Find a Job Now, Start Working Later Does Unemployment Insurance

Find a Job Now, Start Working Later
Does Unemployment Insurance Subsidize Leisure?
(Job market paper)
Marjolaine Gauthier-Loiselle
Princeton University
September 2011
Abstract
Distorting incentives is a major concern when implementing Unemployment Insurance (UI). In particular, UI benefits tend to decrease job search and increase
the reservation wage. Yet, UI could also be prone to moral hazard through another
unexplored channel: postponing job start upon finding a job. This paper develops
a theoretical job search model that allows for a delayed job start. Then, the extent
to which unemployed individuals delay job start after finding a job is assessed using
the Canadian Survey of Labour and Income Dynamics. I find that 17% of all benefits paid are paid to individuals who have already found a job, but have not started
working yet. I find that individuals who accepted an offer before benefit exhaustion
delay job start by 3.9 weeks on average, whereas the average delay is respectively 1.8
and 2.3 weeks for those who accepted a job after exhaustion and for non-recipients.
The survival analysis shows that the job starting rate upon acceptance of a job offer
is much higher both in the month prior to exhaustion and after the benefits are
exhausted, as well as for non-recipients. Although no causal effect can be formally
identified, this suggests that some individuals take advantage of the availability of
Unemployment Insurance benefits to postpone job start.
*I would like to thank my advisor, Henry Farber, Andreas Mueller, as well as participants to the Graduate Labor Workshop and the Public Finance Working Group at
Princeton University for helpful questions and comments. Research was conducted at
McGill’s Quebec Inter-University Center for Social Statistics and Statistics Canada and
I would like to thank Statistics Canada analysts for their great work. I also acknowledge
financial support from the Social Sciences and Humanities Research Council of Canada
and from the Fonds Qubcois de la recherche sur la socit et la culture.
1
Introduction
Unemployment Insurance (UI) serves the goal of providing a safety net in case of a job
loss.1 However, UI benefits create an opportunity for unemployed workers to put less
effort into looking for a job and going back to work. As many researchers have found,
more generous benefits tend to increase unemployment duration (Card and Levine, 2000;
Van Ours and Vodopivec, 2006; Lalive, Van Ours and Zweimueller, 2006; Lalive, 2008).
In traditional job search models, unemployed individuals receiving UI benefits search less
intensively and have higher reservation wages, leading to longer unemployment spells (e.g.
Mortensen,1977).2 Yet, unemployed individuals could also take advantage of UI benefits
through another unexplored channel: postponing job start after accepting a job offer.
Upon finding a job, an unemployed individual receiving UI benefits might be deciding to
take a few extra weeks off work without the stress of finding a job. Although intuitive,
this idea was proposed only recently (Boone and Van Ours, 2009) and little is known
about the magnitude of the tendency to postpone job start and its potential cost for the
society. The goal of this paper is to investigate the importance of the delay between job
offer and job start, as well as its determinants.
The moral hazard induced by Unemployment Insurance has not only been documented
through longer unemployment durations, but also through a spike in the unemployment
exit rate at benefit exhaustion (Moffit, 1985; Katz and Meyer, 1990; Meyer, 1990).3 Postponing job start after accepting an offer could explain, at least partly, these empirical
findings. In fact, when raising the idea that unemployed individuals could strategically
delay job start, Boone and Van Ours (2009) do not study the delay per se, rather, they
want to explain the spike in the job starting rate at benefit exhaustion. Indeed, they
find supporting evidence of their theoretical model, which implies that delaying job start
could cause the spike. However, their data set doesn’t allow them to observe the delay
between job offer and job start, nor do most major data sets. The lack of information on
1
In the literature, the usual term for this type of program is Unemployment Insurance. However, in
1996, the program was renamed Employment Insurance in Canada. To avoid confusion, I will stick to
the traditional name of the program.
2
Chetty (2008) differs in attributing this increase in unemployment duration to liquidity constraints
rather than distortion in search behaviour.
3
Card, Chetty and Weber (2007) point out that the spike is much smaller for the job starting rate
than for the unemployment exit rate.
1
job offer date is probably the main reason why the delay between job offer and job start
still remains undocumented.
This paper investigates the importance of the tendency to delay, both in terms of
frequency and length, as well as its determinants. I first develop a theoretical job search
model that allows for a delay between job offer and job start. Then, I investigate the
delay behaviour and its determinants using the Canadian Survey of Labour and Income
Dynamics. The contribution of this paper is twofold. First, acknowledging the existence
of the delay, there is a need for search models that incorporate this feature. This paper
contributes to the job search literature by developing a non-stationary job search model
that allows for a delay between job offer and job start. Second, it extends the literature
on the effects of Unemployment Insurance on unemployment spells by documenting a new
channel of moral hazard using a unique data set that provides information on job offer
and job start dates along with detailed socio-demographics and administrative tax record
information.
Traditional job search models assume that a job starts as soon as it is accepted, leaving
no room for a delay between job offer and job start. The model presented here builds on
the work of Van den Berg (1990), where employers make take-it-or-leave-it job offers to
unemployed workers. Both his model and my model allow for non-stationarity, although
Van den Berg (1990) model allows for non-stationarity in a more general setting, whereas
I allow non-stationarity in UI benefits only. The core difference is that a job offer entails
both a wage and a start date in my model, whereas an offer consists only of a wage in
Van den Berg (1990). It is important to note that the model developed by Boone and
Van Ours (2009) does allow for delay between job offer and job start, but since it aims
at explaining the spike in the job starting rate at benefit exhaustion, it doesn’t model
acceptance nor rejection of job offers by the worker and, therefore, is not a job search
model per se.
The model implies that there should not be a spike in the job acceptance rate at
benefit exhaustion, but rather the rate should remain high and stable. Empirically, I find
that the job acceptance rate is higher both in the month prior to exhaustion and after exhaustion. Even though the point estimate is larger in the month prior to exhaustion, it is
2
not significantly different from the coefficient after exhaustion, so there is no spike per se.
However, I find a spike in the job starting rate prior to exhaustion as expected from previous studies. The model predicts that jobs with longer delays should be associated with
higher wages for individuals accepting an offer after exhaustion and for non-recipients,
which is confirmed by the data. More generally, the model presented here implies that
unemployed individuals adjust their acceptance or rejection of job offers according to the
start date and their eligibility to UI benefits, leading to a new, unexplored, form of moral
hazard.
In the empirical analysis, I decompose the unemployment spell into two parts: the
duration of unemployment until a job offer is accepted and the delay between job offer
and job start. Although the latter has been left out of the existing literature, I find that
unemployed workers delay job start substantially after accepting a job offer. Individuals
who accepted an offer before benefit exhaustion postpone job start by 3.9 weeks on average, and 54% delay job start by more than two weeks. In comparison, individuals who
accepted an offer after exhaustion delay job start by 1.8 weeks on average and only 35%
of individuals delay job start by more than two weeks. Similarly, individuals who did
not receive UI benefits delay job start by 2.3 weeks on average and 40% delay do so for
more than two weeks. Acknowledging that non-recipients and individuals who accepted
an offer after benefit exhaustion differ from those who accepted an offer before benefit
exhaustion, and thus don’t constitute reliable control groups, the differences in the delay
behaviour remain striking and suggest that the delay has a strategic component, i.e. the
delay is reflective of individuals’ preferences. Overall, 17% percent of all Unemployment
Insurance benefits paid is paid to individuals who have already found a job, but have not
started working yet. Furthermore, even if we allow for a two-week institutional waiting
period before job start, the cost of the delay above the institutional threshold remains as
high as 11% of all benefits paid.
The survival analysis shows that the job starting rate upon job acceptance is much
higher after benefit exhaustion and for non-recipients. This finding provides further evidence that the delay is not solely institutional, but has a strategic component. I also find
that individuals accepting an offer early in their spell are much less likely to resume work
quickly. Personal characteristics such as age, gender and education don’t seem to affect
3
delay behaviour by much. However, having children is correlated with a longer delay
for single parent families in some specifications. Re-employment job characteristics also
seem to matter. Jobs in the public sector are less likely to start quickly after job offer,
and unionized jobs are more likely to start quickly in some specifications. To summarize,
the empirical analysis suggests that some individuals take advantage of the availability of
benefits to postpone job start.
The paper is set-up as follows. Section 2 introduces the theoretical model. Section
3 presents the data and descriptive statistics. Section 4 presents the empirical analysis.
Finally, section 5 concludes.
2
A Job Search Model with Delay
The model developed here extends the non-stationary search model presented by Van den
Berg (1990) to incorporate delay between job offer and job start. The model considers
the acceptance behavior of an unemployed individual eligible to receive UI benefits for
a period of time T at the beginning of his unemployment spell, where job offers consist
of a wage, w, and a start date after a waiting period, τ , and arrive at random intervals
following a homogeneous Poisson process with arrival rate λ.
The model has two important features: non-stationarity and multi-dimensionality
of job offers. First, as in Van den Berg (1990), the non-stationarity implies that the
optimal acceptance rule varies over the course of the unemployment spell. Here, the nonstationarity is introduced by the finite duration of UI benefits, whereas the Van den Berg
(1990) model encompasses a broader class of non-stationarity. Secondly, in the model
presented here, a job offer consists of a wage and a waiting period until the job starts,
τ . Other models also include multi-dimensional job offers. For example, Blau (1991),
Bloemen (2008) and Shephard (2009) considered job offers with wages and hours. I follow Blau (1991) by considering the utility flow associated with all dimensions of the job
offer.4 In that case, the optimal acceptance rule maximizes the expected present value of
the utility of accepting a job net of search cost. This rule is known to have the “reser4
The alternative is to consider the monetary value of the non-wage characteristics.
4
vation utility property”, i.e. an offer is accepted if and only if the utility flow associated
with the offer is above a certain threshold that may vary accordingly with the dimensions
of the offer. Note that since the model is non-stationary, the reservation utility will vary
over the unemployment spell.5
The setting of the model is as follow (a list of the symbols is available in the appendix).
There is an infinite search horizon and job offers arrive at random intervals following a
non-homogeneous Poisson process with a constant, exogenous and known arrival rate, λ.
Workers then accept or reject the offer, but there is no recall of offers previously declined
and workers are not allowed to continue searching after accepting a job offer (this also
precludes on-the-job search). Once a job has started, it lasts forever at a constant wage.
A job offer consists of a wage, w ∈ [0, W ], and a waiting period until the job starts,
τ ∈ [0, M ]. Job offers are random drawings from a wage and wait time distribution with
the distribution function F (w, τ ), the conditional distribution F1 (w|τ ) and the partial distribution F2 (τ ) known and constant over time. For convenience, unemployment duration
and calendar time match, i.e. unemployment starts at t = 0.
The wage is allowed to depend on the delay between job offer and job start, but the
process generating such a relationship is not in the scope of this paper. In particular, both
a positive and a negative relationship could be rationalized. For example, there could be
a negative relationship if firms which know in advance that they will need a new worker at
given date post early offers with a long delay at low wage hoping to get a deal, gradually
increasing the offered wage as the starting date approaches. Alternatively, there could be
a positive relationship if firms which are looking for specific human capital start searching
earlier to ensure a good match and offer a higher wage to compensate for the waiting
period. Another possibility is that early knowledge of a vacancy depends on other firms’
characteristics that are related to wages. In this partial equilibrium search model, I am
agnostic about the process generating the relationship between wages and delay, but I
allow for such a relationship.
5
For a more complete review of job search models, see Rogerson, Shimer and Wright (2005) for a
theory oriented survey and Van den Berg (1999) and Eckstein and Van den Berg (2007) a for survey of
empirical estimations of job search models.
5
Individuals at time t derive utility from leisure, l(t), and consumption, c(t), and there
are no savings or borrowing. When employed, workers consume their wage, w, and enjoy
leisure, l(t) = le . If unemployed, they consume B(t), the sum of their home-production
and benefits if any, and enjoy leisure, l(t) = lu > le . Unemployed individuals are eligible
to receive UI benefits for a period T from the beginning of a new unemployment spell,
thus B(t) = B if t < T . B(t) = b < B if t ≥ T . Note that T and B(t) can vary
from one individual to another, but the subscript indicating the individual is omitted
for simplification. The worker chooses his acceptance strategy such that the implied
consumption and leisure schedule maximizes the expected value of his lifetime utility,
U (c, l). Thus, the worker maximizes:
Z
E(U (c, l)) = E
∞
e−ρ(s−t) u(c(s), l(s))ds
(1)
t
subject to
(c(s), l(s)) =

(w, le )
if working,
(B(s), l )
u
if not working.
where 0 < ρ < ∞ is the worker’s subjective discount rate and u(c(s), l(s)) is the utility
flow with uc > 0, ul > 0, ucc < 0 and ull < 0.
