Discussion Paper No.

592

THE RECALL AND NEW JOB SEARCH
OF LAID-OFF WORKERS:A BIVARIATE PROPORTIONAL HAZARD MODELWITH UNOBSERVED HETEROGENEITY

Bruce Fallick
andKeunkwan Ryu

August 2003

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

The Recall and New Job Search of Laid-oﬀ Workers: A Bivariate
Proportional Hazard Model with Unobserved Heterogeneity
Bruce Fallick
Federal Reserve Board
Washington, D.C. 20551
Telephone: 202-452-3722
Fax: 202-452-5296
E-mail: Bruce.Fallick@frb.gov
andKeunkwan Ryu
Department of Economics
Seoul National University
andISER, Osaka University
E-mail: ryu@snu.ac.kr

Abstract
Workers who lose their jobs can become re-employed either by being recalled totheir previous employers or by finding new jobs. Workers’ chances for recall should
influence their job search strategies, so the rates of exit from unemployment by these
two routes should be directly related. We solve a job search model to establish, intheory, a negative relationship between the recall and new job hazard rates. We
look for evidence in the PSID by estimating a semi-parametric competing risks
model with explicitly related hazards. We find only a small negative behavioral
relationship between recall and new job hazard rates.
KEY WORDS: Lay-oﬀ; Recall; Job search; Hazard rate; Proportional hazard
model; Unobserved heterogeneity; Duration dependence.
JEL Classification Number: J64, C41
Keunkwan Ryu would like to acknowledge financial support of the Korea Research
Foundation. The views expressed are those of the authors and do not necessarily
represent those of the Board of Governors or the staﬀ of the Federal Reserve System.

1. Introduction
Workers who lose their jobs can become re-employed either by being recalled
to their previous employers or by finding new jobs. Each of these routes out of
unemployment has merited the attention of researchers interested in how quickly
job losers return to employment. Although intuition, as well as casual observation,suggests that workers’ prospects for being recalled should influence how hard they
search for new jobs (including which oﬀers they are willing to take), the empiricalliterature on the topic has generally proceeded without taking explicit account of
this interaction.
Katz (1986) recognized that the negative duration dependence observed in theoverall rate of exit from unemployment could be due partly to negative duration
dependence in the recall hazard masking positive dependence in the new job hazard.
He estimated a competing risks duration model that allowed for both routes out of
unemployment, assuming independent Weibull hazard functions and no unobserved
heterogeneity, and found positive duration dependence in the new job hazard. (Seealso Pichelmann and Riedel 1992.)
Han and Hausman (1990) demonstrated that the Weibull assumption was
overly restrictive. They estimated a semi-parametric competing risks model with aflexible baseline hazard function. In addition, they allowed the two types of risks to
be interrelated. While they found no statistically significant relationship between
the two hazard rates, they did find that with their more flexible specification, there
was no evidence of positive duration dependence in the new job hazard.
However, Han and Hausman did not take into account unobserved heterogeneity as such, nor did it attempt to explicitly incorporate the behavioral interaction
between the two routes out of unemployment.
In this paper, we propose an improved specification that incorporates boththese features. We solve a job search model in order to establish, theoretically, anegative behavioral relationship between the recall and the new job hazard rates
that stems from the optimal search strategy of the worker. We then estimate a semiparametric duration model with two competing risks, allowing for both observed andunobserved heterogeneity and for a behavioral relationship between the two risks.
We find positive duration dependence in the new job hazard function, but only asmall negative behavioral relationship between the recall and new job hazards.
Like the current work, both Katz (1986) and Han and Hausman (1990) estimated the objective probability of recall, but lacked any direct measure of workers’
subjective probabilities of recall. In contrast, Katz and Meyer (1990) and Anderson(1992) estimated competing risks models in which self-reported recall expectations
enter the new job hazard function as a covariate. Both studies found that workers’
initial expectations of recall severely depressed the rate at which workers found newjobs, and that this eﬀect diminished over the course of a spell of unemployment.
We view this research and our own work, in which we infer recall expectations from1

observed recall rates, as alternative approaches to answering this question. Eachapproach has its advantages. On the one hand, data on recall expectations allow
workers’ subjective probabilities (which drive search behavior) to diﬀer from observed probabilities, and do not suﬀer from quite the diﬃculties of identificationthat will be an issue in our work. On the other hand, currently available data setsthat include a measure of recall expectations are limited in scope (for example,
including only recipients of unemployment insurance benefits), include only binary
measures of recall expectations, and measure these expectations only at the beginning of the spell, with little indication of how those subjective probabilities maychange as the spell progresses. Moreover, given the survey question, it is not clear
just what is meant when a repondent says that she “expects” to be recalled. Boththe level of confidence and the time frame in which she expects to be recalled areambiguous, which makes interpretation diﬃcult. (See section 7.)
2. Identifying the Behavioral Relationship
Section 3 below presents a theoretical model of job search. Taking into accounthis chances for recall, an unemployed worker chooses how much eﬀort to put into
searching for a new job, and how choosy to be. If he takes a new job too early, hesacrifices the chance of returning to his previous employer. But the longer he waits
before taking a new job, the more income he foregoes. The model characterizes thesearch starting time, search intensity, and the reservation wage partly as functionsof the unemployed worker’s prospects for recall.
We then move on to estimate the joint distribution. The observed unemployment duration will be the minimum of the time to recall and the time to accepting
a new job. We assume that the worker cannot aﬀect her probability of being recalled, except by accepting a new job. Thus, the time to recall is exogenous, but
the time to accepting a new job is endogenous and influenced by the prospects forrecall. Thus, the observed duration is most suitably characterized by a dependentcompeting risks duration model.
However, although the behavioral relationship between the two risks may beclear in theory, in practice the observed relationship between the recall and new job
hazard rates may stem from another source: the direct eﬀect of heterogeneity acrossindividuals. If one believes that “better” workers will be quicker than “poorer”
workers both to be recalled and to find new jobs, then the relationship between thetwo hazard rates induced directly by heterogeneity should be positive. If, instead,prospective new employers are reluctant to hire wrokers laid oﬀ from the types
of jobs that tend to engage in temporary layoﬀs and subsequent recalls, then therelationship between the two hazard rates induced directly by heterogeneity shouldbe negative. In either case, the behavioral relationship should be negative.
To identify these two diﬀerent relationships empirically is not easy. Conceptually, the negative behavioral relationship applies to a given laid-oﬀ worker as her
2chances for recall change over the course of her unemployment spell, or to a set ofworkers who are identical except for the recall probabilities they face, whereas the
directly-heterogeneity-induced relationship applies across diﬀerent (non-identical)
laid-oﬀ workers. In data comprising single spells for many diﬀerent workers — thesort of data a researcher typically confronts — the two types of relationship are
confounded.
Moreover, in such data, the non-behavioral (so to speak) heterogeneity-induced
relationship is likely to dominate the negative behavioral relationship. Consequently, in order to test for the negative behavioral relationship implied by theory,
one needs to carefully control for heterogeneity, both measured and unmeasured. In
this paper, we control for observed heterogeneity by including a rich set of covariates, and control for unobserved heterogeneity using discrete methods suggested by
Heckman and Singer (1984).
Yet the diﬃculties in identifying the behavioral relationship may be more subtle
still. The negative behavioral relationship between the two hazards should manifest
itself in two ways: through the dependence of the overall level of an individual’s newjob hazard on the overall level of the individual’s recall hazard, and through thedependence of the change in his new job hazard over the course of an unemployment
spell on the change in his recall hazard over the course of the same spell. The
distinction is reminiscent of between-group variation vs. within-group variation in
the standard decomposition of variance, if one interprets a group as the weeks
constituting an individual spell of unemployment.
Since our data generally do not include multiple spells for the same individual,
the first manifestation of behavioral relationship — that between the overall levels —and the spurious relationship induced by heterogeneity both show up in comparisonsacross diﬀerent individuals. It may, consequently, be diﬃcult in practice to distinguish between the two. The second manifestation of the behavioral relationship —that over time within a spell — is more distinct.
The variation in recall hazards over time within a spell of unemployment isapparently much smaller than the cross-sectional variation in overall recall hazards.
For example, across persons recall prospects can and do vary from clearly zero, as in
the case of business closings, to almost certain with a recall date specified in advanceby the employer, as one often sees, say, in the auto industry. Accordingly, we
see a trade-oﬀ in empirically identifying the behavioral relationship: The negative
behavioral relationship induced by the variation over time in recall hazards is notconfounded by any competing heterogeneity eﬀect, but may not assert itself sostrongly in the data; whereas the relationship induced by cross-sectional variationin the overall levels of the hazard rates is more muddled, in the sense that it combines
a “behavioral” relationship with a directly heterogeneity-induced relationship, but
because of the large amount of variation in recall prospects across individuals, it
probably has a much stronger presence in the data.
Our estimation procedure is designed to try to separate the two sources ofcross-sectional variation, and then combine the behavioral source of cross-sectional
3

