WORKING PAPER
Job Insecurity, Unemployment Insurance and Onthe-Job Search
Evidence from Older American Workers
Italo Gutierrez
RAND Labor & Population
WR-1085-1
August 2015
This paper series made possible by the NIA funded RAND Center for the Study of Aging (P30AG012815) and the NICHD funded RAND
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Job Insecurity, Unemployment Insurance and Onthe-Job Search
Evidence from Older American Workers
Italo A. Gutierrez, RAND
italo@rand.org
August, 2015
Abstract
In this study I estimate that about 23% to 47% of older American on-the-job seekers search for
another job because they feel insecure at their current employment. I also analyze whether
unemployment insurance (UI) affects this relationship between job insecurity and on-the-job search. I
find evidence that UI discourages on-the-job search, which in turn reduces the probability of starting a
new job at a different employer. The average estimated effects are moderate but they mask important
heterogeneities. On one hand, UI does not affect the search behavior of workers who do not believe to
be at risk of job loss. These workers make up the majority of the employed population over 50. On the
other hand, however, the effects can be substantial for workers with high levels of job insecurity.
JEL Classification Codes: J64, J65, D84
Keywords: on-the-job search; unemployment benefits; job loss expectations; control function methods
1. INTRODUCTION
The effects of unemployment insurance (UI) on job search behavior have been extensively
studied for the case of unemployed individuals. In contrast, we know little about the effects of UI on
the job search behavior of employed workers. To address this issue we first need to acknowledge job
insecurity as an important factor for explaining on-the-job search (OJS). This is usually overlooked in
the standard job search literature, where OJS and job transitions are explained only by a job ladder
motivation. In other words, OJS is motivated by the workers' desire to improve their utility, usually
defined in terms of a combination of wages, promotion opportunities and job amenities. However, in
reality, job insecurity can be the main reason for OJS for a non-trivial fraction of job seekers. For
example, Fujita (2011) documents that the primary reason for OJS for 12% of job seekers in the United
Kingdom (2002-2009) is the fear of losing their jobs. 1 Similarly, Rosal (2003) documents that 27% of onthe-job seekers in Spain (2000) engaged in OJS because of their job instability. 2 Furthermore,
acknowledging the importance of job insecurity for job search decisions might help explain the
substantial share of job-to-job transitions with wage cuts observed in OECD countries. 3 In order to
explore the importance of the job insecurity motivation for OJS I use information from the Health and
Retirement Study (HRS). Although the HRS only surveys individuals who are 50 year and older, its
main advantage is that it collects information on OJS and on job loss expectations. I find that among
older American workers job insecurity can explain 23% to 47% (depending on the estimation method)
of the incidence of on-the-job search. To the best of my knowledge, this is the first study that estimates
the importance of job-insecurity for OJS decisions in the U.S. (either for older workers or for other age
groups).
Given the important role that job insecurity plays in explaining OJS, I also examine whether that
effect is moderated by the availability of UI. Because UI reduces the financial cost of unemployment, it
can also reduce the effect of job insecurity on OJS. As a consequence, workers experiencing job
insecurity may be less likely to look for alternative jobs and thus at higher risk of entering
1
The source is the United Kingdom Labour Force Survey and the sample period is from the first quarter of 2002 to the first
quarter of 2009.
2
The source is the Spanish Survey of Economically Active Population (Encuesta de Poblacion Activa) from the second
quarter of 2000.
3
According to Jolivet et al. (2006) “between 25% and 40%, with substantial variation across countries, of job-to-job
transitions are associated with wage cuts.”
1
unemployment. Understanding better this potential interaction between job insecurity, UI and job
search is important given the substantial evidence that job displacement has persistent negative effects
on earnings (Couch and Placzek, 2010; Fallick, 1996; Jacobson et al., 1993; Kletzer, 1998) and in the case
of older workers it can lead to early exit from the labor force (Chan and Stevens, 1999, 2001). Only a
couple of papers have specifically focused on how UI can alter workers' OJS decisions in the face of job
insecurity (Burgess and Low, 1998; Light and Omori, 2004). 4 This research contributes to this literature
by using information on workers' job loss expectations and potential UI benefits (expressed in terms of
replacement rates) to test two predictions from a simple job search model: i) UI discourages job search
but only for workers who feel at risk of job loss and ii) the effect is larger the higher is the risk of job
loss perceived by the worker. The data provides empirical support for both of these predictions. I also
find supportive evidence from the analysis of employment transitions. I find that UI reduces the
probability that workers move to a new job at a different employer, and this effect is stronger for
workers that report higher levels of job insecurity. In sum, the evidence presented in this research
implies that UI reduces the probability of OJS and therefore affects employment transitions. It also
highlights the importance of taking into account individuals' job insecurity levels as a significant source
of heterogeneity in those effects.
The next section describes more in detail the few previous studies that have looked at how
workers react towards the risk job loss and unemployment and how this behavior can be changed by
UI benefits. Section 3 presents a simple model of OJS and describes the main predictions that I test in
the data. Section 4 describes the data sources and econometric strategy to estimate the effect of UI on
both the probability of OJS and on employment transitions. Section 5 presents the estimation results
and sensitivity analysis, and Section 6 concludes.
2. LITERATURE REVIEW
Workers' job search behavior change with their expectations of job loss, as first evidenced in the
studies on the effects of advanced layoff notifications. Burgess and Low (1992) found that 60.6% of
male workers who received layoff notification searched for alternative jobs before their employment
4
Other research have studied the effect of UI on the risk of unemployment, but do not focus on workers' OJS decisions
(Anderson and Meyer, 1993; Card and Levine, 1994; Christofides and McKenna, 1995, 1996; Feldstein, 1976, 1978; Green
and Riddell, 1997; Green and Sargent, 1998; Jurajda, 2002, 2003; Lalive et al., 2011; Rebollo-Sanz, 2012; Topel, 1983;
Winter-Ebmer, 2003).
2
were terminated. In comparison, only 38.9% of workers who did not receive such notification searched
for a job before termination. Addison and Blackburn (1995) found that the main benefit of providing
advanced layoff notifications is increasing the probability of finding a job before displacement
(especially for white collar males) rather than reducing the length of jobless spells. More recent
evidence from firm closures also indicates that workers' job loss expectations affect their job search
behavior. Lengermann and Vilhuber (2002) found that in the U.S. highly qualified workers tend to
voluntarily separate early from distressed firms before they close. Schwerdt (2011) founds similar
evidence for the Austrian labor market. Fallick and Fleischman (2001) also document, using
information from the Current Population Survey (CPS), that OJS predicts not only job-to-job transitions
but also job-to-unemployment transitions. They report that the probability of transitioning from
employment into unemployment in one month was 5.6% for active searchers versus 0.9% for nonsearchers. This finding indicates that OJS can be motivated by a higher probability of separation. In the
theoretical ground, Tudela and Smith (2012) have developed an equilibrium model to formalize the
idea that workers engage in job search not only to find better paying jobs but also to insure themselves
against the possibility of non-employment. In their model past search experiences becomes capital that
(partially) insures workers against displacement. In other words, if workers get displaced, they can use
their network of contacts as a fallback to avoid unemployment.
The strength of the relationship between job insecurity and job search behavior can be affected
by different institutional arrangements. For example, severance pay requirements and UI benefits
reduce the financial cost of unemployment. Thus, they can also discourage workers from searching for
alternative jobs and avoiding unemployment. These potential effects have been understudied in the
literature. In the case of UI most previous studies focus on the unemployed and on the effects of UI on
the duration of unemployment spells (Krueger and Meyer, 2002; Meyer, 1995). For employed
individuals, previous research has also found an increase in the risk of exiting employment either after
qualifying for UI benefits (Christofides and McKenna, 1995, 1996; Green and Riddell, 1997; Green and
Sargent, 1998; Jurajda, 2002; Rebollo-Sanz, 2012) or after extensions in the duration of potential benefits
(Fitzenberger and Wilke, 2009; Haan and Prowse, 2010; Lalive et al., 2011; Winter-Ebmer, 2003).
3
Although the effects of UI on job search effort could partly explain some of these findings, only a
couple of papers have directly studied this mechanism. 5
The first study on the effect of UI on OJS was done by Burgess and Low (1998). Using data from
displaced workers in Arizona, they found that UI benefits strongly discouraged pre-displacement job
search for workers who received advanced layoff notification and did not expect to be recalled by their
employers. In their study a $10 increase in weekly UI benefits above the sample mean reduced the
likelihood of OJS by 8 percentage points from 59.7% to 51.7%. Conversely, they found no statistically
significant effect of UI on the likelihood of OJS for non-notified workers or for notified workers who
expected to be recalled by their employers. In other words, UI did not change the search behavior of
workers who felt less job-insecure (either because they were not notified about being laid off or because
they believed that unemployment would be only temporary). Although these results are sensible, two
limitations threaten their validity as acknowledged by the authors. First, there is a selection problem
because the study sample was comprised of workers with at least five weeks of unemployment.
Therefore, workers who performed more OJS were less likely to be part of the sample. Second, since all
respondents were unemployed individuals in Arizona in the years 1975-1976 there is no variation in UI
benefits other than that due to the workers’ earnings histories. In other words, there is no exogenous
variation in UI benefits that could be used to identify their effects on OJS.