Diamond (1971) showed that if workers are homogeneous and there is no on-the-job
search, then there is no wage dispersion: all firms post the common reservation wage.
To generate wage dispersion, I will follow Albrecht and Axell (1984) and Eckstein and
Wolpin (1990) and assume that workers differ in their opportunity cost of employment,
and thus have different reservation wages for a given start date. In particular, B(t) and
T are allowed to vary from one individual to another. When workers have different reservation wages, firms will attract different types of workers depending on the wage they
offer. In particular, firms offering a low wage will attract workers with a low reservation
wage, whereas firms offering a high wage will attract both low and high reservation wage
workers. This leads to a non-degenerate wage distribution in equilibrium, when firms are
indifferent between offering low and high wages.
6
2.1
Worker’s problem
In this setting, the unemployed worker has to choose whether to accept or reject the job
offer whenever he receives one. Following the job search literature, the optimal strategy
for the individual is to accept the job that maximizes the expected present value of lifetime utility net of search costs. Even though there is no direct cost of search, there is
an indirect cost in the form of foregone earnings. A job will be accepted if the expected
present value of the lifetime utility of accepting the offer, V e (w, τ, t), is larger than or
equal to the expected present value of lifetime utility of rejecting the offer, V u (t).
The expected present value of lifetime utility of accepting in period t a job that starts
in a period of time τ at wage w is
Z t+τ
e−ρτ
e
V (w, τ, t) =
e−ρ(v−t) u(B(v), lu )dv +
u(w, le ).
ρ
t
(2)
The first term of the equation above represents the value while delaying job start after
accepting a job offer, whereas the second term represents the value once the individual
starts to work.
The job offer arrival process implies that the probability that the next offer arrives
at time s ≥ t conditional on being unemployed at time t has a distribution function
G(s; t) = 1 − e−λ(s−t) . The expected present value of lifetime utility of being unemployed
in period t can then be written as
Z ∞Z s
u
V (t) =
[
e−ρ(v−t) u(B(v), lu )dv + e−ρ(s−t) Ew,τ ;s (max(V e (w, τ, s), V u (s))]dG(s; t).
t
t
(3)
This equation is the expectation over the next job offer’s arrival time of the sum of the
value of being unemployed until the next job offer arrives and the value of the optimal
choice between accepting or rejecting the next offer.
Let ū(τ, t) be the reservation utility, defined as the utility flow such that the unemployed worker is indifferent (in period t) between remaining unemployed or starting to
work in τ periods and receiving a utility flow ū(τ, t) once the job has started. The solution to the worker’s problem is such that any offer (w, τ ) with u(w, le ) ≥ ū(τ, t) will be
accepted in period t. Let Q(u|τ ) = P r(u(w, le ) ≤ u|τ ) be the distribution of the utility
7
flow once the job has started conditional on the delay between job offer and job start.
Note that Q(u|τ ) = F1 (w∗ |τ ), where u = u(w∗ , le ).
Proposition 1. Reservation utility
a. Case t ≥ T :
After benefit exhaustion, the worker’s problem becomes stationary. The reservation
utility is then constant in t, so ū(τ, t) = ū(τ ) and satisfies
λ
ū(τ ) = u(b, lu ) +
ρ
Z
M
0
Z
u(W,le )
e−ρ(z−τ ) (1 − Q(u|z))dudF2 (z).
(4)
ū(z)
Moreover, (i) ū(τ, t) is increasing in τ .
b. Case t < T :
Before exhaustion, ū(τ, t) satisfies
∂ ū(τ, t)
= ρū(τ, t) − ρu(B(t + τ ), lu ) − λ
∂t
Z
0
M
Z
u(W,le )
e−ρ(z−τ ) (1 − Q(u|z))dudF2 (z).
ū(z,t)
(5)
Furthermore, (i) ū(τ, t) is decreasing and concave in t for t < T ,
(ii) ū(τ, t) is decreasing in τ for τ ∈ [0, T − t) if u(B, lu ) > u(w, le ) for the lowest
accepted wage given a start date (increasing otherwise),
(iii) ū(τ, t) is increasing in τ for τ ∈ [T − t, ∞).
Proof. See the appendix.
Proposition 1a implies that when the benefits are exhausted, a job offer is accepted if
the utility flow once the job has started is at least as high as the utility flow when unemployed plus the discounted expected increase in the utility flow from accepting another
offer in the future. Proposition 1a (i) comes from the idea that when the benefits are
exhausted, the worker prefers to start working sooner than later for any acceptable offer.
If it were not the case, the worker would prefer to remain unemployed forever than to
work under those conditions and the offer would be rejected. Therefore, to accept a job
with a delayed start date, the worker would need to be compensated for the lost income
during the delay period by a higher utility flow (i.e. higher wage) once the job has started.
The reservation utility increasing with the delay implies that, after exhaustion, an offer
is more likely to be accepted if the delay is shorter, other things being equal. Moreover,
8
since the marginal value of consumption is positive (uc > 0), the lowest acceptable wage
for a job increases with the delay until job start. Thus, offers with a long delay will be
accepted only if they entail a higher wage. Consequently, a positive relationship between
wages and delay should appear in the data whenever the individual does not receive UI
benefits after accepting a job offer.
Proposition 1b (i) and uc > 0 imply that, as the exhaustion date approaches, the unemployed individual is willing to accept a lower wage for a given delay. Consequently, the
minimum acceptable wage for a given delay decreases over the jobless spell until exhaustion, then remains constant. In particular, the model predicts that the job acceptance
rate is increasing until exhaustion, then remains high and stable. More precisely, the job
acceptance rate in t conditional on not having accepted a job before, θo (t), is simply the
probability of receiving a job offer that is accepted, that is the probability that the wage
and start date offered give a utility flow larger than the reservation utility once the job
starts (Pr(u(w, le ) ≥ ū(τ, t))). Therefore,
Z
M
(1 − Q(ū(z, t)|z))dF2 (z).
θo (t) = λ
(6)
z=0
We can see easily that the job acceptance rate increases whenever the reservation utility
decreases, and vice-versa. Thus, the rate at which job offers are accepted is increasing
until exhaustion, then constant. Consequently, there is no spike in the job acceptance rate
at benefit exhaustion, but rather an increased rate that remains stable after exhaustion.6
Proposition 1b (ii) states the worker would rather delay job start and collect UI benefits than to start working now if the period utility of being unemployed with UI benefits
is large enough. More precisely, the worker is willing to forego future earnings in order to
remain unemployed. As a result, a negative relationship between wage and delay should
emerge from the data. Yet, if u(B, lu ) ≤ ū(τ, t), the intuition becomes similar to that
of proposition 1a: the worker would prefer to start working sooner than later and would
need a higher wage to accept an offer with longer delay. Since only some individuals
6
A richer model including search intensity could generate a spike in the job acceptance rate if leisure
and consumption were substitutes. Then, instead of remaining at a high level following benefit exhaustion,
the job acceptance rate would decrease due to a reduced search effort (increased leisure) to compensate
the reduced consumption.
9
with high value of staying at home with benefits would like to delay, the direction of the
relationship between wage and delay is ambiguous. Finally, proposition 1b (iii) implies
that in the case where the job offer is before exhaustion, but with a delay long enough
that worker resume work after exhaustion (τ ≥ T − t), the worker would rather start to
work sooner than later once the benefits are exhausted and he would want a higher wage
to accept an offer with a slightly longer delay. Yet, the overall effect of delaying could be
either positive or negative. Proposition 1b (iii) only compares job offers with a start date
after exhaustion to those with a further start date. It remains ambiguous whether starting a job a little after exhaustion would be better than starting as soon as the job is offered.
Furthermore, propositions 1b (ii) and (iii) imply that for a given wage and offer time,
the probability that a job is accepted is maximized when the job start date coincides with
exhaustion if the benefits are large enough. Consequently, there are more offers starting
at exhaustion which are accepted and the job starting rate spikes at exhaustion. Similarly, propositions 1b (ii) and (iii) imply that individuals who receive a job offer before
exhaustion are more likely to accept an offer with a longer delay between job offer and
job start.
To summarize, the lowest acceptable utility flow varies according to the delay between
job offer and job start and the UI benefits remaining at the time of job offer. The reservation utility reaches its minimum with respect to time after exhaustion, whereas it reaches
its minimum with respect to delay when the job start date coincides with exhaustion if
the benefits are large enough. Since job offers affect the utility flow only through changes
in wage, we have that the lowest acceptable wage is higher for a long delay if the job
offer is received after exhaustion, whereas the relationship between wages and delay is
ambiguous if the job is offered before exhaustion.
The empirical implications of the model are summarized in the following proposition
and are tested in the empirical analysis (section 4).
Proposition 2. Under the appropriate assumptions on the distribution of (w, τ ) and if
UI benefits are large enough, the model has the following empirical implications:
a. Jobs that start at benefit exhaustion are more likely to be accepted, creating a spike
in the job starting rate at benefit exhaustion.
10
b. There is no spike in the job acceptance rate at benefit exhaustion, rather the job
acceptance rate increases until exhaustion, then remains constant.
c. Longer delays are more likely to be accepted by individuals who receive an offer before
benefit exhaustion.
d. Wages are positively correlated with delay between job offer and job start if the
offer is received after benefit exhaustion, whereas the direction of the correlation is
ambiguous if the offer is received before exhaustion.
The model presented in this section assumes that individuals change their acceptance
decision of a job offer depending on the timing of job start. Therefore, although the delay
between job offer and job start is dictated by the employers, workers take advantage of
UI benefits to accept jobs that start later. So, individuals strategically delay job start in
the sense that the delay is reflective of preferences. The following sections assess whether
this idea of strategic delay is supported empirically.
3
Data and Descriptive Statistics
3.1
Data
To study the delay between job offer and job start, we need a data set that has information
about both the job offer and job start date. This information is provided in the Canadian Survey of Labour and Income Dynamics (SLID), as well as detailed survey data on
demographic characteristics and financial information from administrative tax records.7
The SLID is an annual household survey conducted by Statistics Canada, which follows
households for 6 years. A new panel starts every three years and consists of roughly
30,000 individuals.8 The data used in this paper cover the period from 1993 to 2006.9
Additionally, to account for sampling design and non-random attrition, all results are
7
Respondents need to give permission to be linked with administrative tax records. Over 80% of the
observations were linked with tax records in my sample. A fourth of the remaining observations had
income information collected from the SLID survey and the others had income information completely
imputed by Statistics Canada.
8
More information on the SLID can be found at http://www.statcan.gc.ca.
9
All financial variables are adjusted for inflation using the Consumer Price Index (available from
CANSIM) based on 2002 (CP I2002 = 100).
11
derived using the combined panel weights provided by Statistics Canada.
The sample of jobless spells of adults in the workforce is constructed as follows. The
sample is restricted to individuals from 20 to 65 years old who are neither retired nor
full-time students with at least one jobless spell starting during the survey period. Individuals with a health condition preventing work are excluded from the sample. The
sample also precludes individuals who have been recalled from a previous employer as
their job search behavior is different (Krueger and Mueller, 2010). For the same reason,
individuals not looking for a job at the beginning of their spell because they expect to be
recalled are also excluded.10 To avoid the influence of outliers, spells with delay between
job offer and job start above the 99th percentile are discarded from the sample, so that
the longest delay in the sample lasts 30 weeks. Both UI recipients and non-recipients are
included in the analysis, although it is understood the differences in behaviour can’t be
identified as a causal effect of UI benefits, since the eligibility status and the decision to
apply for benefits are endogenous.