variation with the behavioral over-time variation. The two behavioral sources are
combined in that, at a given point in a spell of unemployment, a person will search
for new job with (presumably) greater intensity if he faces a lower recall hazard
regardless of whether the latter is due to the dissipation of his chances for recall as
time passes, or due to his “inferior” individual or job characteristics to begin with.
This compromise is consistent with the semi-Markov property established in thetheory, that is, a laid-oﬀ worker’s optimal search strategy at any time is a functionof the level of the recall hazard rate at that time, without regard to the path bywhich that level was arrived at.
To control for the “non-behavioral” relationship between the two hazard rates
induced directly by heterogeneity, we allow observed and unobserved individualand job characteristics to enter both the new job and recall hazards in the formof a proportionality term in each hazard function. The proportionality assumption
reflects the idea that ”better” workers are viewed by the previous employer as well as
potential new employers as better prospects than ”poorer” workers throughout the
unemployment spell. Within each proportionality term, measured and unmeasured
individual diﬀerences are captured through covariates and through a pair of randomvariables, respectively.
Once we control for non-behavioral relationship between the new job and recall
hazards generated by measured and unmeasured individual diﬀerences through theproportionality term in each hazard function, we hope to be able to identify the
behavioral negative relationship between new job hazard rates and recall hazard
rates that should obtain both over the course of an unemployment spell for a given
individual and across otherwise similar individuals facing diﬀerent recall prospects.
This behavioral relationship is captured by allowing the recall hazard to influence
the new job hazard directly. The remaining pattern, captured through baseline hazard rates, is supposed to represent the evolution of the hazards over the course of anindividual’s unemployment spell, which is assumed to be common to all individuals.
Of the literature that has attempted to estimate these hazard rates, our econometric framework is closest to that used by Han and Hausman (1990), but diﬀers inthree important respects. First, we introduce unobserved heterogeneity along thelines of Heckman and Singer (1984), whereas Han and Hausman, relying on the evidence of their single-risk estimates, chose not to include unobserved heterogeneity
in their competing risks model. Second, we remain loyal to the initial mixed proportional hazard specification, whereas Han and Hausman deviated from their initialmodel in the competing risks setting by assuming that certain transformations of T1
and T2 follow a bivariate normal distribution, thus avoiding the bivariate extreme
value distribution which would naturally follow from the initial assumption of the
proportional hazard model. Third, and most important, our model specification
allows us to test for the behavioral relationship between the two risks implied by
the theory. Our model is logically consistent, and is also tractable to estimate.
In sum, our paper attempts to make several contributions: Methodologically,(i) both theory and estimation are handled consistently, (ii) methods of identifying
4

behavioral relationships between the recall and new job hazard rates are proposed,and (iii) our empirical model improves upon those of Katz’s and Han-Hausman’s.
Substantively, (iv) we show the new job hazard to be increasing, and (v) we findevidence of an economically small negative behavioral relationship between the recall and new job hazards, leaving in some doubt the negative influence of recall
prospects on new job search behavior.
3. Theoretical Model
One can characterize a laid-oﬀ worker’s optimal search strategy as a trade-oﬀ
between waiting for recall and searching for a new job. Intuitively, if the probabilityof recall is suﬃciently high, it is better not to search for a new job at all and simply
to wait for recall. But, over time, as the chance of recall (presumably) falls, evensuch a worker will start trying to generate new job oﬀers. This search activity
becomes more intense as the probability of recall shrinks, reaching a maximum
when there is no chance of recall at all.
This characterization of the optimal search strategy is a solution to the stochastic optimal control problem that trades-oﬀ the conflicting objectives of, on the one
hand, minimizing search costs and preserving human capital, and on the other hand,minimizing the length of the unemployment spell and thus reducing the earnings
foregone. To characterize this optimal search strategy, we first need to make assumptions about the exogenous stochastic process governing the distribution of thetime to recall. Then we can characterize the optimal behavior of the laid-oﬀ worker.
This characterization plays an important role in deriving the joint distribution of
the time to recall and the time to finding a new job.
First we introduce notation:
w =deterministic wage rate prevailing at the previous job;
Wj ∼ F (·) =random wage rate at a new job;r(t) = recall hazard rate after time t has elapsed since lay-oﬀ, r0 (t) ≤ 01 ;s ∈ S =search intensity of a laid-oﬀ worker, S ⊂ R+ ;c(s) =cost of searching as a function of search intensity,c(0) = 0, c0 (s) > 0, c00 (s) ≥ 0;λ(s) =new job arrival rate as a function of search intensity, λ0 (s) > 0, λ00 (s) < 0;
δ =discount rate;
Tr =time (duration) until recall;
Tj =time (duration) until accepting a new job;T ≡ min(Tr , Tj )=duration of unemployment for a laid-oﬀ worker.
The recall hazard rate r(t) determines the time to recall Tr . We assume here
1

The hazard rate is also referred to in the literature as the failure rate or theage specific death rate.
5