The second study of the effect of UI on OJS is Light and Omori (2004). They formulated a
theoretical model linking UI benefits to OJS and to employment transitions. They tested the predictions
from the model using the 1979 National Longitudinal Survey of Youth (NLSY79). If UI reduces
incentives to perform OJS then higher UI benefits would be associated with a decline in job-to-job (JTJ)
transitions and an increase in job-to-non-employment (JTN) transitions. The authors find evidence of
this effect, although its size is very small. They find that a one standard deviation increase above the
mean in weekly UI benefits reduced the probability of a JTJ transition in the next 15 weeks (for a
worker with 30 weeks of tenure) from 0.047 to 0.045 (or an elasticity of -0.09). A shortcoming in their
study is the lack of a measure of the workers' beliefs about job security. As I discuss in the next section,
UI only reduces the value of OJS if the worker feels vulnerable to job loss. Furthermore, the higher the
5
There is also a relatively well-developed literature on the effect of the imperfect rated UI payroll tax on the probability of
layoff (Anderson and Meyer, 1993; Card and Levine, 1994; Feldstein, 1976; Topel, 1983, 1984), although in this case UI is
postulated to affect employers' layoff decisions rather than workers' job search behavior.
4
risk of job loss, the stronger is the negative effect of UI on the value of job search. Thus, without
allowing the effect of UI to change with the level of job insecurity one would capture the effect for the
average worker, which can be very small. In fact, as suggested by the responses in the Survey of
Economic Expectations (SEE) and in the HRS, the average worker feels relatively secure in the job. 6
Hence, it is not surprising that the effects in Light and Omori (2004) were relatively small.
In this paper, I use the HRS to add new evidence on whether OJS is discouraged by the
generosity of UI. There are two main advantages of using the HRS. First, it contains information on
worker’s expectation of job loss, which allows testing the theoretical prediction that UI have stronger
effects for workers who feel more job-insecure. Second, HRS contains information on OJS and -given its
panel structure- it also contains information on workers’ employment transitions. Therefore, I can
estimate the effect of UI on both outcomes.
3. THEORY AND TESTABLE PREDICTIONS
Mortensen (1977) showed that in a fully dynamic setting the effect of UI benefits on
unemployed individuals' job search effort is ambiguous. An increase in benefits has two opposing
effects: 1) it increases the value of being unemployed, and 2) it increases the value of future
employment since better paying jobs come with better UI benefits – known as the “entitlement effect”.
Mortensen (1977) showed that the first effect reduces the incentives to search for a job and increases the
length of the unemployment spell. This effect is more dominant at the beginning of the spell.
Conversely, the entitlement effect creates incentives for workers to search more because there is higher
reward (in terms of better UI benefits) for finding a good-paying job. This effect decreases the length of
the unemployment spell and dominates when the worker is near the end of the benefit period. UI has
the same ambiguous effect on OJS. On one hand, UI reduces the cost of falling into unemployment. On
the other hand, it increases the payoff from getting a higher-paying job since it comes with better UI
benefits. Therefore, in theory the effect of more generous UI on OJS would be ambiguous. However, for
older workers the second effect is less important for two reasons: First, since the entitlement effect is a
forward-looking effect its importance decreases as the remaining working years also decrease. In my
analysis sample, the average worker is 56 years old. Thus, the length of the remaining working years
6
In the SEE, the average value of the respondent’s expected probability of job loss in the next twelve months is 11% for
workers aged 50 years or older (years 1994 through 1998). In the HRS, the average value is 18% (years 1996 through 2012).
5
until retirement is relatively short. Second, each state in the U.S. sets a maximum level of weekly
unemployment benefits. The entitlement effect does not exist for workers whose potential UI benefits
are already limited by that maximum level. Because earnings usually increase with experience and age,
about 50% of the older workers in my sample have earnings that would put their UI benefits above
their state's maximum level. For these two reasons, I use a simple model that abstracts from the
entitlement effect.
I borrow the model originally proposed by Light and Omori (2004), with a few modifications, to
derive theoretical predictions that I test in the data. 7 The proposed model consists of two periods. 8 In
the first period, the worker is employed and earns
. The maximization problem of the worker is to
decide whether to search on-the-job or not. If the worker decides to search then has to pay a fixed cost
of
, which is distributed among workers with probability function
( ). In each period, the flow
utility is given by the logarithm of the available earnings and the fixed cost of search (if the worker
searches on the job). If a worker searches, the probability of receiving an offer in the second period
equals . Offers come from a known distribution ( ), with density function ( ), and at most one
offer can be received. The worker faces a probability of layoff in period 2 equal to ; and if laid off, the
worker can collect UI benefits equal to
, where is the replacement rate.
If the worker decides not to search for a job, there are two possible scenarios for the second
period: 1) with probability (1
and 2) with probability
) does not lose the job and continuous receiving earnings equal to
loses the job and takes unemployment benefits equal to
;
. Four different
scenarios can occur in the second period if the worker decides to search for a job: 1) with probability
(1
)(1
) does not lose the job and does not receive an offer. In this scenario the worker continues
receiving earnings equal to
; 2) with probability (1
)
the worker loses the job and does not
receive an offer. In this scenario, the worker takes unemployment benefits equal to
probability (1
; 3) with
), the worker does not lose the job and receives an offer. In this scenario the worker
takes the new job as long as the offered wage is greater than
7
; and 4) with probability
, the worker
Light and Omori (2004) model OJS as a continuous outcome, whether in my specification it is modeled as a binary decision
(yes/no) and I introduce a fixed cost of search. I do this modification to fit the available data from HRS (see next section).
Light and Omori (2004) measure the generosity of the unemployment insurance system by the potential UI benefits that a
worker is entitled to if the job is lost. My measure of generosity is the replacement rate, i.e. the fraction of lost earnings
that UI benefits would replace.
8
In a two-period model, there is no entitlement effect by construction since only the immediate future (period 2) matters
for the period 1 decision.
6
loses the job and receives an offer. In this scenario, the worker takes the offer as long as the offered
wage is greater than
. Thus, the maximization problem for the worker in period 1 consists of
deciding whether to search on the job or not, as described below (where
denotes the worker’s time
discount factor):
{
;
{log(
)=
[(1
(1
) + [(1
)(1
) log(
{log(
)
{log(
) log(
)+
) + (1
)
log(
log(
) , log( )} ( )
) , log( )} ( )
)]; log(
)
+
)) +
+
}
(1)
Note that in this model the reservation wage to take a job offer in the second period if the
worker does not lose the job is
, whereas the reservation wage if the worker loses the job is
.
Thus, the expected value of a job offer is larger if the worker loses the job. As a consequence, workers
with higher expectations of layoff are willing to bear a higher maximum search cost to engage in OJS.
This analysis leads to the first testable prediction from the model (the formal proofs of all predictions
are deferred to the Appendix):
Prediction 1: Other things equal, workers with greater probability of job loss are more likely to search on the
job.
Note also that an increase in the replacement rate ( ) reduces the expected value of a job offer
because it increases the reservation wage in case of unemployment, or
. However, this effect does
not matter if there is zero probability of job loss. Conversely, for workers with a positive probability of
job loss, an increase in
reduces the maximum search cost that workers are willing to accept to engage
in OJS and therefore they are less likely to search on the job. Moreover, increases in
have a larger
impact on search decisions the more likely it is that job offers will be measured against the reservation
wage
in period 2. In other words, the effects are larger the higher is the probability of job loss.
This analysis brings the next two predictions from the model:
Prediction 2: An increase in the replacement rate leads to a decrease in the probability of OJS but only for
workers with non-zero probability of layoff (i.e.
> 0).
Prediction 3: The higher the probability of layoff (p), the larger is the negative effect that the replacement rate
has on the probability of OJS (under plausible conditions on ).
7
The model also provides interesting predictions regarding the effect of the replacement rate on
employment transitions, either from the current job to another job or from the current job to nonemployment. Since an increase in the replacement rate decreases the probability of OJS, it will also
decrease the probability of JTJ transitions and, as a result, increase the probability of entering nonemployment. As in the case with OJS, these effects are at work only if the worker has a non-zero risk of
job loss and the effects get stronger the larger is the risk of job loss. Thus, the next prediction from the
model that I test in the data is:
Prediction 4: The replacement rate does not affect the probabilities of employment transitions if the worker is
not at risk of job loss (i.e.
= 0 ). For workers with a non-zero risk of job loss, an increase in the replacement
rate increases the likelihood of falling into non-employment and decreases the likelihood of moving to a new
job. These effects are stronger the larger is the risk of job loss.
Finally, changes in the OJS decision affects the probability of a job-to-job (JTJ) transition
regardless of whether the worker is laid off or not. In comparison, changes in OJS only affect the job-tonon employment (JTN) transition if the worker is laid off. Thus, the final testable prediction from the
model is:
Prediction 5: Given that the worker has a positive probability of job loss ( > 0), the effect of an increase in
the replacement rate is larger (in absolute value) on JTJ transitions than on JTN transitions.
4. DATA AND EMPIRICAL SPECIFICATION
The main data source is the HRS, a nationally representative longitudinal dataset of Americans
over the age of 50. 9 This survey, conducted every two years since 1992, collects information about work
status, earnings, and several job characteristics, among other variables. The HRS also elicits the
subjective probability of job loss through the following question: “Sometimes people are permanently laid
off from jobs that they want to keep. On the (same) scale from 0 to 100 where 0 equals absolutely no chance and
100 equals absolutely certain, what are the chances that you will lose your job during the next year?.” The
median response is zero, which indicates that most workers feel relatively safe in their jobs. Besides
9
The Health and Retirement Study (HRS) data is sponsored by the National Institute on Ageing (grant number
U01AG009740) and was conducted by the University of Michigan.
8
zero, there are also important bunching of responses at 10% and 50%, and to a lesser extent around
90%, which is indicative that responses might be rounded around some focal points (see Figure 1).10
[Figure 1about here]
I include in my analysis workers who are between 50 and 62 years old, but exclude those who
are self-employed. I also exclude observations from states with small sample sizes to avoid
convergence problems in the bootstrapped maximum likelihood. 11 The sample covers the period 19962006 and 2010-2012, since the question on the subjective probability of job loss was not included in the
2008 wave. The resulting initial sample size included 12,526 respondents and 32,309 respondent-year
observations. I dropped 4,229 observations because of missing information regarding on-the-job search,
subjective job loss probability or weekly wages. In order to minimize the number of workers who are
ineligible for UI benefits due to low earnings, I follow Gruber (1997) and drop those cases where the
estimated weekly benefits would be below the state's weekly minimum UI benefits amount. This
accounts only for additional 4 observations being excluded. Finally, I drop observations with missing
values on other controls. The final sample for the analysis includes 10,440 respondents and 23,906
respondent-year observations.