Individuals who quit the labor force at some point during their spell are not necessarily excluded from the sample. The reason is that individuals who found a job but have
not started to work yet are considered unemployed only if the job is to start within the
next four weeks. If the waiting period is longer than four weeks, these individuals are
classified as out of the labor force. Since we are precisely interested in this waiting period,
we have to include individuals with a delay longer than four weeks. However, individuals
out of the labor force for more than a year are excluded from the sample. Consequently,
when I refer to unemployment spells or unemployed individuals in this paper, I do not
refer to the traditional definition that excludes jobless individuals not actively seeking
work. Rather, I respectively refer to unemployment spells and unemployed individuals
as temporary jobless spells and jobless individuals attached to the labor market. Since
the sample includes some individuals not actively seeking work, the observed spells could
be longer on average than it would if the sample were only constituted of unemployed
10
These exclusions imply that the sample does not include individuals who did not look for work
because they expected and are indeed recalled, but also individuals who looked for another job but end
up being re-employed by the same employers, as well as individuals not looking for work at the beginning
of their spell because they expect to be recalled but who are finally re-employed by a different employer.
12
individuals defined in the traditional sense.
Data on both the jobless spells and the re-employment jobs are needed in order to
perform the analysis of the delay between job offer and job start. However, the structure
of the data is such that one can extract the data for job spell history or for jobless spell
history, but the data does not readily include the sequence of jobs and jobless spells.
Thus, I first extracted the data for jobless periods at the individual level, then matched
them with data from previous and following employment using start and end dates of job
and jobless spells, as well as monthly main job identifiers when one of the afore mentioned
dates were unavailable. Similarly, I extracted the SLID data for monthly receipts of UI
benefits and matched it with the employment history. Unfortunately, the data do not include the number of weeks eligible or exhaustion date. Therefore, I imputed the number
of weeks of benefits according to the rules specified under the Unemployment Insurance
program(described in the following section). Then, the number of weeks eligible is used
to compute the exhaustion date, taking into account the two weeks waiting period before
the start of benefits if applicable.
One major concern with survey data is measurement error due to recall. Recalling the
date of a job offer might be especially prone to measurement error. In particular, there is
a distinct bunching on the 1st , 2nd , 15th , 16th , 30th ,and 31st day of the month. Moreover,
32% of individuals report that the job was offered the very same day as it started, and
23% report being offered the job on either Saturday or Sunday, both of which seem much
to high to be the true proportion. One way to deal with the measurement error is to
allow for unobserved heterogeneity in the survival analysis. Moreover, if UI recipients
are more likely to incorrectly report an offer date that is closer to the start date because
they are afraid of penalties, then my estimates would be biased downward. Nonetheless,
in spite of the measurement errors, I do find results indicating that delay has a strategic
component and that its magnitude is considerably large. These findings suggest that the
delay between job start and job offer deserves researchers’ attention and should be studied
with more reliable data in the future.
13
3.2
Unemployment Insurance in Canada
Since 1996, the Canadian UI program is called the “Employment Insurance”. After serving
a two-week waiting period, unemployed workers can receive benefits for a period ranging
from 19 to 50 weeks. The length of benefits varies with the unemployment rate in the
economic region and the number of hours worked. For example, an individual who was
working full-time in the year prior to the spell in a region with an unemployment rate
between 7% and 8% is eligible to 45 weeks of benefits.11
The base replacement rate is 55% of the insurable earnings, up to a maximum benefit
of $413/week.12 The insurable earnings are defined as the average weekly earnings over
the last 26 weeks. However, for those who have not work all weeks, the weekly insured
earnings is calculated by dividing the total earnings in the last 26 weeks by either the
number of weeks worked or the “divisor” number, whichever is the largest. The “divisor”
is a number ranging from 22 to 14 that decreases with the unemployment rate. For
families with income below $25,921, the replacement rate is supplemented up to 80%.
Eligibility to this program depends on the number of hours worked in the previous 52week period or the period since the last unemployment spell (whichever is the shortest).
Depending on the unemployment rate at the time of filing the claim, the minimum number
of insurable hours of work ranges from 420 to 700. For those in the work force for the first
time and those re-entering the work force after an absence of 2 years need 910 hours to
qualify. Moreover, those who quit without just cause, are fired for misconduct, refuse or
are unavailable to accept suitable employment are ineligible for benefits. For more details
on the UI program, see http://www.hrsdc.gc.ca/eng/employment/ei/.
11
Between 420 and 1400 hours worked, an increase of 70 hours worked increases the benefits eligibility
by one week, whereas between 1400 and 1820 hours worked, 35 additional hours increase the benefits
entitlement by one week. Also, for an unemployment rate from 6% to 15%, an increase of one percentage
point of the unemployment rate expands benefit eligibility by two weeks.
12
In 2007, the maximum benefit was increased for the first time since 1996.
14
3.3
Descriptive Statistics
Previous literature looked at the unemployment duration as a whole. For comparability
purpose, I will reproduce this analysis before decomposing the total jobless spell duration
into the time until a job offer is accepted and the subsequent delay until job start. Figure
1 shows the distribution of the completed duration of jobless spells. UI recipients have
longer spell duration than non-recipients, with the median spell lasting 4 months and
the modal spell lasting 3 months, whereas the median spell length for non-recipients is
one month and the modal spell length is less than a month. This is partly due to nonrecipients accepting job offer earlier in their spell than UI recipients as shown in figure
2. In particular, those who expect their spell to be short might not apply to UI benefits,
explaining part of the gap in the spell length. Figure 2 shows the distribution of the
duration of unemployment until a job offer is accepted. The most frequent duration until
a job offer is accepted is less than a month for both UI recipients and non-recipients.
However, non-recipients are much more likely to accept a job in the first month than
recipients, and the median duration until a job offer is accepted less than 2 months for
non-recipients, whereas it is over 4 months for recipients. In general, the distribution
of duration until a job offer is accepted is more left skewed than the distribution of the
total duration of the spells. Among those who accepted an offer within the first month of
the unemployment spell, over 80% of non-recipients start working within the first month
of their spell, whereas this proportion is only a half for UI recipients. This discrepancy
between job offer and job start durations for UI recipients brings us to the core of the
paper: the delay between job offer and job start.
In this section, simple descriptive statistics are presented to give a global idea of the
size of the delay and strategic acceptance behaviour. The more detailed empirical analysis
is presented in section 4 and supports the findings of the descriptive statistics. Figure 3
shows the distribution of the delay between job offer and job start. Figure 3 reveals that
a large fraction of individuals don’t delay job start at all. In fact, the delay between job
offer and job start is less than a week for about a third of UI recipients and a little less
than 40% of non-recipients. The modal waiting period is 4 weeks for those who do not
start working right away for both recipients and non-recipients. Although most of those
who delay do so for less than 5 weeks, 6% of UI recipients postpone their job start by
more than two weeks compared to 2% for non-recipients. As a result, the distribution of
15
delay is more right skewed for UI recipients.
To get a better grasp at the effect of UI benefits on postponing job start, one can
separate UI recipients into two categories: individuals who accepted their job offer before
exhaustion and those who accepted it after. Although neither individuals who accepted an
offer after exhaustion, nor non-recipients constitute a valid control group for identifying
a causal effect of UI benefits on the delay between job offer and job start, they constitute
a useful start point for comparison purposes.13 Table 1 presents the average delay for the
different groups. The average time between job offer and job start is 3.9 weeks for those
who accepted an offer before exhaustion, whereas it is respectively 1.8 and 2.3 weeks for
those who accepted an offer after exhaustion and non-recipients. Noting that the average
delay for both comparison groups is about two weeks, I will use this cut-off as reference
point for the remaining parts of the paper. This reference point could be thought of as an
“institutional” threshold, i.e. the part of the delay that results from the institutional constraints rather than personal preferences. Not surprisingly, individuals who accepted an
offer before exhaustion are more likely to delay for more than two weeks. More precisely,
table 1 shows that 54% of individuals who accepted an offer before exhaustion postpone
job start by more than two weeks, respectively 19 and 14 percentage points more than
those who accepted an offer after exhaustion and non-recipients. Consequently, not controlling for other characteristics, individuals who receive UI benefits after accepting a job
offer are more likely to postpone job start.
Of course, individuals who accepted an offer after exhaustion and non-recipients are
different from individuals who accepted an offer before exhaustion. In particular, one
obvious difference between those who accept a job before and after exhaustion is the
timing of job offer. Table 1 also presents the average delay by offer time. If we restrict
the sample to those who accepted the offer after at least 20 weeks of unemployment, we
still find that those who accepted an offer before exhaustion delay more than those who
accepted an offer after exhaustion and non-recipients.14 Indeed, in that case, the average
delay drops to 2.7 weeks, still 0.9 weeks (50%) more than the average delay for those with
13
A structural estimation or an exogenous variation in the benefits level or eligibility would be necessary
to identify causal effects.
14
I use 20 weeks as the cut-off because it is the minimum length of benefits eligibility in my sample.
16
an offer after exhaustion and 0.7 weeks (39%) more than non-recipients with an offer after
20 weeks unemployed. Similarly, the proportion of individuals with at least two weeks
between job offer and job start drops to 45% for individuals who accepted an offer before
exhaustion, still 10 percentage points more than those who exhausted their benefits at job
offer and non-recipients with an offer after 20 weeks unemployed. Moreover, if we restrict
the sample to individuals who accepted the job offer in less than 20 weeks unemployed,
those who received UI benefits after accepting a job offer delay by 4.5 weeks on average, almost twice as much as non-recipients.15 Similarly, the fraction of individuals who
postpone job start by more than two weeks reaches 59% for those who accepted an offer
before exhaustion, 17 percentage points more than non-recipients. Figure 4 illustrates
the finding that individuals who continue to receive UI benefits after accepting an offer
delay job start for a longer time and that this finding is robust to controlling for offer time.
Table 1 and figure 4 also put in evidence the effect of the timing of job offer on the
duration of the delay until job starts. Those who accepted a job offer in the first 20 weeks
of their spell delay more than individuals who accepted an offer later in their spell. For UI
recipients who accepted an offer before exhaustion, the average delay is 4.5 weeks if the
offer was accepted in the first 20 weeks of the spell, which is 40% longer than when the
job is offered after 20 weeks of unemployment, and they are 14 percentage point (25%)
more likely to delay for more than two weeks. The pattern, though similar, is less pronounced for non-recipients: the average delay is 0.3 weeks (15%) longer and individuals
are 7 percentage point (17%) more likely to delay for more than two weeks if the offer is
accepted in the first 20 weeks of the spell. This finding is consistent with a decreasing
marginal value of leisure or increasing credit constraints as the spell progresses. In both
case, additional leisure would be less valuable than consumption later in the spell and
some individuals would prefer to work than delay job start.
As mentioned before, individuals who accepted an offer before exhaustion differ from
those who accepted an offer after exhaustion and from non-recipients. Table 2 presents
summary statistics for the different groups. In particular, non-recipients are more likely
to be women, college graduates, are on average younger (explained by tighter rules for
15
Such a comparison is not possible for those who accepted the offer after exhaustion, as all individuals
who received UI were eligible to at least 20 weeks in my sample.
17
UI eligibility if they never qualified before). Non-recipients also have higher average reemployment wage than the wage prior to the spell and have much shorter spells (14.7
weeks). On the other hand, individuals who accepted an offer after exhaustion are less
educated, experience a large decrease in their average wage upon re-employment and have
very long spell (58.7 weeks) on average. The average spell for those who accepted a job
offer before exhaustion is 20.8 weeks. Furthermore, not only do the different comparison
groups differ on observable characteristics, but they are also likely to differ on unobservable characteristics. For example, eligible non-recipients might be more motivated to find
a job and start working than recipients if the reason they choose not to receive UI benefits
is because they expect their spell to be short. Thus, it is not possible to identify a causal
effect of receiving benefits from the analysis presented here. In order to identify causal
effects, one would need to proceed to a structural estimation of the model presented in
section 2 or to find an exogenous variation in benefits availability. Although neither comparison group constitutes a good control, the regularity and consistency of the results can
shed some light on the effect of UI benefits on the delay behavior.
A relevant question at this point is whether individuals strategically postpone resuming work or if this results solely from institutional constraints. Even though in the model
delay between job offer and job start are fixed by the employers, individuals can change
their acceptance behaviour based on their preferences. Any delay that is reflective of
individuals’ preferences is “strategic” in that sense. In particular, if the delay between
job offer and job start were entirely driven by institutional constraints, the delay would
not be affected by whether the individual receives UI benefits after job offer, nor the
time unemployed at job offer. The empirical findings presented in this section go in the
opposite direction, which suggests that at least part of the delay might be strategic rather
than institutional.