that the recall hazard rate r(t) is monotonically decreasing, r0 (t) ≤ 0. Whether or
not one searches for new job, and, if one does search, how much search eﬀort one
puts forth, determine the cost of search and the arrival rate of new job oﬀers. The
cost of searching, c(s), is an increasing function of the search intensity s, s ≥ 0,with increasing marginal cost. The benefit of searching is generating new job oﬀers.
New jobs arrive according to a non-homogeneous Poisson process with intensityλ(s). This arrival rate λ(s) is an increasing function of s. But the marginal benefitof search in terms of the marginal increase in the new job arrival rate is assumed to
be decreasing in s. The new job arrival rate and the reservation wage level (to be
defined below) will determine the hazard rate for finding a new job, and thus theduration Tj leading to accepting a new job.
Between the two competing duration variables, Tr and Tj , only the minimum,
T = min(Tr , Tj ) is realized and observed, with its source identified.
Given his discount rate δ, a laid-oﬀ worker maximizes expected discounted
future income from time zero to infinity by pursuing an optimal search strategy.
The choices open to the worker at each instant are whether or not to search for a
new job, how much eﬀort to put into the search activity, and whether to take a newjob once oﬀered.
The optimal search strategy determines the time until a new job Tj endogenously. Given the infinite horizon and the stationarity of other elements of thesearch problem, the environment is stationary conditional on the recall hazard rate.
Of course, the recall hazard rate itself is decreasing over time, introducing an element of unconditional non-stationarity. Thus, not conditional on the recall hazard
rate, the optimal search strategy changes over time, but once the recall hazard rate
is given, the optimal search strategy can be characterized purely as a function of
the recall hazard rate, independent of the time elapsed since lay-oﬀ. In this way,
the optimal job search strategy satisfies a semi-Markov property, a property crucial
for empirical identification of the behavioral relationship.
Let us formalize some of the above statements into assumptions:
Assumption 1. The recall hazard rate is monotonically decreasing for eachlaid-oﬀ worker, r0 (t) ≤ 0.
In the empirical analysis, we will estimate r(t) without imposing this monotonicity assumption, and then test whether the estimated pattern is consistent withthe monotonicity assumption.
Assumption 2. A new job, once turned down, cannot be “recalled” later on(search without “recall”).
Note that here we write “recall” with quotation marks. This “recall”, as usedin the literature, means an option to accept previous job oﬀers at a later time, andis an altogether diﬀerent concept from the recall to the previous job that we are
analyzing in this paper. In the traditional stationary search model, such as Lippman
and McCall (1976a,b), search with “recall” and search without “recall” result in6the same optimal search strategy on the part of the worker: Under stationarity, arational economic agent has no reason to revise his previous accept/reject decision,
implying that an oﬀer once turned down will never be “recalled.” Therefore, theoption of “recall” will never be exercised, and there is no diﬀerence between the
search strategies with and without “recall.”But here, the chance of being recalled to one’s previous employer is decreasingover time, introducing non-stationarity into the environment, and causing searchwith “recall” to diﬀer from search without “recall.” Through Assumption 2, we
restrict our consideration to the search without “recall.” However, the main pointof the model — that the new job hazard should be decreasing in the recall hazard— would obtain without this assumption, and our empirical specification does notembody this assumption.
Assumption 3. An oﬀer to be recalled is always accepted.
Assumption 3 says that value of recall is higher than the value of continuing
to search, at any level of the recall hazard rate. This condition is more likely to besatisfied as the wage prevailing at recall is higher relative to the expected wage at
new jobs, as the new job wage distribution has less variation, as the discount rateincreases, and as the new job arrival rate decreases.
In practice, an oﬀer of recall may not always be accepted, and in our data, wecannot identify whether a worker has received and declined an oﬀer of recall before
taking a new job. However, in our judgment the probability that a worker will turndown recall is low. So, for simplicity, we adopt Assumption 3 in our model. It
would be interesting to extend the model by relaxing this assumption, but that isbeyond the scope of the current work.
Once a new job oﬀer arrives, the unemployed worker evaluates the oﬀered wage
rate. If it is high enough, he will take the new job. Otherwise, he will turn down
the oﬀer, and continue searching for another new job while also waiting for recall.
In contrast, by assumption 3, a laid-oﬀ worker will always accept an oﬀer of recall.
Assumption 4. The cost function c(s) is increasing from an initial level ofzero and is convex with respect to search intensity s: c(0) = 0, c0 (s) > 0, c00 (s) ≥ 0.
The new job arrival rate function λ(s) is increasing but at a decreasing rate: λ0 (s) >0, λ00 (s) < 0. A new job oﬀers a random wage W which is distributed according toa distribution function F (·). Wages are independent across oﬀers.
Assumption 4 posits the typical positive and increasing marginal cost function
c (s), and the typical positive but decreasing marginal product function λ0 (s). Wageoﬀers are assumed i.i.d. according to a distribution function F (·).
Under these assumptions, one can show that the optimal search strategy of an
unemployed worker over time is characterized by Theorem 1, and that one unemployed worker’s optimal search intensity is diﬀerent from another’s when the two
are faced with diﬀerent recall hazard rates, as stated in Theorem 2.
07Theorem 1. (search strategy of an unemployed worker over time)
The optimal search strategy is characterized by nondecreasing search intensity andnonincreasing reservation wage, leading to a nondecreasing new job hazard rateover the duration of an unemployment spell. If the initial recall hazard rate is highenough, it is optimal not to search for a new job at all until a certain amount oftime has elapsed since lay-oﬀ. Because the recall hazard rate is decreasing over time,a laid-oﬀ worker will increase search eﬀort over time, and will accept any new job
oﬀering a wage higher than the reservation wage at that time. The reservation wage
is nonincreasing over time, reflecting the fact that the laid-oﬀ worker is more willingto accept new jobs as the recall hazard rate falls. (proof in the appendix)
Theorem 2. (comparison of two unemployed workers’ search behavior) Suppose that there are two unemployed workers, say A and B, where A is facedwith a uniformly higher recall hazard rate schedule than B over the course of theirunemployment spells. Then, A will begin to search for a new job later in the spellthan will B. At any point in the spell at which both A and B are searching for newjobs, A will search less intensely than B. (proof in the appendix)
These two theorems allow us to identify the behavioral relationship between
the recall hazard and the new job hazard in empirical implementation.
4. Empirical Model
Our task is to develop an empirical model that allows one to test whether
recall hazard rates are decreasing, whether new job hazard rates are increasing, andwhether recall hazards depress new job hazards.
However, as described in section 2, there are diﬀerences across workers in characteristics and circumstances that cause their hazard rates to move together in a
non-behavioral way. For example, a worker disemployed during a boom may face ahigher recall probability, and also will find a new job more easily, than an otherwise
identical worker disemployed during a recession. To take an opposite example, aworker with a large amount of firm-specific human capital may face higher recall but
lower new job hazard rates than a worker with more general skills. Thus heterogeneity can generate a spurious (with respect to the theory) cross-sectional relationship,
either positive or negative, between the recall and new job hazard rates.
If we observed many unemployment spells for each individual, it would be easier
to identify the negative relationship between the two hazards rates. However, as
is typically the case, in our data we observe many individuals for only one spell(and often only part of that). Under these circumstances, the spurious positive
relationship between the hazards across individuals may dominate the negative
behavioral relationship, resulting in a positive overall observed relationship. The
nature of the data, then, requires careful attention to be paid to heterogeneity,
both measured and unmeasured, if we hope to uncover the negative behavioral
8relationship.
The trick is to find a way to separately identify the spurious cross-sectional
relationship arising directly from heterogeneity from the behavioral relationshipthat arises from the worker’s reaction to that heterogeneity. In the empirical model
presented below, we employ essentially two identifying assumptions, beyond thestandard assumptions of the proportional hazard model.
First, we allow individual heterogeneity, measured and unmeasured, to generate
any pattern of cross-sectional relationships between the two hazard rates by letting
individual and job characteristics enter into the recall and new job hazard functions
with free coeﬃcients, and by introducing random variables representing unobserved
heterogeneity into both hazard functions without restricting their correlation acrossthe hazards. However, we allow only a single combined eﬀect of the recall hazard
rate on the new job hazard rate, since it is only this total recall hazard, not its
individual determinants, that ought to influence new job search behavior.
Second, we assume that workers unemployed due to plant closings or to theends of seasonal or temporary jobs have no recall prospects and are aware that they
have none. Econometrically, this restriction serves the same purpose as the more
typical exclusion restrictions in a two-equation system, by forcing these variables tohave a larger impact on the recall hazard than on the new job hazard in a particular
fashion determined by our prior knowledge of the world.
Let z = {z1 , z2 , · · ·} denote a collection of observed individual and job characteristics aﬀecting the recall and new job hazard rates in weeks {1, 2, · · ·} after
the loss of a job. Let e and v denote two possibly correlated random variables
capturing unmeasured heterogeneity in the recall and the new job hazard rates,
respectively. z controls for observed heterogeneity, whereas e and v are intended toaccount for remaining individual diﬀerences. Higher draws of e and v mean thatthe corresponding worker faces a better chance of recall and finding a new job,
respectively.
Workers who lost their jobs due to plant closings or the end of seasonal or
temporary jobs are assumed to face a recall hazard rate of zero throughout theirunemployment spell (with a few exceptions, described in note 5 below). To distinguish these workers from those who may have recall prospects, we define anindicator variable 1nohope , which takes value one if the worker was dismissed due toeither plant closing or end of seasonal or temporary job and zero otherwise. These
workers will presumably start searching for new jobs immediately after becoming
unemployed.
Consider a worker characterized by a vector (z, e, v). We model the recall
hazard rate of this worker as:r(t|z, e, v) = r(t|z, e) = (1 − 1nohope )r0 (t) exp(xt β + e),(6)where the value of 1nohope can be determined from information in z, and xt is asubset of zt influencing the recall hazard rate at week t for potentially recall-able
workers.
9

This specification has the form of a mixed proportional hazard model. The(mixed) proportionality part, (1 − 1nohope ) exp(xt β + e), controls for observed andunobserved heterogeneity. The proportional hazard assumption reduces the duration dependence of recall hazard rate for each individual worker to the duration
dependence of the common baseline hazard function, simplifying the task of testing
assumptions about duration dependence.2
To anticipate our description of the data in section 5, the observed heterogeneity
term z includes numerous socio-economic variables, year dummies, three region
dummies, seven industry dummies, and five occupation dummies. Additionally, z
includes a dummy variable for whether the worker received unemployment insurance(UI) benefits, and its interaction with each of two benefit exhaustion points at 26
and 39 weeks. These interaction terms serve to control for spikes in the exit rates
observed in our data for UI recipients (see Katz 1986 or Han and Hausman 1990).
A realization of z and e defines a conditional distribution of Tr through theconditional recall hazard rate r(t|z, e). From fr (t|z, e)/Sr (t|z, e) = r(t|z, e), we
derive Sr (t|z, e) = exp[−R(t|z, e)], where Sr (t|z, e) = P r(Tr ≥ t|z, e) is the conditional recall survival function, fr (t|z, e) is the corresponding conditional recall
Rt
density function, and R(t|z, e) = 0 r(u|z, e) du is the integrated recall hazard rate.
Note that z will be observed both by the individual worker and econometricians,
but e will not be observed by the econometrician. Thus, we obtain an unconditional
distribution of Tr by taking the expectation of the above quantities with respect tothe stochastic nature of e: Sr (t|z) = Ee Sr (t|z, e).
In section 3, we derived the new job hazard rate as a solution to an optimal
control problem, given an exogenously specified recall hazard rate: the new job
hazard rate is λ(s(r)) · [1 − F (wr∗ )] when the recall hazard rate is r.
Note that the derived new job hazard rate, being the product of new job arrival
rate and the probability that the oﬀered wage exceeds the reservation wage, would
not in general be in a proportional hazard form, even if, as we have assumed, therecall hazard rate is in a proportional hazard form. A fully structural approach
would specify λ(s) as a function of s, and characterize s(r) and wr∗ in terms of r. In
this paper, we take a reduced-form approach (i) modeling the new job hazard rate
as a function of the recall hazard rate as well as additional time and heterogeneity
components, and then (ii) testing the structural search implications ex post. Thisapproach allows us to specify the recall and the new job hazard rates flexibly at thesacrifice of theoretical neatness.
To capture the theoretical implication that the new job hazard rate “reacts”
to the recall hazard rate, we explicitly model the new job hazard rate as a functionof the recall hazard rate. Any other duration dependence in the new job hazard
2

Given the computational demands inherent in our model, one can easily imagine
how diﬃcult it would be to test for duration dependence for each individual without
invoking the proportionality assumption. In section 6 we test the proportionality
assumption using the methods in Ryu (1994), and fail to reject it.
10

rate will be captured by a baseline hazard rate for new jobs. Thus we can test forany time pattern in the new job hazard rate that remains after controlling for theeﬀect of changing recall hazard rate and the eﬀects of measured and unmeasured
heterogeneity. Specifically, we model the new job hazard rate asj(t|z, e, v) = j(t|z, v) = j0 (t) exp(zt γ + a · (1 − 1nohope )r0 (t)ext β + v).

