Eﬀects of job mobility on the unemployment risk

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Effects of job mobility on the unemployment risk

Jurriaan J.M. Prins Master thesis Econometrics

August 22, 2010

Supervisors:

Prof. dr. R.J.M. Alessie (Rijksuniversiteit Groningen) Dr. A. Heyma (SEO Economisch Onderzoek, Amsterdam) Co-assessor:

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Acknowledgments

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Abstract

Though it is generally assumed that job mobility positively relates with employability, no empirical evidence exist so far. This paper studies the effect of job mobility on employabil-ity by explicitly modeling employabilemployabil-ity in terms of the individual probabilemployabil-ity of making a transition from employment to unemployment. Specific emphasis lies on voluntary and in-voluntary job mobility as the effect will most likely differ. The analysis takes into account that the relation between job mobility and employability may be endogenous and that employment durations with exit to unemployment is potentially censored by transitions made to employment. In addition, we control for the observed and unobserved differences in the workers’ productivity profiles by including a rich set of explanatory variables and allow for unobserved heterogeneity.

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1 Introduction

Employability is worldwide an important political issue as it is considered to be a necessary condition for high levels of labour participation, which is one of the driving forces behind eco-nomic growth. For the Netherlands and many other EU countries, high labour participation is of particular importance with respect to the sustainability of the Welfare State, which is challenged by a rapid aging population. Since the major costs of social services are financed through the labour force, an aging population requires that costs will have to be carried by fewer people. In addition, European countries have stated in the Lissabon treaty that Europe should be world’s leading knowledge economy, which implies that labour participation should grow to 70% of the population. Meanwhile, globalisation, increasing international competi-tion and rapid technological developments increase the dynamics in produccompeti-tion and labour. Firms are expected to grow and decline faster, implying that employees have to change jobs more often and move more frequent between industries and occupations. This may seem even more difficult to achieve when an aging labour force already leads to a higher job replacement level.

One of the ways in which governments respond to these challenges is to stimulate the dy-namics on the labour markets. The idea is that job mobility contributes to both the level of human capital and search capital of individuals, increasing the probability that individuals reach more optimal productivity levels. Human capital is the set of skills that is acquired during a job and it may increase by switching jobs regularly. This implies that not only new knowledge is acquired, but it also makes individuals employable in different segments of the labour market. Similarly, search capital is the level of labour market experience and is used in finding a new or better job. Since job mobility contributes to the level of search capital, people with a relatively high level of search capital are able to find a job more easily and pos-sibly avert unemployment. According to an advisory committee1to the Dutch government on increasing future labour participation, job mobility is one of the instruments that may help to keep the labour force employable in the long run. In short, this means that workers have to switch jobs more often and more easily, reduce time spent in unemployment and participate longer on the labour market.

The main question in this paper is whether job mobility does in fact have a positive effect on the employability of individuals. If so, a high level of job mobility is expected to reduce the risk of becoming unemployed, ceteris paribus. Using a Dutch panel with people’s labour market history, we study the effect of job mobility on employability by modeling employability in terms of the probability of making a transition from employment to unemployment (also referred to as the unemployment risk). We express job mobility as the number of (past) job transitions per year.

In order to answer this question we have to take into account that the relation between job mobility and employability is ambiguous. A high level of job mobility may result from a number of dismissals and it is unlikely that this kind of job mobility contributes to human capital. Therefore, we take into account whether job transitions were made voluntary or involuntary. One may argue that, in case the job transitions from the past were involuntary, possibly including intermediate periods of unemployment, job mobility does not contribute to the worker’s human capital level and hence, does not decrease the unemployment risk. On the contrary, voluntary job mobility may decrease the unemployment risk as it is more likely

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that it reflects a movement towards a better job.

In the empirical analysis we use a Mixed Proportional Hazard (MPH) model. With this we take into account that the probability of making a transition from employment to unemploy-ment depends on the elapsed job duration and that the observed exit rate to unemployunemploy-ment may be explained by (un)observed explanatory variables. The hazard specifies the probability of leaving a certain state conditional on the time being in that state. It is called proportional, because observed and unobserved explanatory variables are allowed to have a multiplicative effect on the hazard rate to unemployment while leaving the shape of the hazard the same for all individuals.

