solve the decision problem for each type.

The probability that high (low) types perceive themselves as high (low) types equals B

= 0.84 in the baseline model.

The cross-sectional bias becomes smaller (B

= 0.89) in the model with high depreciation. However, with no perceived

depreciation in both models (B

= 0), the under-estimation of the depreciation is more pronounced in the latter.

in our model is explained by biased beliefs. We view this as a clear lower bound as we focus only on

systematic biases in beliefs but ignore random errors in perceptions as an additional source of bias.

6 Conclusion

This paper analyzes job seekers’ perceptions about their employment prospects and how these percep-

tions relate to employment outcomes. We have oﬀered three sets of results:

We have documented empirically (1) that reported beliefs have strong predictive power for actual job

ﬁnding, (2) that job seekers are over-optimistic in their beliefs, particularly the long-term unemployed,

and (3) that job seekers do not revise their beliefs downward when remaining unemployed.

We have then developed a novel framework, where we show how the relation between beliefs and

ex-post realizations can be used to disentangle heterogeneity and duration dependence in true job

ﬁnding rates. Using this framework, we ﬁnd that the reported beliefs reveal a substantial amount of

heterogeneity in true job ﬁnding rates, accounting for most of the observed decline in job ﬁnding rates

over the spell of unemployment. Moreover, we ﬁnd that job seekers’ beliefs are systemically biased and

under-respond to diﬀerences in job ﬁnding rates across job seekers. Job seekers with low job ﬁnding are

over-optimistic and select into long-term unemployment without adjusting their beliefs downward.

We have also shown in a model of job search how biases in beliefs contribute to the slow exit

out of unemployment and the incidence of long-term unemployment. Unemployed workers with worse

employment prospects are over-optimistic, setting their reservation wage too high and not suﬃciently

adjusting it as the unemployment spell progresses. Calibrating this model, we ﬁnd that this mechanism

signiﬁcantly increases the incidence of long-term unemployment.

Our analysis demonstrates the broader value of having data on both expectations and realizations

for the same individuals over time. In our context, the data allow us to learn about job seeker’s true

employment prospects, providing us with a novel identiﬁcation strategy to separate dynamic selection

and true duration dependence, with well-known implications with regard to a broad range of labor

market policies. Further, the data allow us to learn about biases in the perceived employment prospects

and to study their interplay with behavior in determining unemployment outcomes. We believe this

opens up an important area of research with again wide-ranging policy implications. Our ﬁndings for

example raise the question of whether biases in beliefs amplify the rise of long-term unemployment

in recessions. If unemployed workers fail to adjust their beliefs about their employment prospects in

response to developments in the aggregate labor market, the lack of a behavioral response is likely to

lead to greater unemployment levels than would otherwise be the case.

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Online Appendix (Not for Publication)

A Survey Questions

A.1 Survey of Consumer Expectations

Question about 12-Month Job Finding Prospect

What do you think is the percent chance that within the coming 12 months, you will ﬁnd a job that you

will accept, considering the pay and type of work?

[Ruler & box]

Question about 3-Month Job Finding Prospect

And looking at the more immediate future, what do you think is the percent chance that within the

coming 3 months, you will ﬁnd a job that you will accept, considering the pay and type of work?

[Ruler & box]

A.2 Krueger-Mueller Survey

Question about 1-Month Job Finding Prospect

What do you think is the percent chance that you will be employed again within the next 4 weeks?

Please move the red button on the bar below to select the percent chance, where 0% means ’absolutely

no chance’ and 100% means ’absolutely certain’.

Survey of Unemployed Workers in New Jersey

Week of: 1/31/10 - 2/6/10

[SRI Note: This page is shown every fourth week.]

Next we would like to ask you a few questions related to your chances of finding a job. If

you have already found a job, you can go on to the next page.

What do you think is the percent chance that you will be employed again within the next 4 weeks?

Please move the red button on the bar below to select the percent chance, where 0% means

'absolutely no chance' and 100% means 'absolutely certain'.

[SRI Note: This question is omitted the first time the page is displayed.]

During the last 4 weeks, did anything happen that made you more or less optimistic about your

chances of finding a job? Please select all that apply.

How many weeks do you estimate it will actually take before you will be employed again?

[q52a] Do you think your chances of finding a job would increase if you spent more time searching

for a job?

[SRI Note: If yes, display q52b]

How many weeks do you estimate it would take to become employed again if you spent an

additional hour searching for a job every day?

5. Job search activities and job

offers (continued)

Absolutely no chance

100%

Absolutely certain

[q53a] I spent more time searching for a job than usual

[q53b] I spent less time searching for a job than usual

[q53c] I realized that the impact of my search efforts is different from what I expected

[q53d] I realized that there are more jobs available than I expected

[q53e] I realized that there are fewer jobs available than I expected

[q53f] I realized that many jobs pay less than I would be willing to accept

[q53g] I realized that many employers think I'm not qualified for the position available

[q53h] Other [q53_spec] Please specify:

[q51]

Weeks:

Yes

[q52b]

Weeks:

Previous Next

Finish Later

[NB: Initial position on bar is randomized.]

Question about Expected Duration

How many weeks do you estimate it will actually take before you will be employed again?

Weeks

B Descriptive Statistics and Sample Comparisons

This appendix provides additional descriptive statistics for both surveys, for the main samples used

in the analysis and a series of sub-samples. Table B1 shows statistics for the SCE, while Table B2

shows statistics for the KM survey. In both tables, column 1 shows the full sample of unemployed,

column 2 shows the main sample used in the longitudinal analysis and column 3 shows the main sample

used for the analysis of predictive power of beliefs. The samples statistics are very similar across the

diﬀerent main samples, except for the sample in column 3 for the KM survey, which is substantially

smaller and somewhat selected. Columns 4 and 5, shows descriptive statistics for the short- and the

long-term unemployed. The long-term unemployed in both surveys are older and more female, though

little diﬀerences exist by education. Finally, columns 6 and 7 show descriptive statistics separately

by number of surveys completed. In the SCE, attrition appears to be non-random with respect to

education, though survey weights adjust for this. Reassuringly, the monthly job ﬁnding rate is similar

across the two samples. In the KM survey, attrition also appears non-random, but again survey weights

adjust for this. Moreover, the sample in column 7 with two surveys or more, which is the variation we use

for the longitudinal analysis in the KM data, is similar to the full weekly panel, which is representative

of the UI population in New Jersey over the survey period.

Table B1: Sample Comparison in the SCE

Unemployed: Unemployed:

Full Main samples Sub-samples of sample (2)

(in %) sample (1) (2) (3) (4) (5) (6) (7)

High-School Degree or Less 34.9 44.5 42.1 43.7 42.1 42.0 46.6 39.4

Some College Education 31.4 32.4 32.6 30.3 30.3 34.5 35.9 30.6

College Degree or More 33.7 23.1 25.4 26.0 27.6 23.5 17.5 29.9

Ages 20-34 23.1 25.4 23.8 21.2 29.4 19.1 29.9 20.3

Ages 35-49 34.0 33.5 34.4 33.1 34.5 34.4 32.8 35.4

Ages 50-65 42.9 41.1 41.7 45.7 36.1 46.5 37.4 44.2

Female 51.3 59.3 58.0 55.3 53.3 62.0 60.6 56.6

Black 11.1 19.1 18.2 14.3 17.9 18.5 19.9 17.2

Hispanic 9.6 12.5 12.2 11.0 13.2 11.4 11.3 12.8

Monthly job ﬁnding rate — 18.7 18.2 17.3 24.2 13.2 18.9 18.0

# respondents 12,200 948 882 494 513 479 395 487

# respondents w/ > 1 survey 10,147 534 477 278 260 239 166 311

# survey responses 84,174 2,597 2,281 1,201 1,070 1,211 756 1,525

Notes: All samples are restricted to ages 20-65. Survey weights are used to compute the descriptive statistics. The

table shows descriptive statistics for the full sample in the SCE, including those employed and out of the labor force,

as well as statistics for (1) all unemployed, (2) all unemployed where the sample was trimmed from observations

with inconsistent elicitations between the 3-month and the 12-month probability, and (3) the same sample as in

(2) but in addition limited to interviews with at least 3 consecutive monthly follow-up interviews (used to measure

3-month job ﬁnding). Sample (2) is the baseline sample in our paper and sample (3) is used for the analysis of the

predictive power of beliefs in Section 3.3. Sub-sample (4) consists of unemployed workers of durations 0-6 months

and sub-sample (5) of unemployed workers of duration of 7 or more months. Sub-sample (6) consists of those in the

main sample (2) with less than 9 interviews over the 12 months of the SCE and sub-sample (7) consists of those in

the main sample (2) with at least 9 interviews over the 12 months of the SCE.

Table B2: Sample Comparison in the KM Survey

Monthly panel: Monthly panel:

Weekly Main samples Sub-samples of (2)

(in %) panel (1) (2) (3) (4) (5) (6) (7)

High-School Degree or Less 32.6 32.5 32.4 30.2 32.8 32.3 39.6 29.3

Some College Education 38.0 37.4 37.4 36.7 37.0 37.5 38.0 37.1

College Degree or More 29.5 30.1 30.2 33.0 30.2 30.2 22.4 33.7

Ages 20-34 35.3 38.1 38.7 21.7 44.9 35.7 55.1 31.4

Ages 35-49 36.5 35.4 34.8 31.8 35.8 34.3 31.8 36.2

Ages 50-65 28.2 26.5 26.5 46.4 19.3 30.0 13.1 32.4

Female 48.1 48.6 47.3 42.7 46.2 47.8 50.2 46.0

Black 22.8 24.4 24.1 15.2 23.0 24.6 30.7 21.1

Hispanic 23.6 27.5 27.8 16.9 33.7 24.9 31.8 26.0

Monthly job ﬁnding rate 11.1 10.3 10.5 10.5 13.5 9.5 — 9.2

# respondents 4,939 2,384 2,278 552 397 1,884 744 1,534

# respondents w/ > 1 survey 3,835 1,422 1,296 121 175 1,118 0 1,296

# survey responses 27,021 4,803 4,435 734 572 3,863 744 3,691

Notes: All samples are restricted to unemployed workers, ages 20-65. Survey weights are used to compute the

descriptive statistics. The table shows descriptive statistics for the full weekly panel of the KM survey, as well

as statistics for (1) the full monthly panel with elicitations about job ﬁnding , (2) the same sample as in (1)

but trimmed for observations with inconsistencies between the elicitation of the 1-month probability and the

expected remaining duration, and (3) the same sample as in (2) but in addition limited to interviews with at

least 4 consecutive weekly follow-up interviews (used to measure 1-month job ﬁnding). Sample (2) is the baseline

sample in our paper and sample (3) is used for the analysis of the predictive power of beliefs. Sub-sample (4)

consists of unemployed workers of durations 0-6 months and sub-sample (5) of unemployed workers of duration of

7 or more months. Sub-sample (6) consists of those in the main sample (2) with only 1 interview in the monthly

panel and sub-sample (2) consists of those with more than 1 interview in the monthly panel.

C Theoretical Derivations in Conceptual Framework

This appendix provides the derivations underlying the characterizations in Section 3.1.

Decomposition of Duration Dependence We ﬁrst establish the following result linking the

expectations at diﬀerent durations:

d+1

i,δ

) = E

i,δ

) −

cov

i,δ

, T

i,d

)

1 − E

i,d

)

. (20)

To obtain this expression, we note ﬁrst that

i,d

) =

i,d

di =

i,d



i,d

− S

i,d+1

i,d



di,

i,d

− S

i,d+1

di = 1 −

d+1

where S

i,d

refers to the survival rate to duration d for individuals of type i. We can then re-write

d+1

i,δ

) =

i,d+1

d+1

i,δ

di =

d+1

i,d

(1 − T

i,d

)

i,δ

1 − E

i,d

)



i,d

i,δ

di −

i,d

i,δ



1 − E

i,d

)







i,d

i,δ

di −

i,d

i,δ

−

i,d

i,δ

di −

i,d

i,δ







1 − E

i,d

)

i,δ

) (1 − E

i,d

)) − cov

i,d

, X

i,δ

)} ,

= E

i,δ

) −

cov

i,d

, X

i,δ

)

1 − E

i,d

)

which proves the earlier statement.

The decomposition of the observed duration dependence immediately follows from applying equation

(20) to the average job ﬁnding. That is,

i,d

) − E

d+1

i,d+1

) = E

i,d

− T

i,d+1

) +

cov

i,d

, T

i,d+1

)

1 − E

i,d

)

where

cov

i,d

, T

i,d+1

) = cov

i,d

, T

i,d

+ (T

i,d+1

− T

i,d

))

= var

i,d

) − cov

i,d

, T

i,d

− T

i,d+1

) .