(7)

Observed heterogeneity appears anew in the new job hazard specification, with
its own set of coeﬃcients, as one would not expect the eﬀects of worker and job
characteristics on recall and new job finding to be the same. For example, union
members may be more likely to be recalled, but less likely to find new jobs. If
so, the union dummy variable will appear in the recall hazard rate with positive
coeﬃcient, but in the new job hazard rate with a negative coeﬃcient. We allow forthis diﬀerential impact for all variables. Also, to see whether job loss due to plantclosing or end of seasonal or temporary jobs have an eﬀect on speeding up new job
search in addition to their influence via the recall hazard rate, we allow z to include
plant closing status and temporary/seasonal status in addition to variables in x.
To control for unobserved heterogeneity in the new job hazard rate, we introduce
another discrete random variable v, which may be correlated with e. The correlation
between e and v, if any, would reflect the spurious relationship between the recall
and new job hazard rates arising from unmeasured heterogeneity.
The introduction of a · (1 − 1nohope )r0 (t)ext β as an argument in the new job
hazard specification is intended to capture one of the major implications of the job
search model developed in the previous section. We introduce this term under theassumption that agents know their overall recall chances — to the extent that it isdetermined by measured heterogeneity — and react to this knowledge when looking
for new jobs. We assume that agents do not know the realization of e and thus do
not react to this term. This assumption is of course open to question, but is notcritical for our results.
If a turns out to be negative, it implies that a laid-oﬀ worker whose chance ofrecall is lower is, in response, more enthusiastic about finding a new job, and searches
more intensely or with a lower reservation wage. The lower probability of recall
may derive from the time that has elapsed since the lay-oﬀ, or from unfavorable
individual or job characteristics; the result is the same. In the extreme case, workers
who lost their jobs due to a plant closing or the end of a temporary job exhibit
the strongest behavioral reaction because they have no chance of being recalled
throughout their spells of unemployment.
In addition, we are interested in seeing whether r0 (t) and j0 (t) display any duration dependence of their own. If our job search theory is a reasonable descriptionof behavior, then the behavioral relationship between the recall hazard rate and the
new job hazard rate should be captured through the negative coeﬃcient of a. But
we have no particular expectation for a remaining temporal pattern in j0 (t), once
we control for (1 − 1nohope )r0 (t)ext β in the specification of the new job hazard rate.
11

To save on the number of parameters to be estimated, we restricted the recall
and new job baseline hazard functions each to be a step function, with the number ofsteps considerably smaller than the number of weeks in the duration data. Also, toavoid odd behavior in the estimated baseline hazard functions due to the sparsity ofobservations at longer durations, we right-censored any observations whose reported
duration is longer than or equal to 60 weeks. The lengths of the steps are identical
for the two hazard functions. After considerable experimentation, we chose a step
function with 12 steps: the first three steps are each 2 weeks long, the second three
are each 3 weeks long, the third three are each 4 weeks long, and the final three
are each 11 weeks long. The lengths of the steps are increasing because the data
become sparser as duration increases. This choice appears to represent a goodbalance between flexibility and tractability.
Assuming that the baseline hazard functions are constant within each step butvary across steps, let us define rk and jk as rk = log r0 (t) and jk = log j0 (t) fortime t within step k, k = 1, · · · , 12. Note that the rk ’s and jk ’s are unrestricted,
whereas r0 (t) and j0 (t) are restricted to be positive. Then, r1 , · · · , r12 are twelve
free parameters characterizing the recall baseline hazard function, and j1 , · · · , j12
are twelve free parameters characterizing the new job baseline hazard function.
Thus, each baseline hazard function is approximated as a step function with twelve
steps covering durations from one to sixty weeks. From (6) and (7), we have, fork = 1, · · · , 12,r(t|z, e) = (1 − 1nohope ) exp(rk + xt β + e), for t in step k,j(t|z, v) = exp(jk + zt γ + a(1 − 1nohope )erk +xt β + v), for t in step k.

(8)Now, let us write down the likelihood contribution of each observation according
to the duration and outcome of its unemployment spell. An observation will takeone of the following three forms:(i) An unemployment spell is terminated due to recall in the tth time interval.
In this case, we assign to the observation P r(t − 1 < Tr ≤ t, Tj > Tr ), which will
be bounded by P r(t − 1 < Tr ≤ t, Tj > t) and P r(t − 1 < Tr ≤ t, Tj > t − 1). Since
the length of an interval in our data is just one week and, accordingly, a worker’s
chance of receiving both a recall and an acceptable new job oﬀer in the same interval
is quite small, all three probabilities will be approximately equal. While the twobounds are easy to compute, the true probability is relatively involved to compute(see Han and Hausman 1990, Fallick 1991, McCall 1996). So, we approximate thetrue probability P r(t − 1 < Tr ≤ t, Tj > Tr ) as P r(t − 1 < Tr ≤ t, Tj > t − 1).
(ii) An unemployment spell is terminated due to taking a new job in the tthtime interval. In this case, we assign to the observation P r(Tr > Tj , t − 1 < Tj ≤ t),which will be bounded by P r(Tr > t, t − 1 < Tj ≤ t) and P r(Tr > t − 1, t − 1 <Tj ≤ t). We will approximate the true probability P r(Tr > Tj , t − 1 < Tj ≤ t) as
P r(Tr > t − 1, t − 1 < Tj ≤ t).
12

(iii) An unemployment spell is still going on at the end of the tth interval. In
this case, we assign to the observation P r(Tr > t, Tj > t).
As mentioned above, for those workers unemployed due to plant closings or theend of temporary or seasonal jobs, we assume that the probability of recall is zerothroughout the unemployment spell. If such a spell is terminated due to taking a
new job in the tth time interval, we assign P r(Tr > Tj , t − 1 < Tj ≤ t) = P r(t − 1 <Tj ≤ t) after imposing r(u|z, e) = 0 for all u. On the other hand, if such a spell is stillgoing on at the end of the tth interval, we assign P r(Tr > t, Tj > t) = P r(Tj > t).
To derive the probabilities in (i)-(iii) above from the hazard rates specified in
Rt(8), it is useful to define the integrated hazard rates, R(t|z, e) = 0 r(u|z, e) du andRt
J(t|z, v) = 0 j(u|z, v) du, for the recall and the new job hazard rates, respectively.
Assuming that z is constant within each week (which is the case in our data), these
integrations reduce to summations by virtue of the assumed step nature of thebaseline hazard functions,
R(t|z, e) =J(t|z, v) =

t
X

u=1
t
X
u=1

r(u|z, e),(9)j(u|z, v), t = 0, 1, · · · , 60,

where R(0|z, e) = J(0|z, v) = 0. The conditional survival probabilities are,Sr (t|z, e) = P (Tr > t|z, e) = exp[−R(t|z, e)],Sj (t|z, v) = P (Tj > t|z, v) = exp[−J(t|z, v)].

(10)

Recall that Tr and Tj are correlated through the search strategies of laid-oﬀ
workers as well as through heterogeneity across workers. If our model is wellspecified, in the sense that these relationships are fully reflected in the specificationof r(t|z, e) and j(t|z, v), then it is reasonable to assume that Tr and Tj are independent given r(t|z, e) and j(t|z, v).
Under this assumption of conditional independence, we have
P r(t − 1 < Tr ≤ t, Tj > t − 1|z, e, v) = [Sr (t − 1|z, e) − Sr (t|z, e)]× Sj (t − 1|z, v),
P r(Tr > t − 1, t − 1 < Tj ≤ t|z, e, v) = Sr (t − 1|z, e)
× [Sj (t − 1|z, v) − Sj (t|z, v)],
P r(Tr > t, Tj > t|z, e, v) = Sr (t|z, e)Sj (t|z, v).

(11)

We do not observe the realization of (e, v), so we must take the expectation of theabove quantities with respect to the stochastic nature of (e, v). Assume that e and13

v follow a discrete bivariate distribution that takes value (el , vm ) with probability
plm , l = 1, · · · , M and m = 1, · · · , M. Here, M denotes the number of support
points for each of e and v. This approach has been advocated by Heckman andSinger (1984). We estimate the model with M = 1 (no unobserved heterogeneity),
M = 2, and M = 3, and chose an “optimal” M according to the Schwarz Bayesian
information criterion (e.g., Stock and Watson 2003).
Because 0 ≤ plm ≤ 1 (m = 1, · · · , M), for computational convenience we
represent plm ’s in terms of qlm ’s as follows:
eqlm
plm = PM PM
l=1

qlm
m=1 e

, l, m = 1, · · · , M.