Though the class of MPH models gives a suitable framework for modeling the unemployment risk, estimating the effect of job mobility on employability may still be difficult for several reasons. First of all, the relation between job mobility and employability is endogenous. Not only may job mobility affect employability, employability may affect the level of job mobility as well. If job switching adds to employability, the individual might switch jobs even more easily as he has become more attractive to other employers. On the other hand, the current level of employability may be strongly correlated with the past level of employability, which affects the current level of job mobility. This endogenous relation (reversed causality) is hard to isolate from the identification of the effect of job mobility on employability. To tackle this problem, we specifically consider the effect of past job mobility on the current level of em-ployability. Secondly, during employment one faces not only the risk of unemployment, but also the probability of making a transition to another job and possibly avoid unemployment. This implies that a job duration may exit to another job or to unemployment but only one of these durations is observed (competing risks). If these processes have different determinants this may lead to an incorrect inference of job mobility regarding the transition rate to un-employment. In order to correctly estimate the effects of job mobility, we jointly model the transition rate to unemployment and employment. Thirdly, though we aim to explain the observed differences in the exit rate to (un)employment by including explanatory variables that capture the individual specific level of employability, the possible presence of unobserved heterogeneity may affect the transition rate as well. For example, involuntary job mobility may indicate a relatively low employable worker with a relative high unemployment risk. On the other hand, voluntary job transitions may indicate that a job applicant is highly talented and that he switched jobs as soon as an employer offered him a better job. The presence of unobserved heterogeneity may have far-reaching consequences on the coefficients of job mobil-ity as low employable individuals may have shorter job durations and higher unemployment risk, leaving us with a sample of high employable workers that are probably better able to avoid unemployment.

In summary, we estimate the effects of job mobility on the unemployment risk and account for the fact that: (1) the relation between job mobility and employability is endogenous; (2) jobs may exit into another job or unemployment (competing risks); (3) unobserved differ-ences in employability levels may affect the hazard rates. A rich set of control variables is used to capture the individual specific level of employability (also referred to as the worker’s productivity profile).

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2.2. In Section 3 we discuss the data and we explain in detail how we define the duration variables and the measures of job mobility. In this section we also define our estimation sam-ple and give an overview of the control variables we use for capturing the worker’s specific productivity profile. In Section 4 we discuss the econometric model in more detail and in Section 5 we present the results. Finally, we conclude in Section 6.1.

2 Theoretical framework

This section gives an overview of the existing literature on job mobility and employability. Since little empirical research is done on the effects of job mobility on the unemployment risk, we first consider some economic theories that explain the relation between job mobility and employability in a broader perspective. This helps us identify the possible effects of job mobility on the unemployment risk. In section 2.2 we give a short overview of the econometric literature on duration analysis. Our main focus lies on three econometric issues related with estimating the effect of job mobility on the unemployment risk: (1) The fact that the relation between job mobility and employability is endogenous; (2) one may make a transition to another job instead of making a transition to unemployment and (3) the presence of unobserved heterogeneity. This framework is used to setup an econometric model to estimate the effects of job mobility.

2.1 The relation between job mobility and employability

There are several theoretical models that help to identify the relation between job mobility and employability. Most well known theory is the theory of human capital (Becker (1962)). It explains a reciprocal relation between job mobility and employability. On one hand, the theory of human capital predicts an accumulation of human capital during a job, which contributes to the worker’s productivity profile and induces a certain level of job mobility. Job, firm, occupational and industry specific skills are acquired during the time spend in a job, making the worker more attractive to other employees. A worker might switch jobs when the accumulation of human capital and associated wages in his current job is less than the discounted cash flow of future earnings that is offered by other employees (Becker (1962), Acemoglu and Pischke (1998)). On the other hand, job mobility itself may contribute to the level of human capital. According to Hall (1982), about two-third of all lifetime job changes occur in the first ten years of people’s career. Since most job specific knowledge is achieved in the first few years of a job, switching jobs on a regular basis should sustain a human capital growth. By job switching, not only new knowledge is acquired, but it also increase the diversity of skills which makes workers more employable in different segments of the labour market.

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words, the job search theory predicts that job mobility increase the employability of workers, and hence reduce the unemployment risk.