Table 1 shows the mean and the standard deviation of outcomes and selected covariates of
interest in the final sample. The average individual is 56 years old and women represent 57% of the
sample. On average, the subjective probability of job loss is 18% and about 12% of workers report to be
looking for a new job. The average potential replacement rate (i.e. the fraction of lost earnings that UI
benefits would replace) is 42%. This variable is constructed using the worker’s weekly earnings ( ), the
states' nominal replacement fraction ( ) and the state's limit on weekly benefits in each year
(
). Given that I previously excluded workers with calculated benefits below the state statutory
minimum amount, each worker potential replacement rate is determined by equation (2) below: 12
10
Manski and Molinari (2010) and Kleinjans and van Soest (2010) found evidence of rounding responses for subjective
probability questions in the HRS, with the extent of rounding differing across respondents.
11
States included in the analysis are Alabama, Arizona, Arkansas, California, Colorado, Connecticut, Florida, Georgia, Illinois,
Indiana, Iowa, Kansas, Kentucky, Louisiana, Maine, Maryland, Massachusetts, Michigan, Minnesota, Mississippi, Missouri,
Nebraska, Nevada, New Hampshire, New Jersey, New York, North Carolina, North Dakota, Ohio, Oklahoma, Oregon,
Pennsylvania, South Carolina, Tennessee, Texas, Virginia, Washington, West Virginia, Wisconsin and Wyoming.
12
Note that I use pre-tax levels of earnings and benefits, whereas Gruber (1997) uses after-tax levels. I use pre-tax levels so
that the replacement rate is only a function of the two main legislated parameters regarding UI benefits in a state/year: the
nominal replacement rate and the maximum level of weekly benefits. Pre-tax levels avoid bringing into the calculation
other household characteristics that can affect the tax rate. It is also worth noticing that Gruber uses after-tax dollars to
9
{ × ,
=
}
(2)
[Table 1 about here]
To test the theoretical predictions from Section 3, I start by modelling the probability that an
employed individual
at time
is looking for another job. Denote by
,
the latent index in a probit
model for the likelihood that an employed individual is looking for another job. As shown in equation
(3), I model
,
as a function of the subjective probability of job loss (
replacement rate if the job is lost (
,
=
+
,
), the potential wage
) and the interaction of these two variables.
,
,
+
,
+
,
×
,
+
,
+
(3)
,
Since the replacement rate is a function of the worker’s earnings, I need to disentangle the effect
of earnings from the effect of the replacement rate itself on the probability of OJS. Thus, I also added a
fifth-order polynomial in wages to the model to account for the fact that wages determine
nonlinear way. In addition to wages, vector
in a
,
controls for other characteristics that may affect job
,
search decisions such as age, gender, race and ethnicity, education attainment, occupation category
(white, pink or blue collar), self-reported health, part-time employment, industry, employer-sponsored
health insurance, job-related stress and physical requirements (heavy lifting). It also contains a set of
state and year dummy variables.
The theoretical model not only gives predictions about the effect of
,
on the probability of
OJS, but also on how it affects employment transitions. This is of particular importance for
understanding the extent to which UI might affect unemployment and the rate of transitions between
jobs. In order to test the predictions from the theoretical model, I use a multinomial probit to analyze
how
,
,
,
and their interaction predicts employment in the next wave ( + 1). I define three possible
employment outcomes in
+ 1: i) non-employment, ii) employment at a new employer, and iii)
continued employment at the current employer. Denote by
likelihood of each employment outcome
,,
>
for all
,,
the latent variable that measures the
,,
in the next wave. Outcome
. The empirical specification for
, ,,
will occur in the next wave if
is similar to the one for
,
, as
shown in equation (4):
,,
=
+
,
+
,
+
,
×
,
+
,
+
,,
(4)
account for the fact that UI benefits became taxable within his period of analysis (1968-1987). In contrast, in my period of
analysis (1996-2012) there was no change in the tax treatment status of UI benefits.
10
Addressing potential endogeneity
Both
,
and
,
can be determined by unobserved factors that also affect job search decisions or
employment transitions. For example,
pessimism). In the case of
can correlate with unobserved personality traits (such as
,
, a shortcoming of controlling for wages is that they are endogenous and
,
can correlate with other workers’ and jobs’ unobserved characteristics (e.g. high productivity). To
address the potential endogeneity in
,
and
,
(and their interaction) I employ a control function (CF)
approach (and drop wages from the controls vector
,
). An advantage of the CF approach is that it can
be more efficient than standard instrumental variables (IV) approaches, albeit at the cost of assuming
that one has modelled correctly the conditional mean of the error term (Wooldridge, 2007; Wooldridge,
2015). Another advantage is that an IV approach cannot be applied directly in some non-linear models
like the multinomial probit. Conversely, CF methods can be easily applied in non-linear models and
are computationally simple (Wooldridge, 2015). To apply CF methods, I need to model the conditional
mean for the error terms in equations (4) and (5). I start by modelling the reduced-form equation for
and
,
,
as:
,
,
The terms
,
and
,
=
=
+
+
,
,
+
+
+
,
+
,
,
,
+
+
(5)
,
(6)
,
in equations (5) and (6) are exogenous variables in the sense that are
uncorrelated with the unobserved components
,
,
,,
,
,
and
,
. The variable
,
measures
whether the employer has downsized recently. Downsizing is posited to increase subjective
expectations of job loss by reasons that are exogenous to the workers. The HRS asks respondents
whether their employers have downsized since the last interview or since they started working if they
were hired between waves. 13 The fraction of workers in the sample that reports downsizing is around
25% in the late 1990s and early 2000s and increases sharply to 40% in the 2010 wave. In Gutierrez and
Michaud (2015), we document that the average rates of downsizing reported in the HRS are consistent
with the available information in studies that use firms’ employment records. Table 2 shows that, as
13
The question is worded as follows: “Has your employer experienced a permanent reduction in employment since [last
interview month and year/ month and year respondent started job/ 2 years ago]?,” with interviewers coding references to
downsizing and permanent layoffs as “yes” and those to temporary layoffs as “no”.
11
expected, workers whose employer has downsized recently report on average a subjective probability
of job loss that is 7.4 percentage points higher than that for workers at non-downsizing employers, after
controlling for observed characteristics.
The variable
,
measures states’ generosity in UI benefits for workers above 50. I construct it
following Gruber (1997) simulated instrument approach (see also Currie and Gruber (1996a, b)). To
attain a large enough sample per state of workers above 50, I pool three waves (2001, 2003 and 2005) of
the Current Population Survey (CPS) Annual Social and Economic Supplement (ASEC) and keep the
employed individuals in each state that are over 50 years old. Then I use this pooled sample and the
information on each state’s UI rules to calculate the average potential replacement rates (APRR) for the
working population over 50 years old, for each state and year in the period 1996-2012. In other words, I
keep the sample of workers within a state fixed across years and use the corresponding state-year UI
benefit rules for calculating the APRR. 14 I calculate separate APRR for men and women in each stateyear combination because men on average have higher earnings. Therefore, men are more likely to be
affected by the limit on weekly benefits and to have lower replacement rates. Table 2 shows that the
APRR is a strong predictor of
,
, even after controlling for observed characteristics including gender,
year and state dummies. Notice that after controlling for these characteristics, the remaining variation
in the APRR that is used for identification purposes comes from changes in the benefits rules (i.e., the
nominal replacement rate and the maximum weekly benefits) over time within a state and from a stategender interaction. To illustrate the first source of variation, Table 3 shows a selection of states with
small, medium and large range in their APRR over the sample period. A potential concern is that the
variation in benefit rules is correlated with economic conditions that can also affect job search decisions
or employment transitions. To deal with this potential problem of “legislative endogeneity”, I follow
Gruber (1997) and control for states’ unemployment rates (although the empirical results are robust to
whether they are included in the analysis). Regarding the second source of variation, I also run
separate models for men and women obtaining similar results.
14
I use the sample of workers in each state to calculate the APRR rather than a national sample as in Gruber (1997). I do
this because the effect of the UI maximum weekly benefits on the replacement rate will depend on the average income of
workers (over 50), which can differ significantly across states.
12
Next, following Rivers and Vuong (1988) and Petrin and Train (2010) in their application of CF
methods to probit and multinomial probit models, respectively, I assume that
,
,
,
,,
,
and
,
are joint normally distributed, such that:
,
|
,
,
|
,,
,
,
,
,
=
,
,
,
,
|
=
,
,
,
,,
,
,
|
,
,
,
,
,
,
,
=
,
,
,
,
,
,
,
,
|
=
,
,
=
,
,,
,
|
,
,
+
(7)
,
=
,
,
+
,
(8)
The first equality in equations (7) and (8) follows from the reduced-form relationships for the
endogenous variables in equations (5) and (6). The second equality in equations (7) and (8) holds
because
,
,
,
,
are independent of the unobserved components
,
(7) and (8) suggest that we can control for the endogeneity in
,
and
,
,
,
,,
,
,
,
. Equations
,
by having
,
and
as
,
additional controls in the model specifications of equations (3) and (4). This leads to the following twostep estimation procedure (Wooldridge, 2015). First, estimate equations (5) and (6) and obtain the
residuals
,
and
,
. Then add these residuals to the main probit and multinomial probit equations. I
bootstrap this two-step procedure to obtain valid standard errors for all of the coefficients.