The advantage
this representation is that qlm is not bounded, −∞ < qlm < ∞.
PM ofP
Of course, l=1 M
m=1 plm = 1, so normalization is necessary, and we choose toimpose q11 = 0.
Some normalization is also required to estimate the overall level of each hazard
rate, as the “intercepts” in the baseline hazard rates, the constant terms in x and z,
and the unobserved heterogeneity terms (e and v) are redundant if left unrestricted.
We use the baseline hazard function to estimate the overall level of each hazard rate,and impose restrictions on the other two “intercepts”, by excluding the constantterm from both x and z and setting e1 = v1 = 0.
By taking the expectation with respect to e and v, one derives
P r(t − 1 < Tr ≤ t, Tj > t − 1) = Ee,v P r(t − 1 < Tr ≤ t, Tj > t − 1|z, e, v)
=

M
M X
X

plm [Sr (t − 1|z, el ) − Sr (t|z, el )]Sj (t − 1|z, vm ),

M
M X
X

plm Sr (t − 1|z, el )[Sj (t − 1|z, vm ) − Sj (t|z, vm )],l=1 m=1

P r(Tr > t − 1, t − 1 < Tj ≤ t) = Ee,v P r(Tr > t − 1, t − 1 < Tj ≤ t|z, e, v)=

l=1 m=1(12)

P r(Tr > t, Tj > t|z) = Ee,v P r(Tr > t, Tj > t|z, e, v)
=

M
M X
X

plm Sr (t|z, el )Sj (t|z, vm ).

l=1 m=1

These unconditional (with respect to e and v) probabilities will form our likelihood
function. The resulting likelihood function will be a function of β, γ, a, rk ’s, jk ’s,
el ’s, vm ’s, and qlm ’s, with the normalizations e1 = 0, v1 = 0, and q11 = 0 .
To summarize, the recall hazard rate and the new job hazard rate are related
through two channels: (i) individual optimization implies a behavioral relationshipacross time and across individuals, as predicted by the search model; and (ii) heterogeneity across individuals and jobs may induce a non-behavioral relationship
14

directly. The first channel will be captured by the sign of a. We expect a to be
negative, implying that when the recall hazard rate is lower, due either to the passage of time since the lay-oﬀ or to individual or job characteristics, the new job
hazard rate is higher as the worker adjusts his new job search behavior. The second channel, individual heterogeneity, will be captured in two ways. For measured
heterogeneity z, we allow diﬀerential impacts of numerous individual covariates inthe two hazards: β and γ are not restricted to be equal for the variables in x. For
unmeasured heterogeneity, we model (e, v) as following a general discrete bivariate distribution, which allows unmeasured heterogeneity to aﬀect the two hazards
diﬀerently. If the type of person who is more likely to be recalled to his previous
job is also likely to find a new job faster for reasons not related to his optimal
new job search strategy, holding measured heterogeneity constant, then we would
expect e and v to be positively correlated. (Recall that using a diﬀerent approach,assuming a bivariate log-normal distribution, Han and Hausman found a positive,
but statistically insignificant, relationship.)Once we estimate the model, we will be interested in (i) the temporal patterns in
rk ’s and jk ’s, that is, duration dependence, (ii) the behavioral relationship betweenr(t|x, e) and j(t|z, v), that is, the coeﬃcient a, (iii) the relationship between β andγ, and (iv) the joint distribution of e and v, (including the “optimal” value for M).
Before moving on to describe the data, we note that an alternative empiricalstrategy would be to control for the direct eﬀects of heterogeneity in estimating
the recall and new job hazards, but to attempt to avoid confusing the spurious
and behavioral relationships between the two hazards by estimating the influenceof changes in the recall hazard on the new job hazard rate only over the course ofan unemployment spell, while leaving aside the influence on the new job hazard of
diﬀerences from person to person in recall hazard schedules.
In work not reported here, we pursued this strategy. That is, we estimated amodel in which only the baseline recall hazard rate, stripped of all heterogeneity
terms, can influence the new job hazard rate directly via the behavioral term (theterm that takes the coeﬃcient a). The estimates described a negative behavioral
relationship between the two hazards over the course of a spell of unemployment.
However, the finding was fragile, and not statistically significant at conventional
levels. We attribute this to not having enough variation over time in recall hazard
rates to allow us to convincingly identify the behavioral negative relationship bylooking at the time-variation alone. One has to make use of the cross-sectionalvariation as well.
5. Data
Our data are drawn from Waves XIV, XV, and XVI (interview years 1981-83) ofthe Panel Study of Income Dynamics (PSID), the same source used by Katz (1986),
Han and Hausman (1990), and Idson and Valletta (1996). Our sample comprises
15

heads of households who lost a job due to plant closings, the end of seasonal or
temporary jobs, or because they were “laid oﬀ” (either permanently or temporarily)
or fired. Each observation refers to the last spell of unemployment experienced
during the year previous to the interview, or else to a spell of unemployment thatwas ongoing at the time of the interview. Specifically, those who were employedor on temporary layoﬀ at the time of the interview were asked, referring to theirlast spell of unemployment in the calendar year previous to the interview, “Howmany weeks was it before you returned to work?” They were then asked whether
that spell of unemployment ended by returning to the same employer. Answers tothese two questions allow us to assign a value to the unemployment duration, andto distinguish between spells leading to recalls and spells leading to new jobs.3
Those who were unemployed (and not on temporary layoﬀ) at the time of theinterview were asked ”How long have you been looking for work?” When available,
we used the answers to these questions as the spell durations which are rightcensored. In the case of those still on temporary layoﬀ at the date of the interview,
however, durations were typically approximated by subtracting the reported monthin which the spell began from the interview month.4
We further restricted the sample to people who were between 21 and 64 yearsof age at the time of the interview, who were in the labor force every year from1980 to 1983 and were not exclusively self-employed during those years, and toobservations that were not missing data for any of the variables described below.
We artificially censored spells at 60 weeks of unemployment: any observations with
reported durations of 60 weeks or more were treated as still unemployed after 59
weeks. In addition, the questions do not allow us to identify with confidence spellswith durations of zero weeks. Therefore, we retain in the sample only unemployment
spells that are reported to have lasted at least 1 week, and renormalized all the
durations so that, for computational purposes, they span 0 to 59 weeks. Thus, theestimated hazard for the first week really refers to the hazard for the second week,
and so on.
In the end, we were left with a sample of 1403 observations, 274 of which ended
in a new job, 718 of which ended in a recall (that is, a return to the same employer),and 411 of which were still unemployed (censored) at the time of the survey or wereartificially censored at 59 weeks. Of the total of 1403 observations, 156 began witha plant closing or a temporary or seasonal job ending, and are accordingly assumed
to have recall hazard rates of zero throughout the spell.53Since those on temporary layoﬀ at the time of the interview may have completed
the last spell of unemployment in the previous year, they are not necessarily on
temporary layoﬀ for the purposes of our sample.
4
The nature of the questions is such that, in some cases, the reason for the
separation (which we used to distinguish job losses from quits) may not refer to thesame episode that generated the recorded spell of unemployment. This is not likely
to be often true, but does add some uncertainty to our results.
5
In practice, the spell of unemployment whose cause the survey identifies is
16

The explanatory variables are as follows. All but “temp/seasonal job ended”
and “plant closed” appearing in both hazard functions. That is, z includes all thevariables below, whereas x includes all the variables other than “tempseas” and“closed”, which enter the recall hazard only through the “nohope” variable. The
industry and occupation variables refer to the job that was lost.
SOCIO-ECONOMIC VARIABLES:age (at time of interview, in years)
male (= 1 if male, = 0 if female)education (years of schooling at time of interview)
white (= 1 if white, = zero otherwise)
UI benefit (= 1 if received UI benefits during spell, = 0 otherwise)
married (= 1 if married at time of interview, = 0 otherwise)
county unemployment rate (unemployment rate in county of residence)home ownerwhip (= 1 if owns own home, = 0 otherwise)
veteran (= 1 if a veteran, = 0 otherwise)
spouse employed (= 1 if spouse had a job at interview date, = 0 otherwise)
YEAR DUMMY VARIABLES:
y82 = 1 if wave XV (1982 interview year), = 0 otherwise
y83 = 1 if wave XVI (1983 interview year), = 0 otherwise
VARIABLES DESCRIBING LOST JOB
plant closed (= 1 if plant closed, = 0 otherwise)
temp/seasonal job ended (= 1 temporary or seasonal job ended, = 0 otherwise)
union member (= 1 if member of a union, = 0 otherwise)
job tenure (years at the lost job)
REGION DUMMY VARIABLES:
northeast (resided in the Northeast in previous year)
northcentral (resided in the North Central in previous year)
south (resided in the South in previous year)
INDUSTRY DUMMY VARIABLES:
finance/insurance/realtor (includes several other service industries)
trans/comm/utility (transportation, communications, utilities)
construction
durable manufacturing
miningnot necessarily the last spell of unemployment in the calendar year previous to
the interview (the latter being the spell to which the duration measures refer).
As a consequence, a small number of observations who reported a plant closing
or a temporary or seasonal job ending also reported having returned to the same
employer following the last spell in the previous year. We coded such observations
as normal layoﬀs since the answers given probably referred to diﬀerent spells.
17

nondurable manuracturingretail/wholesale (retail or wholesale trade)(The omitted category includes agriculture, forestry, fisheries, recreation andpersonal services.)
OCCUPATION DUMMY VARIABLES:
managment/admin (management, administration)
clerical/sales/service
craft
operatives
professional/technical(The omitted category includes laborers and farm occupations.)
Table 1 shows the sample mean and the sample standard deviation of eachexplanatory variable used in the paper.
(Table 1 here.)
6. Results
As we have emphasized so far, adequate controls for heterogeneity are important for testing the behavioral implications of search theory using data on single
unemployment spells for many individuals. We assume that u and v follow a discrete
bivariate distribution with the same number of points of support for each term. We
experimented with 1, 2, 3, and 4 points of support. Some unobserved heterogeneity
is clearly indicated. The Schwarz Bayesian information criterion strongly recommends 2 points of support (SBIC = -4093 vs. -4213 for 3 points), while the the
Akaike information criterion is indiﬀerent between 2 and 3 points. Adding a fourth
point of support to each hazard’s heterogeneity term improved the log-likelihood
trivially. Accordingly, we will feature the estimates from the mixed proportional
hazard model allowing for two points of support of unmeasured heterogeneity, shownin table 2. The values for e1 and v1 are normalized to zero, and the signficicance ofthe e2 and v2 terms attests to the importance of unobserved heterogeneity.
We tested the validity of the proportional hazard assumption using the methodsuggested by Ryu (1994). That is, one can test the proportionality assumption by
testing the equivalence of two sets of estimates, one estimated using the original
weekly duration data and the other estimated using a more aggregated version of
the same duration data. In our case, we aggregated the unemployment duration
data according to the baseline steps). According to the joint chi-square test, wecannot reject the proportionality assumption. Judging by individual t-tests, only
the local unemployment rate (ructy) turns out to have a non-proportional impacts
on the new job hazard rates. It significantly depresses the new job hazard rates
at an earlier period after lay-oﬀ. But such an eﬀect dies out over time, generating18