Lower Bound on Heterogeneity We ﬁrst note that

cov

i,d

, F

i,d

) = E

i,d

) − E

i,d

) E

i,d

)

= E

i,d

)) − E

i,d

) E

i,d

)

= E

i,d

× 1|T

i,d

) Pr (F

i,d

= 1|T

i,d

) + E

i,d

× 0|T

i,d

) Pr (F

i,d

= 0|T

i,d

)) − E

i,d

) E

i,d

)

= E

i,d

)) − E

i,d

) E

i,d

)

= E

i,d

) − E

i,d

) E

i,d

)

= cov

i,d

, T

i,d

) .

Now we can use the Cauchy-Schwarz inequality,

var

i,d

) var

i,d

) ≥ cov

i,d

, T

i,d

)

= cov

i,d

, F

i,d

)

Hence, we have derived the ﬁrst lower-bound on the variance in job ﬁnding rates,

var

i,d

) ≥

cov

i,d

, F

i,d

)

var

i,d

)

We next use Proposition 3 in Morrison and Taubinsky [2019] to derive a second lower-bound using

two measurements of the beliefs, Z

i,d

and Z

i,d

, which requires that both are independently distributed

conditional on T

i,d

(i.e., Z

i,d

⊥ Z

i,d

) and have the same conditional expectation (i.e., E



i,d



α (T

i,d

))). Following the proof in Morrison and Taubinsky [2019], we ﬁrst note that

cov



i,d

, Z

i,d



= E



i,d



− E



i,d





i,d



= E



i,d



− E

(α (T

i,d

)) E

(α (T

i,d

))

= E



α (T

i,d

)



− E

(α (T

i,d

))

= var

(α (T

i,d

)) and

cov



i,d

, Z

i,d



= cov

i,d

, α (T

i,d

)) .

So we can combine these expressions with the Cauchy-Schwarz inequality,

var

i,d

) var

(α (T

i,d

)) ≥ cov

i,d

, α (T

i,d

))

to derive the lower bound

var

i,d

) ≥

cov



i,d

, Z

i,d



cov



i,d

, Z

i,d



cov



i,d

, Z

i,d



Note that if the two measurements are positively correlated, conditional on T

i,d

, the lower bound

argument continues to hold, since then cov



i,d

, Z

i,d



≥ var (α (T

i,d

)).

Linear Beliefs Model For the linear beliefs model, we have

i,d

) = b

+ b

i,d

) for any d.

Hence, it trivially follows that

d+1

i,d+1

) − E

i,d

)

d+1

i,d+1

) − E

i,d

)

The variance in job ﬁnding is thus identiﬁed by

var

i,d

) =

× cov

i,d

, Z

i,d

) =

d+1

i,d+1

) − E

i,d

)

d+1

i,d+1

) − E

i,d

)

× cov

i,d

, Z

i,d

)

We also note that with two elicitations Z

i,d

and Z

i,d

that are both some linear transformation of

i,d

= b

+ b

i,d

+ ε

i,d

our earlier lower bound becomes tight,

var

i,d

) =

cov



i,d

, Z

i,d



cov



i,d

, Z

i,d



cov



i,d

, Z

i,d



But this is only the case when the error terms are independently distributed. The covariance ratio

becomes a lower bound when the error terms are positively correlated.

Persistence in Job Finding For the linear beliefs model, it naturally follows that

cov

d+1

i,d+1

, Z

i,d

) = b

cov

d+1

i,d+1

, T

i,d

) .

This term relates to the dynamic selection term contributing to the duration dependence in job ﬁnding,

but is backward-looking rather than forward-looking. We characterize this relationship in case the job

ﬁnding probability consists of a permanent term and a random transitory term, independently drawn

every period,

i,d

= T

+ τ

i,d

Here, the forward-looking covariance simpliﬁes to the variance in the persistent component,

cov

i,d+1

, T

i,d

) = var

) .

The backward-looking covariance can be re-expressed as

cov

d+1

i,d+1

, T

i,d

) = cov

d+1

+ τ

i,d+1

, T

+ τ

i,d

)

= E

d+1

((T

+ τ

i,d+1

) (T

+ τ

i,d

)) − E

d+1

+ τ

i,d+1

) E

d+1

+ τ

i,d

)

= E

d+1

((T

+ τ

i,d+1

) (T

+ τ

i,d

) |T

)]

−E

d+1

+ τ

i,d+1

)] E

d+1

+ τ

i,d

)]

= E

d+1



+ T

i,d



− E

d+1

) E

d+1

+ τ

i,d

)

= var

d+1

) + cov

d+1

, τ

i,d

)

Here, we can apply the characterization of the conditional expectation in (20) to re-express

cov

d+1

, τ

i,d

) = E

d+1

i,d

) − E

d+1

) E

d+1

(τ

i,d

)

= E

i,d

) −

cov

i,d

, T

i,d

)

1 − E

i,d

)

− E

d+1

)



(τ

i,d

) −

cov

(τ

i,d

, T

i,d

)

1 − E

i,d

)



= −



i,d



1 − E

i,d

)

+ E

d+1

)

var

(τ

i,d

)

1 − E

i,d

)

= −

1 − E

i,d

)





i,d



− E



i,d



− (E

d+1

) − E

)) var

(τ

i,d

)



= −

1 − E

i,d

)



cov



, τ

i,d



− (E

d+1

) − E

)) var

(τ

i,d

)



d+1

) − E

)

1 − E

i,d

)

var

(τ

i,d

)

= −

var

) var

(τ

i,d

)

[1 − E

i,d

)]

where we have used

cov

i,d

, T

+ τ

i,d

) = E



i,d



+ E



i,d



− E

i,d

) E

) − E

i,d

) E

(τ

i,d

)

= E



i,d



d+1

) − E

) = −

cov

, T

)

1 − E

i,d

)

and

cov



, τ

i,d



= E



i,d



− E



i,d



= 0.

Hence, we have

cov

d+1

i,d+1

, T

i,d

) = var

d+1

) −

var

) var

(τ

i,d

)

[1 − E

i,d

)]

while instead

cov

d+1

i,d+1

, T

i,d+1

) = var

d+1

) + var

d+1

(τ

i,d+1

) = var

d+1

) + var

(τ

i,d

)

Putting the two expressions together, we obtain

cov

d+1

i,d+1

, T

i,d+1

) − cov

d+1

i,d+1

, T

i,d

) = var

(τ

i,d

)

1 −

var

)

[1 − E

i,d

)]

which shows that the diﬀerence in the contemporaneous covariance and lagged covariance is increasing

in the variance in transitory shocks, but decreasing in the variance in the permanent shocks. Combined

with

cov

i,d

, T

i,d

) = var

) + var

(τ

i,d

)

and, for the linear beliefs model,

cov

d+1

i,d+1

, Z

i,d

) = b

cov

d+1

i,d+1

, T

i,d

)

cov

d+1

i,d+1

, Z

i,d+1

) = b

cov

d+1

i,d+1

, T

i,d+1

)

cov

d+1

i,d

, Z

i,d

) = b

cov

i,d

, T

i,d

)

we can use the diﬀerence in contemporaneous and lagged covariance to get an estimate of the variance

in transitory shocks.

D Additional Empirical Results

In this appendix, we provide additional results on the empirical analysis that we refer to in the paper for

both the SCE and the KM survey. More precisely, we provide (1) additional details on the distributions

of elicitations and their correlations, (2) additional details and a series of robustness checks on the

predictive power of beliefs and the non-parametric lower bounds, (3) additional details on the biases

in beliefs and a detailed robustness analysis of the longitudinal changes in beliefs, (4) evidence on the

relationship of beliefs, job search eﬀort and reservation wages in the KM data, and (5) evidence on the

relationship between beliefs and indicators of labor market tightness in the SCE.

D.1 Elicited Beliefs about Job Finding

Figure D1: Histogram of Elicitations of the 12-Month Job Finding Probability in the SCE

0 .5 1 1.5 2

Density

0 .2 .4 .6 .8 1

Prob(Employed in 12 Months)

Figure D2: Histogram of Elicitations of the Expected Remaining Duration in the KM survey

0 .05 .1 .15

Density

0 20 40 60 80 100

Expected Remaining Duration, in Weeks

Figure D3: Comparison of Kernel Density Estimates for Alternative Forms of Elicitations

Correlation = 0.76

0 1 2 3 4

Density

0 .2 .4 .6 .8 1

Prob(Find Job in 12 Months)

Elicited Probability

Imputed from Prob(Find Job in 3 Months)

Correlation = 0.65

0 .5 1 1.5 2

Density

0 .2 .4 .6 .8 1

Prob(Find Job in 1 Month)

Elicited Probability

Imputed from Elicited Weeks Until Employed

Figure D4: Ratio of Imputed Probabilities and Elicited Probabilities based on Alternative Forms of

Elicitations in the SCE (top panel) and KM Survey (bottom panel)

0 .4 .8 1.2

Density

0 1 2 3 4

Imputed Prob(Find Job in 12 Months)/Elicited Prob(Find Job in 12 Months)

0 .2 .4 .6 .8

Density

0 1 2 3 4

Imputed Prob(Find Job in 1 Month)/Elicited Prob(Find Job in 1 Month)

Note: See the main text and Figure D3 for details on the imputed probabilities.

D.2 Job Finding Beliefs and Outcomes

In this section, we provide additional details on the analysis of the predictive value of beliefs, a series of

robustness checks of the ﬁndings in Table 2 in the paper as well as the results for the KM survey. The

section also shows additional estimates of the non-parametric lower bounds in the SCE as well as the

lower bound estimates for the KM survey.

Table D1: Regressions of Realized Job Finding Probabilities on Elicitations (Showing Controls)

(1) (2) (3) (4)

Prob(Find Job in 3 Months) 0.586*** 0.464*** 0.501***

(0.073) (0.069) (0.092)

Prob(Find Job in 3 Months) x LT Unemployed -0.258*

(0.142)

LT Unemployed -0.078

(0.094)

Female -0.134** -0.114** -0.071

(0.055) (0.050) (0.046)

Age 0.017 0.018 0.019

(0.017) (0.015) (0.013)

Age*Age -0.0003 -0.0003* -0.0003*

(0.0002) (0.0002) (0.0001)

High-School Degree 0.216* 0.142 0.111

(0.130) (0.124) (0.101)

Some College 0.136 0.098 0.075

(0.121) (0.120) (0.095)

College Degree 0.117 0.054 0.031

(0.121) (0.119) (0.096)

Post-Graduate Education 0.139 0.059 0.034

(0.128) (0.126) (0.105)

Other Education 0.487* 0.388 0.329*

(0.267) (0.261) (0.197)

HH income: $30,000-$59,999 0.127** 0.111** 0.095**

(0.055) (0.053) (0.048)

HH income: $60,000-$100,000 0.182*** 0.189*** 0.150**

(0.058) (0.057) (0.060)

HH income: $100,000+ 0.151* 0.156** 0.113

(0.079) (0.072) (0.082)

Race/Ethnicity: Hispanic -0.022 -0.049 -0.062

(0.073) (0.067) (0.063)

Race/Ethnicity: African-American 0.157** 0.087 0.088

(0.078) (0.078) (0.070)

Race/Ethnicity: Asian 0.081 0.137 0.157*

(0.100) (0.084) (0.092)

Race/Ethnicity: Other -0.145* -0.131* -0.125**

(0.076) (0.073) (0.060)

Constant 0.121*** 0.171 -0.104 -0.062

(0.040) (0.402) (0.363) (0.329)

Observations 1,201 1,201 1,201 1,201

0.131 0.148 0.218 0.259

Notes: The table shows the results in Table 2 in the paper with controls. Robust standard errors (clustered at

the individual level) are in parentheses. Asteriks indicate stat. signiﬁcance at the *0.1, **0.05 and ***0.01 level.