5. RESULTS
5.1. Probability of OJS
Table 4 shows the probit coefficients (column 1 to 3) and the CF probit coefficients (column 4 to
6) for modelling the probability of OJS. In both approaches, I start with a model that does not include
the interaction term
significant effect of
,
,
×
,
. This model allows me to test whether I am able to detect a statistically
without modelling any heterogeneity in that effect. I found that, as predicted by
the model, an increase in
,
reduces the probability of OJS on average. However, the effects are
statistically indistinguishable from zero. This does not come as a surprise since most individuals in the
sample report a zero or very small subjective probability of job loss (Figure 1) and for them changes in
,
should have no effect on their OJS decisions (Prediction 2). Conversely, the coefficient for
,
is
positive and strongly significant both in the probit and in the CF probit models. This suggests that
workers with higher expectation of job loss are more likely to be searching for other jobs, as predicted
by the theory (Prediction 1). Although technically the coefficients in the probit and the CF probit
models cannot be compared directly since they are standardized by different standard deviations
(Wooldridge, 2007; Wooldridge, 2015), it is interesting to notice that the main effect for
13
,
is
substantially larger in the CF probit model whereas the coefficient for
,
is relatively similar in both
approaches. The same conclusion arises from computing the marginal effects that I present later, which
are comparable across models. This pattern implies that controlling for a polynomial in wages (and
state dummies) in the probit models eliminates much of the endogenous variation in
is still endogenous variation in
,
,
, but that there
, even after controlling for observed worker and employer
characteristics.
Next, I introduce the interaction term
,
×
,
to the probit and CF probit models. Their
coefficients are negative and statistically significant in both models, while the main effects for
,
smaller than before and remain not statistically significant. These results imply that increases in
get
,
decreases the probability of OJS but only for workers with non-zero expectations of job loss (i.e.,
,
> 0) and that the effect is larger the higher the subjective probability of job loss. These findings
were also predicted by the theoretical model (Predictions 2 and 3).
Given the supporting empirical evidence for the predictions from the theory, I estimate next a
model that imposes no effects of
main effect for
and
×
,
,
,
,
on workers with
,
= 0. Notice that this amounts to restricting the
to be zero. In both the probit and the CF probit models, the new coefficients for
,
in the restricted models (columns 3 and 6) are very close to those in the unrestricted
models (columns 2 and 5). Moreover, in the probit as in the CF probit, likelihood ratio tests confirm
that the unrestricted and restricted models fit the data equally well.
[Table 4 about here]
Table 5 shows the marginal effects. For simplicity, I only show the marginal effects from the
restricted models. I chose these models because the theory and the empirical evidence indicate that the
effect of
,
should be zero when
,
= 0. Furthermore, as discussed above, the restricted models fits
the data equally well as the unrestricted models, but provides more precise marginal effect estimates. I
find that an increase of 25 percentage points in
,
(about one standard deviation) increases the average
probability of OJS by 3.51 percentage points (or by about 29%) in the probit model, and by 11.31
percentage points (or by 93.3%) in the CF probit model. As seen in Table 4, the effect is much larger in
the CF probit model, although it is still of considerable magnitude in the probit model. In fact, I
calculate that the average probability of OJS if I eliminate the job insecurity mechanism (i.e. if I set
,
= 0 for everyone) is 9.4% in the probit model and 6.4% in the CF probit model. When compared to
14
the proportion of workers in the sample who claim to be searching for a job (about 12%), it implies that
job-insecurity might be the main motivation for job search for about 23% to 47% (depending on the
estimation approach) of older on-the-job seekers in the U.S. Thus, job insecurity is clearly an important
factor for OJS.
I also calculate the effect on the probability of OJS of an increase of 12.5 percentage points in
,
(about one standard deviation). I calculate the sample average effect and also the predicted average
effects at different levels of
,
. The results are shown in panel B of Table 5. The sample average effects
are relatively small, a decrease of around 0.52 to 0.62 percentage points in the probability of searching.
As predicted by the theoretical model and suggested by the coefficients in Table 4, the effects are larger,
albeit still moderate, when job insecurity levels are higher. For example when
in
,
,
= 0.90, the increase
is predicted to decrease the probability of searching on the job by 3.8 percentage points (or by
15%) in the probit model and by 3.29 percentage points (or by 4.8 %) in the CF probit model.
[Table 5 about here]
5.2. Employment transitions
Now I turn to the estimation of the effects of
,
and
,
on employment transitions between
waves. As discussed earlier, I use a multinomial probit approach and a CF multinomial probit
approach to model the probability of three outcomes in the next wave: i) non-employment, ii)
employment at a new employer, and iii) continued employment at the current employer. I define the
last outcome as the base scenario for fitting the models. Table 6 shows the estimated multinomial probit
coefficients. Note that the sample size is smaller than before because there is no information available
on next period outcomes for the 2012 wave. The estimation results highlight again the importance of
modelling the heterogeneity in the effects of
term
,
×
,
,
. Specifically, I find that the coefficient on the interaction
in the equation for employment at a new employer (in the next wave) is strongly
significant. Also, as with the probit models, the coefficients in the restricted model (that restrict the
main effects of
,
to be equal to zero) are similar to the ones in the full model and the likelihood-ratio
test confirms that both models explain the data just as well. This supports the theoretical prediction
that
,
should only affect employment transitions when
,
> 0 (Prediction 4). I use the restricted
model to estimate the marginal effects, which are presented in Table 7. I find that
,
is a predictor of
both the risk of non-employment and of having a job at a new employer in the next wave, even after
15
controlling for observed characteristics. Although not explicitly considered among the testable
predictions in Section 3, these finding are also supported by the theoretical model. I find that a 25
percentage points increase in
,
raises the probability of transitioning into non-employment by the
next wave in 1.88 percentage points and of having a job at a new employer in 2.52 percentage points. In
other words, per each percentage point increase in
,
, the actual probability of separation (adding
both outcomes) increases by 0.18 percentage points. This effect, albeit statistically strong, seems small.
An explanation might be that individuals tend to be pessimistic about their job loss probabilities. This
was pointed out by Stephens (2004) who finds that although
,
has a strong predictive power of actual
job separation, individuals in the HRS tend to overstate that probability. This is particularly true for
individuals that report high probabilities of job loss (see Figure 2)
I also find that increases in
,
are associated with lower probabilities of moving to a new
employer (panel B in Table 7). The sample average effect is moderate, but the predicted average effects
become substantial at higher levels of job insecurity, in accordance to Prediction 4 from the theoretical
model. On average, a 12.5 percentage points increase in
,
reduces the probability of changing jobs by
0.77 percentage points (or -7.2%). In comparison, when
,
= 0.90, a similar increase in
,
is predicted
to reduce the probability of having a job at a new employer by 4.9 percentage points (or -24.3%).
Opposite to these results, the effects of
values of
,
,
on the on the probability of non-employment are low at all
. These findings are a direct consequence of the interaction term
,
×
,
having a small
coefficient on the latent risk for transitioning into non-employment and a much larger coefficient on the
latent risk for having a job at a new employer (see Table 6). Prediction 5 from the theoretical model
provides the insight for understanding this difference. A reduction in the probability of OJS (caused by
an increase in
,
) has an impact on the probability of finding a new job regardless of whether the
worker is laid off or not. In comparison, a reduction in the probability of OJS only has an impact in the
probability of transitioning into non-employment if the worker is actually laid off. If the worker is not
laid off, there are not consequences in terms of non-employment. Thus, even though changes in
,
can
significantly affect workers’ job search decisions and job changes, they will have a small effect on
entering non-employment if individuals tend to overstate their actual risk of jobs loss. As discussed
earlier, this seems to be the case for HRS respondents. This finding is robust to alternative
specifications of the non-employment outcome, in particular including any reported non-employment
spell between waves.
16
[Table 6 and Table 7 about here]
Table 8 presents the CF multinomial probit coefficients. The main difference with the
multinomial probit coefficients in Table 6 is that
,
has a stronger effect on the risk of being non-
employed by the next wave, and a smaller, negative (opposite sign) and statistically significant effect
on the probability of changing employers (see for example the model with no interactions). The
marginal effects presented in Table 9 confirm these findings. A 25-percentage points increase in
,
leads to an increase of 8.89 percentage points (or 60.5%) in the probability of being non-employed by
the next wave and to a reduction of 5.25 percentage points (or 49.3%) in the probability of working at a
different employer. These are much larger effects than the marginal effects found in the multinomial
probit model (Table 7) and of opposite sign in the case of the probability of changing employers. A
possible explanation is that downsizing may be associated with fewer job opportunities (for example, if
downsizing is associated with weaker local economies or lower demands for a specific industry or
occupation). Evidence towards this explanation arises from that fact that workers at downsizing
employers report a lower subjective probability of being able to find a similar job. The HRS asks
workers “Suppose you were to lose your job this month. What do you think are the chances that you could find
an equally good job in the same line of work within the next few months?” The sample mean answer is 47%
and downsizing is associated with a reduction of 7.1 percentage points, after controlling for observed
characteristics. Also, if I control for the expected job finding probability in the CF multinomial probit
model, the effect of
,
on the probability changing employers is still negative but much smaller and
statistically significant only at the 10% level. However, I prefer not to control for this variable in the
main specifications since it can be endogenous. The fewer employment opportunities associated with
downsizing can also explain why the effects of
also smaller –at all levels of
,
,
on the probability of moving to a new employer are
- in the CF multinomial probit model than in the multinomial probit.
Notice, however, that this is true when the effects are measured in percentage points, but not when
measured in percentage change. An increase in
,
still leads to a substantial decrease in the probability
of moving to a new job when measured in percentage change for individuals with high levels of job
insecurity (for example when
,
= 0.90). Finally, the effects of
,
on the probability of being non-
employed by the next wave continue to be not statistically significant, as it was in the multinomial
probit model.