non-proportionality. We cannot reject proportionality for any other coeﬃcients.6(Table 2 here.)Among the explanatory variables, note that membership in a union increases
the recall hazard while decreasing the new job hazard.7 Job tenure significantly
increases the recall hazard rates whereas its impact on the new job hazard rates isnegative but not statistically significant.
Note also that having lost one’s job due to a plant closing has a significant
positive eﬀect on the new job hazard rate. But, having lost one’s job due to ending ofa seasonal or temporary job — a variable that has often appeared as having a positive
influence on new job finding in the literature — is not estimated to have a significant
eﬀect on the new job hazard rate. This would not imply that those displaced byending of seasonal or temporary jobs behave no diﬀerently than those laid-oﬀ forother reasons, however. They all have zero recall chances (by assumption), and thisaﬀects their new job hazards so long as the coeﬃcient a is not zero.
By comparing estimated coeﬃcients for each of the individual covariates in therecall and new job hazard functions, we observe that with respect to several characteristics (namely, sex, race, UI recipiency, and geography), people who are fasterto find new jobs are also faster to be recalled, a “spurious” positive relationshipbetween the two hazard rates arising from heterogeneity alone. This contrasts withthe estimated eﬀects of union membership, job tenure, and plant closings, which,as noted above, have opposite signs for the two hazards.
The model included interactions for UI receipt at weeks 26 and 39. The usual
spikes seen at the UI benefit exhaustion points (26th and 39th weeks) are confirmedby the positive coeﬃcient estimates of the UI interaction terms at 26 and 39 weeks(coeﬃcients ui26 and ui39), the first two of which are significantly positive.
In this model, the behavioral coeﬃcient a is estimated to be significantly negative, but small. A sense of the size of this estimated eﬀect of the prospect for recall
on new-job finding can be gathered from graphs 1 and 2. The graphs present therecall and new job hazard rates in percentage terms (after exponentiating the log
hazard rates), at the mean of the explanatory variables. The solid line in graph 2
shows how the estimated new job hazard changes over the course of a spell of unemployment for an individual with no chance of recall at any time (that is, 1nohope =1).
The dashed line shows how the estimated new job hazard changes over a spell for
an individual with the estimated recall hazard depicted in Graph 1. The diﬀerence
between the lines reflects our esitmate of a.
Graphs 1 and 2 here.
6

Detailed test results are available upon request.
This is the direct eﬀect of union membership on the new job hazard rate;union membership may also aﬀect the new job hazard indirectly by raising therecall hazard, but this is manifested exclusively through the behavioral coeﬃcient
a.
7

19

The importance of our treatment of unobserved heterogeneity for this result
is demonstrated in Table 3. The table shows the estimates of the behavioral coefficient for the 4 diﬀerent specifications that allow for successively greater degrees
of unobserved heterogeneity by allowing successively more points of support for its
discrete distribution.
(Table 3 here.)In the specification with just 1 point of support for the unobserved heterogeneity term, which is to say, the specification that assumes no unobserved heterogeneity, the estimate of the a coeﬃcient is far more negative than in those specifications
wherein unmeasured heterogeneity is taken into account. While once some unobserved heterogeneity is allowed (i.e., at least 2 points of support), the estimate is
not very sensitive to the the number of support points assumed.8
All in all, while our empirical results support the prediction of the theory that
there should be a negative behavioral relationship between the recall and the newjob hazard rates, but the estimated correlation is not large.
Clearly, then, one must adequately control for both measured and unmeasured
heterogeneity in order to identify the behavioral relationship between these two avenues for leaving unemployment. Drawing general inferences about behavior fromdata on single spells of many heterogeneous individuals is a challenging task, andwe do not doubt that better data are likely to be more useful than better econometric techniques for estimating the theoretical implications of job search models,a situation familiar to researchers in many areas. (For example, see Lalonde 1986
on evaluating the eﬀectiveness of job training programs.) Nevertheless, we obtain
empirical results consistent with the theoretical predictions by applying econometric tools to the sort of less-than-ideal data with which one is most often confronted.
The sensitivity of our findings to the introduction of unobserved heterogeneity, andtheir robustness to varying the degree of unobserved heterogeneity gives us confidence that our procedure was adequate to the task.
Graphs 1 and 2 also indicate that we find limited duration dependence in thehazard rates. The estimated recall hazard rate exhibits negative duration dependence, as posited in our theoretical model and documented by previous researchers.
However, the recall hazard rate only begins to decline after about 6 months following
a lay-oﬀ; the rate is flat, or even increasing, over the first 6 months of unemployment.
This suggests that it would be very diﬃcult to identify the behavioral influence ofrecall chances on the new job hazard by looking at the relationship over time alone.
Cross-sectional variation is critical.
The new job hazard rate is more or less increasing over the course of theunemployment spell, but not uniformly so.
8

We were unable to estimate the standard error of the coeﬃcient in the casewith four points of support.
20

7. Our Estimates compared to Katz and Meyer’s
Except in the case where only observed heterogeneity is modeled, our estimateof the behavioral impact of recall prospects on the new job hazard appears to beconsiderably smaller than that reported in Katz and Meyer (1990; KM hereafter)or Anderson (1992). However, comparing the estimates is not straightforward.
Recall that KM’s measure of recall expectations is a zero-one indicator variable for
expecting recall or not expecting recall. According to KM’s estimates, a person who”expects recall” has a new job hazard rate that is 60% to 75% as large as a person
who does not expect recall. But it is not clear just what it means to “expect recall”
in this context. Neither the likelihood of recall nor the time frame is specified.9 In
addition, our model deals with a recall hazard rate rather than an indicator variable.
For both reasons, comparing our estimates to theirs is best done by example. And
the task is made easier by positing constant recall hazard rates.
According to our estimates, a reduction in the new job hazard similar in size tothat found by KM for someone expecting recall relative to someone not expecting
recall would arise from a constant recall hazard rate of 40% to 50% relative toa recall hazard rate of zero (that is, to having no recall prospects at all, such as
would be true if nohope=1). But how well does a recall hazard rate of 40% to
50% correspond to “expecting recall”? One way to guage this is that a constantrecall hazard rate of this magnitude would imply that an individual has a 99%
chance of having been recalled by 6-10 weeks of unemployment, with a mean timeuntil-recall of 2 to 2-1/2 weeks. If this is a good description of the typical recall
prospect faced by someone who “expects recall” at the time of the layoﬀ, then ourestimates are of a similar magnitude to KM’s. As an alternative, if one thinksthat someone “expecting recall” at the time of the layoﬀ corresponds better to his
having, say, a 99% chance of being recalled within a year and a mean time-until
recall of 10 weeks, then a better comparision would be with an individual with aconstant recall hazard rate of 10%. According to our estimates, such an individual
would have a new job hazard that is 92% as large as a person with no prospects forrecall, a considerably smaller diﬀerence than that estimated by KM, although stillenough to raise a person’s mean time-until-new-job by 9%.
How can we reconcile our results with those of KM? If we ourselves were asking
the survey question in KM’s data, we would have in mind a recall hazard rate
more in the neighborhood of 10% than 50% when we asked whether the respondent
expects to be recalled. In this case, we would interpret our estimate of the behavioral
response to those expectations of recall as being much smaller than KM’s. However,the survey respondents may have a higher probability or diﬀerent time frame inmind. In particular, workers who expect recall may be overly optimistic, reacting
to an “ex ante” subjective recall hazard rate that is larger than the “ex post”
9