Table D2: Regressions of 3-Month UE Transition Rate on Perceived Job Finding: Robustness Checks

Panel A. Linear Regressions w/o Demographic Controls

(0) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Prob(Find Job 0.586*** 0.710*** 0.587*** 0.553*** 0.624*** 0.444*** 0.653*** 0.574*** 0.567*** 0.503*** 0.345***

in 3 Months) (0.073) (0.088) (0.073) (0.075) (0.079) (0.097) (0.143) (0.075) (0.106) (0.172) (0.109)

Cohort & Time F.E. x

Observations 1,201 1,200 989 1,356 1,066 408 295 1,201 369 184 648

0.131 0.125 0.159 0.121 0.151 0.076 0.184 0.159 0.137 0.094 0.046

Panel B. Linear Regressions w/ Demographic Controls

(0) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Prob(Find Job 0.464*** 0.580*** 0.458*** 0.445*** 0.493*** 0.322*** 0.428*** 0.442*** 0.450*** 0.499*** 0.235**

in 3 Months) (0.069) (0.086) (0.070) (0.071) (0.073) (0.101) (0.121) (0.070) (0.108) (0.168) (0.101)

Demogr. Controls x x x x x x x x x x x

Cohort & Time F.E. x

Observations 1,201 1,200 989 1,356 1,066 408 295 1,201 369 184 648

0.218 0.213 0.253 0.205 0.236 0.198 0.322 0.251 0.257 0.333 0.203

Notes: Survey weights are used in all regressions. All samples are restricted to unemployed workers, ages 20-65. Column (0) show the baseline estimates; in column (1),

we instrument the 3-month probability with the 12-month probability (or rather its equivalent in terms of a 3-month probability); in column (2), we exclude answers equal

to 50%; in column (3), we do not trim the sample for inconsistent answers between the 3- and 12-month elicitation (i.e., where the 3-month probability was higher than

the 12-month probability); in column (4), we only include one unemployment spell for each person; in column (5), we include only one observation for each person (=the

ﬁrst observation in the survey); in column (6), we only include those individuals who entered the survey as employed and became unemployed during the survey period; in

column (7) we control for survey-cohort, calendar-year and month-of-the year ﬁxed eﬀects; in column (8), we only include those unemployed for 3 months or less; in column

(9), we only include those unemployed for 4-6 months; and in column (10), we only include those unemployed for 7 months or more. Robust standard errors (clustered at the

individual level) are in parentheses. Asteriks indicate statistical signiﬁcance at the *0.1, **0.05 and ***0.01 level.

Table D3: Linear Regressions of Realized Job Finding on Elicitations (KM Survey)

Panel A. Dependent Variable: Monthly Job Finding Rate

Prob(Find Job in 1 Month) 0.260** 0.266*** 0.382***

(0.109) (0.094) (0.131)

Prob(Find Job in 1 Month) x LT Unemployed -0.283

(0.180)

LT Unemployed 0.077*

(0.045)

Controls x x

Observations 650 650 650 650

0.039 0.189 0.224 0.234

Panel B. Dependent Variable: Monthly Job Finding Rate

Expected Duration (Inverted) 0.402 0.294 0.513

(0.178)** (0.090)*** (0.140)***

Expected Duration (Inverted) x LT Unemployed -0.493

(0.157)***

LT Unemployed 0.145

(0.056)***

Controls x x

Observations 650 650 650 650

0.080 0.189 0.223 0.249

Notes: Survey weights are used in all regressions. All samples are restricted to unemployed workers in the

KM survey, ages 20-65, with 4 consecutive weekly interviews following the belief question. For the purpose of

comparability across the columns in the table, the samples are restricted to the same number of observations,

i.e., where all control variables and both elicitations are observed. Expected duration (inverted) is calculated

as 1 − (1 −

)

, where x is the elicited expected remaining duration of unemployment (in weeks). Controls are

dummies for gender, race, ethnicity, household income brackets (4), educational attainment (6), and age and age

squared. Robust standard errors (clustered at the individual level) are in parentheses. Asteriks indicate statistical

signiﬁcance at the *0.1, **0.05 and ***0.01 level.

Figure D5: Averages of Actual Job Finding Probabilities, by Bins of Elicited Probabilities (KM Survey)

0 .1 .2 .3 .4 .5

Realized Monthly Job Finding Rate

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1

Elicited Prob(Employed in 1 Month)

Mean of Realized Monthly Job Finding Rate

95% Confidence Interval

0 .1 .2 .3 .4 .5

Realized Monthly Job Finding Rate

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1

Expected Duration (Inverted)

Mean of Realized Monthly Job Finding Rate

95% Confidence Interval

Table D4: Lower Bounds: Additional Estimates (SCE)

Residualized Short-term

Full sample (full sample) unemployed

Lower bound measure based on: Value S.e. Value S.e. Value S.e.

... 3-month elicitations only 0.032 (0.009) 0.016 (0.005) 0.031 (0.012)

... 12-month elicitations only 0.028 (0.008) 0.013 (0.004) 0.016 (0.009)

... 3- and 12-month elicitations 0.038 (0.010) 0.019 (0.006) 0.029 (0.013)

... controls only 0.036 (0.009) 0.020 (0.006) 0.043 (0.012)

... controls and 3-month elicitations 0.053 (0.010) 0.030 (0.007) 0.059 (0.014)

... controls and both elicitations 0.054 (0.010) 0.031 (0.007) 0.060 (0.014)

Notes: Standard errors are bootstrapped with 2,000 replications. For the results in the second column, in a

ﬁrst stage, beliefs (in rows 1 to 3) and the predicted values (in rows 4 to 6) are regressed on three dummies

for unemployment duration (4-6 months, 7-12 months and 13+ months) and then, in a second stage, the

residual of the regression is used to compute the lower bounds. The sample in the third column includes only

those unemployed with a duration of 3 months or less.

Table D5: Lower Bounds Based on KM Survey

Lower bound measure based on: Value S.e.

... 1-month elicitation only 0.0039 (0.0035)

... elicited duration (inverted) only 0.0081 (0.0086)

... both elicitations 0.0085 (0.0076)

... controls only 0.0192 (0.0137)

... controls and both elicitations 0.0233 (0.0143)

Notes: Standard errors are bootstrapped with 2,000 replications.

D.3 Biases in Beliefs

D.3.1 Average Bias by Duration

The following table shows the statistics in the SCE underlying the Figure 3 in the paper. It also shows

the corresponding statistics in the KM survey.

Table D6: Comparison of Perceived and Realized Job-Finding Probabilities

Perceived Job- Realized Job-

Finding Probability Finding Rate Sample Size

Panel A. SCE (3-month horizon)

Full Sample 0.491 (0.014) 0.408 (0.022) 1,201

Duration 0-3 months 0.616 (0.028) 0.642 (0.037) 369

Duration 4-6 months 0.529 (0.031) 0.472 (0.050) 184

Duration 7-12 months 0.530 (0.024) 0.333 (0.045) 198

Duration 13+ months 0.354 (0.015) 0.221 (0.027) 450

Panel B. KM Survey (1-month horizon)

Full sample 0.256 (0.019) 0.105 (0.022) 734

Duration 0-6 months 0.256 (0.042) 0.135 (0.043) 79

Duration 7-12 months 0.283 (0.031) 0.116 (0.048) 158

Duration 13+ months 0.232 (0.028) 0.076 (0.022) 497

Notes: Survey weights are used for all statistics. All samples are restricted to unemployed workers, ages 20-65. The

KM sample is further restricted to interviews where the belief questions were administered. Standard errors are in

parentheses. Duration refers to self-reported duration in the SCE and duration of weeks of beneﬁt receipt in the KM

survey. The SCE sample for this table is restricted to individuals with 4 consecutive interviews. Actual job ﬁnding is

measured in the SCE as the fraction of individuals who reported being employed in month t+1, t+2 or t+3, where t is

the month of the interview where the belief was reported. The KM sample is restricted to those who have not accepted

a job in the same or any previous interviews and are not working at the time of the interview. Actual job ﬁnding in

the KM survey is measured as the fraction accepting a job oﬀer or working in an interview at any point in the 31 days

following the interview where the belief was reported.

D.3.2 Job Finding Beliefs by Duration: Robustness

In this section, we provide additional details on the robustness analysis of our longitudinal results in

Table 4 and Figure 4 in the main paper.

We probe the robustness of the ﬁnding that beliefs are not revised downward in several ways and

also evaluate potential forces that may underlie the (weakly) increasing beliefs about job ﬁnding proba-

bilities. First, we check whether the results in column 4 of Table 4 hold for other measures of perceived

job ﬁnding. In the KM survey, we ﬁnd that the expected remaining duration decreases with duration of

unemployment when controlling for individual ﬁxed eﬀect. This is obviously consistent with an increas-

ing probability over the spell of unemployment as reported in Table 4. For the purpose of comparison

with the probability question, we take the inverse of the expected duration question and convert it into

a 4-week probability, assuming that the probability is constant over the spell of unemployment (see

footnote 20 for details). Table D8 reports these results. We ﬁnd that the coeﬃcient is 0.013, which is

close to the estimate based on the probability question (0.022). Using the 12-month probabilities in the

SCE, the coeﬃcient on unemployment duration is negative but insigniﬁcant and very close to zero with

an estimate of −0.0027 (0.0065). The point estimate implies that the 12-month probability decreases

by 3.2 percentage points over a 12-month period, which is almost trivial.

The ﬁrst columns in Tables D7 and D8 report results where we exclude answers of 50 percent, results

where we exclude answers of 100 percent, results where we do not trim outlier answers as discussed

further above, and results where we use self-reported duration of unemployment as the independent vari-

able. While individuals increase their perceived job ﬁnding probability as they approach re-employment,

the result remains if we exclude individuals who ﬁnd and accept a job within the next 4 weeks in the

KM survey. Neither is the estimate aﬀected when we exclude individuals who reported a job oﬀer in

a previous interview but did not accept it (see Table D8). Across all these diﬀerent speciﬁcations, the

results are very similar.

We also ﬁnd that our results are robust to controlling for changes in aggregate labor market con-

ditions during our sample period. For the SCE, which uses a rotating panel, controlling for changes in

the national, state unemployment rates or quarterly GDP growth has little eﬀect on our estimate of

the duration dependence in perceived job ﬁnding rates. More importantly, we also run a speciﬁcation

with individual ﬁxed eﬀects and ﬁxed eﬀects for calendar time, and ﬁnd that the results are not af-

fected. Even though calendar time and duration are collinear in a given spell, this model is identiﬁed in

the presence of multiple unemployment spells per person. The results are very similar to our baseline

speciﬁcation, demonstrating that aggregate time trends are unlikely to drive our longitudinal results on

perceived job ﬁnding. Note that, for the KM survey, the sample period coincides for all job seekers, so

calendar time and time spent unemployed are collinear and thus it is problematic to include the state

or local unemployment rate into the ﬁxed eﬀect regression. As discussed in Krueger and Mueller [2011],

however, the unemployment rate in NJ was nearly constant over the period of the survey (October 2009

through April 2010) between 9.5 and 9.8 and did not drop below 9.4 until August 2011, so it seems

unlikely that people perceived the job market to improve over the sample period.

Finally, one may be concerned that the beliefs are not elicited for individuals who get discouraged

and drop out of the labor and that as a consequence our longitudinal estimates are upward biased.

While this is a potential concern in the SCE where individuals were asked the belief questions only

when unemployed, we’d like to start by emphasizing that this is not the case for the KM survey, where

individuals were followed and their perceptions were elicited independently of whether they indicated

searching for a job or not. To further assess this issue in the SCE, we split the sample into those

unemployment spells that were interrupted by or ended with a transition into out of the labor force.

We ﬁnd a negligent longitudinal decline for those spells with a UN transition of 0.0022 percentage points

per month (or 2.6 percentage points per year). We further assess this issue by imputing the longitudinal

decline for the months where the individual was reported to be out of the labor force based on the

longitudinal decline in the months unemployed. We then re-estimate our regression with spell ﬁxed

eﬀects but now including those survey months where a person was reported out of the labor force as

part of the same spell. As the last column in Panel B of Table D7 shows, the resulting coeﬃcient on

unemployment duration remains positive and becomes even signiﬁcant, suggesting that even for the

SCE, our longitudinal results are not biased upward. Note that the nature of this exercise is somewhat

diﬀerent from the one further above, as the imputation procedure implies that we give more weight to

individuals with more or longer transitions into out of the labor force.

The lack of updating over the spell seems pervasive across diﬀerent groups of job seekers. When

we regress the gradient of perceptions over the spell of unemployment, we ﬁnd few characteristics that

correlate signiﬁcantly with it. For example, in the KM survey, measures of impatience, risk aversion or

available savings do not correlate with the beliefs gradient.

We ﬁnd a positive within-person correlation

between liquidity constraints and the perceived probability - a job seeker reports a higher job ﬁnding

probability when liquidity constraints become binding - but controlling for liquidity constraints does

not attenuate the positive impact of duration on beliefs.

To conclude, we have done extensive robustness checks and ﬁnd that our results of the lack of

negative updating of beliefs over the unemployment spell is a very robust result in both the SCE and

the KM survey.

Impatience in the KM survey is measured by the choice of a $20 incentive payment at the beginning of the survey over

the option of a $40 incentive payment after the ﬁrst 12 weeks of the survey. Risk aversion is elicited as the willingness to

take risks on a scale from 0 to 10.