Further evidence of strategic delay is provided by figure 5, which shows the behaviour
of the job acceptance and job starting rate around benefit exhaustion.16 As suggested
16
The hazard rates are computed as the number of individuals who exit a state in a given month divided
by the number of individuals remaining in that state at the beginning of the month, where the states are
respectively not having accepted an offer and not having started to work. In figure 5, the horizontal axis
denotes the time to exhaustion at the end of the month used for computation.
18
by the theoretical model, the job starting rate spikes at benefit exhaustion. Indeed, the
job starting rate more than doubles at exhaustion. The model also predicts that there
would be no spike in the job acceptance rate. However, this prediction is not validated
by the data, even though the spike in the job offer rate is much smaller than that in the
job starting rate (an increase of 15.7% compared to 111.8% for the job starting rate).
The fact that the job starting rate increases much more than the job acceptance rate at
benefit exhaustion suggests that individuals take advantage of UI benefits by strategically postponing job start after accepting an offer. While not shown in the figure, the
job starting rate among individuals with a pre-existing offer increases by 61% to reach
84% in the month prior to exhaustion (compared to an average monthly rate of 57% before exhaustion and 77% after exhaustion). Of course, the suggestive evidence presented
here do not account for differences in individuals characteristics, but the idea that delay
has a strategic component holds when including these differences in the empirical analysis.
4
Empirical Analysis
4.1
Methodology
Following the existing literature, I first estimate a reduced-form equation of the job starting rate. Then I decompose the total duration of the jobless spell, ts , into two components,
the duration until a job offer is accepted, to , and the duration of delay between job offer
and job start, τ , and estimate a reduced-form equation for each of them.
For the purpose of the empirical analysis, each of the duration observed in the data
is assumed to come from a mixed proportional hazard model (MPH). The proportional
hazard (PH) model was first suggested by Cox (1972). This econometric model assumes
that the probability of leaving a state is affected proportionally by the covariates. The
MPH builds on the PH model by allowing for unobserved heterogeneity. The MPH was
introduced by Lancaster (1979) who applied it to unemployment duration. Lancaster
points out that not controlling for unobserved heterogeneity can lead to attenuation bias
and that it is especially important in the case of omitted variables or measurement errors.
Since our data set is particularly prone to measurement errors, allowing for unobserved
19
heterogeneity will have a large impact on the estimates. It is important to realize that this
analysis does not estimate the structural parameters of the model presented in section
2, and can’t distinguish between the job arrival rate and the job acceptance rate. Moreover, the proportional hazard model is not consistent with the theoretical model except
in some limited cases. This reduced-form analysis is nonetheless informative about the
determinants of delay and the role UI plays in it.
The first equation to be estimated is that of the job starting rate, i.e. the probability
that a job starts at time t, conditional on being unemployed at that time.17 This estimation relates to the total duration of unemployment and is done solely for descriptive and
comparability purposes. This estimation is inconsistent with the subsequent estimation
of the sequential model. Following the literature, the job starting rate at duration t in
the jobless spell is assumed to be
θs (t|xs , us ) = hs (t) exp(x0s βs )us
(7)
where xs are observed characteristics at the beginning of the spell, us is the unobserved
heterogeneity with a distribution Gamma (1, σ) and hs is the time-dependence. Note
that us and xs are assumed to be independent. To allow for some flexibility, I assumed a
piecewise constant baseline hazard. I also included an indicator variable for being in the
month prior to benefit exhaustion and another for having exhausted the benefits. Thus,
the time-dependence can be written as
X
µsk Imk (t) + γs Ispike (t) + δs Iexh (t)),
hs (t) = exp(
(8)
k
where Imk is an indicator for being in the k th month since the beginning of the jobless
spell, Ispike (t) is an indicator for being in the month prior to exhaustion and Iexh (t) is an
indicator for having exhausted UI benefits. Note that Ispike (t) and Iexh (t) are identified
by the variation in UI benefit entitlement and take the nil value if the individual did not
receive UI during the spell. An indicator variable for receiving UI at some point during
the spell is included in the vector of observed characteristics.
17
The literature typically uses the term “job finding rate” to refer to the rate at which individuals start
working. Since the goal of my paper is precisely to recognize that finding a job (i.e. accepting an offer)
differs from starting to work, I use the term “job starting rate”. Moreover, to avoid confusion with the
previous literature, I use“job acceptance rate” to refer to the rate at which individuals find a job.
20
The second equation to be estimated is that of the job acceptance rate, i.e. the
probability that a job offer is accepted at time t, conditional on not having accepted a
job offer before. The rate at which unemployed individuals accept job offers after being
jobless for a duration t is assumed to be
θo (t|xo , uo ) = ho (t) exp(x0o β)uo
(9)
where xo are observed characteristics at the beginning of the spell, including an indicator
for receiving UI, uo is the unobserved heterogeneity with a distribution Gamma (1, σ)
and ho is the time-dependence. Again, uo and xo are assumed to be independent. The
baseline hazard is assumed piecewise constant and the time-dependence also includes an
indicator variable for being in the month prior to benefit exhaustion and another for
having exhausted the benefits. Thus, the time-dependence can be written as
ho (t) = exp(
X
µok Imk (t) + γo Ispike (t) + δo Iexh (t)),
(10)
k
where Imk is an indicator for being in the k th month since the beginning of the jobless
spell, Ispike (t) is an indicator for being in the month prior to exhaustion and Iexh (t) is
an indicator for having exhausted UI benefits, both of which take the nil value for nonrecipients. Identification of the effect of benefit exhaustion and time effect is possible
because of the variability in the number of weeks of benefits. If all individuals had the
same length of benefit, it would be impossible to distinguish time-effect from exhaustion
effect.
The third equation to be estimated is that of the rate at which unemployed individuals
start working after having accepted a job offer, i.e. the probability that a job starts at a
duration τ after accepting a job offer, conditional on not having resumed work yet. The
job starting rate upon acceptance at duration τ is assumed to be
θ(τ |xτ , to , uτ ) = h(τ ) exp(x0τ β + λto )uτ
(11)
where to is the duration in unemployment until job offer, xτ are observed characteristics,
assumed independent from the unobserved heterogeneity, uτ ∼ Gamma (1, σ). The
baseline hazard is still assumed piecewise constant at the week level (rather than the
month in the case of the job acceptance rate). The time-dependence can then be defined
21
as
h(τ ) = exp(
X
µk Iwk (τ ) + γIspike (τ ) + δIexh (τ )),
(12)
k
where Iwk is an indicator for being in the k th week since the job was offered, Ispike (t) is an
indicator for being in the month prior to exhaustion and Iexh (t) is an indicator for having
exhausted UI benefits.
Observed characteristics controlled for vary from one specification to another. First,
all specifications include an indicator for not receiving UI benefits during the spell. There
are three other categories of control variables. The first set of regressors includes the
unemployment rate in the UI economic region, as well as province and year at the start of
the spell. Some specifications also include personal characteristics at the start of the spell:
age group, sex, family status (marital status and children), and highest level of education.
The last set of control variables, re-employment job characteristics, applies only to the
estimation of the job starting rate upon acceptance. It consists of a set of indicators for
being a union member, being employed in the public sector, and being employed in a large
firm (more than 500 employees). Some specifications also include occupation dummies to
control for the possibility that some jobs imply a long waiting period until job start (ex:
professors and teachers).
Furthermore, in the analysis of the delay between job offer and job start, the duration
of unemployment until job offer is included as a control in the form of a set of dummy variables indicating whether the offer was accepted within a month, within at least a month
and less than three months, within at least three months and less than six months. Not
controlling for the job offer time would likely bias upward the effect of exhausting benefits.
Effectively, the longer an individual has been unemployed at job offer, the less likely he
is to value delay before job start (assuming a decreasing marginal value of leisure), but
at the same time the longer an individual has been unemployed at job offer, the more
likely he has exhausted UI benefits. This creates an artificial correlation between benefit
exhaustion and delay if not controlling for time until job offer. However, for the time until
job offer to be exogenous, we need to make the restrictive assumption that the unobserved
heterogeneity uo and u are uncorrelated.
22
Some individuals have not accepted a job offer at the end of the period of observation
and are thus right-censored. Right-censoring is taken into account in the log likelihood
as follows
N
X
logL =
[ci logθ(ti |x) + logS(ti |x)],
(13)
i=1
where t ∈ (ts , to , τ ) is the completed duration or censoring time of the duration of interest (subscripts denoting the type of duration are dropped for convenience), i is an
observation,ci indicates whether the duration is complete for observation i, and S(ti |x)
is the survivor function (probability that the duration lasts at least ti ). The survivor
function can be written as

 exp[−exp(x0 β) R t h(s)ds] without unobserved heterogeneity
0
S(t|x) =
 [1 + σ 2 exp(x0 β) R t h(s)ds]−1/σ2 with u ∼ Γ(1, σ).
(14)
0
However, there is no right-censoring in the estimation of the job starting rate upon acceptance, since whenever the offer date is observed, so is the job start date. Additionally,
individuals who dont accept an offer by the end of the survey period never begin the delay
duration, and are therefore excluded from the estimation of the job starting rate upon acceptance. The parameters of equations (7) to (11) are estimated by maximum-likelihood
using the above equations (13 and 14).
Another consideration is that more than a third of individuals have more than one
unemployment spell over the 6-year period of the panel. Thus, I allow for correlation
in the error terms by clustering the standard errors at individual level. However, the
unobserved heterogeneity is assumed uncorrelated across spells for the same individual.
The piecewise constant time-dependence is flexible and has been shown to be more
robust to assumptions about the distribution of the unobserved heterogeneity (Han and
Hausman (1990), Ridder (1987), Trussel and Richards (1985) ). Thus, even though the
unobserved heterogeneity is assumed to be gamma distributed, the results should remain
similar would another distribution be assumed. As a robustness check, I present results
from Cox regressions for all durations in the appendix (table A1). Cox regression is a nonparametric method based on the rank and doesn’t make assumptions about heterogeneity.
23
However, it does not estimate the underlying baseline hazard, so it can’t be used to predict
the delay were UI benefits less generous. Finally, results from Probit regressions of the
probability of delaying more than two weeks are also presented in the appendix (table A2).
4.2
Results
The empirical analysis has two goals. First, it aims at testing the implications of the
theoretical model regarding the shape of the job acceptance and job starting rates around
benefit exhaustion. Second, it gives a first assessment of the determinants of delay between job offer and job start.
The first implication of the model states that the job starting rate should spike at
benefit exhaustion (proposition 2a). This prediction is due to individuals having a lower
reservation wage for jobs starting around exhaustion. Table 3 contains estimates of the
job starting rate.18 Indeed, table 3 reveals that the job starting rate is much higher in
the month preceding exhaustion. More precisely, without accounting for unobserved heterogeneity, the job starting rate increases by over 300% in the month prior to exhaustion,
but only by 200% after benefit exhaustion, creating a spike in the job starting rate before
benefit exhaustion (table 3, columns 1-3). Yet, not accounting for unobserved heterogeneity can lead to attenuation bias (Lancaster, 1990). When allowing for unobserved
heterogeneity, the magnitude of the estimated hazard ratio increases by more than 25%
both in the month prior to exhaustion and after exhaustion. However, although the job
starting rate remains higher in the month prior to exhaustion, it is not significantly higher
than that after exhaustion. Moreover, the job starting rate is higher for non-recipients
than for UI recipients with at least a month of benefits left. Estimates range from a job
starting rate 206% to 270% higher for non-recipients without and with unobserved heterogeneity respectively. The findings are robust to controlling for personal characteristics
(columns 3 and 6). Women and high school drop-outs have a lower job starting rate,
whereas individuals aged 25 to 34 years old have a higher job starting rate. Family status
and the unemployment rate at the beginning of the spell do not have much impact on the
job starting rate. This estimation replicates what has been done in previous studies and
18
Estimates are presented in log form, so the hazard ratio is eβ̂ .
24
is not consistent with the estimation of the subsequent model which separates the time
until a job offer is accepted and the delay until job start.