The survey questions is “do you expect to be called back to work by any ofyour past employers?” (KM, p. 978).
21

realized hazard rate that we estimate. If this is the explanation, it suggests thatlaid-oﬀ workers would increase their search eﬀorts if they were made better awareof their true prospects for recall. Of course, we may simply not have done a goodjob of estimating the ex post recall hazard rate. But note that in KM’s data andespecially in Anderson, a substantially greater fraction of persons initially expected
recall than ended up being recalled.
Another possibility is the treatment of unobserved heterogeneity. KM assume
that unobserved heterogeneity is distributed according to a gamma distribution
and that it is independent across risks. They found that their results were notvery sensitive to whether or not they controlled for unobserved heterogeneity ornot. But perhaps those assumptions are overly restrictive. In the current study, we
assume that unobserved heterogeneity has a discrete distribution, which Heckman
and Singer (1984) argue is better than the gamma assumption. We also allow theunobserved heterogeneity to be correlated across the two risks. In sharp contrast
to KM’s results, we found that the estimate of the influence of the recall hazard on
the new job hazard rate is 10 times larger when we do not control for unobserved
heterogeneity as when we do (table 2). This may be due to our less restrictive
assumptions.10 If so, then oﬃcials designing programs for laid-oﬀ workers need not
be particularly concerned that job search assistance, for example, would be wasted
on those on temporary layoﬀ.
8. Concluding Remarks
In this paper, we derive theoretically a negative behavioral relationship between
recall hazard rates and new job hazard rates. In order to identify the behavioral
relationship separately from the spurious relationship induced by individual heterogeneity, we use theoretical implications as identifying restrictions and try to control
adequately for both observed and unobserved heterogeneity. We find evidence of anegative behavioral relationship between the recall and new job hazards. Althoughcomparisons are not straightforward, the estimated relationship in this paper appears to be much weaker than that reported in Katz and Meyer (1990) or Anderson(1992), raising questions about its true magnitude, and highlighting the likelihoodthat laid-oﬀ workers tend to hold unrealistically optimistic views of their chances forrecall. If so, then policy might be well directed towards encouraging employers togive their employees a better idea of their prospects for recall, perhaps by providing
10

It is also possible that KM do not find unobserved heterogeneity to be important because their sample is less heterogeneous than ours to begin with. However,this is not entirely clear. On the one hand, KM’s sample comprises only UI recipients, which would make it less heterogeneous, and comes from administrative datathat may include less measurement error that could create artificial heterogeneity
in the data. On the other hand, our sample includes only heads of households (asdefined by the PSID).
22

a record of the quantity and spped of recalls during past episodes of layoﬀs.
In addition, we find positive duration dependence in the new job hazard, andsome negative duration dependence in the recall hazard, once heterogeneity has
been accounted for. However, to our surprise, we find no indication that the recall
hazard rate declines over the first six months of an unemployment spell.
The current analysis suggests at least two avenues for further work on this topic.
One would be to include multiple spells per individual in the analysis, presumably
using a richer source of data. Another would be to attempt a fully structural
approach to estimating the duration model. This would involve (i) specification of
F (w) and λ(s), and (ii) characterization of s(r) and wr∗ in terms of r, which would
require solving the value function using numerical techniques. These and otherpossibilities are left for future research.

23

Appendix: Proof of Theorems 1 and 2
When the two unemployed workers A and B in theorem 2 face the same environment in terms of new job arrival rates, oﬀered wage distribution, and searchcosts — that is, if they are identical in all respects except their recall hazard rates— then the proofs of theorem 1 and 2 are virtually the same. It suﬃces to provethat a lower recall hazard rate leads one to search for new job more intensely. If
a lower recall hazard rate corresponds to a later time in a spell of unemployment
spell for a single unemployed worker, then the proof covers theorem 1, whereas if alower recall hazard rate applies to one individual faced with a lower recall hazard
than another individual, then it covers theorem 2. So, the following proof applies
to both theorems.
Let Q(r) be the expected discounted future income over [0, ∞) when the current
recall hazard rate is r and when the laid-oﬀ worker follows the optimal searchstrategy. This Q(r) represents the value of optimal search strategy as a function of
the current recall hazard rate, the so-called value function.
Using Bellman’s optimality principle, we can write Q(r) as:
Q(r) = max[−c(s)dt + e−δdt {rdt · w/δs∈S+(1 − rdt)[λ(s)dtE[max(Wj /δ, Q(r − br dt))] + (1 − λ(s)dt)Q(r − br dt)]}]= max[−c(s)dt + e−δdt {rdt · w/δs∈S+(1 − rdt)[Q(r − br dt) + λ(s)dt ·

Z ∞
wr∗

(w/δ − Q(r − br dt))dF (w)]}],(1)
where wr∗ is determined from wr∗ /δ = Q(r −br dt) and br is defined as br = |∂r(t)/∂t|evaluated at t = r−1 (r).
Note that the infinite future [0, ∞) is divided into the immediate future [0, dt)
and the rest of time [dt, ∞). Under this decomposition, we can interpret each termon the right hand side of the above value function as follows. When the search
eﬀort is s, the worker incurs the search cost c(s)dt over the interval [0, dt). The
value in the rest of the future [dt, dt + ∞) is determined diﬀerently according towhether or not the worker receives notice of recall during the interval [0, dt). If
he receives recall notice (which happens with probability rdt), he will accept recall
and the resulting value is w/δ. If he does not receive recall notice, which happens
with probability 1 − rdt, his choice of action depends on whether he receives a newjob oﬀer (happening with probability λ(s)dt) or not (happening with probability
1 − λ(s)dt). When he has a new job oﬀer in hand, he will compare the expecteddiscounted future income from the new job, Wj /δ, with the value of continuingsearch under a reduced recall hazard rate, Q(r − br dt). When he has not received
a new job oﬀer, his future value of search is just Q(r − br dt).
By using the facts (i) e−δdt = 1−δdt+o(dt), where X = o(dt) if limdt→0 X/dt =24

0, (ii) Q(r − br dt) = Q(r) − br Q0 (r)dt + o(dt), and (iii) the monotonicity of Q(r),Q0 (r) ≥ 0, we can express the above value function as follows:
Q(r) = o(dt) + max[−c(s)dt + (1 − δdt){rdt · w/δ
s∈S
Z ∞
(2)
0
+(1 − rdt)[Q(r) − br Q (r)dt + λ(s)dt(w/δ − Q(r) + br Q0 (r)dt)dF (w)]}].
wr∗

After dividing both hand sides of (2) by dt and letting dt → 0, we have:"

0 = max −c(s) + rw/δ − (r + δ)Q(r) − br Q0 (r) + λ(s)
s∈S

Z ∞
wr∗

#

(w/δ − Q(r))dF (w)(3)
By taking derivative of the right hand side of (3) with respect to the searchintensity s, one has:000 = −c (s) + λ (s)

Z ∞
wr∗

(w/δ − Q(r))dF (w),(4)

where wr∗ is determined from wr∗ /δ = Q(r). That is, wr∗ = δQ(r). If the first-ordercondition (4) is satisfied at a positive search intensity s > 0, that solution is the
optimal search intensity. On the other hand, no search will be optimal if00

c (0) ≥ λ (0)

Z ∞
wr∗

(w/δ − Q(r))dF (w).

(40 )Note that these necessary first-order conditions (4) and (4’) for optimal search arein fact suﬃcient as well thanks to Assumption 4.
The condition (4’) for the corner solution (s = 0) is more likely to be satisfied
if the current recall hazard rate r is high, and wr∗ is consequently large. Let r∗ be
the threshold level of the recall hazard rate such that if the current recall hazard
rate is higher than r∗ it is optimal not to search at all, and otherwise it is optimal
to search. Obviously, r∗ will be determined as a solution to (4’) when the inequality
is replaced by an equality.
Since wr∗ = δQ(r), we have ∂wr∗ /∂r = δQ0 (r) > 0, which implies that as therecall hazard rate is lower the reservation wage is lower as well. The recall hazard
rate can be lower due to the passage of time for an individual unemployed worker, or
due to inferior individual characteristics when comparing two workers at the sametime.
For the interior solution case (r ≤ r∗ R), the first order condition (4) equates the∞marginal benefit of search intensity, λ0 (s) w∗ (w/δ −Q(r))dF (w), with the marginalr
cost of search intensity, c0 (s).
25Let the solution be s(r). One can easily see that as r decreases, the optimal
search intensity increases, implying that s(r) is decreasing in r. By plugging in the
optimal search intensity s(r) back into (3), one derives:
Q(r) =

R∞−c(s(r)) + rw/δ − br Q0 (r) + λ(s(r)) w∗ w/δdF (w)rr + δ + λ(s(r))[1 − F (wr∗ )].

(5)Consider the case where r > r∗ . When the recall hazard rate is suﬃciently
high, it is optimal not to search for a new job at all: s = 0, a corner solution. In
this case, the laid-oﬀ worker just waits to be recalled without paying any searchcost, c(0) = 0, and receives new job oﬀers at the minimum possible rate, λ(0). Using
these observations, we have from (5)Q(r) =

R∞
rw/δ − br Q0 (r) + λ(0) w∗ w/δ dF (W )rr + δ + λ(0)[1 − F (wr∗ )], for r > r∗ .

(50 )Now consider the case where r = 0. Once the recall hazard rate hits zero, it
can decline no further and the problem becomes stationary. This corresponds to the
Lippman and McCall type traditional job search model under stationarity. Notethat Q0 (0) = 0, or, more precisely, Q(0 − b0 dt) = Q(0) (since b0 = 0). Therefore,
00(w/δ − Q(0))dF (w),(400 )

R∞−c(s(0)) + λ(s(0)) w∗ w/δdF (w)(500 )

0 = −c (s) + λ (s)And
Q(0) =Z ∞w0∗0

δ + λ(s(0))[1 − F (w0∗ )].