Table D7: Linear Regressions of Elicitations on Unemployment Duration, Robustness Checks (SCE)

Dependent Variable (Unless Otherwise Stated in Footnote): Prob(Find Job in 3 Months)

Panel A. (1) (2) (3) (4) (5) (6) (7) (8) (9)

Unemployment Duration, in Months 0.0022 -0.0027 0.0034 0.0012 -0.0004 0.0006 -0.0001 0.0024 0.0017

(0.0064) (0.0065) (0.0068) (0.0065) (0.0043) (0.0068) (0.0003) (0.0021) (0.0016)

F.E. S S S S S S S I I & T

Observations 2,281 2,280 2,597 1,890 2,096 1,912 2,278 2,281 2,281

0.824 0.835 0.789 0.868 0.790 0.813 0.823 0.806 0.827

Panel B. (10) (11) (12) (13) (14) (15) (16) (17) (18)

Unemployment Duration, in Months 0.0021 0.0033 0.0023 0.0022 0.0014 0.0011 -0.0022 0.0057 0.0096***

(0.0063) (0.0069) (0.0064) (0.0064) (0.0094) (0.0046) (0.0053) (0.0104) (0.0032)

F.E. S S S S S S S S S

Observations 2,281 2,278 2,278 2,281 1,070 1,211 765 1,516 3,059

0.824 0.824 0.824 0.824 0.876 0.806 0.812 0.825 0.672

Notes: Survey weights are used in all regressions. All samples are restricted to unemployed workers, ages 20-65, in the SCE. Column (1) reports the baseline results from

Column 4 in Table 4; column (2) reports results where use the 12-month probability as dependent variable; column (3) reports the results where we did not trim the sample for

inconsistent answers between the two survey questions (i.e., where the 3-month probability was larger than the 12-month probability); in column (4) we excluded answers with a

probability of 50 percent; in column (5) we excluded answers with a probability of 100 percent; in column (6) we excluded answers where the person was employed at the next

interview; column (7) reports results with self-reported duration as the independent variable; column (8) reports results with individual ﬁxed eﬀects (I) instead of spell ﬁxed

eﬀects (S); column (9) reports results where we control for individual ﬁxed eﬀects (I) and calendar time (T) ﬁxed eﬀects (month of survey); columns (10)-(13) control for the

national unemployment rate, the state unemployment rate, the change in the state unemployment rate and quarterly GDP growth (in this order); column (14) reports results for

those unemployed 6 months or less; column (15) reports results for those unemployed more than 6 months; column (16) reports results for spells with a transition into out of

the labor force; column (17) reports results for continuous unemployment spells ending in a UE transition; column (18) reports results where missing elicitations in months out

of the labor force are linearly inter- or extrapolated from months when unemployed. Robust standard errors (clustered at the spell level) are in parentheses. Asteriks indicate

statistical signiﬁcance at the *0.1, **0.05 and ***0.01 level.

Table D8: Linear Regressions of Elicitations on Unemployment Duration, Robustness Checks (KM Survey)

Dependent Variable (Unless Otherwise Stated in Footnote):

Prob(Employed in 4 Weeks) (1) (2) (3) (4) (5) (6) (7) (8) (9)

Unemployment Duration, 0.022 0.013 0.020 0.021 0.022 0.020 0.017 0.021 0.030

in Months (0.008)** (0.008) (0.008)** (0.009)** (0.008)** (0.008)** (0.008)** (0.008)** (0.014)**

Person Fixed Eﬀects x x x x x x x x x

Observations 4,435 4,269 4,486 3,862 4,292 4,105 4,044 4,272 4,435

0.902 0.887 0.913 0.920 0.890 0.900 0.900 0.900 0.902

Notes: Survey weights are used in all regressions. All samples are restricted to unemployed workers, ages 20-65, in the KM survey. Column (1) reports the baseline results

from Table 4; Column (2) uses the inverse of the expected duration question as dependent variable (see footnote 20 in the maintext for details); Column (3) reports the results

where we did not trim the sample for inconsistent answers between the two survey questions (i.e., where the diﬀerence between the probability question and the inverse of the

remaining duration was more than 75 percentage points apart); Column (4) reports results where we excluded answers with a probability of 50 percent; Column (5) reports

results where we excluded probabilities of 80 percent or more; Column (6) reports the results where we excluded answers where the person reported in the following 4 weeks

that she or he accepted a job or was working; Column (7) reports the results where we excluded answers where the respondent had previously received but not accepted a job

oﬀer; Column (8) reports results with self-reported duration as the independent variable; Column (9) reports results where we control for the monthly unemployment rate in

New Jersey as reported by the BLS. Robust standard errors (clustered at the individual level) are in parentheses. Asteriks indicate statistical signiﬁcance at the *0.1, **0.05

and ***0.01 level.

Figure D6: Perceived Job Finding Probabilities, by Time since First Interview

A. Elicitation of 12-Month Probability (SCE)

−.2 −.15 −.1 −.05 0 .05 .1 .15

Prob(Find Job in 12 Months)

0 1 2 3 4 5 6

Time Since First Interview (in Months)

Within and Across Spell Changes

−.2 −.15 −.1 −.05 0 .05 .1 .15

Prob(Find Job in 12 Months)

0 1 2 3 4 5 6

Time Since First Interview (in Months)

Within Spell Changes Only

B. Inverse of Elicited Expected Duration (KM Survey)

−.15 −.1 −.05 0 .05 .1 .15

Prob(Find Job in 1 Month)

0 1 2 3 4

Time Since First Interview (in Months)

Within and Across Spell Changes

−.15 −.1 −.05 0 .05 .1 .15

Prob(Find Job in 1 Month)

0 1 2 3 4

Time Since First Interview (in Months)

Within Spell Changes Only

Figure D7: Average Perceived Monthly Job Finding Rate, by Duration of Unemployment and by Cohort

(KM Survey)

A. Averages of Elicited Probability (Raw)

0 20 40 60 80

Percent

0 5 10 15 20 25

Unemployment Duration, in Months

1−Month Probability

0 20 40 60 80

Percent

0 5 10 15 20 25

Unemployment Duration, in Months

Inverse of Elicited Expected Duration

B. Averages of Elicited Probability (Removing Individual Fixed Eﬀects)

0 20 40 60 80

Percent

0 5 10 15 20 25

Unemployment Duration, in Months

1−Month Probability

0 20 40 60 80

Percent

0 5 10 15 20 25

Unemployment Duration, in Months

Inverse of Elicited Expected Duration

Note: The ﬁgure shows averages for each month of unemployment duration and by cohort. The ﬁgures in Panel A show

raw averages, whereas the ﬁgures in Panel B show averages after removing individual ﬁxed eﬀects and adding the average

for each cohort. The ﬁgures does not show averages for month-cohort bins with less than 10 observations.

D.3.3 Further Evidence on Elicited Beliefs

In this section, we provide some evidence on the relationship between eliced beliefs and job search

behavior as reported in the KM survey. We also report some evidence on how job-seekers’ beliefs

respond to aggregate indicators of labor market tightness in the SCE.

Table D9 reports the results of regressions on reported search behavior in the KM data. We ﬁnd

that across job seekers, the self-reported reservation wage bears a negative association with the 1-month

probability though statistically insigniﬁcant, whereas time spent on job search activities is a positive

predictor of the elicited 1-month probability (signiﬁcant at the 1 percent level). Overall, these results are,

at least qualitatively, in line with what one could expect from a simple search model with a reservation

wage choice and endogenous search eﬀort: the reservation wage has a negative eﬀect on the probability

of accepting and thus ﬁnding a job, whereas search eﬀort increases the probability of ﬁnding a job. The

causality, however, may well run in the opposite direction. Job seekers who update positively on the

probability of receiving a job oﬀer are likely to increase their reservation wage. Indeed, we ﬁnd some

evidence for this in column 4: controlling for individual ﬁxed eﬀects, job seekers who decrease their

reservation wage, reduce at the same time their expected remaining duration, though for the 1-month

probability question the relationship remains small and insigniﬁcant. Reverse causality may confound

the relationship between job ﬁnding beliefs and search eﬀort as well. Controlling for individual ﬁxed

eﬀects, the correlation between perceived job ﬁnding and search disappears.

When deciding how hard to search, the perceived returns to search are key as well (Spinnewijn

[2015]). The survey gauges job seekers’ perceived control by asking whether they could increase their

job ﬁnding chances by spending more time searching for a job. Interestingly, the vast majority of job

seekers state that they cannot. Table D9 shows, controlling for search eﬀort, that workers who report

a positive return to search at the margin also report higher job ﬁnding probabilities.

We revisit the question on the role of beliefs for job search in our structural analysis in Section

5, where we specify a search model allowing for heterogeneous beliefs about the primitives of the job

search environment and calibrate this model targeting the true and perceived job ﬁnding in our data.

Note that our analysis in the statistical model in Section 4 abstracts from job search decisions and does

not rely on any assumption about how beliefs aﬀect job search either.

Table D10 shows workers’ perceptions respond to aggregate indicators of job ﬁnding in the SCE. We

ﬁnd that for unemployed individuals there is no signiﬁcant relationship between the national or state-

level unemployment rate and the 3-month perception, though standard errors are relatively large. We do

ﬁnd, however, a highly signiﬁcant positive correlation with the elicited probability that the stock market

will rise and a highly signiﬁcant negative correlation with the elicited probability that the unemployment

rate will rise. This suggests that unemployed job seekers take into account their perceptions about

aggregate conditions when expressing their perceptions about individual job ﬁnding (or vice versa),

but their perceptions about aggregate conditions seem ill-informed. Interestingly, when looking at the

sample of employed, who were asked the same 3-month perception question for the hypothetical situation

where they become unemployed, there is a strongly negative and signiﬁcant correlation between the 3-

month perception and the national or state-level unemployment rate. For the state-level results, where

the standard errors are lower, we can reject the hypothesis that the unemployed’s perceptions respond

as much as the employed’s perceptions to the state-level unemployment rate. At the same time, the

correlation between the perceived individual job ﬁnding and the perceived aggregate conditions is very

similar for the employed and unemployed. Overall, the results seem to suggest that unemployed workers’

perceptions under-react to aggregate indicators of their employment prospects.

Table D9: Linear Regressions of Elicited Perceptions on Time Spent on Job Search and the Reservation Wage

(KM Survey)

Dependent variable: Prob(Find Job in 1 Month) Expected Duration (Inverted)

(1) (2) (3) (4)

Dummy for Control Belief 0.0884 -0.0109 0.1053 0.0533

(0.0253)*** (0.0230) (0.0197)*** (0.0307)*

Time Spent on Job Search (Hours per Week) 0.0013 -0.0014 0.0011 0.0008

(0.0006)** (0.0011) (0.0006)* (0.0014)

Log(Hourly Reservation Wage) -0.0304 -0.0109 -0.0477 0.1346

(0.0346) (0.0758) (0.0298) (0.0812)*

Reservation Commuting Distance (in min) -0.0002 -0.0009 -0.0008 -0.0003

(0.0006) (0.0013) (0.0005)* (0.0013)

Controls x x

Individual F.E. x x

N 3,992 4,087 3,911 3,990

R2 0.129 0.915 0.097 0.891

Notes: Survey weights are used in all regressions. All samples are restricted to unemployed workers, ages 20-65, in the KM survey.

Expected duration (inverted) is calculated as 1 − (1 −

)

, where x is the elicited expected remaining duration of unemployment (in

weeks). The dummy for control belief is set to one for respondents who believe that chances of ﬁnding a job increase if they spent

more time searching. Robust standard errors (clustered at the individual level) are in parentheses. Asteriks indicate statistical

signiﬁcance at the *0.1, **0.05 and ***0.01 level.

Table D10: Linear Regressions of Macroeconomic Measures on Elicitations (SCE)

Panel A. Unemployed Individuals:

Elicited 3-Month Probability (1) (2) (3) (4)

National Unemployment Rate 0.812

(1.369)

National Job Openings Rate 2.597

(2.460)

State Unemployment Rate -0.236 -0.561

(0.832) (0.763)

Elicited Prob(Rise in US Unemployment) 0.165***

(0.039)

Elicited Prob(Rise in Stock Prices) -0.079*

(0.042)

Demographics x x x x

State FE x x

Observations 2,593 2,593 2,593 2,569

0.103 0.102 0.175 0.187

Panel B. Employed Individuals:

Elicited (Conditional) 3-Month Probability (1) (2) (3) (4)

National Unemployment Rate -2.699***

(0.366)

National Job Openings Rate 1.528**

(0.637)

State Unemployment Rate -2.789*** -2.901***

(0.244) (0.270)

Elicited Prob(Rise in US Unemployment) 0.217***

(0.014)

Elicited Prob(Rise in Stock Prices) -0.096***

(0.014)

Demographics x x x x

State FE x x

Observations 58,295 58,295 58,295 57,860

0.054 0.055 0.066 0.075

Notes: Survey weights are used in all regressions. All samples are restricted to unemployed workers, ages 20-

65, in the SCE. Robust standard errors (clustered at the individual level) are in parentheses. Asteriks indicate

statistical signiﬁcance at the *0.1, **0.05 and ***0.01 level.