[Table 8 and Table 9 about here]
17
5.3. Specification checks
I test the robustness of the findings to alternative estimation approaches and model
specifications. First, I model the probability of OJS using four alternative linear models: i) an ordinaryleast-squares (OLS) model where I control for wages; ii) a CF OLS model that follows the same
approach describe earlier; iii) a individuals’ fixed effects (FE) model; iv) and a standard two-step leastsquares (2SLS) model. Table 10 shows the estimation results for the four models. I find that the main
effects for
,
are positive as predicted by the theory and statistically significant in the OLS, CF OLS
and FE models. I also find that the interaction terms
,
×
,
are negative as predicted by the theory,
but they are not statistically significant in any model. This might be explained by the loss in efficiency
and higher standard errors resulting from using linear approaches to model a binary outcome.
Evidence in favor of this explanation comes from the fact that if I extend the sample to include workers
up to 65 years old (an additional 3,473 observations), the interaction terms remain negative, are of
similar magnitudes, and become statistically significant at the 10% confidence level in the OLS and FE
models. This finding highlights the attractiveness of CF methods for controlling endogeneity when
modelling non-linear outcomes. The coefficients for
,
, and
,
×
,
are not statistically significant in
the 2SLS model (even if I expand the sample size by including individuals up to 65 years old). Note
that the standard errors in the 2SLS approach increase substantially in comparison to the other models.
This highlights another advantage of CF methods, already discussed earlier. CF methods can be more
efficient than standard IV approaches, albeit at the cost of assuming that one has modelled correctly the
conditional mean of the error term.
Next, I test whether the estimation results in the CF probit method and in the CF multinomial
probit method are sensitivity to the inclusion of controls. I do this because although employer
downsizing can be consider an exogenous event from the workers’ perspective, the selection of
workers that remain employed at downsizing employers is likely to be non-random. In Gutierrez and
Michaud (2015) we found suggestive evidence of positive selection of “survivor” workers at
downsizing employers. They tend to be younger, more educated, more likely to be white-collar and
full-time employees, and have higher tenure at their jobs. Also, downsizing employers are more likely
to provide health insurance and pension benefits, which might indicate higher-quality jobs and thus
reinforce a positive selection of workers at these employers. I find similar effects of
,
and
,
on the
probability of searching for another job and on employment transitions regardless of whether I control
18
for observed characteristics. Thus, to the extent that effects are similar with and without controls,
omitted confounders are unlikely to significantly bias the results in the CF models.
I also estimate separate models for men and women. 15 Table 11 presents the reduced-form
regressions for
,
and
,
, and Table 12 presents the marginal effects from the CF restricted models.
We observe that increases in
,
have similar strong effects on the probability of OJS for both men and
women. I also find that increases in
,
reduce the probability of OJS in similar magnitudes for men and
women, although the effects are only statistically significant for men. Interestingly, however, I find that
increases in
,
reduce the probability of transitioning to a new job in similar magnitudes for men and
women and are statistically significant for both groups. As with the case of the pooled sample, I find
that
,
do not affect the probability of transitioning into non-employment by the next wave for either
men or women.
6. CONCLUSION
In this study I document that about 23% to 47% of older American on-the-job seekers search for
another job because they feel insecure at their current employment. I also analyze how unemployment
insurance (UI) affects the relationship between job insecurity and job search. The theoretical model
presented in Section 3 predicts that an increase in the generosity of UI, measured by a higher
replacement rate (or the fraction of lost wages replaced by UI benefits), reduces the value of OJS
because it reduces the financial burden of unemployment. Thus, an increase in the replacement rate
should reduce the probability that a worker searches for another job. The model also predicts that this
effect should exist only for workers who believe that are at risk of job loss. Even more, the effect should
be larger the higher is the worker's perceived risk of job loss. Using information on workers' subjective
probability of job loss, job search activity and potential replacement rates (based on earnings and state
of residency), I find that the empirical evidence supports these predictions. I find that an increase in the
potential replacement rate discourages OJS, which in turn reduces the probability of starting a job at a
new employer. These effects are only statistically significant for workers who report a non-zero
subjective probability of job loss and they increase as the subjective probability of job loss gets larger.
15
I dropped observations from the state of Maine (2 observations) in the gender-specific analysis to avoid convergence
problems.
19
I also find that because older American workers feel relative secure in their jobs, the sizes of the
average estimated effects are moderate. For example, an increase of 12.5 percentage points in the
potential replacement rate (about one standard deviation) reduces the probability of OJS by 4.3% or
5.1% (depending on the estimation approach), and reduces the probability of moving to a new job by
about 7%. Thus UI have a moderate effect on the average rate at which older workers change jobs.
However, these moderate effects mask important heterogeneities. On one hand, as discussed above, UI
does not affect the search behavior of workers who do not believe to be at risk of job loss. On the other
hand, the effects can be substantial for workers with higher levels of job insecurity. Depending on the
estimation approach, a similar increase in the potential replacement rate is predicted to reduce the
probability of OJS by 4.8% or 15.0% for workers with a subjective probability of job loss of 90%; and
their probability of changing employers is predicted to decrease by 24.3% or 32.8%.
It is also worth noticing that I do not find that changes in UI potential replacement rates affect
the probability of older workers transitioning into non-employment, even for those who report high
levels of job insecurity. This finding is robust to whether employment is measured in the next wave or
by looking at any non-employment spells between waves. A plausible explanation is that older
American workers tend to overestimate their actual job loss probability. Therefore, the effects of UI
potential replacement rates on workers’ decision to search on-the-job matter more for the likelihood of
changing employers than for becoming unemployed. Still, it is plausible that the effects of UI on
transitioning into unemployment might be larger for younger workers who are less attached to their
employers. The evidence presented here warrants more study on the interaction between job
insecurity, job search and UI benefits, particularly for young and prime-age workers.
ACKNOWLEDGMENTS
This paper has been funded in part with federal funds from the U.S. Department of Labor under
contract number DOLJ111A21738. It has also been supported by a grant from the National Poverty
Center at the University of Michigan, which is supported by award #1 U01 AE000002-03 from the U.S.
Department of Health and Human Services, Office of the Assistant Secretary for Planning and
Evaluation. The contents of this publication do not necessarily reflect the views or policies of the
Department of Labor or of any agency of the Federal Government, nor does mention of trade names,
commercial products, or organizations imply endorsement of same by the U.S. Government.
20
I thank Jeffrey Smith, Charlie Brown, Melvin Stephens, Brian McCall and Daniel Hamermesh
for comments on earlier versions of this paper. I also thank seminar participants at the University of
Michigan for helpful suggestions. Special thanks to Michael Nolte, Janet Keller and all the staff at the
Health and Retirement Survey at the Institute for Social Research for their help and assistance through
this project. All errors are my own.
REFERENCES
Addison, J.T., Blackburn, M. Advance Notice and Job Search: More on the Value of an Early Start. Industrial
Relations. 1995;34;242-262.
Anderson, P.M., Meyer, B.D. Unemployment Insurance in the United States: Layoff Incentives and Cross
Subsidies. Journal of Labor Economics. 1993;11;S70-S95.
Burgess, P.L., Low, S.A. Preunemployment Job Search and Advance Job Loss Notice. Journal of Labor Economics.
1992;10;258-287.
Burgess, P.L., Low, S.A. How do Unemployment Insurance and Recall Expectations Affect On-The-Job Search
among workers who Receive Advance Notice of Layoff? Industrial and Labor Relations Review. 1998;51;241-252.
Card, D., Levine, P.B. Unemployment Insurance Taxes and the Cyclical and Seasonal Properties of
Unemployment. Journal of Public Economics. 1994;53;1-29.
Chan, S., Stevens, A.H. Employment and Retirement Following a Late-Career Job Loss. American Economic
Review. 1999;89;211-216.
Chan, S., Stevens, A.H. Job Loss and Employment Patterns of Older Workers. Journal of Labor Economics.
2001;19;484-521.
Christofides, L.N., McKenna, C.J. Unemployment Insurance and moral hazard in employment. Economics Letters.
1995;49;205-210.
Christofides, L.N., McKenna, C.J. Unemployment Insurance and Job Duration in Canada. Journal of Labor
Economics. 1996;14;286-312.
Couch, K.A., Placzek, D.W. Earning Losses of Displaced Workers Revisited. American Economic Review.
2010;100;572-589.
Currie, J., Gruber, J. Health Insurance Eligibility, Utilization of Medical Care, and Child Health. The Quarterly
Journal of Economics. 1996a.
Currie, J., Gruber, J. Saving Babies: The Efficacy and Cost of Recent Changes in the Medicaid Eligibility of
Pregnant Women. Journal of Political Economy. 1996b;1263-1296.
Fallick, B.C. A Review of the Recent Empirical Literature on Displaced Workers. Industrial and Labor Relations
Review. 1996;50;5-16.
Fallick, B.C., Fleischman, C.A. The Importance of Employer-to-Employer Flows in the U.S. Labor Market. 2001.
Feldstein, M. Temporary Layoffs in the Theory of Unemployment. Journal of Political Economy. 1976;84;937958.
Feldstein, M. The Effect of Unemployment Insurance on Temporary Layoff Unemployment. American Economic
Review. 1978;68;834-846.
21
Fitzenberger, B., Wilke, R.A. Unemployment Durations in West Germany Before and After the Reform of the
Unemployment Compensation System during the 1980s. German Economic Review. 2009;11;336-366.
Fujita, S. Reality of on-the-Job Search. Reserve Bank of Philadelphia. 2011.
Green, D.A., Riddell, W.C. Qualifying for Unemployment Insurance: An Empirical Analysis. Economic Journal.
1997;107;67-84.
Green, D.A., Sargent, T.C. Unemployment Insurance and Job Durations: Seasonal and Non-Seasonal Jobs.
Canadian Journal of Economics. 1998;31;247-278.