The second implication of the model states that the job acceptance rate should not
spike at benefit exhaustion, but rather gradually increase up to exhaustion then remain
high and stable (proposition 2b). This prediction is due to individuals having lower
reservation wage for any given job start date after benefit exhaustion. Table 4 contains
estimates of the job acceptance rate.19 Indeed, table 4 confirms an increase in the hazard rate during the month preceding exhaustion of more than 220%, and this increase
is sustained after exhaustion at a level of about 170% (although the difference is not
statistically significant). As before, the increase in the job acceptance rate is a little
higher when allowing for unobserved heterogeneity. Furthermore, the increase in the job
acceptance rate at benefit exhaustion is much smaller than that of the job starting rate.
Thus, the increase in the job acceptance rate can’t explain all of the variation in the
job starting rate in the month prior to benefit exhaustion and after exhaustion. Again,
the job acceptance rate is higher for non-recipients than for UI recipients with at least a
month of benefits left, with estimates ranging from 158% to 171%. Finally, these findings
are robust to controlling for region, year and unemployment rate at the beginning of the
spell and personal characteristics. As for the job starting rate, women and high school
drop-outs have a lower job acceptance rate, whereas individuals aged 25 to 34 years old
have a higher job acceptance rate (columns 3 and 6).
The discrepancy between the increase in the job acceptance rate and the spike in the
job starting rate hints that the delay between job offer and job start might play a role in
explaining the spike in the job starting rate at benefit exhaustion. Moreover, estimating
the effect of UI and timing of job offer on the job starting rate upon acceptance enables
us to assess whether delay has a strategic component. In particular, the third implication
of the model states that delay should be shorter if the offer is accepted after exhaustion (proposition 2c). This implies that the job starting rate upon acceptance should be
higher after benefit exhaustion. Table 7 contains estimates of the job starting rate upon
acceptance.20 The job starting rate is more than 150% higher both in the month prior
19
Estimates are presented in log form, so the hazard ratio is eβ̂ .
20
Estimates are presented in log form, so the hazard ratio is eβ̂ .
25
to exhaustion and once the benefits are exhausted (table 5). Controlling for unobserved
heterogeneity increases the coefficient by about a third. These results imply that delays
are shorter if the offer is accepted near or after exhaustion, as predicted by the model.
Furthermore, the job starting rate conditional on having accepted a job offer is also much
higher for non-recipients than recipients with a least one month of benefits left. Besides,
the timing of job offer also matters for predicting the delay. Individuals who accepted
an offer in the first month of their jobless spell have a job starting rate upon acceptance
about 40% lower than those who accepted an offer later in their spell. This proportion
reaches 55% when including unobserved heterogeneity. Results are robust to controlling
for personal and re-employment job characteristics (columns 2 and 4), as well as occupation (columns 3 and 6). The lower job starting rate for jobs offered early in the spell
could reflect either a decreasing marginal value of leisure or a credit constraint further in
the spell. In either case, it provides evidence that the delay between job offer and job
start has a strategic component.
On the other hand, part of the delay that could be qualified as institutional. In particular, re-employment job characteristics have an effect on the job starting rate upon
acceptance. In particular, jobs in the public sector are less likely to start quickly upon
acceptance,21 whereas unionized jobs are more likely to start quickly (not significant if
including unobserved heterogeneity). Moreover, single parents have a lower job starting
rate upon acceptance (significant only when including unobserved heterogeneity). A single
parent postponing job start could also be qualified as institutional delay if it takes time to
make childcare arrangements prior to starting a job. As a robustness check, results from
Cox regressions and Probit regressions of the probability of delaying more than two weeks
are presented in the appendix (table A1 and A2 respectively). Both the Cox regressions
and the Probit regressions support the idea that individuals receiving UI after accepting
a job offer postpone job start for a longer period.
21
This finding is robust to excluding individuals in teaching occupations.
26
4.3
Cost of the delay
The empirical analysis showed that individuals substantially postpone job start after accepting job offer. This delay has a cost for the Unemployment Insurance program, since
benefits are paid until the job starts, sometimes long after the job is accepted. Table
6 presents the cost of delaying job start as a fraction of all benefits paid. The amount
of benefits paid to individuals still receiving UI while postponing job start accounts for
16.9% of all benefits paid. To compute this, I multiplied the weekly benefits by the number of weeks of UI benefits received after job offer, then summed it for all individuals and
divided by the total amount of benefits paid. If we do the same computation allowing for
an institutional delay of two weeks, then 10.7% of all benefits paid are paid to individuals
who delay in excess of the institutional threshold. Hence, the delay between job offer and
job start implies a large cost for the UI program even without accounting for the lost
income tax revenue for the government.
Of course, this estimates doesn’t control for differences in observed characteristics.
Using estimates from the survival analysis, I predict the delay as if UI were exhausted
for all individuals when accepting a job offer and, alternatively, as if all individuals were
non-recipients. Then, I compute the “excess” delay as the difference between the actual
delay and the predicted delay. Without unobserved heterogeneity, I find that about 8.2%
of all benefits paid are paid to individuals postponing job start after job offer in excess
than predicted had they exhausted their benefits before job offer. This fraction reaches
12.1% when taking unobserved heterogeneity into account. Similarly, without controlling
for heterogeneity, 8.5% of all benefits paid are paid to individuals postponing job start
in excess than predicted were they non-recipients. This proportion reaches 12.5% when
including unobserved heterogeneity. Therefore, the “excess” delay accounts for half to
three fourth of the total cost of delay (16.9% of all benefits paid). Although this cost
seems considerable, it could be mitigated by efficiency gains if receiving UI benefits enables unemployed workers to accept better jobs starting later rather than accepting lower
paid jobs starting earlier. The following subsection test this hypothesis, as well as the
model prediction that wages and delay should be positively correlated for offers accepted
after exhaustion.
27
4.4
Efficiency gains
Postponing job start after job offer implies substantial costs for the UI program, and one
should be concerned that individuals receiving benefits strategically delay job start after
accepting a job offer. However, the overall cost might be much lower than estimated if
receiving UI enables unemployed workers to accept jobs that start later and are a better
match, rather than to accept the jobs that start the soonest. One way to assess the quality
of a match is by looking at the re-employment wage.
Table 7 contains regressions of the re-employment wage. There is a positive correlation
with the number of weeks between job offer and job start of an order of about 1%, and this
result is robust to including job characteristics and occupation (columns 1-3). However,
the positive relationship between wages and delay is driven by individuals who accepted
an offer after exhaustion and by non-recipients rather than by efficiency gains from receiving UI after accepting an offer. When interactions of delay and indicator variables for
accepting an offer after exhaustion and not receiving UI during the spell are included in
the model, the relationship between wages and delay disappears for those accepting an
offer before exhaustion (columns 4-6). Therefore, the possibility of postponing job start
while receiving UI benefits doesn’t lead to efficiency gains in terms of wages. However,
as predicted by the model, the effect of postponing job start on wages is positive (1.6%
to 2.5%) for non-recipients and for those accepting an offer after exhaustion. This result
supports the model’s prediction that wages and delay should be positively correlated for
offers accepted after benefit exhaustion and for non-recipients (proposition 2d). Intuitively, when individuals don’t receive benefits, they would rather start to work sooner
than later and will ask for a compensation to delay job start. To conclude, the analysis
of wages doesn’t support the hypothesis of efficiency gains from postponing job start, but
supports the prediction of a model in which individuals strategically postpone job start
to take advantage of the UI benefits.
4.5
Liquidity effect
The effect of Unemployment Insurance on the delay between job offer and job start could
be interpreted as a distortion in the marginal incentives or as a liquidity effect (Chetty,
28
2008). Intuitively, constrained individuals should be less inclined to delay than nonconstrained individuals other things being equal. When constrained, the marginal value
of consumption is higher than that of leisure, and delaying job start is less desirable.
Table 8 presents the average delay for different indicators of liquidity constraint. Following Chetty(2008) and Krueger and Mueller(2010), I define an individual to be liquidity
constrained if either his earnings are below the low-income margin, has a mortgage or is
the single earner of the household. Overall, liquidity constrained individuals start to work
0.5 weeks before unconstrained individuals upon finding a job. This gap is a little smaller
if we look at the average for each indicator separately. The striking result of table 8 is
that the difference between constrained and unconstrained individuals is mostly driven by
those who accepted an offer before exhaustion. If Unemployment Insurance were affecting
the delay through a liquidity effect, it should have a larger impact on liquidity constrained
individuals and receiving UI should not change the average delay for unconstrained individuals. Yet, the difference between individuals who received UI benefits after accepting
an offer and those who didn’t is larger for unconstrained individuals. The findings are
very similar if we look at the fraction who delay at least two weeks.
The cumulative distribution of the delay by liquidity constraint (figure 6) shows that
the distribution of the delay is very similar for both liquidity constrained and unconstrained individuals who don’t receive UI benefits after accepting a job. However, liquidity constrained individuals who receives benefits after accepting the job offer are more
likely to work at any duration after accepting a job than unconstrained individuals. This
suggests that moral hazard might be more important than liquidity effect in explaining
the correlation between the delay and Unemployment Insurance.
Table 9 shows the estimated parameters of the job starting rate by liquidity constraint.
The point estimates for constrained and unconstrained subsamples are not statistically
different. This finding confirms that the liquidity effect is not driving the relationship
between UI and delay, but rather that UI changes the marginal incentives to return to
work by providing a subsidy to delay job start.
29
5
Conclusion
Unemployment Insurance can alter job search behaviour and lead to longer unemployment
spells. The effect of UI on unemployment duration has been extensively documented, but
traditionally, it was assumed to be caused by an increase in the duration until a job offer
is accepted. This paper suggests that this is only part of the story. UI also affects another
component of the unemployment spell: the delay between job offer and job start.
In this paper, I developed a theoretical model where firms make job offers that include a wage and a start date. In this model, UI recipients are indifferent between a job
start now at a higher wage or a job start later at a lower wage but which enables them
to enjoy leisure subsidized by UI benefits. Once the benefits are exhausted, they would
rather start working now, and will accept a job that starts later only if the wage is high
enough to compensate for lost income while waiting for the job to start. Indeed, in the
data, longer delays are correlated with higher wages only for those who accepted an offer
after benefit exhaustion and for non-recipients. The model predicts that delay would be
longer on average for individuals accepting an offer before benefit exhaustion, which is
confirmed by the data. The model also rationalizes the empirical finding of a spike in the
job starting rate at benefit exhaustion, as suggested by Boone and Van Ours (2009). The
model predicts that the rate at which job offers are accepted increases until exhaustion
and remains stable thereafter. Thus, it can’t account for the empirical finding of a small
spike in the job offer rate. However, since the spike in the job starting rate is much more
pronounced than that in the job acceptance rate, the delay between job offer and job start
can explain at least part of the spike in the job starting rate.
The main contribution of this paper is to document the behaviour of postponing job
start after accepting a job offer, which has not been studied before. I find that individuals
who accepted an offer before benefit exhaustion delay job start by 3.9 weeks on average,
whereas the average delay is respectively 1.8 and 2.3 weeks for those who accepted a
job after exhaustion and those who did not receive benefits. Moreover, 54% of individuals with an offer accepted prior to exhaustion postpone job start by at least two weeks,
compared to 35% and 40% for those with an offer after exhaustion and non-recipients
respectively. Overall, this implies that 17% of all benefits paid are paid to individuals
30
who have already found a job, but have not started working yet. Moreover, half to three
quarters of the cost of delaying job start is due to delay in excess of the predicted delay
were the benefits exhausted at job offer or were the individuals not receiving UI at all.
Although no causal effect can be formally identified, this at least suggests that the delay
between job offer and job start is not solely driven by the employer side; rather some
individuals take advantage of the availability of benefits to postpone job start.
The empirical analysis also studied the determinants of delay. Receiving benefits
has a large negative impact on the job starting rate upon accepting a job. Although
no causal effect is identified, it supports the idea that individuals strategically postpone
job start. Similarly, the timing of job offer matters: accepting a job offer early in the
spell decreases the job starting rate upon acceptance. This finding could reflect either
a decreasing marginal value of leisure or it could reflect a credit constraint as the spell
progresses. In both cases, postponing job start would be less valuable further in the spell.
In any case, the effect of the timing of job offer on the job starting rate provides further
evidence that the delay between job offer and job start has a strategic component. However, personal characteristics such as age and gender don’t seem to affect the job starting
rate upon acceptance. Education has a non-monotonic effect and this effect varies across
specifications. In some specifications, single parents have a lower job starting rate upon
acceptance, which could be due to institutional constraints such as arranging for childcare. Another evidence of the presence of an institutional delay is that re-employment
job characteristics are correlated with the job starting rate upon acceptance. Jobs in the
public sector are less likely to start quickly after the offer, whereas unionized jobs are
more likely to start quickly in some specifications.