E Statistical Framework

E.1 Model Fit and Estimation Results for Restricted Models

In this section, we provide additional details regarding the estimation of the statistical model in the

paper. Table E1 shows details on the model ﬁt for the baseline model. Table E2 shows additional details

on the restricted versions of the model discussed in the paper and shown in Table 6.

Table E1: Matched Moments

Value in

Moment Symbol Data Model

Mean of 3-Month Job Finding Rates:

... at 0-3 Months of Unemployment m

0.642 0.646

... at 4-6 Months of Unemployment m

0.472 0.456

... at 7 Months of Unemployment or More m

0.256 0.262

Mean of 3-Month Elicitations (Deviation from Actual):

... at 0-3 Months of Unemployment m

− m

−0.026 −0.027

... at 4-6 Months of Unemployment m

− m

0.057 0.058

... at 7 Months of Unemployment or More m

− m

0.153 0.147

Mean of Monthly Innovations in Elicitations m

0.008 0.006

Variance of Elicitations s

0.093 0.093

Covariance of Elicitations and Job Finding c

Z,F

0.054 0.056

Covariance of Elicitations and Job Finding in 3 Months c

d+3

0.025 0.024

Table E2: Parameter Estimates and Model Fit for Restricted Versions of the Model

(1) (2) (3) (4) (5) (6)

A. Parameter Estimates Baseline θ = 0 No heterog. σ

= 0 b

= 1 b

= 0

and Selected Moments: in T

i,d

= 1

E(T

) 0.403 0.405 0.318 0.419 0.294 0.332

V ar(T

) 0.044 0.051 0.000 0.070 0.019 0.019

0.334 -0.275 0.000 0.000 0.201 0.245

θ 0.017 0.000 0.106 -0.044 0.012 0.015

0.265 0.269 0.341 0.27 0.065 0.000

0.55 0.538 0.349 0.543 1.000 1.000

0.453 0.453 0.442 0.454 0.374 0.38

V ar

i,0

) 0.076 0.079 0.000 0.085 0.051 0.047

V ar

) 0.057 0.065 0.000 0.085 0.040 0.033

V ar

i,0

) 0.081 0.082 0.066 0.083 0.087 0.085

TD 0.459 0.454 0.430 0.452 0.301 0.315

LD 0.070 0.000 0.430 -0.116 0.054 0.071

1 − LD/T D (in %) 84.71 100.00 0.000 125.67 82.20 77.53

B. Model Fit: Data (1) (2) (3) (4) (5) (6)

Targeted Moments:

0.642 0.646 0.640 0.598 0.63 0.571 0.627

0.472 0.456 0.446 0.460 0.418 0.464 0.520

0.256 0.262 0.263 0.218 0.262 0.321 0.373

− m

-0.026 -0.027 -0.027 -0.049 -0.018 0.064 0.000

− m

0.057 0.058 0.062 0.041 0.078 0.066 -0.001

− m

0.153 0.147 0.148 0.199 0.151 0.066 0.00

0.008 0.006 0.007 -0.013 0.006 0.004 0.006

0.093 0.093 0.092 0.069 0.092 0.098 0.099

Z,F

0.054 0.056 0.056 0.012 0.054 0.059 0.058

d+3

0.025 0.024 0.025 0.010 0.029 0.034 0.034

Weighted SSR 0.470 0.695 49.198 2.514 12.251 21.613

Notes: The total decline (TD) in 3-month job ﬁnding is deﬁned as E

i,0

) − E

i,12

). The longitudinal

decline (LD) in 3-month job ﬁnding is deﬁned as E

i,0

− T

i,12

) .

E.2 Robustness

In this section, we study the robustness of our results when using alternative speciﬁcations, alternative

moments, and alternative functional forms and distributions. Tables E3 and E4 show results for various

robustness checks discussed brieﬂy in the paper.

First, we assess the estimated heterogeneity in our statistical model using the heterogeneity that

is not predictable using observable characteristics. The robustness check we perform is to estimate

the model on a set of residualized moments, i.e., the moments obtained from the residuals of a set of

linear regressions of the 3-month belief question and of the 3-month job ﬁnding rate on the same set

of demographic controls as in Table 2. The estimation results are shown in Table E4 and the moments

in Table E5 . Overall, the estimation results are very similar to the baseline, with the role played by

true duration dependence being again close to zero. Of course, the extent of ex-ante heterogeneity is

estimated to be smaller in this robustness check, as the eﬀects of observables are parsed out from all

moments. We also obtain a comparable estimate for the slope coeﬃcient b

of 0.559, which suggests that

the relationship between observed heterogeneity in job ﬁnding and beliefs is similar as the relationship

between unobserved heterogeneity in job ﬁnding and beliefs.

Second, we probe the robustness of our ﬁndings to alternative assumptions about the functional

form and distributions as well as extensions of the model, as reported in Tables E3 and E4. Without

discussing these estimates in detail, the table shows that the parameter estimates are very stable across

all of the results reported in the table. In particular, our results are robust to assuming that T

follows

the Gamma distribution (2), and to assuming that ε follows a bounded normal distribution, which

no longer satisﬁes mean-independence of the error term (3). Our results are also robust to assuming

piecewise linear duration dependence instead of geometric depreciation (4), extending the horizon of the

model to 5 years (5), and doing both (6). We also extend the model to allow for completely persistent

elicitation errors (i.e., ε

i,d

= ε

) and ﬁnd that it has no impact on our estimation results (7). This is

also true when we extend the model to allow for bunching at 0, 0.5 and 1 of the elicited beliefs, by

imposing on the baseline model that any belief in the intervals (0, 0.1], [0.4, 0.6] resp. [0.9, 1) are reset

to the bunching points 0, 0.5 resp. 1. Despite these relatively strong assumptions about the nature of

bunching, the results of the estimation appear not to be aﬀected (8). This suggests that the variations in

elicitations across (rather than within) these intervals is the dominant source of variation that is relevant

for identiﬁcation of the key parameters in the model. We also report the results for a model (9), where

a share α of individuals has random elicitations (Z

i,d

= b

+ ε) and a share 1 − α correctly perceives

their job ﬁnding prospects (Z

i,d

= T

i,d

). The model results are very similar to our baseline, and the

value of 1 − α is close to the value of b

, suggesting that b

in our baseline may instead capture the

share of individuals who perceive their job ﬁnding prospects correctly. Our results are also very similar

when using the residualized data moments as discussed before (10), or when excluding individuals with

recall expectations when generating the data moments (11). Furthermore, the results do not change

either when restricting the set of moments by using only 0-6 and 7+ months for the time intervals and

dropping the mean of monthly innovations, so that the model is exactly identiﬁed (12), or when using

the inverse of the bootstrapped variances on the diagonal of the weighting matrix (and zero otherwise)

instead of the full variance-covariance matrix as the weighting matrix (13).

Finally, in (14) we show the results for the extended model, where

θ 6= θ, as discussed in detail in

the paper. The targeted moments and the model ﬁt are reported in Table E6. Figures E1 and E2 show

the estimated duration dependence in actual and perceived job ﬁnding for both the baseline model and

the extended model. Overall, the duration depdencence in both actual job ﬁnding and the bias looks

very similar across the two models. For this reason, not surprisingly, the ﬁt of the restricted model in

column 15 of Table E4 where

θ = θ is close to the ﬁt of the unrestricted version of the extended model

in column 14.

To sumarize, we ﬁnd that our results for the baseline model are very robust to alternative assump-

tions about functional form and distributional assumptions as well as to extensions of our baseline

model.

Table E3: Robustness Checks

(1) (2) (3) (4) (5) (6) (7) (8) (9)

A. Parameter Estimates Baseline Gamma Normal Linear Horizon=5y Horizon=5y Persistent Bunching Share α w/

and Selected Moments: T

ε Depreciation Lin. Depr. errors rand. elicit.

E(T

) 0.403 0.401 0.405 0.406 0.380 0.383 0.401 0.404 0.405

V ar(T

) 0.045 0.044 0.044 0.046 0.038 0.041 0.041 0.042 0.043

0.334 0.335 0.358 0.334 0.321 0.299 0.378 0.373 0.353

θ 0.017 0.018 0.02 0.017 0.007 0.003 0.025 0.026 0.022

0.265 0.263 0.236 0.265 0.269 0.269 0.259 0.271 0.586

0.550 0.553 0.619 0.549 0.542 0.540 0.556 0.536 0.543*

0.453 0.452 0.287 0.453 0.455 0.455 0.466 0.439 0.483

V ar

i,0

) 0.076 0.076 0.078 0.077 0.072 0.073 0.077 0.076 0.076

V ar

) 0.057 0.056 0.056 0.058 0.053 0.056 0.053 0.053 0.055

V ar

i,0

) 0.081 0.081 0.08 0.081 0.081 0.082 0.084 0.081 0.08

TD 0.459 0.459 0.462 0.464 0.414 0.418 0.460 0.463 0.464

LD 0.070 0.075 0.083 0.071 0.030 0.013 0.107 0.111 0.094

100 − 100LD/T D 84.71 83.56 82.15 84.82 92.66 96.79 76.73 76.11 79.76

B. Model Fit: Data (1) (2) (3) (4) (5) (6) (7) (8) (9)

Targeted Moments:

0.642 0.646 0.646 0.648 0.646 0.643 0.642 0.647 0.649 0.648

0.472 0.456 0.457 0.457 0.452 0.478 0.473 0.459 0.461 0.457

0.256 0.262 0.262 0.261 0.263 0.255 0.256 0.260 0.261 0.259

− m

-0.026 -0.027 -0.026 -0.027 -0.027 -0.025 -0.025 -0.028 -0.028 -0.029

− m

0.057 0.058 0.058 0.058 0.060 0.050 0.051 0.057 0.057 0.059

− m

0.153 0.147 0.146 0.148 0.147 0.153 0.153 0.148 0.147 0.149

0.008 0.006 0.006 0.006 0.007 0.008 0.008 0.006 0.007 0.007

0.093 0.093 0.093 0.093 0.093 0.093 0.092 0.092 0.093 0.092

Z,F

0.054 0.056 0.056 0.056 0.056 0.055 0.055 0.056 0.056 0.056

d+3

0.025 0.024 0.024 0.024 0.024 0.024 0.025 0.023 0.023 0.023

Weighted SSR 0.4698 0.4598 0.4660 0.6032 0.0289 0.0427 0.4320 0.4262 0.3731

Notes: The total decline (TD) in 3-month job ﬁnding is deﬁned as E

i,0

) − E

i,12

). The longitudinal decline (LD) in 3-month job ﬁnding is deﬁned as E

i,0

− T

i,12

*In this model, a share α of individuals has random elicitations (Z

i,d

= b

+ ε) and a share 1 − α correctly perceives their job ﬁnding prospects (Z

i,d

= T

i,d

). We report

the estimated value of 1 − α instead of b

Table E4: Robustness Checks (Diﬀerent Targeted Moments)

(1) (10) (11) (12) (13) (14) (15)

Parameter Estimates Baseline Residualized Excluding Exact Diagonal Extended Extended

and Selected Moments: Moments Recall Identiﬁcation W Model w/

θ = θ

E(T

) 0.403 0.348 0.403 0.404 0.403 0.421 0.412

V ar(T

) 0.045 0.022 0.043 0.048 0.045 0.048 0.042

0.334 0.279 0.360 0.279 0.341 0.477 0.484

θ 0.017 0.011 0.022 0.012 0.016 0.022 0.035

θ — — — — — 0.037 0.035

0.265 0.258 0.265 0.269 0.273 0.291 0.270

0.550 0.559 0.548 0.543 0.538 0.518 0.542

0.453 0.425 0.453 0.456 0.456 0.459 0.455

V ar

i,0

) 0.076 0.053 0.076 0.076 0.077 0.091 0.087

V ar

) 0.057 0.036 0.054 0.062 0.057 0.057 0.051

V ar

i,0

) 0.081 0.071 0.081 0.081 0.081 0.083 0.083

TD 0.459 0.332 0.462 0.462 0.460 0.482 0.480

LD 0.070 0.048 0.095 0.046 0.068 0.089 0.151

1 − LD/T D (in %) 84.71 85.5 79.49 90.08 85.25 81.64 68.46

Weighted SSR 0.470 0.260 0.487 0.000 0.204 3.999 4.141

Notes: In this table, the Weighted SSR refers to diﬀerent sets of moments, so they cannot be compared across speciﬁcations in this table.