Gruber, J. The Consumption Smoothing Benefits of Unemployment Insurance. American Economic Review.
1997;87;192-205.
Gutierrez, I.A., Michaud, P.-C. 2015. Employer Downsizing and Older Workers' Health. Institute for the Study of
Labor (IZA), Discussion Paper 9140. 2015.
Haan, P., Prowse, V. The Design of Unemployment Transfers: Evidence from a Dynamic Structural Life-Cycle
Model. IZA Discussion Paper Series. 2010.
Jacobson, L.S., LaLonde, R.J., Sullivan, D.G. Earning Losses of Displaced Workers. The American Economic
Review. 1993;83;685-709.
Jolivet, G., Postel-Vinay, F., Robin, J.-M. The Empirical Content of the Job Search Model: Labor Mobility and
Wage Distributions in Europe and the US. European Economic Review. 2006;50;877-907.
Jurajda, S. Estimating the effect of unemployment insurance compensation on the labor market histories of
displaced workers. Journal of Econometrics. 2002;108;227-252.
Jurajda, S. Unemployment Insurance and the Timing of Layoffs and Recalls. Labour. 2003;17;383-389.
Kleinjans, K.J., van Soest, A. Nonresponse and Focal Point Answers to Subjective Probability Questions. IZA
Discussion Paper No. 5272. 2010.
Kletzer, L.G. Job Displacement. Journal of Economic Perspectives. 1998;12;115-136.
Krueger, A.B., Meyer, B.D., 2002. The Labor Supply Effects of Social Insurance, in: Auerbach, A., Feldstein, M.
(Eds.), Handbook of Public Economics. North-Holland, pp. 2327-2392.
Lalive, R., van Ours, J.C., Zweimüller, J. Equilibrium unemployment and the duration of unemployment benefits.
Journal of Population Economics. 2011;24;1385-1409.
Lengermann, P.A., Vilhuber, L. Abandoning the sinking ship: The composition of worker flows prior to
displacement. Center for Economic Studies, US Census Bureau. 2002.
Light, A., Omori, Y. Unemployment Insurance and Job Quits. Journal of Labor Economics. 2004;22;159-188.
Manski, C.F., Molinari, F. Rounding Probabilistic Expectations in Surveys. Journal of Business \& Economics
Statistics. 2010;28;219-231.
McCall, B.P. The Impact of Unemployment Insurance Benefit Levels on Recipiency. Journal of Business \&
Economic Statistics. 1995;13;189-198.
Meyer, B.D. Lessons from the U.S. Unemployment Insurance Experiments. Journal of Economic Literature.
1995;33;91-131.
Mortensen, D.T. Unemployment Insurance and Job Search Decisions. Industrial and Labor Relations Review.
1977;30;505-517.
Petrin, A., Train, K. A Control Function Approach to Endogeneity in Consumer Choice Models. Journal of
Marketing Research. 2010;47;3-13.
22
Rebollo-Sanz, Y. Unemployment insurance and job turnover in Spain. Labour Economics. 2012;19;403-426.
Rivers, D., Vuong, Q.H. Limited information estimators and exogeneity tests for simultaneous probit models.
Journal of Econometrics. 1988;39;347-366.
Rosal, O.D. La Busqueda De Empleo De Los Ocupados. Intensidad Y Motivos. Estudios de Economia Aplicada.
2003;21;151-174.
Schwerdt, G. Labor turnover before plant closure: Leaving the sinking ship vs. Captain throwing ballast
overboard. Labour Economics. 2011;18;93-101.
Stephens, M.J. Job Loss Expectations, Realizations, and Household Consumption Behavior. Review of Economics
and Statistics. 2004;86;253-269.
Topel, R.H. On Layoffs and Unemployment Insurance. American Economic Review. 1983;73;541-559.
Topel, R.H. Experience Rating of Unemployment Insurance and the Incidence of Unemployment. Journal of Law
and Economics. 1984;27;61-90.
Tudela, C.C., Smith, E. Search Capital. CESifo Working Papers. 2012.
Winter-Ebmer, R. Benefit duration and unemployment entry: A quasi-experiment in Austria. European Economic
Review. 2003;47;25-273.
Wooldridge, J. 2007. What’s New in Econometrics? Lecture 6: Control Functions and Related Methods. NBER
Summer Institute. 2007.
Wooldridge, J.M. Control Function Methods in Applied Econometrics. Journal of Human Resources. 2015;50;420445.
23
50%
45%
40%
35%
30%
25%
20%
15%
10%
5%
0%
0%
1% - 5%
6% - 10%
11% - 15%
16% - 20%
21% - 25%
26% - 30%
31% - 35%
36% - 40%
41% - 45%
46% - 50%
51% - 55%
56% - 60%
61% - 65%
66% - 70%
71% - 75%
76% - 80%
81% - 85%
86% - 90%
91% - 95%
96% - 100%
% of observations
Figure 1: Distribution of the Subjective Probability of Job Loss
Reported Probability of Job Loss
Data Source: HRS, 1996-2006 and 2010-2012.
100%
80%
60%
40%
20%
91% - 100%
81% - 90%
71% - 80%
61% - 70%
51% - 60%
41% - 50%
31% - 40%
21% - 30%
11%-20%
0%
0% - 10%
Probability leaving employer
Figure 2: Subjective Probability of Job Loss and Average Probability of Job Separation
Subjective Probability of Job Loss
Non-Downsizing
Downsizing
24
45° line
Table 1: Sample means of outcomes and selected covariates
Mean
Standard
Deviation
0.12
0.15
0.75
0.11
0.33
0.35
0.43
0.31
0.18
0.42
0.25
0.13
0.40
56.38
0.57
0.06
3.33
0.49
Outcomes:
On-the-Job Search (1=yes; 0=no)
Employment transition: to non-employment
Employment transition: same employer
Employment transition: Different employer
Covariates:
Subjective probability of job loss (from 0 to 1)
Potential replacement rate (from 0 to 1)
State average potential replacement rate (from 0 to
1)
Age (in years)
Female
Data source: HRS, 1996-2006 and 2010-2012.
Note: Other controls include race and ethnicity, weekly earnings, education, occupation, part-time
employment status, industry, whether employer provides health insurance, levels of stress at job,
requirements of lifting heavy loads at work, and state and year dummies.
Table 2: Reduced form regressions for endogenous variables
Downsizing (
,
)
State average potential replacement
rate (APRR or , )
# Observations
Subjective
probability
of job loss
( ,)
Potential
replacement
rate ( , )
0.074***
(0.004)
-0.008***
(0.001)
0.054
(0.054)
23,906
0.792***
(0.060)
23,906
Data: HRS, 1996-2006 and 2010-2012.
Notes: Controls include age, gender, education, occupation, part-time employment, partlyretired employment, industry, whether employer provides health insurance, levels of stress at
job, requirements of lifting heavy loads at work, and state and year dummies. Standard errors
(in parentheses) were clustered at the state level. *** denotes p-value <0.01, ** denotes p-value
<0.05, * denotes p-value<0.1.
25
Table 3: Variation in States Average Potential Replacement Rates
All
State
Min
ND
33.9%
AR
Median
Males
Max
Min
37.3%
38.9%
33.9%
40.0%
42.2%
46.9%
PA
41.8%
43.9%
NC
39.9%
42.5%
Median
Females
Max
Min
Median
Max
34.3%
37.3%
37.3%
38.0%
38.9%
40.0%
41.3%
42.3%
42.1%
46.2%
46.9%
49.1%
41.8%
43.3%
44.2%
43.6%
48.5%
49.1%
47.7%
39.9%
41.9%
42.6%
42.4%
47.0%
47.7%
TX
38.2%
40.3%
46.1%
38.2%
39.0%
40.3%
40.3%
44.9%
46.1%
NJ
42.2%
45.5%
53.0%
42.2%
44.7%
45.9%
45.2%
51.8%
53.0%
CO
40.2%
44.5%
51.5%
40.2%
43.3%
44.6%
44.1%
49.8%
51.5%
FL
32.2%
37.6%
43.5%
32.2%
36.0%
38.1%
32.2%
41.8%
43.5%
TN
31.9%
36.9%
43.6%
31.9%
35.4%
37.1%
31.9%
42.4%
43.6%
KS
37.6%
40.4%
50.0%
37.6%
39.2%
40.7%
40.0%
48.7%
50.0%
VA
28.3%
35.5%
44.6%
28.3%
32.9%
37.0%
33.0%
40.5%
44.6%
CA
27.6%
37.6%
44.6%
27.6%
36.0%
39.7%
32.2%
38.3%
44.6%
KY
40.1%
46.8%
57.5%
40.1%
45.1%
47.2%
43.6%
56.2%
57.5%
NH
29.2%
38.2%
46.8%
29.2%
37.0%
39.1%
35.9%
44.9%
46.8%
MI
16.1%
37.7%
47.3%
16.1%
36.0%
38.2%
16.1%
45.5%
47.3%
Note: Author calculations using the CPS March Supplement (2001, 2003 and 2005)
Table 4: Effect of Job Insecurity and Potential Replacement Rate on On-the-Job Search
(Probit Coefficients)
Probit
Subjective prob. of job
loss ( , )
Potential rep. rate
( ,)
Probit CF
Main
effects
only
Main and
interactio
n effects
0.756***
(0.042)
-0.336
(0.286)
1.237***
(0.171)
-0.113
(0.309)
1.258***
(0.156)
-1.078***
(0.353)
-1.127***
(0.327)
Interaction term
( , × ,)
Restricte
d Model
Main
effects
only
Main and
interactio
n effects
2.467***
(0.411)
-0.308
(0.760)
2.863***
(0.469)
-0.103
(0.764)
2.877***
(0.448)
-0.931***
(0.353)
-0.942***
(0.338)
Restricte
d Model
,
-1.737***
(0.416)
-1.717***
(0.414)
-1.726***
(0.394)
,
1.674**
(0.733)
23,906
1.652**
(0.714)
23,906
1.551***
(0.172)
23,906
# Observations
23,906
23,906
23,906
Data: HRS, 1996-2006 and 2010-2012.