Even though the cost implied by postponing job start is considerably high, the cost
could be mitigated by efficiency gains. For example, receiving UI could enable unemployed workers to accept a better job that starts later by providing a subsidy during the
waiting period. Yet, this hypothesis is not supported by the regressions of wage on the
delay between job offer and job start. In particular, there is a positive correlation between wages and delay, but only for those who accepted the offer after benefit exhaustion
and for non-recipients, but not for individuals who still receive UI benefits after they accepted the offer. Furthermore, this result confirms the model prediction that wages should
31
be positively correlated with delay for jobs offered after exhaustion and for non-recipients.
Finally, the effect of Unemployment Insurance on the delay between job offer and job
start is larger for individuals who are not liquidity constrained, suggesting that UI distorts
the marginal incentives to resume work rather than acting through a liquidity effect.
Unfortunately, the data don’t allow to assess the effect of economic conditions on the
delay behaviour. Although there were fluctuations in the unemployment rate during the
period covered by the data, there was no recession in Canada during the 1993-2006 period.22 Thus, one can hardly generalize the results to a deeper economic downturn, such
as the Great Recession in the United States. Consequently, even though I didn’t find a
statistically significant effect of the unemployment rate on the duration of the delay, it is
very possible that unemployed individuals resume work more quickly when offered a job
in an economic downturn, limiting the undesirable effects of UI benefits on unemployment
duration. Moreover, jobs accepted later in the spell are more likely to start quickly, suggesting that the delay would be shorter during an economic downturn, when the job offer
arrival rate is low. Finally, if the length of the delay were to stay the same both in period
of economic growth and in recessions, the relative importance of the cost of delaying job
start would be mechanically much smaller in a period of recession, where the spells are
longer. Thus, the cost of the delay between job offer and job start should be more of a
concern in periods of expansion and might be negligible during deep economic downturns
like the Great Recession.
This paper is the first to study of the delay between job offer and job start. More
research has to be done in order to establish causal effects. Moreover, it will be important
to proceed to a structural estimation of the model’s parameters for policy simulation.
This will enable answering important questions such as how the government can improve
the UI system to make it less prone to strategic delay. It would also be interesting to look
at the efficiency gains of postponing job start for the employers. Do firms post vacancies
early to ensure a good match? Do they try to get their share of the pie by offering a lower
wage to UI recipients who would like to postpone job start?
22
Only a reduced growth (below 2% in 1996, 2001 and 2003)
32
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33
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34
A
Proofs
Proof. Proposition 1
a. Case t ≥ T :
After exhaustion, the problem becomes stationary, so V u (t) = V u and V e (w̄(τ ), τ, t) = V e (w̄(τ ), τ ).
Equations 2 and 3 respectively simplifiy to
V e (w, τ ) =
1 − e−ρτ
e−ρτ
u(b, lu ) −
u(w, le )
ρ
ρ
and
V
u
Z
∞
Z
[
=
s
e−ρ(v−t) u(b, lu )dv + e−ρ(s−t) Ew,τ (max(V e (w, τ ), V u )]dG(s; t)
t
t
u(b, lu )
λ
+
Ew,τ (max(V e (w, τ ), V u )
λ+ρ
λ+ρ
u(b, lu ) λ
+ Ew,τ (max(V e (w, τ ) − V u , 0).
=
ρ
ρ
=
Worker is indifferent between accepting or rejecting a job if V e (w̄(τ ), τ ) = V u . Substituting using
the equations above we get
1 − e−ρτ
e−ρτ
u(b, lu ) λ
u(b, lu ) −
ū(τ ) =
+ Ew,τ (max(V e (w, τ ) − V u , 0)
ρ
ρ
ρ
ρ
where Ew,τ (max(V e (w, τ ) − V u , 0)) can be rewritten as
Z
M
Z
0
u(W,le )
(V e (w, z) − V e (w̄(z), z)dQ(u|z)dF2 (z)
ū(z)
Z
M
Z
u(W,le )
=
[(
0
Z
ū(z)
M
Z
M
Z
u(W,le )
=
0
Z
ū(z)
u(W,le )
=
0
ū(z)
e−ρz
1 − e−ρz
e−ρz
1 − e−ρz
u(b, lu ) −
u(w, le )) − (
u(b, lu ) −
ū(z))]dQ(u|z)
ρ
ρ
ρ
ρ
e−ρz
[u(w, le ) − ū(z)]dQ(u|z)dF2 (z)
ρ
e−ρz
(1 − Q(u|z))dudF2 (z) by integration by parts.
ρ
Plugging it in the previous equation and rearranging gives equation 4.
(i) It is easy to see that ū(τ ) is strictly increasing in τ as long as ρ > 0.
b. Case t < T :
Taking the derivative with respect to time of equation 3, we have
dV u (t)
= −u(B(t), lu ) − λEw,τ (max(V e (w, τ, t) − V u , 0)) + ρV u (t)
dt
Taking the derivative with respect to time of V u (t) = V e (w̄(τ ), τ, t), we have
Z t+τ
dV u (t)
e−ρτ ∂ ū(τ, t)
−ρτ
=e
u(B(t + τ ), lu ) − u(B(t), lu ) + ρ
e−ρ(v−t) u(B(v), lu )dv +
.
dt
ρ
dt
t
35
Equating the two equations above, rearranging and substituting using equation 3 gives
∂ ū(τ, t)
ρ
= ρū(τ, t) − ρu(B(t + τ ), lu ) − λ −ρτ Ew,τ (max(V e (w, τ, t) − V u , 0))
dt
e
Z M Z u(W,le ) −ρz
e
ρ
[(1 − Q(u|z))dudF2 (z)]
= ρū(τ, t) − ρu(B(t + τ ), lu ) − λ −ρτ
e
ρ
ū(z,t)
0
by integration by parts (see a.)
(i) Define the ū∗ (τ, t) as the optimal reservation wage at time t if the environment remains stationary
after t, i.e.
Z Z
λ M u(W,le ) −ρ(z−τ )
∗
e
(1 − Q(u|z))dudF2 (z)
ū (τ, t) ≡ u(B(t), lu ) +
ρ 0
ū∗ (z,t)
For t < T , we have
ū∗ (τ, t) −
λ
ρ
Z
M
Z
0
u(W,le )
e−ρ(z−τ ) (1 − Q(u|z))dudF2 (z) = u(B, lu )
ū∗ (z,t)
> u(b, lu )
λ
= ū(τ, T ) −
ρ
Z
0
M
Z
u(W,le )
e−ρ(z−τ ) (1 − Q(u|z))dudF2 (z).
ū(z,T )
R M R u(W,le ) −ρ(z−τ )
Noting that x − λρ 0 x
e
(1 − Q(u|z))dudF2 (z) is an increasing function of x, it implies that
ū∗ (τ, t) > ū(τ, T ) for all t < T . The remaining of the proof follows the intuition of Van den Berg (1990).
More precisely, the discrepancy between ū∗ (τ, t) and ū(τ, t) arises only because of the anticipation of a
change in the benefit level. As the exhaustion date approaches, the positive discounting and the decrease
in the probability of finding a job before exhaustion increase the effect of the anticipation and, thus,
increase the difference between ū∗ (τ, t) and ū(τ, t). However, since the benefits are stationary before
increases in absolute
exhaustion, ū(τ, t) is the only variable that changes before exhaustion, so ∂ ū(τ,t)
∂t
2
∗
−
value (i.e. the sign of ∂ ū(τ,t)
is the same as that of ∂ ū(τ,t)
∂t2
∂t ). In particular, limt→T ū (τ, t) > ū(τ, T )
implies that the reservation utility is decreasing, and thus concave.
(ii) & (iii) Worker is indifferent between accepting or rejecting a job if V e (w̄(τ ), τ, t) = V u (t). Deriving
both sides, we get
e−ρτ ∂ ū(τ, t)
e−ρτ u(B(t + τ ), lu ) − e−ρτ ū(τ, t) −
=0
ρ
∂τ
which can be rewritten
∂ ū(τ, t)
= ρ[u(B(t + τ ), lu ) − ū(τ, t)].
∂τ
The sign of the RHS of the equation depends on whether ū(τ, t) is larger than u(B(t + τ ), lu ). Note
that for τ ∈ [T − t], u(B(t + τ ), lu ) = u(b, lu ) is smaller than the utility flow for any accepted offer
(otherwise the offer would not be accepted), so the RHS is positive.
36
B
Notation Summary
w ∈ [0, W ]
τ ∈ [0, M ]
F1 (w|τ )
F2 (τ )
λ
t
to
ts
lt
le
lu
l
ct
c
B(t)
b
B
T
ρ
u(ct , lt )
U (c, l)
V e (w, τ, t)
V u (t)
ū(τ, t)
Q(u|τ )
w̄(τ, t)
θo (t)
θs (t)
θτ (z)
wage
delay between job offer and job start
wage distribution conditional on delay
probability distribution of delay between job offer and job start
offer arrival rate
time elapsed since the beginning of unemployment spell
duration of unemployment spell at job offer
duration of unemployment spell at job start
leisure in period t
leisure if employed
leisure if unemployed
leisure schedule, i.e. l = (l1 , l2 , ..., lt , ...)
consumption in period t
consumption schedule, i.e. c = (c1 , c2 , ..., ct , ...)
consumption if unemployed in period t
home production and other source of income if UI benefits are exhausted
home production and unemployment benefits if not exhausted
benefit exhaustion
worker subjective discount rate
utility flow in period t
Life-time utility
value of being employed in τ periods at wage w in period t
value of being unemployed in period t
reservation utility for a job start in τ periods in period t
conditional distribution of utility flow once the job has started
reservation wage for a job start in τ periods in period t
job acceptance rate (conditional on not having accepted a job before)
job starting rate in period t (conditional on not having started working yet)
job starting rate conditional on having accepted a job offer z periods ago and not having started working ye
37
Figure 1: Distribution of jobless spell durations (completed spells)
Figure 2: Distribution of jobless spell durations at job offer (completed spells)
38
Figure 3: Distribution of delay between job offer and job start (completed spells)
Figure 4: Cumulative distribution of delay between job offer and job start (completed spells)
39
Figure 5: The spike in the job acceptance and the job starting rate at benefit exhaustion
Figure 6: Cumulative distribution of delay by liquidity constraint
40
Table 1: Delay for those who accepted the offer before exhaustion, after exhaustion and
non-recipients
Total
Offer time
<20 weeks ≥ 20 weeks
Mean delay between job offer and job start (weeks)
Offer before exhaustion
3.9
4.5
2.7
Offer after exhaustion
1.8
1.8
Non-recipients
2.3
2.3
2.0
Total
2.7
2.9
2.2
Fraction with delay longer than 2 weeks
Offer before exhaustion 0.54
0.59
0.45
Offer after exhaustion
0.35
0.35
Non-recipients
0.40
0.42
0.35
Total
0.44
0.46
0.36
Table 2: Mean of control variables and other selected variables
Offer before exhaustion
Personal characteristics (at the beginning of the spell)
Age
38.8
Women
0.41
Single without child
0.28
Married without child
0.21
Married with children
0.44
Single parent
0.08
Highschool drop-out
0.16
Highschool graduate
0.32
College graduate
0.07
Region
Atlantic
0.23
Quebec
0.37
Ontario
0.25
Prairies
0.10
British Columbia
0.06
Re-employment job characteristics (at job start)
Union
0.24
Public sector
0.09
Large firm
0.21
Wage
14.39
Other characteristics
Previous wage
14.61
Observed spell length (weeks)
20.8
Observations
5289
41
Offer after exhaustion
Non-recipients
Right-censored
39.4
0.44
0.33
0.19
0.41
0.07
0.21
0.27
0.04
35.7
0.46
0.35
0.16
0.43
0.07
0.16
0.32
0.11
41.0
0.51
0.34
0.18
0.42
0.06
0.21
0.29
0.09
0.21
0.18
0.38
0.11
0.13
0.10
0.24
0.37
0.17
0.12
0.15
0.23
0.38
0.14
0.10
0.18
0.08
0.27
13.85
0.16
0.08
0.23
15.52
15.19
58.7
1161
15.12
14.7
8860
23.4
2191
Table 3: Mixed proportional hazard estimates - job starting rate
(1)
(2)
UI benefits
Exhausted Benefits
0.7735***
0.7877***
(0.1288)
(0.1240)
< 1 month left
1.1611***
1.1388***
(0.1711)
(0.1702)
Non-recipient
0.7213***
0.7338***
(0.0593)
(0.0577)
Personal characteristics (at the beginning of the spell)
20-24 years old
(5)
(6)
0.7727***
(0.1191)
1.1131***
(0.1673)
0.7611***
(0.0568)
1.5702**
(0.6632)
1.7003***
(0.4360)
0.9917***
(0.1389)
1.0767***
(0.2738)
1.3706***
(0.2568)
0.8660***
(0.1038)
1.1106***
(0.2660)
1.3962***
(0.2833)
0.9089***
(0.1060)
-0.0057
(0.0066)
Gamma
-1.8935***
(0.4774)
Yes
Yes
9.518e+07
-4.759e+07
17501
15310
0.0533
(0.1367)
0.3296***
(0.1240)
0.1409
(0.1215)
0.1175
(0.1246)
-0.2508***
(0.0762)
0.0562
(0.0920)
-0.0371
(0.0952)
-0.0761
(0.1184)
0.2151**
(0.1029)
0.1705*
(0.0966)
0.2676*
(0.1539)
-0.0035
(0.0067)
Gamma
-1.8162***
(0.4085)
Yes
Yes
9.430e+07
-4.715e+07
17501
15310
No
-0.0052
(0.0055)
No
No
Yes
9.690e+07
-4.845e+07
17501
15310
Yes
Yes
9.534e+07
-4.767e+07
17501
15310
Yes
Yes
9.451e+07
-4.725e+07
17501
15310
35-44 years old
45-54 years old
Women
Married without child
Married with children
Single parent
High-school graduate
Some post-secondary
College graduate
Unemployment rate
Region and year dummies
Months in unemployment dummies
BIC
Log-likelihood
Number of spells
Number of completed spells
(4)
0.0143
(0.1085)
0.2464***
(0.0932)
0.0874
(0.0952)
0.0846
(0.1001)
-0.2252***
(0.0641)
0.0388
(0.0761)
-0.0485
(0.0784)
-0.0565
(0.0936)
0.1740**
(0.0807)
0.1438*
(0.0758)
0.2145*
(0.1225)
-0.0030
(0.0055)
No
25-34 years old
Unobserved heterogeneity
Log σ 2
(3)
Gamma
-1.2708***
(0.3094)
No
Yes
9.646e+07
-4.823e+07
17501
15310
Notes: Log relative-hazard form. Significance level: *** 1% , ** 5%, *10%.