See Table E5 for the residualized moments targeted in the estimation of the results reported in column 4. The total decline (TD) in 3-month

job ﬁnding is deﬁned as E

i,0

) − E

i,12

). The longitudinal decline (LD) in 3-month job ﬁnding is deﬁned as E

i,0

− T

i,12

Table E5: Matched Moments (Residualized)

Value in

Moment Symbol Data Model

Mean of 3-Month Job Finding Rates:

... at 0-3 Months of Unemployment m

0.642 0.641

... at 4-6 Months of Unemployment m

0.513 0.525

... at 7 Months of Unemployment or More m

0.369 0.373

Mean of 3-Month Elicitations (Deviation from Actual):

... at 0-3 Months of Unemployment m

− m

−0.026 −0.025

... at 4-6 Months of Unemployment m

− m

0.042 0.026

... at 7 Months of Unemployment or More m

− m

0.098 0.094

Mean of Monthly Innovations in Elicitations m

0.009 0.006

Variance of Elicitations s

0.078 0.078

Covariance of Elicitations and Job Finding c

Z,F

0.036 0.038

Covariance of Elicitations and Job Finding in 3 Months c

d+3

0.020 0.020

Notes: The sample is restricted to unemployed workers, ages 20-65, in the SCE. Moments are computed

based on residuals from a regression on dummies for gender, race, ethnicity, household income, educational

attainment, and age and age squared. Note that the raw mean of the variables in the full sample is added to

the residual.

Table E6: Matched Moments (Extended Model)

Value in

Moment Symbol Data Model

Mean of 3-Month Job Finding Rates:

... at 0-3 Months of Unemployment m

0.642 0.656

... at 4-6 Months of Unemployment m

0.472 0.452

... at 7 Months of Unemployment or More m

0.256 0.250

Mean of 3-Month Elicitations (Deviation from Actual):

... at 0-3 Months of Unemployment m

− m

−0.026 −0.030

... at 4-6 Months of Unemployment m

− m

0.057 0.060

... at 7 Months of Unemployment or More m

− m

0.153 0.157

Mean of Monthly Innovations in Elicitations m

0.008 0.009

Variance of Elicitations:

... at 0-6 Months of Unemployment s

0.098 0.091

... at 7 Months of Unemployment or More s

0.073 0.079

Covariance of Elicitations and Job Finding:

... at 0-6 Months of Unemployment c

0.056 0.055

... at 7 Months of Unemployment or More c

0.025 0.029

Covariance of Elicitations and Job Finding in 3 Months c

d+3

0.025 0.021

Notes: The sample is restricted to unemployed workers, ages 20-65, in the SCE.

Figure E1: Duration Dependence in Job Finding in Baseline and Extended Model

(a) Baseline Model

0 2 4 6 8 10 12

Duration of Unemployment, in Months

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

3-Month Job Finding Probability

Observed Duration Dependence in Job Finding Rates

True Duration Dependence in Job Finding Rates

(b) Extended Model

0 2 4 6 8 10 12

Duration of Unemployment, in Months

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

3-Month Job Finding Probability

Observed Duration Dependence in Job Finding Rates

True Duration Dependence in Job Finding Rates

Figure E2: Duration Dependence in Biases in Perceptions in Baseline and Extended Model

(a) Baseline Model

0 2 4 6 8 10 12

Duration of Unemployment, in Months

-0.2

-0.15

-0.1

-0.05

0.05

0.1

0.15

0.2

3-Month Perception - 3-Month Job Finding Rate

Observed Duration Dependence in Biases in Perceptions

True Duration Dependence in Biases in Perceptions

(b) Extended Model

0 2 4 6 8 10 12

Duration of Unemployment, in Months

-0.2

-0.15

-0.1

-0.05

0.05

0.1

0.15

0.2

3-Month Perception - 3-Month Job Finding Rate

Observed Duration Dependence in Biases in Perceptions

True Duration Dependence in Biases in Perceptions

E.3 Identiﬁcation

In this section, we provide further details on the identiﬁcation of the parameters in the statistical model.

We proceed in two steps:

First, we prove that in a two-period version of the statistical model, where σ

= 0, all other

parameters are a function of moments with an empirical counterpart in the data and thus are identiﬁed.

Second, we provide a formal identiﬁcation argument in the two-period model where σ

> 0, and

then show that in the full model a monotone relationship exists between σ

and the moment c

d+3

conditional on having identiﬁed all other parameters of the model.

Third, we extend the two-period model to allow for

θ 6= θ and prove that in the version of this

model, where σ

= 0, all other parameters are a function of moments with an empirical counterpart in

the data and thus are identiﬁed. We then show in the full model that a monotonic relationship exists

between

θ and the moments c

and s

, conditional on having identiﬁed all other parameters of

the model.

E.3.1 Identiﬁcation in two-period model with σ

= 0

Proposition 2. In a two-period version of the statistical model with measurement error, var(ε), that is

independent of T

i,d

and with σ

= 0, the parameters b

, b

, and θ as well as the mean and the variance

of the persistent component of job ﬁnding rates, E(T

) and var(T

), and the variance of the elicitation

error, var(ε), are identiﬁed by the moment conditions for: (1) the means of the elicitations in period

1 and 2, m

and m

, (2) the means of the job ﬁnding rates in period 1 and 2, m

and m

, (3)

the covariance of job ﬁnding and elicitations in period 1, c

, and (4) the variance of elicitations in

period 1, s

Proof. We start by assuming that there are only two periods, and that σ

= 0. In this case, we can

write down the moment conditions for the moments mentioned in the proposition above as:

= b

+ b

) (21)

= b

+ b

(1 − θ)E

) (22)

= E

) (23)

= (1 − θ)E

) (24)

= cov

i,1

, b

) (25)

= b

var

) + var(ε) (26)

where sub-indices 1 and 2 on the moments stands for the sample of survivors. Note that E

) = E(T

)

and var

) = var(T

), i.e. the moments for the sample of survivors in period 1 correspond to the

population moments. The ﬁrst two moments directly pin down b

and b

− m

(27)

= m

−

− m

(28)

Then, we can write:

= cov

i,1

, b

)

= b

i,1

) − E

i,1

)]

= b

i,1

)) − E

)

]

= b

) − E(T

)

]

= b

var

) = b

var(T

) (29)

Hence, we can pin down the mean and the variance of T

from moment conditions (23) and (29):

E(T

) = m

(30)

var(T

) =

− m

(31)

We next note that we can re-write the expected value of T

, conditional on survival to period 2 as:

) =



(1 − T

)



1 − E(T

)

) − E

)

1 − E

)

)(1 − E

)) − var

)

1 − E

)

(32)

Substituting this into the moment condition for m

, we get:

= (1 − θ)

)(1 − E

)) − var

)

1 − E(T

)

(33)

Rearranging and using equation (30), we get:

θ = 1 −

(1 − m

)

(1 − m

) − var

)

= 1 −

(1 − m

)

(1 − m

) −

−m

= 1 −

− m

)(m

(1 − m

))

(1 − m

) − (m

− m

(34)

Finally, given b

, we can solve for var(ε) by using the moment condition for s

var(ε) = s

−

− m

(35)

Since var(ε) is increasing in σ

, the equation implies a value for σ

In conclusion, equations 27, 28, 30, 31, 34 and 35 solve parameters b

, b

, θ and moments E(T

var(T

) and var(ε) for any distribution of these variables as function of moments that we observe in

the data (m

, m

, c

and s

). The two-period model with σ

= 0 is thus identiﬁed.

Proposition 3. In a two-period version of the statistical model with both a measurement error, ε, that

is independent of T

i,d

, as well as a non-classical measurement error of the form η = c

+ c

i,d

, and

with σ

= 0, the parameters

= b

+ c

, and θ as well as the mean and the variance of the

persistent component of job ﬁnding rates, E(T

) and var(T

), and the variance of the classical elicitation

error, var(ε), are identiﬁed by the moment conditions for: (1) the means of the elicitations in period

1 and 2, m

and m

, (2) the means of the job ﬁnding rates in period 1 and 2, m

and m

, (3)

the covariance of job ﬁnding and elicitations in period 1, c

, and (4) the variance of elicitations in

period 1, s

Proof. As argued in the main text of the paper, the model continues to be identiﬁed exactly in the

presence of non-classical measurement error, as long as it is a linear in T

. The proof is almost trivial,

as we can re-express equations 21, 22, 25 and 26 from above as:

= (b

+ c

) + (b

+ c

) (36)

= (b

+ c

) + (b

+ c

)(1 − θ)E

) (37)

= cov

, (b

+ c

) (38)

= (b

+ c

)

var

) + var(ε) (39)

or:

) (40)

(1 − θ)E

) (41)

= cov

) (42)

= (

)

var

) + var(ε) (43)

These moment conditions are identical to the ones in the model without non-classical measurement

error, except that we replaced b

and b

with

and

. It follows from the proof for Proposition 2

that the parameters

, θ and moments E(T

), var(T

) and var(ε) are functions of moments that

we observe in the data (m

, m

, c

and s

). The two-period model with σ

= 0 and

non-classical measurement error of the form η = c

+ c

is thus identiﬁed.

E.3.2 Identiﬁcation of σ

Our conjecture is that in a two-period version of the statistical model with measurement error, ε, that

is independent of T

i,d

, with transitory shocks to job ﬁnding, τ

i,d

, that are independent of T

, and with

G(T

) following a two-parameter distribution, the parameters b

, b

, θ, and σ

as well as the mean and

the variance of the persistent component of job ﬁnding rates, E(T

) and var(T

), and the variance of the

elicitation error, var(ε), are identiﬁed by the moment conditions for: (1) the means of the elicitations

in period 1 and 2, m

and m

, (2) the means of the job ﬁnding rates in period 1 and 2, m

and m

(3) the covariance of job ﬁnding and elicitations in period 1, c

, (4) the covariance of job ﬁnding in

period 2 and elicitations in period 1, c

, and (5) the variance of elicitations in period 1, s

We again consider a model with only two periods, period 1 and 2. In this case, we can write down

the moment conditions for the moments mentioned in the proposition above as:

= b

+ b

+ τ

i,1

) (44)

= b

+ b

(1 − θ)E

+ τ

i,2

) (45)

= E

+ τ

i,1

) (46)

= (1 − θ)E

+ τ

i,2

) (47)

= cov

, b

+ τ

i,1

)) (48)

= cov

, b

+ τ

i,1

)) (49)

= b

var

+ τ

i,1

) + var(ε) (50)

The ﬁrst two moments again directly pin down b

and b

− m

(51)

= m

−

− m

(52)

We can again re-write the expectation conditional on survival to period 2, now of T

+ τ

i,1

, as:

+ τ

i,1

) =



+ τ

i,1

)(1 − T

− τ

i,1

)



1 − E

+ τ

i,1

)

) − E

(τ

i,1

)

1 − E

)

)(1 − E

)) − var

) − var

(τ

i,1

)

1 − E

)

(53)

because E

(τ

i,1

) = E

i,1

) = 0. Similarly, we obtain

+ τ

i,2

) =

)(1 − E

)) − var

)

1 − E

)

(54)

because E

(τ

i,1

) = E

i,2

) = E

i,1

) = E

(τ

i,1

i,2

) = 0. Hence, we can re-write:

= cov

i,1

, b

+ τ

i,1

))

= b

i,1

+ τ

i,1

)) − E

+ τ

i,1

)]

= b

i,1

+ τ

i,1

)|T

, τ

i,1

)) − E

+ τ

i,1

+ τ

i,1

)]

= b

((T

+ τ

i,1

)(T

+ τ

i,1

)|T

, τ

i,1

)) − E

+ τ

i,1

+ τ

i,1

)]

= b

((T

+ τ

i,1

)

) − E

+ τ

i,1

+ τ

i,1

)]

= b

((T

+ 2T

i,1

+ τ

i,1

) − E

)]

= b

((T

) + E

(τ

i,1

) − E

)]

= b

[var

) + var

(τ

i,1

)] (55)

because E

i,1

) = 0. Similarly, we obtain:

= cov

i,2

, b

+ τ

i,1

))

= b

i,2

+ τ

i,1

)) − E

i,2

+ τ

i,1

)]

= b

i,2

+ τ

i,1

)|T

, τ

i,1

)) − (1 − θ)E

+ τ

i,2

+ τ

i,1

)]

= b

((1 − θ)(T

+ τ

i,2

)(T

+ τ

i,1

)) − (1 − θ)E

+ τ

i,2

+ τ

i,1

)]

= b

(1 − θ)[E

((T

+ τ

i,2

)(T

+ τ

i,1

)) − E

+ τ

i,2

+ τ

i,1

)]

= b

(1 − θ)

) − E

i,1

)

1 − E

)

−



) −

var

)

1 − E

)



) −

var

) + var

(τ

i,1

)

1 − E

)



where the last equality uses the same steps as before to re-write the conditional expectation. Re-

arranging terms and using m

= E

), m

= (1 − θ)

−

var

)

1−m

and b

−m

, we get:

= b

(1 − θ)

var

) + m

− E

) − E

i,1

)

1 − m

− b



−

1 − m



− m

(1 − m

)

(1 − m

) − var(T

)

var

) + m

− E

) − E

i,1

)

1 − m

−

− m

+ m

1 − m

− m

(1 − m

)

(1 − m

) − var(T

)

var

) + m

− E

)

1 − m

−

− m

+ m

1 − m

Using equation (55) to get var

) =

− var

(τ

i,1

), we can rearrange the equation above, to get:

− m

(1 − m

)

(1 − m

) −

−m

+ var

(τ

i,1

)

−m

− var

(τ

i,1

) + m

− E

)

1 − m

−

− m

+ m

1 − m

For two-parameter distributions of T

where E

) is either implicitly or explicitly deﬁned by the

ﬁrst two moments of the distribution, we can deﬁne a function h(., .), such that E

) = h(E

), var

)),

and thus:

− m

(1 − m

)

(1 − m

) −

−m

+ var

(τ

i,1

)

−m

− var

(τ

i,1

) + m

− h(m

−m

− var

(τ

i,1

))

1 − m

−

− m

+ m

1 − m

(56)

While it is not possible to solve explicitly for σ

, we note that for h

≤ 0, the right-hand side of the

equation (56) above depends negatively on σ

, and thus a solution for σ

exists.