We can interpret Q(0) = w0∗ /δ as the value of permanent lay-oﬀ. In our empirical
implementation, this value applies to those workers who lost their jobs due to plantclosing or end of seasonal or temporary jobs, for whom we assume that no recall ispossible.
From the above discussions, we reach the following conclusions regarding thehazard rate for terminating the unemployment spell by taking a new job, viewed asa function of the recall hazard rate. Let us denote the function by j(r). This hazard
rate is a product of the new job arrival rate and the probability that the oﬀered wage
exceeds the reservation wage: j(r) = λ(s(r))·[1−F (wr∗ )]. Since λ0 (s) > 0, s0 (r) ≤ 0,and ∂wr∗ /∂r > 0, we have j 0 (r) ≤ 0. That is, the new job hazard rate is increasing
as the recall hazard rate decreases. This behavioral negative relationship holds bothacross time for an individual unemployed worker (Theorem 1) and across diﬀerent
workers at the same time (Theorem 2).

26

References
Anderson, P. (1992), “Time-varying Eﬀects of Recall Expectation, a Reemployment
Bonus, and Job Counseling on Unemployment Durations,” Journal of Labor
Economics, 10, 99-115.
Fallick, B. (1991), “Unemployment Insurance and the Re-employment of Displaced
Workers,” Review of Economics and Statistics, 73, 228-235.
Han, A. K., and Hausman, J. A. (1990), “Flexible Parametric Estimation of
Duration and Competing Risk Models,” Journal of Applied Econometrics,
5, 1-28.
Heckman, J., and Singer, B. (1984), “A Method for Minimizing the Impact ofDistributional Assumptions in Econometric Models for Duration Data,”
Econometrica, 52, 271-320.
Idson, Todd L. and Robert G. Valletta (1996), “Seniority, Sectoral Decline, andEmployee Retention: An Analysis of Layoﬀ Unemployment Spells,”
Journal of Labor Economics, 14, 654-76.
Katz, L. (1986), “Layoﬀs, Recall and the Duration of Unemployment,” Working
Paper No. 1825, NBER, Cambridge, Massachusetts.
Katz, L., and B. Meyer (1990), “Unemployment Insurance, Recall Expectations,and Unemployment Outcomes,” Quarterly Journal of Economics, 105,
973—1002.
LaLonde, R. (1986), “Evaluating the Econometric Evaluations of Training Programswith Experimental data,” American Economic Review, 76, 604—620.
Lippman, S., and J. McCall (1976a), “The Economics of Job Search: A Survey,”
Economic Inquiry, 14, 155-89 and 347-68.
Lippman, S., and J. McCall (1976b), “The Economics of Job Search: A Survey:
Part I,” Economic Inquiry, 14, 155-189.
McCall, B. (1996), “Unemployment Insurance Rules, Joblessness, and Part-time
Work,” Econometrica, 64, 647-682.
Pichelmann, K., and M. Riedel (1992), “New Jobs or Recalls? Flow Dynamics inAustrian Unemployment Reconsidered,” Empirica - Austrian Economic
Papers, 19, 259-74.
Ryu, K. (1994), “Group Duration Analysis of the Proportional Hazard Model:
Minimum Chi-square Estimators and Specification Tests,” Journal of theAmerican Statistical Association, 89.
Stock, J. and M. Watson (2003), Introduction to Econometrics, Addison Wesley.
Sueyoshi, G. (1992), “Semi-parametric Proportional Hazards Estimation ofCompeting Risks Models with Time-varying Covariates,” Journal of
Econometrics, 51, 25-58.

27

Table 1. Selected Statistics of the Sample
variable nameage
maleeducation
white
UI benefit
marriedcounty unemployment ratehome ownershipveteranspouse employed
union member
job tenure
northeast
north central
southfinanace/insurance/realtor
trans/comm/utility
construction
durable manufactureminingnondurable manufacture
retail/wholesale
management/admin
clerical/sales/service
craftsoperatives
professional/technicalclosedtempseas28

mean SD
34.90 10.76
0.85
0.36
11.35 2.24
0.54
0.50
0.66
0.47
0.69
0.46
9.52
3.82
0.49
0.50
0.25
0.43
0.38
0.49
0.41
0.49
49.36 68.46
0.12
0.33
0.28
0.45
0.44
0.50
0.10
0.31
0.07
0.26
0.15
0.35
0.34
0.47
0.03
0.17
0.15
0.36
0.10
0.31
0.04
0.21
0.16
0.36
0.23
0.42
0.41
0.49
0.04
0.20
0.08
0.27
0.03
0.17

Table 2. Estimates of Recall and New Job Hazard Rates
r +xβ(each week in step t: r(t) = ert +xβ+e and j(t) = ejt +zγ+a∗e t +v
where the first three steps are each 2 weeks long, the second three 3 weeks
long, the third three 4 weeks long, and the final three 11 weeks long.)
TYPE
recallnew job

VARIABLE
r1
r2
r3
r4
r5
r6
r7
r8
r9
r10
r11
r12
y82
y83
j1
j2
j3
j4
j5
j6
j7
j8
j9
j10
j11
j12
y82
y83
a

PARAMETER
-0.70
-0.60
-0.89
-0.59
-0.63
0.00
-0.61
-0.07
-0.35
-0.99
-1.19
-1.18
-0.43
-0.54
-1.40
-0.89
-1.28
-1.02
-1.30
-0.63
-0.64
-1.32
-0.46
-0.47
-0.51
0.48
-0.22
-0.75
-0.62

29

SE
0.602
0.611
0.618
0.623
0.639
0.639
0.661
0.662
0.714
0.697
0.822
0.905
0.155
0.147
0.908
0.943
0.970
0.950
1.024
1.026
1.046
1.116
1.095
1.135
1.159
1.228
0.207
0.208
0.242

T-VALUE
-1.15
-0.99
-1.44
-0.95
-0.99
0.00
-0.92
-0.11
-0.49
-1.42
-1.45
-1.30
-2.77
-3.66
-1.54
-0.94
-1.32
-1.07
-1.27
-0.61
-0.61
-1.18
-0.42
-0.41
-0.44
0.39
-1.07
-3.60
-2.55

Table 2. (continued)
TYPE

VARIABLE
e1
e2

PARAMETER
SE
0.00
-3.28
0.195

T-VALUE-16.85

v1
v2

0.00
-1.70

0.486

-3.49

q11
q12
q21
q22

0.00
-0.05
-0.23
0.28

1.332
0.700
0.870

-0.04
-0.33
0.32

30

Table 2. (continued)
TYPE
recall (x)VARIABLE
age
maleeducation
white
UI benefit
marriedcounty unemployment ratehome ownershipveteranspouse employed
union member
job tenure

PARAMETER
0.005-0.482-0.0210.639-0.8420.168-0.0140.491-0.079-0.383
0.680
0.005

SE
0.007
0.239
0.030
0.133
0.139
0.202
0.015
0.134
0.147
0.137
0.134
0.001

T-VALUE
0.71
-2.01
-0.72
4.80
-6.06
0.83
-0.90
3.67
-0.54
-2.80
5.07
4.83

northeast
north central
south-0.699-0.487
0.047

0.223
0.197
0.192

-3.13
-2.47
0.25

finanace/insurance/realtor
trans/comm/utility
construction
durable manufactureminingnondurable manufacture
retail/wholesale-1.486-1.213-0.4620.667-0.7401.173-0.966

0.397
0.398
0.350
0.332
0.483
0.344
0.375

-3.74
-3.05
-1.32
2.01
-1.53
3.41
-2.57

management/admin
clerical/sales/service
craftsoperatives
professional/technical

0.067-0.2910.161-0.035-0.105

0.380
0.275
0.217
0.204
0.364

0.18
-1.06
0.74
-0.17
-0.29

UI26
UI39

1.75
0.55

0.398
0.920

4.40
0.60

31

Table 2. (continued)
TYPE
new job (z)VARIABLE
age
maleeducation
white
UI benefit
marriedcounty unemployment ratehome ownershipveteranspouse employed
union member
job tenure
northeast
north central
south

PARAMETER-0.035-0.4800.061
0.856-0.6480.330-0.048
0.006
0.424
0.001
-0.386-0.001-0.801-1.092-0.367

SE
0.010
0.307
0.041
0.196
0.192
0.247
0.026
0.187
0.195
0.188
0.203
0.002
0.289
0.285
0.218

T-VALUE
-3.43
-1.57
1.49
4.37
-3.38
1.34
-1.82
0.03
2.17
0.01
-1.90
-0.88
-2.78
-3.83
-1.68

finance/insurance/realtor
trans/comm/utility
construction
durable manufactureminingnondurable manufacture
retail/wholesale-0.080-0.5470.166-0.524-0.554-0.017-0.259

0.413
0.439
0.400
0.402
0.539
0.433
0.400

-0.19
-1.24
-0.42
-1.30
-1.03
-0.04
-0.65

management/admin
clerical/sales/service
craftsoperatives
professional/technical-0.072-0.2300.121-0.333
0.317

0.375
0.316
0.262
0.282
0.397

-0.19
-0.73
0.46
-1.18
0.80

plant closed
temp/seasonal job end
UI26
UI39

0.462
-0.227
1.79
1.93

0.263
0.390
0.450
0.712

1.76
-0.58
3.99
1.31

32

Table 3. How the Estimates of ”a” Change for differing level of control forunobserved heterogeneity
Unobserved Heterogeneity
12
3
4

Estimate of ”a”
-7.09
-0.62
-0.77
-0.78

33

SE(a)
3.06
0.24
0.65

t-Value
-2.32
-2.55
-1.17

34