Standard errors in parenthesis. σ 2 is the variance of unobserved heterogeneity.
42
Table 4: Mixed proportional hazard estimates - job acceptance rate
(1)
(2)
UI benefits
Exhausted Benefits
0.5274***
0.5536***
(0.1303)
(0.1244)
< 1 month left
0.8303***
0.8148***
(0.1741)
(0.1721)
Non-recipient
0.4584***
0.4759***
(0.0660)
(0.0633)
Personal characteristics (at the beginning of the spell)
20-24 years old
(5)
(6)
0.5357***
(0.1218)
0.7975***
(0.1684)
0.4955***
(0.0609)
0.7297***
(0.2375)
0.9469***
(0.2296)
0.5362***
(0.0909)
0.6272***
(0.1737)
0.8574***
(0.1860)
0.5058***
(0.0807)
0.6279***
(0.1791)
0.8466***
(0.1864)
0.5296***
(0.0806)
-0.0063
(0.0063)
Gamma
-3.0294***
(1.0398)
Yes
Yes
7.525e+07
-3.763e+07
17501
15310
0.0995
(0.1360)
0.2437**
(0.1215)
0.0971
(0.1181)
0.1186
(0.1297)
-0.1513**
(0.0708)
0.0373
(0.0886)
-0.1033
(0.0836)
-0.1353
(0.1058)
0.2286***
(0.0855)
0.1722**
(0.0825)
0.3363**
(0.1411)
-0.0034
(0.0064)
Gamma
-2.9007***
(0.9361)
Yes
Yes
7.470e+07
-3.735e+07
17501
15310
No
-0.0064
(0.0060)
No
No
Yes
7.666e+07
-3.833e+07
17501
15310
Yes
Yes
7.527e+07
-3.764e+07
17501
15310
Yes
Yes
7.473e+07
-3.736e+07
17501
15310
35-44 years old
45-54 years old
Women
Married without child
Married with children
Single parent
High-school graduate
Some post-secondary
College graduate
Unemployment rate
Region and year dummies
Months in unemployment dummies
BIC
Log-likelihood
Number of spells
Number of completed spells
(4)
0.0835
(0.1234)
0.2207**
(0.1094)
0.0843
(0.1085)
0.1074
(0.1197)
-0.1472**
(0.0664)
0.0317
(0.0825)
-0.1037
(0.0777)
-0.1307
(0.0984)
0.2112***
(0.0788)
0.1639**
(0.0750)
0.3081**
(0.1236)
-0.0037
(0.0060)
No
25-34 years old
Unobserved heterogeneity
Log σ 2
(3)
Gamma
-2.0787***
(0.4885)
No
Yes
7.655e+07
-3.828e+07
17501
15310
Note: Log relative-hazard form. Significance level: *** 1% , ** 5%, *10%.
Standard errors in parenthesis. σ 2 is the variance of unobserved heterogeneity.
43
Table 5: Mixed proportional hazard estimates - job starting rate upon acceptance
(1)
(2)
(3)
UI benefits
Exhausted Benefits
0.5913***
0.4528***
0.4384***
(0.1011)
(0.1099)
(0.1125)
< 1 month left
0.5802**
0.4583*
0.4972**
(0.2538)
(0.2528)
(0.2268)
Non-recipient
0.4479***
0.5213***
0.5441***
(0.0690)
(0.0667)
(0.0652)
Job offer time (from the beginning of the unemployment spell)
< 1 month
-0.4769*** -0.4796***
(0.0708)
(0.0709)
[1-3) months
0.1414
0.1354
(0.1316)
(0.1309)
[3-6) months
-0.0402
-0.0565
(0.1530)
(0.1514)
Re-employment job characteristics (at job start)
Union
0.1785**
0.1653**
(0.0736)
(0.0723)
Public sector
-0.3002***
-0.2744**
(0.1033)
(0.1143)
Large firm
-0.0465
-0.0096
(0.0759)
(0.0737)
Personal characteristics (at the beginning of the spell)
20-24 years old
0.1398
0.1112
(0.1357)
(0.1340)
25-34 years old
-0.0611
-0.0758
(0.1185)
(0.1171)
35-44 years old
-0.0677
-0.0433
(0.1208)
(0.1208)
45-54 years old
-0.0113
-0.0388
(0.1185)
(0.1189)
Women
-0.0040
-0.0150
(0.0641)
(0.0672)
Married without child
0.0395
0.0381
(0.0897)
(0.0868)
Married with children
0.0169
0.0163
(0.0842)
(0.0816)
Single parent
-0.1462
-0.1695
(0.1166)
(0.1181)
High-school graduate
0.1147
0.1181
(0.0871)
(0.0873)
Some post-secondary
0.1298
0.1431*
(0.0822)
(0.0820)
College graduate
0.0582
0.1301
(0.1402)
(0.1478)
Unemployment rate
0.0064
0.0080
0.0073
(0.0065)
(0.0063)
(0.0064)
Unobserved heterogeneity
No
No
No
Log σ 2
Region and year dummies
Weeks since job offer dummies
Occupation dummies
BIC
Log-likelihood
Number of completed spells
Yes
Yes
No
1.192e+08
-5.958e+07
15310
Yes
Yes
No
1.159e+08
-5.793e+07
15310
Yes
Yes
Yes
1.151e+08
-5.755e+07
15310
(4)
(5)
(6)
0.7781***
(0.1439)
0.8423**
(0.3446)
0.5348***
(0.0968)
0.6451***
(0.1591)
0.6899**
(0.3466)
0.7645***
(0.1135)
0.6611***
(0.1678)
0.7355**
(0.3503)
0.8478***
(0.1203)
-0.7703***
(0.1195)
0.2408
(0.2270)
-0.1629
(0.2530)
-0.8203***
(0.1228)
0.2722
(0.2216)
-0.2253
(0.2699)
0.0948
(0.1262)
-0.4014**
(0.1762)
-0.0518
(0.1257)
0.0603
(0.1172)
-0.3030*
(0.1815)
0.0291
(0.1256)
0.0127
(0.2210)
-0.2108
(0.2022)
-0.1897
(0.1947)
-0.1327
(0.1966)
0.0099
(0.1026)
0.0073
(0.1392)
-0.0371
(0.1300)
-0.3758*
(0.2097)
0.2281*
(0.1380)
0.1580
(0.1397)
0.0872
(0.2484)
0.0156
(0.0099)
Gamma
-1.0355***
(0.2066)
Yes
Yes
No
1.148e+08
-5.740e+07
15310
-0.0398
(0.2245)
-0.2420
(0.2011)
-0.1680
(0.2053)
-0.1769
(0.2085)
0.0172
(0.1116)
0.0042
(0.1359)
-0.0534
(0.1313)
-0.4491**
(0.2124)
0.2345*
(0.1401)
0.1663
(0.1383)
0.2635
(0.2679)
0.0169
(0.0103)
Gamma
-0.8845***
(0.1171)
Yes
Yes
Yes
1.139e+08
-5.697e+07
15310
0.0123
(0.0096)
Gamma
-1.0679***
(0.1156)
Yes
Yes
No
1.192e+08
-5.958e+07
15310
Note: Log relative-hazard form. Significance level: *** 1% , ** 5%, *10%.
44variance of unobserved heterogeneity.
Standard errors in parenthesis. σ 2 is the
Table 6: Cost of delay as a fraction of all benefits paid
Fraction of benefits paid while the recipient is delaying job start
” in excess of 2 weeks
” in excess of predicted delay were benefits exhausted at job offer
without unobserved heterogeneity (specification 2)
with unobserved heterogeneity (specification 4)
” in excess of predicted delay if all were non-recipients
without unobserved heterogeneity (specification 2)
with unobserved heterogeneity (specification 4)
0.169
0.107
0.082
0.121
0.085
0.125
Table 7: OLS regressions of log wage
Delay (weeks)
(1)
0.0101***
(0.0028)
(2)
0.0092***
(0.0028)
(3)
0.0080***
(0.0028)
-0.1256***
(0.0483)
0.2826***
(0.0524)
-0.3136***
(0.0612)
0.0151***
(0.0047)
-0.0003***
(0.0001)
0.0866**
(0.0390)
0.2237***
(0.0408)
0.5447***
(0.0724)
-0.1366***
(0.0425)
0.2298***
(0.0432)
-0.2895***
(0.0533)
0.0165***
(0.0043)
-0.0003***
(0.0001)
0.0656*
(0.0345)
0.1889***
(0.0370)
0.4953***
(0.0662)
0.2746***
(0.0327)
0.1635***
(0.0360)
0.1372***
(0.0361)
No
Yes
0.37
15297
-0.1287***
(0.0380)
0.1946***
(0.0399)
-0.2573***
(0.0478)
0.0133***
(0.0037)
-0.0002***
(0.0001)
0.0730**
(0.0312)
0.1554***
(0.0334)
0.3801***
(0.0610)
0.2878***
(0.0307)
0.1327***
(0.0407)
0.0996***
(0.0292)
Yes
Yes
0.46
15297
Delay (weeks) if non-recipient
Delay (weeks) if offer after exhaustion
Non-recipient
Offer after exhaustion
Women
Married
Married women
Potential experience
Potential experience (squared)
High-school graduate
Some post-secondary
College graduate
Union
Public sector
Large firm
Occupation dummies
Region and year dummies
R2
Observations
No
Yes
0.29
15297
(4)
0.0026
(0.0033)
0.0201***
(0.0065)
0.0250*
(0.0131)
-0.0362
(0.0350)
-0.0463
(0.0707)
-0.1257***
(0.0477)
0.2823***
(0.0516)
-0.3120***
(0.0605)
0.0145***
(0.0048)
-0.0003***
(0.0001)
0.0853**
(0.0389)
0.2203***
(0.0405)
0.5430***
(0.0710)
No
Yes
0.29
15297
(5)
0.0027
(0.0036)
0.0184***
(0.0063)
0.0216*
(0.0131)
-0.0143
(0.0309)
-0.0483
(0.0485)
-0.1378***
(0.0422)
0.2286***
(0.0427)
-0.2861***
(0.0530)
0.0161***
(0.0043)
-0.0003***
(0.0001)
0.0651*
(0.0347)
0.1880***
(0.0370)
0.4950***
(0.0653)
0.2792***
(0.0323)
0.1557***
(0.0347)
0.1366***
(0.0354)
No
Yes
0.38
15297
Notes: Significance level: *** 1% , ** 5%, *10%. Standard errors in parenthesis.