A solution also exists

for h

≤

h, where

h is some positive number, as long as

h is smaller than some upper bound

Having solved for var

(τ

i,1

), when a solution to equation (56) exists, we can then ﬁnd a solution for

the mean and variance of T

) = m

(57)

var

) =

− m

− var

(τ

i,1

) (58)

Rearranging and using equation (47), we also get:

θ = 1 −

(1 − m

)

(1 − m

) −

−m

+ var

(τ

i,1

)

(59)

As before, given b

, we can also solve for var(ε) by using the moment condition for s

var(ε) = s

−

− m

(60)

In conclusion, if a solution exists to equation (56), implicitly deﬁning σ

, we can solve for parameters

, b

, σ

, and θ as well as the mean and variance of the persistent component of job ﬁnding rates,

E(T

) = E

) and var(T

) = var

), as a function of the moments m

, m

, c

Note σ

is monotonically increasing in but not equal to var

(τ

i,1

), because of the boundary conditions.

Figure E3: The relationship between σ

and the moment c

d+3

in the estimated sub-model

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

0.02

0.022

0.024

0.026

0.028

0.03

0.032

d+3

Model

Data

, s

, as shown in equations 51, 52, 57, 58, 59 and 60.

To provide further evidence on identiﬁcation of the parameter σ

, we now proceed by showing that

in the context of our estimated model (i.e., with more than two periods), there is a monotone mapping

between the parameter σ

and the moment C

d+3

. More precisely, we estimate a sub-model of the

baseline version of our statistical model for diﬀerent levels of σ

, by targeting all of the same moments

except C

d+3

. Figure E3 shows that there is a monotone relationship between the level of σ

and the

covariance of elicitations and the 3-month forward job ﬁnding rates in this estimated sub-model, which

shows that our parameter σ

is identiﬁed by the moment C

d+3

in the full (baseline) model.

E.3.3 Identiﬁcation in extended model with

θ 6= θ

Proposition 4. In a two-period version of the extended version of the statistical model with

θ 6= θ and

with measurement error, ε, that is independent of T

i,d

, but with σ

= 0, the parameters b

, b

, θ,

θ as

well as the mean and the variance of the persistent component of job ﬁnding rates, E(T

) and var(T

and the variance of the elicitation error, var(ε), are identiﬁed by the moment conditions for: (1) the

means of the elicitations in period 1 and 2, m

and m

, (2) the means of the job ﬁnding rates in

period 1 and 2, m

and m

, (3) the covariance of job ﬁnding and elicitations in period 1, c

(4) the variance of elicitations in period 1, s

, and (5) a statistic that depends on all these moments

as well as the variance of eliciations in period 2, s

, and the covariance with job ﬁnding in period 2,

Proof. We assume that there are only two periods, and that σ

= 0. In this case, we can write down

the moment conditions for the moments mentioned in the proposition above as:

= b

+ b

) (61)

= b

+ b

(1 −

θ)E

) (62)

= E

) (63)

= (1 − θ)E

) (64)

= cov

i,1

, b

) (65)

= cov

i,2

, b

) (66)

= b

var

) + var(ε) (67)

= b

(1 −

θ)

var

) + var(ε) (68)

where sub-indices 1 and 2 on the moments stands for the sample of survivors. Note that E

) = E(T

)

and var

) = var(T

), i.e. the moments for the sample of survivors in period 1 correspond to the

population moments. One can express the additional moment condition (66) as follows:

= cov

i,2

, b

(1 −

θ)T

)

= b

(1 −

θ)[E

i,2

) − E

i,2

)E(T

)]

= b

(1 −

θ)[E

i,2

)) − (1 − θ)E

)

]

= b

(1 −

θ)(1 − θ)[E

) − E

)

]

= b

(1 −

θ)(1 − θ)var

)

Re-arranging the moment conditions 61-67 and using equations (29) and (32), we thus get:

= b

+ b

(69)

= b

+ b

1 −

1 − θ

(70)

= E

) (71)

= (1 − θ)

−

var

)

1 − m

(72)

= b

var

) (73)

= b

(1 −

θ)(1 − θ)var

) (74)

= b

var

) + var(ε) (75)

= b

(1 −

θ)

var

) + var(ε) (76)

The mean of the job ﬁnding rate, E(T

) = E

), is directly identiﬁed by moment condition in equation

(71).We then take the diﬀerence of the ﬁrst two moment conditions:

− m

= b



−

1 −

1 − θ



(77)

which gives b

as a function of moments, θ and

θ. Next combine equations 73 and 75 and equations 74

and 76, to get:

= b

+ var(ε) (78)

= b

1 −

1 − θ

+ var(ε) (79)

and taking the diﬀerence, we get:

− s

= b

−

1 −

1 − θ

) (80)

Taking the ratio of equation 77 and 80, we get:

− m

− s

−

1−

1−θ

−

1−

1−θ

(81)

Rearranging:

− m

− s

−

1 −

1 − θ

) = m

−

1 −

1 − θ

(82)

Rearranging further:

− m

− s

− m

= −

1 −

1 − θ

− m

− s

1 −

1 − θ

(83)

Rearranging further:

1 −

1 − θ

−m

−s

− m

−m

−s

− m

(84)

Equation 84 deﬁnes the ratio of

1−

1−θ

as a function of moments only. Using the ratio, one can rearrange

equation 77 to get b

as a function of moments only:

− m

−

1−

1−θ

(85)

Using b

, one can use equation 61 to get b

as a function of moments only:

= m

− b

(86)

Using b

, one can use equation 73 to get var(T

) = var

) as a function of moments only:

var(T

) =

(87)

Using b

and var(T

), one can use equation 75 to get var(ε) as a function of moments only:

var(ε) = s

− b

var(T

) (88)

Using var(T

), one can use equation 64 to get θ as a function of moments only:

θ =

− m

)(1 − m

) − var(T

)

(1 − m

) − var(T

)

(89)

Using θ and equation 84, we get

θ as a function of moments only:

θ = 1 − (1 − θ)

−m

−s

− m

−m

−s

− m

(90)

In conclusion, equations 85 (together with equation 84), 86, 63, 87, 88, 89 and 90 solve parameters

, b

, θ,

θ and population moments E(T

), var(T

) and var(ε) for any distribution of these variables

as function of moments that we observe in the data (m

, m

, c

, s

and the ratio in

equation 84). The two-period model with σ

= 0 and

θ 6= θ is thus identiﬁed.

To provide evidence on the identiﬁcation of the parameter

θ in the full version of the model that we

estimate with the data, we proceed by showing that in the context of our estimated model (i.e., with

more than two periods and σ

> 0), there is a monotone mapping between

θ and the covariance in

duration interval 7+, c

as well as a monotone mapping between

θ and the variance of elicitations

in duration interval 7+, s

. More precisely, we estimate a sub-model of the extended version of

our statistical model, where

θ 6= θ, for diﬀerent levels of

θ, targeting all the same moments except

and s

. Figure E4 shows that there is a monotone relationship between the level of

θ and the

covariance of elicitations and job ﬁnding rates in duration interval 7+ as well as a monotone relationship

between level of

θ and the variance of elicitations in duration interval 7+. This shows that both of these

moments provide variation that identiﬁes the parameter

θ in the full (extended) model.

Figure E4: The relationship between

θ and moments c

and s

in the estimated sub-model

-0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

0.005

0.01

0.015

0.02

0.025

0.03

0.035

|d>6

Model

Data

-0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

0.065

0.07

0.075

0.08

0.085

0.09

0.095

0.1

|d>6

Model

Data

F Structural Model

This section provides further details on the derivations and Proposition in the theoretical analysis and

the calibration and counterfactual analysis in the numerical analysis in Section 5.

F.1 Theoretical Analysis

In a stationary setting (with θ = 0), we have for any individual

i,d

= λ

[1 − F (R

)].

Now dropping subindices, we can consider the impact on the job ﬁnding rate T of inﬁnitesimal changes

in λ and

λ,

dT = [1 − F (R)]dλ − λf(R)

λ,

A change in λ does not trigger a change in the reservation wage R since it is only the perceived arrival

rate that informs the agent’s reservation wage. Rearranging this equation we get,

dλ

= 1 − λ

f(R)

1 − F (R)

dλ

To unpack the

term we consider the determination of the reservation wage. The reservation wage

is deﬁned by U = V (R), where

U =u(b

) +

1 + δ

max



U +

[V (w) − U ]dF (w)]



V (w) =u(w) +

1 + δ



(1 − σ)



V (w) + λ

(V (x) − V (w))dF (w)

+ σU



Assuming σ = λ

= 0, we can write,

V (R) =

1 + δ

u(R)

and thus

1 + δ

u(R) = u +

1 + δ

max



1 + δ

u(R) +



V (w) −

1 + δ

u(R)



dF (w)



We can totally diﬀerentiate this condition with respect to R and

λ, applying the envelope theorem to

the right hand side (i.e., dU/dR = 0) and assuming no job separation risk and no on-the-job search

such that V (w) = (1 + δ)u(w)/δ,

(R)

1 −

1+δ

dR =

1 + δ





u(w)

1 −

1+δ

−

u(R)

1 −

1+δ



dF (w)



λ.

So, we can conclude

1 + δ





u(w) − u(R)

(R)



dF (w)



Combining this with our earlier result, we ﬁnd

dλ

= 1 −

1 + δ

λf(R)



u(w)−u(R)

(R)



dF (w)

1 − F (R)

dλ

= 1 −

1 + δ

f(R)

1 − F (R)



u(w) − u(R)

(R)



w ≥ R



dλ

≡ 1 − κ

dλ

This corresponds to equation (17) in the main text.

F.1.1 Proof of Proposition 1

First, we consider the introduction of heterogeneity. That is, we assume λ

λ + dλ

for j = h, l with

dλ

= −dλ

≈ 0, but we keep θ = 0. We also assume an equal share of high and low types, φ = 1/2.

Now for small diﬀerences in actual and perceived arrival rates, we can approximate

≈ T +

dλ

λ[1 − F (R)] + [1 − F (R)]dλ

−

λf(R)

λ[1 − F (R)] + [1 − F (R)]

dλ

− κd

Following the derivations in the conceptual framework (see Appendix C), we can write

d+1

)

= 1 −

var

)

) [1 − E

)]

Given the mean-preserving spread in the arrival rates, we have

) ≈

λ[1 − F (R)],

We also have

var

) ≈ var



[1 − F (R)]

dλ

− κd



= [1 − F (R)]

var

dλ

− κd

= [1 − F (R)]

var

(dλ) + κ

var





− 2κcov



dλ, d

i

where

cov



dλ, d



= B





+ B

(1 − φ)





+ (1 − B) φλ

+ (1 − B

) (1 − φ) λ

−

= B

var

(dλ) + (1 − B

)

−

= [2B

− 1] var

(dλ) .

The last equality follows since var

(dλ) =

− λ

for φ = 1/2.

Hence,

var

) = [1 − F (R)]



1 + κ

− 2κ [2B

− 1]



var

(dλ) .

Small changes in the dispersion leave the expected job ﬁnding rate unaﬀected to a ﬁrst-order, but do

increase the variance in job ﬁnding rates. However, the increase in the dispersion is scaled and has a

smaller impact on the variance in job ﬁnding rates, the higher B

. The ﬁrst part of the Proposition

immediately follows.