Notes: Controls include age, gender, education, occupation, part-time employment, partly-retired employment, industry, whether employer
provides health insurance, levels of stress at job, requirements of lifting heavy loads at work, and state and year dummies. Standard errors
(in parentheses) were clustered at the state level. Standard errors for the Probit CF approach were calculated from 500 bootstrap replications
clustered at the state level; *** denotes p-value <0.01, ** denotes p-value <0.05, * denotes p-value<0.1.
26
Table 5: Effect of Job Insecurity and Potential Replacement Rate on On-the-Job Search
(Marginal Effects- Restricted Model)
Probit
CF Probit
Percentage Percentage
points
change
Percentage Percentage
points
change
A. Effect of 25 percentage points increase in
Average effect
3.51***
29.0%
(0.18)
93.3%
(1.75)
B. Effect of 12.5 percentage points increase in
Average effect
,
11.31***
,
-0.62***
(0.18)
-5.1%
-0.52***
(0.18)
-4.3%
If
,
= 0.25
-0.68***
(0.20)
-5.4%
-0.67***
(0.24)
-4.0%
If
,
= 0.50
-9.8%
,
= 0.75
If
,
= 0.90
-1.94***
(0.71)
-3.07***
(1.07)
-3.29***
(1.17)
-5.7%
If
-1.66***
(0.49)
-2.92***
(0.87)
-3.80***
(1.13)
-13.3%
-15.0%
-5.5%
-4.8%
Data: HRS, 1996-2006 and 2010-2012.
Notes: Controls include age, gender, education, occupation, part-time employment, partly-retired employment, industry,
whether employer provides health insurance, levels of stress at job, requirements of lifting heavy loads at work, and state
and year dummies. Standard errors (in parentheses) were clustered at the state level. Standard errors for the Probit CF
approach were calculated from 500 bootstrap replications clustered at the state level; *** denotes p-value <0.01, ** denotes
p-value <0.05, * denotes p-value<0.1.
27
Table 6: Effect of Job Insecurity and Potential Replacement Rate on Employment Transitions
(Multinomial Probit Coefficients)
Main effects only
Subjective
prob. of job
loss ( , )
Potential rep.
rate ( , )
Interaction
term ( , ×
,
# Observations
Main and interaction
effects
Restricted Model
Outcome:
Nonemployment
Outcome:
Different
Employer
Outcome:
Nonemployment
Outcome:
Different
Employer
Outcome:
Nonemployment
Outcome:
Different
Employer
0.636***
0.896***
0.949***
1.991***
1.052***
1.957***
(0.065)
(0.067)
(0.241)
(0.360)
(0.238)
(0.340)
-0.747*
(0.430)
-0.261
(0.368)
-0.635
(0.435)
0.216
(0.399)
-0.709
-2.483***
-0.941*
-2.405***
(0.505)
(0.738)
(0.500)
(0.691)
18,910
18,910
18,910
18,910
)
18,910
18,910
Data: HRS, 1996-2006 and 2010-2012.
Notes: Controls include age, gender, education, occupation, part-time employment, partly-retired employment, industry, whether employer
provides health insurance, levels of stress at job, requirements of lifting heavy loads at work, and state and year dummies. Standard errors
(in parentheses) were clustered at the state level. *** denotes p-value <0.01, ** denotes p-value <0.05, * denotes p-value<0.1.
28
Table 7: Effect of Job Insecurity and Potential Replacement Rate on Employment Transitions
(Marginal Effects – Multinomial Probit Restricted Model)
Outcome:
Non-employment
Percentage Percentage
points
change
Outcome:
Different Employer
Percentage Percentage
points
change
A. Effect of 25 percentage points increase in ,
12.8%
Average effect
1.88***
2.52***
(0.25)
23.7%
(0.20)
B. Effect of 12.5 percentage points increase in ,
-0.9%
Average effect
-0.13
-0.77***
(0.20)
(0.25)
-1.5%
If , = 0.25
-0.23
-0.95***
(0.26)
(0.30)
-2.4%
If , = 0.50
-0.41
-2.23***
(0.57)
(0.73)
-2.5%
If , = 0.75
-0.48
-3.82***
(0.93)
(1.28)
-2.3%
If , = 0.90
-0.46
-4.90***
(1.17)
(1.67)
-7.2%
-8.4%
-15.6%
-21.4%
-24.3%
Data: HRS, 1996-2006 and 2010-2012.
Notes: Controls include age, gender, education, occupation, part-time employment, partly-retired employment,
industry, whether employer provides health insurance, levels of stress at job, requirements of lifting heavy loads at
work, and state and year dummies. Standard errors (in parentheses) were clustered at the state level. Standard errors
for the Probit CF approach were calculated from 500 bootstrap replications clustered at the state level; *** denotes pvalue <0.01, ** denotes p-value <0.05, * denotes p-value<0.1.
29
Table 8: Effect of Job Insecurity and Potential Replacement Rate on Employment Transitions
(CF Multinomial Probit Coefficients)
Main effects only
Subjective
prob. of job
loss ( , )
Potential rep.
rate ( , )
Interaction
term ( , ×
,
Main and interaction
effects
Restricted Model
Outcome:
Nonemployment
Outcome:
Different
Employer
Outcome:
Nonemployment
Outcome:
Different
Employer
Outcome:
Nonemployment
Outcome:
Different
Employer
2.113***
-0.920*
2.397***
0.157
2.235***
-0.054
(0.534)
0.908
(1.788)
(0.516)
0.782
(1.183)
(0.596)
1.029
(1.739)
(0.632)
1.357
(1.167)
(0.516)
(0.637)
-0.670
(0.544)
-2.561***
(0.704)
-0.587
(0.514)
-2.450***
(0.705)
)
,
-1.494***
(0.532)
1.856***
(0.541)
-1.481***
(0.533)
1.909***
(0.574)
-1.356***
(0.453)
2.071***
(0.559)
,
-0.890
(1.833)
18,910
0.201
(1.204)
18,910
-0.918
(1.766)
18,910
0.086
(1.219)
18,910
0.098
(0.190)
18,910
1.424***
(0.263)
18,910
# Observations
Data: HRS, 1996-2006 and 2010-2012.
Notes: Controls include age, gender, education, occupation, part-time employment, partly-retired employment, industry, whether employer
provides health insurance, levels of stress at job, requirements of lifting heavy loads at work, and state and year dummies. Standard errors
(in parentheses) were calculated from 500 bootstrap replications clustered at the state level. *** denotes p-value <0.01, ** denotes p-value
<0.05, * denotes p-value<0.1.
30
Table 9: Effect of Job Insecurity and Potential Replacement Rate on Employment Transitions
(Marginal Effects – CF Multinomial Probit Restricted Model)
Outcome:
Non-employment
Percentage Percentage
points
change
Outcome:
Different Employer
Percentage Percentage
points
change
A. Effect of 25 percentage points increase in ,
60.5%
Average effect
8.89***
-5.25***
(1.93)
(1.77)
B. Effect of 12.5 percentage points increase in ,
0.1%
Average effect
0.02
-0.82***
If
,
= 0.25
If
,
= 0.50
If
,
= 0.75
If
,
= 0.90
-49.3%
(0.20)
-0.12
(0.28)
-0.46
(0.72)
-0.98
(1.24)
-1.31
(1.52)
-0.6%
-1.5%
-2.2%
-2.5%
(0.18)
-0.85***
(0.19)
-1.16***
(0.31)
-1.07***
(0.37)
-0.91**
(0.38)
-7.7%
-8.0%
-17.0%
-26.7%
-32.8%
Data: HRS, 1996-2006 and 2010-2012.
Notes: Controls include age, gender, education, occupation, part-time employment, partly-retired employment,
industry, whether employer provides health insurance, levels of stress at job, requirements of lifting heavy loads at
work, and state and year dummies. Standard errors (in parentheses) were clustered at the state level. Standard
errors for the Probit CF approach were calculated from 500 bootstrap replications clustered at the state level; ***
denotes p-value <0.01, ** denotes p-value <0.05, * denotes p-value<0.1.
31
Table 10: Effect of Job Insecurity and Potential Replacement Rate on OJS
(Linear Models)
Subjective prob. of job
loss ( , )
Potential rep. rate (
,
)
Interaction term
( , × ,)
OLS
CF OLS
FE
2SLS
0.215***
(0.040)
0.014
(0.056)
0.525***
(0.097)
-0.011
(0.137)
0.166***
(0.049)
0.029
(0.080)
0.604
(0.480)
0.023
(0.234)
-0.104
(0.085)
-0.091
(0.079)
-0.158
(0.109)
-0.280
(1.121)
,
-0.321***
(0.084)
,
0.279**
(0.134)
# Observations
23,906
23,906
23,906
23,906
Data: HRS, 1996-2006 and 2010-2012.
Notes: Controls include age, gender, education, occupation, part-time employment, partlyretired employment, industry, whether employer provides health insurance, levels of stress
at job, requirements of lifting heavy loads at work, and state and year dummies. Standard
errors (in parentheses) were clustered at the state level. Standard errors for the CF approach
were calculated from 500 bootstrap replications clustered at the state level; *** denotes pvalue <0.01, ** denotes p-value <0.05, * denotes p-value<0.1.
Table 11: Reduced form regressions for endogenous variables, by gender
Males
Females
Subjective
Potential
probability
replacement
of job loss
rate ( , )
( ,)
Subjective
Potential
probability
replacement
of job loss
rate ( , )
( ,)
0.061***
-0.011***
0.082***
-0.007***
State average
potential replacement
rate (APRR or , )
(0.006)
-0.030
(0.002)
1.066***
(0.006)
0.102**
(0.002)
0.869***
(0.089)
(0.055)
(0.045)
(0.037)
# Observations
10,225
10,225
13,640
13,640
Downsizing (
,
)
Data: HRS, 1996-2006 and 2010-2012.