45
(6)
0.0022
(0.0035)
0.0160***
(0.0060)
0.0227
(0.0149)
-0.0230
(0.0271)
-0.0331
(0.0521)
-0.1279***
(0.0376)
0.1944***
(0.0394)
-0.2558***
(0.0476)
0.0129***
(0.0038)
-0.0002***
(0.0001)
0.0722**
(0.0314)
0.1539***
(0.0335)
0.3825***
(0.0602)
0.2905***
(0.0303)
0.1285***
(0.0392)
0.0992***
(0.0286)
Yes
Yes
0.46
15297
Table 8: Mean delay by different indicator of liquidity constraint
Liquidity constrained Low-income
No
Yes
No
Yes
Mean delay between job offer and job start (weeks)
Offer before exhaustion 4.43
3.56
3.99 3.15
Offer after exhaustion
2.07
1.72
1.83 1.85
Non-recipients
2.38
2.20
2.27 2.18
Total
3.05
2.54
2.76 2.42
Fraction with delay longer than 2 weeks
Offer before exhaustion 0.58
0.51
0.55 0.47
Offer after exhaustion
0.40
0.32
0.35 0.32
Non-recipients
0.41
0.40
0.40 0.42
Total
0.47
0.43
0.44 0.43
Single earner
No
Yes
Mortgage
No
Yes
3.93
1.79
2.30
2.76
3.74
1.95
2.12
2.55
4.33
1.94
2.19
2.83
3.47
1.55
2.28
2.57
0.54
0.37
0.41
0.45
0.52
0.30
0.38
0.41
0.56
0.33
0.39
0.44
0.51
0.34
0.41
0.43
Table 9: Mixed proportional hazard estimates by liquidity - job starting rate upon acceptance
Liquidity constrained
Exhausted Benefits
< 1 month
Non-recipient
Completed spells
Not liquidity constrained
Exhausted Benefits
< 1 month
Non-recipient
Completed spells
Unobserved heterogeneity
Personal characteristics
Job characteristics
Occupation dummies
Region and year dummies
Weeks since job offer dummies
(1)
(2)
(3)
(4)
(5)
(6)
0.5203***
(0.1106)
0.8423***
(0.2438)
0.3786***
8011
0.5348***
(0.1146)
0.8905***
(0.2346)
0.3688***
8011
0.3790**
(0.1536)
0.7455***
(0.2444)
0.4736***
8011
0.7188***
(0.1708)
1.2128***
(0.4479)
0.4841***
8011
0.7659***
(0.1767)
1.2433***
(0.4615)
0.4718***
8011
0.6636***
(0.2414)
1.1808**
(0.5160)
0.9318***
8011
0.6678***
(0.1820)
0.4109
(0.3835)
0.5100***
(0.1042)
7299
No
No
No
No
Yes
Yes
0.7016***
(0.1775)
0.4898
(0.3717)
0.4945***
(0.0910)
7299
No
Yes
Yes
No
Yes
Yes
0.6440***
(0.2080)
0.3219
(0.3708)
0.5680***
(0.0903)
7299
No
Yes
Yes
Yes
Yes
Yes
0.6897***
(0.2126)
0.4204
(0.4014)
0.5236***
(0.1224)
7299
Gamma
No
No
No
Yes
Yes
0.8204***
(0.2192)
0.5663
(0.4452)
0.5815***
(0.1172)
7299
Gamma
Yes
Yes
No
Yes
Yes
0.9106***
(0.2451)
0.4638
(0.4515)
0.8917***
(0.1692)
7299
Gamma
Yes
Yes
Yes
Yes
Yes
Notes: Log relative-hazard form. Significance level: *** 1% , ** 5%, *10%. Standard errors in
parenthesis.
46
47
Job starting rate
(2)
(3)
n.a.
No
No
2.742e+05
-1.371e+05
17501
15310
-0.0047
(0.0055)
n.a.
Yes
No
2.736e+05
-1.367e+05
17501
15310
0.0220
(0.1098)
0.2553***
(0.0944)
0.0957
(0.0968)
0.0847
(0.1001)
-0.2207***
(0.0652)
0.0552
(0.0775)
-0.0305
(0.0818)
-0.0494
(0.0963)
0.1807**
(0.0831)
0.1499*
(0.0774)
0.2211*
(0.1259)
-0.0024
(0.0056)
n.a.
Yes
No
2.731e+05
-1.364e+05
17501
15310
n.a.
No
No
2.156e+05
-1.078e+05
17501
15310
-0.0055
(0.0060)
n.a.
Yes
No
2.151e+05
-1.075e+05
17501
15310
0.6676***
(0.1324)
0.7819***
(0.1710)
0.4973***
(0.0647)
(3)
0.0984
(0.1250)
0.2354**
(0.1106)
0.1033
(0.1099)
0.1206
(0.1199)
-0.1439**
(0.0672)
0.0471
(0.0834)
-0.0908
(0.0798)
-0.1275
(0.0988)
0.2112***
(0.0795)
0.1662**
(0.0760)
0.3150**
(0.1252)
-0.0028
(0.0060)
n.a.
Yes
No
2.148e+05
-1.072e+05
17501
15310
0.6445***
(0.1267)
0.7670***
(0.1682)
0.5151***
(0.0629)
Job acceptance rate
(2)
0.6627***
(0.1362)
0.7900***
(0.1729)
0.4820***
(0.0667)
(1)
0.0032
(0.0060)
n.a.
No
No
2.621e+05
-1.310e+05
17501
15310
0.1273
(0.1121)
-0.0292
(0.0985)
-0.0074
(0.1042)
0.0025
(0.1005)
-0.0235
(0.0523)
0.0638
(0.0723)
0.0196
(0.0693)
-0.1047
(0.1017)
0.0929
(0.0773)
0.1702**
(0.0709)
0.0566
(0.1121)
0.0035
(0.0057)
n.a.
Yes
No
2.668e+05
-1.332e+05
17501
15310
0.0977
(0.0661)
-0.2643***
(0.0867)
-0.0509
(0.0593)
0.5099***
(0.0916)
0.4673**
(0.2123)
0.4049***
(0.0601)
0.1211
(0.1092)
-0.0198
(0.0946)
-0.0287
(0.0984)
0.0054
(0.0958)
-0.0212
(0.0529)
0.0577
(0.0715)
0.0143
(0.0708)
-0.1147
(0.1049)
0.1106
(0.0745)
0.1561**
(0.0681)
0.0688
(0.1118)
0.0051
(0.0056)
n.a.
Yes
No
2.664e+05
-1.330e+05
17501
15310
0.0924
(0.1082)
-0.0395
(0.0934)
-0.0141
(0.0979)
-0.0192
(0.0957)
-0.0333
(0.0546)
0.0527
(0.0677)
0.0127
(0.0679)
-0.1285
(0.1053)
0.1108
(0.0741)
0.1632**
(0.0677)
0.1126
(0.1141)
0.0050
(0.0056)
n.a.
Yes
Yes
2.664e+05
-1.329e+05
17501
15310
0.1555**
(0.0628)
-0.2314**
(0.0934)
-0.0187
(0.0593)
-0.3444***
(0.0596)
0.0444
(0.0951)
-0.0206
(0.1281)
-0.3480***
(0.0604)
0.0471
(0.0981)
-0.0164
(0.1297)
0.1581**
(0.0651)
-0.2813***
(0.0885)
-0.0415
(0.0617)
0.3815***
(0.0984)
0.3809**
(0.1890)
0.4697***
(0.0574)
0.3900***
(0.0954)
0.3491*
(0.2106)
0.4492***
(0.0597)
Job starting rate upon acceptance
(2)
(3)
(4)
0.4655***
(0.0899)
0.4630**
(0.2165)
0.4121***
(0.0640)
(1)
Log relative-hazard form. Significance level: *** 1% , ** 5%, *10%. Standard errors in parenthesis.
Unobserved heterogeneity
Region and year dummies
Occupation dummies
BIC
Log-likelihood
Number of spells
Number of completed spells
Unemployment rate
College graduate
Some post-secondary
High-school graduate
Single parent
Married with children
Married without child
Women
45-54 years old
35-44 years old
25-34 years old
Personal characteristics (at the beginning of the spell)
20-24 years old
Large firm
Public sector
Re-employment job characteristics (at job start)
Union
[3-6) months
[1-3) months
0.9428***
0.9411***
0.9161***
(0.1331)
(0.1281)
(0.1219)
< 1 month
1.0789***
1.0622***
1.0416***
(0.1635)
(0.1618)
(0.1605)
Non-recipient
0.7546***
0.7658***
0.7916***
(0.0597)
(0.0585)
(0.0580)
Job offer time (from the beginning of the unemployment spell)
< 1 month
UI benefits
Exhausted Benefits
(1)
Table A.1: Cox regressions
Table A.2: Probit regressions of the probability of delaying job start for at least two weeks
(1)
(2)
UI benefits
Offer after exhaustion
(3)
-0.4840*** -0.4924***
-0.3900**
(0.1572)
(0.1525)
(0.1579)
Non-recipient
-0.3480*** -0.3531*** -0.4780***
(0.0835)
(0.0818)
(0.0844)
Job offer time (from the beginning of the unemployment spell)
< 1 month
0.4657***
(0.0901)
[1,3) months
-0.1338
(0.1291)
[3,6) months
0.2473
(0.1952)
Re-employment job characteristics (at job start)
Union
0.0033
-0.0599
(0.1098)
(0.1058)
Public sector
0.2039*
0.2304*
(0.1232)
(0.1219)
Large firm
0.1192
0.0935
(0.0956)
(0.0964)
Personal characteristics (at the beginning of the spell)
20-24 years old
0.0396
0.0538
(0.1532)
(0.1552)
25-34 years old
0.1680
0.1504
(0.1299)
(0.1295)
35-44 years old
0.1947
0.2168
(0.1339)
(0.1325)
45-54 years old
0.1982
0.2010
(0.1353)
(0.1332)
Women
-0.0387
-0.0226
(0.0772)
(0.0768)
Married without child
-0.1166
-0.1170
(0.1088)
(0.1113)
Married with children
0.0504
0.0481
(0.1007)
(0.1017)
Single parent
0.2000
0.2107
(0.1454)
(0.1446)
High-school graduate
-0.1098
-0.1305
(0.1103)
(0.1061)
Some post-secondary
-0.1111
-0.1110
(0.1077)
(0.1052)
College graduate
-0.0024
-0.0331
(0.1615)
(0.1624)
Unemployment rate
-0.0161**
-0.0152**
-0.0167**
(0.0075)
(0.0074)
(0.0074)
Occupation dummies
No
No
No
Region and year dummies
Yes
Yes
Yes
bic
4.441e+07
4.394e+07
4.289e+07
ll
-2.220e+07 -2.197e+07 -2.144e+07
Number of spells (completed)
15310
15310
15310
(4)
-0.3848**
(0.1550)
-0.5235***
(0.0815)
0.4582***
(0.0873)
-0.1513
(0.1264)
0.2648
(0.1977)
-0.0215
(0.1027)
0.1565
(0.1209)
0.0423
(0.0913)
0.0741
(0.1531)
0.1565
(0.1284)
0.2055
(0.1312)
0.2306*
(0.1329)
-0.0319
(0.0794)
-0.1330
(0.1029)
0.0377
(0.0990)
0.2174
(0.1435)
-0.1385
(0.1006)
-0.1267
(0.1017)
-0.1492
(0.1588)
-0.0171**
(0.0074)
Yes
Yes
4.203e+07
-2.102e+07
15310
Standard errors in parenthesis. Significance level: *** 1% , ** 5%, *10%.
48