Second, we consider the introduction of geometric depreciation of the true and perceived arrival

rates,

d+1

=(1 − θ)λ

d+1

=(1 − B

θ)

We can write,

d+1

=(1 − θ)

1 − F (R

d+1

)

1 − F (R

)

⇒



d+1



dθ

= −

1 − F (R

d+1

)

1 − F (R

)

+ (1 − θ)



1−F (R

d+1

)

1−F (R

)



dθ

Unpacking the last term, we ﬁnd



1−F (R

d+1

)

1−F (R

)



dθ

f(R

)[1 − F (R

d+1

)]

dθ

− f(R

d+1

)[1 − F (R

)]

d+1

dθ

[1 − F (R

)]

f(R

)

1−F (R

d+1

)

1−F (R

)

dθ

− f(R

d+1

)

d+1

dθ

1 − F (R

)

f(R

d+1

)

d+1

dθ

1 − F (R

)



f(R

)

f(R

d+1

)

1 − F (R

d+1

)

1 − F (R

)

dθ

d+1

dθ

− 1



We now look at the reaction of the respective reservations wage to the depreciation parameter. The

reservation wage is characterized by V (R

) = U

where,

V (R

) =

1 + δ

u(R

)

= u(b

) +

1 + δ

max



d+1

+ (1 − B

θ)



V (w) − U

d+1



dF (w)



so substituting the former into the latter for U

, U

d+1

,and V (w) gives,

1 + δ

u(R

) = u(b

) +

max



u(R

d+1

) + (1 − B

θ)



u(w) − u(R

d+1

)



dF (w)



Total diﬀerentiation yields,

1 + δ

)dR

= −

(1 − B

θ)

d−1



u(w) − u(R

d+1

)



dF (w)dθ . . .

. . . +

d+1

)

d+1

dθ

dθ −

(1 − B

θ)

d+1

)

d+1

dθ

dθ,

Hence, we ﬁnd

dθ

1 + δ



− d

1 − B



1 − B

1 − θ





u(w) − u(R

d+1

)



w > R



d+1

)

(1 −

)

d+1

dθ



and, then by iterating, we get

dθ

= −

1 + δ

1 − B

∞

s=d



k=d

[1 −

]

1 −



s+1

)



1 − B

1 − θ





u(w) − u(R

s+1

)



w > R



Starting from θ ≈ 0, the reservation wage, arrival rate, and job ﬁnding rate are approximate constant

and the perceived arrival rate equals the actual arrival rate. Denoting by R and T = λ [1 − F (R)] the

reservation wage and the job ﬁnding for the stationary type, where we have dropped the subindex 0 in

the notation, we can write

d+1

dθ



θ=0

= −

1 + δ

T E



u(w) − u(R)

(R)



w > R



∞

s=d+1



(1 − λ)

s−d−1



and thus

dθ

d+1

dθ



θ=0

∞

s=d−

(1 − λ)

s−d

∞

s=d+1

(1 − λ)

s−d−1

d + (1 − λ)

∞

s=d+1

(1 − λ)

s−d−1

∞

s=d+1

(1 − λ)

s−d−1

d + (1 − λ)



d+1

1−λ



d+1

1−λ

< 1,

which proves that the reservation wage responds more at longer durations. The last equality above

follows from expanding the power series as follows:

∞

s=d+1

(1 − λ)

s−d−1

s =d + 1 + (1 − λ)(d + 2) + (1 − λ)

(d + 3) + (1 − λ)

(d + 4) + . . . ,

=(d + 1)(1 + (1 − λ) + (1 − λ)

+ (1 − λ)

+ . . .) + (1 − λ) + 2(1 − λ)

+ . . . ,

d + 1

+ (1 − λ)(1 + (1 − λ) + (1 − λ)

+ (1 − λ)

+ . . .) + (1 − λ)

+ 2(1 − λ)

+ . . . ,

d + 1

1 − λ

+ (1 − λ)

(1 + (1 − λ) + (1 − λ)

+ . . .) + (1 − λ)

+ 2(1 − λ)

+ . . . ,

d + 1

1 − λ

(1 − λ)

+ . . . ,

d + 1

1 − λ

(1 + (1 − λ) + (1 − λ)

+ (1 − λ)

+ . . .),

d + 1

1 − λ

Hence, putting things together and starting from θ ≈ 0, we have



d+1



dθ



θ=0

= − 1 +

f(R)

d+1

dθ



θ=0

1 − F (R)



dθ

d+1

dθ



θ=0

− 1



= − 1 +

f(R)

1 − F (R)

1 + δ

T E



u(w) − u(R)

(R)



w > R



d + 1

1 − λ



. . .



1 −

d + (1 − λ)



d+1

1−λ



d+1

1−λ



= − 1 +

f(R)

1 − F (R)



1 +

1 − λ



1 + δ

T E



u(w) − u(R)

(R)



w > R



1 + δ



u(w) − u(R)

(R)



w > R



f(R) − 1,

− 1.

Moreover, since

= 0 for θ = 0, we also have



d+1



dθdB



θ=0

> 0.

This proves the second part of the Proposition.

F.2 Numerical Analysis

Table F1 shows the 8 moments that we target in the calibration of our structural model. As in the

statistical model, the targeted moments include the actual and perceived job ﬁnding rates for the short,

medium and long-term unemployed. We additionally target an average job acceptance rate underlying

the job ﬁnding rates of 0.71, as estimated by Hall and Mueller [2018] using the KM survey. As we

already estimated the true duration dependence in our statistical model using elicited beliefs moments,

instead of targeting these again, we directly target a moment capturing the depreciation in job ﬁnding,

i.e., the average of the ratio of true job ﬁnding when long-term vs. short-term unemployed within a

spell (i.e., E

i,d

)/E

i,d

) for a given spell). We simulate this moment using the baseline estimation

of our statistical model, obtaining a value of .895. We also gauge the robustness of our results to the

rate of depreciation and recalibrate the model targeting a ratio .75, which is below any estimate we

obtain in the statistical model (excluding the speciﬁcation in which we do not allow for heterogeneity).

We set the perceived duration dependence B

equal to 0 in both speciﬁcations.

Table F2 Panel A shows the set parameter values. We set the separation rate at 0.02 per month,

corresponding the average separation rate in the SCE. We set arrival rate of job oﬀers for employed

workers at 0.15, in line with recent evidence in Faberman et al. [2017] also using the SCE. We assume that

wages are log-normally distributed, with a standard deviation of the logged distribution of σ

= 0.24 as

estimated by Hall and Mueller [2018] with the KM survey data. We normalize the median of the wage

oﬀer distribution to 1. We also assume an annual discount factor 0.996 and CRRA preferences with

relative risk aversion equal to 2. Panel B of Table F2 shows the remaining 7 parameters of our model

, B

, λ

, φ, θ, b

} that are estimated by targeting the vector of 8 moments. We ﬁnd that the

uniform bias parameter B

is negative, but the average bias is still positive. This is due to the share of

low types perceiving themselves as high, who remain unemployed for the longest. The probability that

high (low) types perceive themselves as high (low) types equals B

= 0.84 in the baseline speciﬁcation.

As we assume that no duration dependence is perceived (B

= 0), the corresponding cross-sectional

bias becomes smaller in the model where we target high true duration dependence (B

= 0.89).

The

estimated parameters minimize the sum of squared diﬀerences between data moments and simulated

moments from the model. Table F1 shows that we closely match our targeted moments. We also obtain

plausible values for standard labor market statistics; the elasticity of the unemployment duration with

respect to unemployment beneﬁts is 0.62, which is within the range of estimates in the literature (see

Schmieder and von Wachter [2016]). The elasticity of the reservation wage equals .44, which corresponds

to estimates in Feldstein and Poterba [1984] and Fishe [1982]. The elasticity of the equilibrium wage

equals .04, which is arguably low, but still higher than recent estimates in Jaeger et al. [2020]. The

monthly rate of job-to-job transitions equals 0.024, which is within the range considered by Hornstein

et al. [2011].

We have also extended our model with a type-speciﬁc bias in the perceived arrival rates. This relaxes the restrictions

of our stylized model that on average the low-type job seekers are more optimistic than the high-type job seekers. However,

the estimated type-speciﬁc biases are very close, suggesting that this restriction is not binding.

We also performed sensitivity checks when changing incidental parameters, including the arrival rate of job oﬀers

for the employed, the dispersion of the wage distribution and the level of risk aversion, which all change the relative

value of unemployment to employment. For the baseline model, it is mainly the parameter b

aﬀecting the ﬂow value

of unemployment that adjusts, while the other parameter estimates remain very similar. The other parameter estimates

Table F3 shows the impact of eliminating the biases in beliefs on the average unemployment durations

and the share of long-term unemployed. The intermediate columns consider the elimination of one bias

at a time, the last column the elimination of all biases simultaneously. From Panel A, which shows

the results for the baseline model, we see that eliminating all biases lowers the average unemployment

duration, but this eﬀect is numerically very small. Despite the small impact on the overall duration, the

impact on the share of LT unemployed is substantial, which decreases by 8.2 percent (2.4 percentage

points) when all biases are eliminated. Panel B shows the results for the model calibrated with high

depreciation rate. The eﬀect on the average unemployment duration is somewhat larger, at around 0.15

months. However, eliminating the biases reduces the share of LT unemployed by 2.6 percentage points,

which is slightly higher than in the baseline model. Overall, the model’s prediction that biased beliefs

contribute substantially to the high incidence of LT unemployment is robust to the relative importance

of heterogeneity vs. depreciation in the arrival rates.

become more sensitive in the model with high depreciation.

We note that these counterfactual results remain very similar when changing incidental parameters (i.e., wage oﬀer

distribution, arrival rates, risk aversion) in the baseline calibration, but are somewhat sensitive in the calibration with high

depreciation.

Table F1: Targeted Data Moments and Corresponding Moments in Structural Model

Moments Data

Baseline

Model

High Depreciation

Model

Mean of 3-Month Job Finding Rates:

... at 0-3 Months of Unemployment 0.642 0.642 0.640

... at 4-6 Months of Unemployment 0.472 0.470 0.474

... at 7 Months of Unemployment or more 0.256 0.259 0.255

Mean of 3-Month Elicitations:

... at 0-3 Months of Unemployment 0.616 0.614 0.615

... at 4-6 Months of Unemployment 0.529 0.537 0.535

... at 7 Months of Unemployment or more 0.409 0.404 0.405

Acceptance Rate: 0.710 0.716 0.715

True Duration Dependence:

... Baseline Depreciation 0.895 0.895 -

... High Depreciation 0.75 - 0.751

Table F2: Calibrated Parameters

Parameters Symbol

Baseline

Model

High Depreciation

Model

A. Set Parameters

Median of wage oﬀer distribution µ

1 1

Std. dev. of logged wage oﬀer distribution σ

0.24 0.24

Exogeneous job loss probability σ 0.02 0.02

Arrival rate when employed λ

0.15 0.15

Discount rate δ 0.004 0.004

Coeﬃcient of relative risk aversion γ 2 2

Longitudinal bias B

0 0

B. Estimated Parameters

Uniform bias B

-0.014 -0.050

Cross-sectional bias B

0.84 0.89

Low-type arrival rate λ

0.12 0.16

High-type arrival rate λ

0.63 0.67

Share of high-types φ 0.78 0.74

Depreciation in arrival rate θ 0.019 0.046

Unemployed consumption b

0.52 0.52

Table F3: Comparative Statics in Structural Model

Calibrated

Model

Eliminating Biases

= 0 B

= 1 B

= 1

= 0

= 1

A. Baseline Model

Unemployment duration 4.01 4.07 4.01 3.90 3.95

Share of LT unemployed 0.295 0.297 0.275 0.289 0.271

B. High Depreciation Model

Average unemployment duration 3.99 4.15 3.99 3.75 3.85

Share of LT unemployed 0.294 0.299 0.278 0.278 0.267

Figure F1: Comparative Statics: True vs. Perceived Changes in Arrival Rates

A. Impact of Arrival Rates on Duration

B. Impact of Heterogeneity on LT Incidence

Figure F1: Comparative Statics: True vs. Perceived Changes in Arrival Rates (continued)

C. Impact of Depreciation on LT Incidence

Notes: Panel A plots the average unemployment duration as a function of actual and perceived arrival rates, changing

them in the same way for all types relative to the baseline model. Panel B plots the share of long-term unemployment (i.e.,

the share of unemployed workers who are unemployed for longer than 6 months) as a function of the spread of true arrival

rates (while preserving the mean arrival rate) and the correlation between the perceived and true arrival rates. Panel C

plots the share of long-term unemployment as a function of the true and perceived depreciation rate. The output in the

last two panels corresponds to results (i) and (ii) in Proposition 1.