Notes: Controls include age, education, occupation, part-time employment, partly-retired employment, industry,
whether employer provides health insurance, levels of stress at job, requirements of lifting heavy loads at work,
and state and year dummies. Standard errors (in parentheses) were clustered at the state level. *** denotes p-value
<0.01, ** denotes p-value <0.05, * denotes p-value<0.1.
32
Table 12: Effects by Gender of Job Insecurity and Potential Replacement Rate on OJS and
Employment Transitions
(Marginal Effects – Restricted Model)
Probability of
OJS
Pct.
points
Pct.
change
Employment Transitions
Outcome:
Outcome:
Different
Non-employment
Employer
Pct.
Pct.
Pct.
Pct.
points
change
points change
I. Males
Avg. effect
I.A. Effect of 25 percentage points increase in
61%
13.24*** 104.3%
9.01**
(2.44)
Avg. effect
,
-6.86**
(3.39)
-59.4%
-0.78***
(0.27)
-6.7%
(3.59)
I.B. Effect of 12.5 percentage points increase in
0.6%
-0.57**
-4.5%
0.09
(0.23)
,
(0.27)
If
,
= 0.50
-2.17**
(0.87)
-5.1%
-0.20
(1.02)
-0.6%
-0.99**
(0.43)
-14.5%
If
,
= 0.90
-2.97**
(1.37)
-3.7%
-0.75
(2.17)
-1.3%
-0.72
(0.47)
-30.8%
-3.98**
-39.9%
II. Females
Avg. effect
II.A. Effect of 25 percentage points increase in
9.51***
64.6%
10.53***
90.2%
(2.45)
Avg. effect
If
,
= 0.50
If
,
= 0.90
(2.26)
(2.02)
II.B. Effect of 12.5 percentage points increase in
-0.3%
-0.43
-3.7%
-0.04
(0.38)
-1.57
(1.40)
-2.87
(2.51)
,
(0.30)
-0.63
(1.10)
-1.62
(2.24)
-4.9%
-4.5%
33
-2.0%
-3.0%
,
-0.88***
(0.26)
-1.33***
(0.47)
-1.13*
(0.62)
-8.8%
-20.0%
-38.4%
A. APPENDIX: THEORETICAL MODEL AND PREDICTIONS
Model set up
The following model is an adaptation of the model initially proposed by Light and Omori
(2004). The model consists of two periods. In the first period, the worker is employed and earns
. The
maximization problem of the worker is to decide whether to search on-the-job (OJS) or not. If the
worker decides to search, then has to pay a fixed cost of , which is distributed among workers with
probability function
( ). In each period, the flow utility is given by logarithm of the available
earnings and the fixed cost of job search (if the worker searches on the job).
If a worker searches, the probability of receiving an offer in the second period equals . Offers
come from a known distribution
( ) and at most one offer can be received. The worker faces a
probability of layoff in period 2 equal to ; and if laid off, the worker can collect UI benefits equal to
, where
is the current wage of the worker in period 1 and is the effective replacement rate.
If the worker decides not to search for a job, there are two possible scenarios for the second
period: 1) with probability (1
and 2) with probability
) does not lose the job and continuous receiving earnings equal to
;
. Four different
loses the job and takes unemployment benefits equal to
scenarios can occur in the second period if the worker decides to search for a job: 1) with probability
(1
)(1
) does not lose the job and does not receive an offer. In this scenario the worker continues
receiving earnings equal to
; 2) with probability (1
)
the worker loses the job and does not
; 3) with
receive an offer. In this scenario, the worker takes unemployment benefits equal to
probability (1
), the worker does not lose the job and receives an offer. In this scenario the worker
; and 4) with probability
takes the new job as long as the offered wage is greater than
, the worker
loses the job and receives an offer. In this scenario, the worker takes the offer as long as the offered
. Thus, the maximization problem for the worker in period 1 consists of
wage is greater than
deciding whether to search on the job or not. More formally, the maximization problem of the worker
can be formulated as described below (where
{
;
{log(
)=
[(1
(1
is the worker’s discount factor) :
) + [(1
)(1
) log(
{log(
)
{log(
) log(
)+
) + (1
)
log(
log(
) , log( )} ( )
) , log( )} ( )
34
}
)]; log(
)
+
)) +
+
(A.1)
The optimal decision for the worker is to search in period 1 if the fixed search cost
reservation level
is below a
, which is a function of the worker’s wage, job loss expectations and the
is given by equation (A.2) below, where
replacement rate. An expression for
[log( )
( )=
)] ( )
log(
+ (1
[log( )
)
Hence, the probability that a worker engages in OJS is given by
=( ,
log(
, , , , ):
)] ( )
(A.2)
( ) , or the probability that
the idiosyncratic fixed cost of search is below the maximum cost the worker is willing to accept to
search on the job.
Model predictions
The following predictions hold in the model:
Prediction 1: Other things equal, workers with greater probability of job loss are more likely to search on the
job.
Proof. Equation (A.3) below shows that the derivative of
with respect to the expected
probability of job loss ( ) is unambiguously positive:
( )
=
×
[log( )
log( ×
[log( )
)] ( )
log(
Given that the probability of performing OJS is given by
density function
)] ( )
>0
(A.3)
( ) , and that the probability
( ) is always positive, then equation (A.4) below completes the proof of
Prediction 1:
( )
( )
( ) ×
=
>0
(A.4)
Prediction 2: An increase in the replacement rate leads to a decrease in the probability of OJS but only for
workers with non-zero probability of layoff (i.e.
> 0).
Proof. Equations (A.5) and (A.6) below show the derivative of
and of the probability of OJS
with respect to :
( )
[1
=
( )
=
( ×
)]
( )
( ) ×
35
0
(A.5)
0
(A.6)
The derivatives are zero if
= 0. Thus, changes in the replacement rate have no effect on the
probability of OJS if the worker is not at risk of job loss. If
is positive, then an increase in the
replacement rate will decrease the maximum search cost an employed worker is willing to accept,
everything else equal, and thus will reduce the probability that the worker engages in OJS.
Prediction 3: The higher the probability of layoff (p), the larger is the negative effect that the replacement rate
has on the probability of OJS (under plausible conditions on ).
Proof. Equation (A.7) below shows the cross-derivative of
( ) with respect of
equation (A.8) shows the cross-derivative of the probability of OJS with respect to
( )
[1
=
( )
=
( ×
( ) ×
and :
)] < 0
( )
and , whereas
(A.7)
( )
+
( )
×
( )
×
( )
(A.8)
Equation (A.7) shows that the effect of an increase in the replacement rate ( ) on reducing the
maximum search cost an individual is willing to accept gets larger (more negative) at higher levels of
job loss expectations ( ). However, the effect of
with higher levels of
on the probability of OJS can be larger or smaller
. In other words, the sign of equation (A.8) is ambiguous. However, under
condition (A.9) below, the sign of
( )
would be unambiguously negative.
( )
( )
( )
( )
>
( )
×
( )
(A.9)
Condition (A.9) is a smoothness condition requiring that if the rate of change in the probability
density function () is negative, then it should be bounded by the right-hand side term of condition
(A.9). In other words, condition (A.9) requires that () varies smoothly around
( ).
Prediction 4: The replacement rate does not affect the probabilities of employment transitions if the worker is
not at risk of job loss (i.e. = 0 ). For workers with a non-zero risk of job loss, an increase in the replacement
rate increases the likelihood of falling into non-employment and decreases the likelihood of moving to a new
job. These effects are stronger the larger is the risk of job loss.
Proof. Equations (A.10) and (A.11) state the probabilities that workers experience a job-to-job
(JTJ) transition or a job-to-non-employment (JTN) transition in period 2, respectively:
36
(
( ) { [1
| )=
(
| )=
( ×
( ) [1
1
)] + (1
( ×
)[1
(
)]}
(A.10)
)]
(A.11)
After taking the derivatives of (A.10) and (A.11) with respect to the replacement rate , the
( ) is the probability density function of the wage offer
following equations are obtained, where
distribution ( ):
(
| )
( )
=
(
| )
(
| )
[1
( ×
)[1
)]
(
( ×
( )
= 0, and negative if
is zero if
( ×
( )
)]}
)
(A.12)
)
(A.13)
(
> 0. Similarly,
| )
is zero if
= 0, and
> 0. Now, I take the cross-derivatives of equations (A.12) and (A.13) with respect to :
positive if
| )
( )
=
{ [1
| )
( )
=
( )
)
[1
( ×
)] + (1
( ×
( ×
( )
(
)] + (1
( ×
( )
=
Thus,
(
{ [1
( )
+
( ×
)[1
(
( ×
)]
( )
( )
)]} +
{ (
)
)
( ×
( ×
)}
(A.14)
( )
)
[1
)
( ×
)]
(A.15)
Under the smoothness condition in equation (A.9), and as long as
derivatives in equations (A.14) and (A.15) as
(
| )
< 0 and
(
| )
> 0, we can sign the cross-
> 0.
Prediction 5: Given that the worker has a positive probability of job loss ( > 0), the effect of an increase in
the replacement rate is larger (in absolute value) on JTJ transitions than on JTN transitions.
Proof. We can re-write the absolute value of (A.12) as:
(
| )
( )
=
{ [1
)] + (1
( ×
)[1
(
)]} +
( )
( ×
)
(A.16)
Subtracting (A.13) from (A.16) we have:
(
| )
(
| )
=
( )
(1
37
)[1
(
)]
0
(A.17)
Again, equation (A.17) equals zero when
is zero and is positive when
38
is positive.