However, the relation between job mobility and employability may not always be positive. There is extensive empirical evidence that the need for job change declines with age, experience and, most importantly, with the tenure of job duration (Farber (1999); Mincer and Jovanovic (1981); Parson (1978)). Rosen (1976) suggest that, as job duration increases, the worker will have a concentration of human capital that is specific to the current job and difficult to be transferred to new jobs, making job searches longer and more selective. In addition, one may argue that a relatively high level of job mobility may indicate at workers that are not able to maintain long-term working relations to the firm. This may reduce the employer’s incentives to invest in on-the-job training and education, which lowers the worker’s human capital growth. If so, the worker’s value on the labour market decreases and it will be harder to find a new job. Althought the relation between job mobility and employability is ambiguous, the relation will most likely differ between voluntary job mobility and involuntary job mobility. As switching jobs may considered as a human capital investment of the employee, it is more likely that voluntary job mobility contributes to employability and reduce the unemployment risk. Involuntary job transitions are not likely to increase human capital.

This relation can also be explained by the signaling theory (Spence (1973)). This theory states that, in case no prior information is available, both employers and employees signal secondary information which is used to judge whether there is a good match. More specifically, Hirshleifer (1973), defines a job as an inspection good, which is used in the decision making process of employers and employees. Job interviews or Curriculum Vitae’s reveals information about people’s job history, such as the number of employment relations in the past, their length and probably, how they ended (voluntary or involuntary) which can be used to inform the employer about the expected productivity of the job applicant. People are likely less employable in case job transitions were involuntary and moreover, if they are followed by periods of unemployment. Apparently, they didn’t manage to prevent unemployment or to switch to a job of their preferences. Since this is a negative signal for the employer, it may lead to even longer periods of unemployment. On the other hand, voluntary job transitions, without intermediate periods of unemployment may indicate that the job applicant is highly talented and that he switched jobs as soon as an employer offered him a better job.

So far, only a few studies have quantified the effects of job mobility on employability. These studies generally express employability in terms of wage levels. Topel and Ward (1992) finds evidence that the evolution of wages is an important determinant of job changes. In his study, job switching increases the early-career wage growth by one-third. Bartel and Borjas (1982) and Mincer and Jovanovic (1981) find the same relation, but the wage gains decline with age. Becker and Hills (1983) show that the long run net effect of the job mobility of teenage men on future adult wages is positive. Since the human capital theory predicts a positive relation between wages and employability (Burdet (1978); Jovanovic (1979)), job mobility may indeed lead to better employable workers.

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involuntary job mobility. Voluntary job mobility is more likely to increase human capital than involuntary job mobility. We expect that voluntary job mobility reduces the unemployment risk, while involuntary job mobility increases the unemployment risk. Since voluntary and involuntary job mobility may indicate at low and high employable workers it makes clear the importance to include observed and unobserved variables that capture the individual productivity profile. We explain how we deal with these issues in the following section.

2.2 Econometric framework

Employability includes a wide range of economic interpretations. It can be related, for in-stance, to education, working experience or wages. In order to quantify the effects of job mobility we first have to define employability. In this paper we define the employability of an individual as the probability of making a transition from employment to unemployment, also referred to as the unemployment risk. High employable workers have a low unemployment risk, whereas low employable workers have a high unemployment risk. The advantage of using this measure of employability is that all other measures of employability (education, working experience, wages etc.) are allowed to have an individual contribution to the transition rate to unemployment as they can be included in the empirical model. In addition, we have to define what we mean by job mobility. This will be done in Section 3.3.

Already mentioned in the previous section, the probability of making a transition to unem-ployment (or emunem-ployment) depends on the tenure of the job (duration dependence). This implies that we have to model employability conditional on the time spent in the job. More specifically, consider the duration of a job to be stochastic and denoted by T . Given an individual who was employed for a time t, the probability that a transition to unemployment is made in the interval t + dt after t equals P (t ≤ T < t + dt|T ≥ t). The hazard function of T is defined as the probability that a job spell is completed at t given that it has not been completed before t, as a function of t. With T continuous and letting dt → 0 the hazard can be written as,

θ(t) = lim

dt↓0

P (t ≤ T < t + dt|T ≥ t)

dt .

In general, three important assumptions are made in the analysis of durations. First is on which way explanatory variables enter the model. The class of Mixed Proportional Hazard (MPH) model, developed by Lancaster (1979), plays a central role in duration analysis. The MPH model assumes that individual differences in the hazard rate can be explained by ob-served explanatory variables x and unobob-served variables v. The hazard function is modeled by, a so-called, baseline hazard that gives the shape of the hazard function for any given individual and a systematic part of explanatory variables. In other words, the MPH model allows only the level of the hazard function to differ across individuals. Usually it is used to provide estimates of particular variable of interest on the duration variable. For example, Atkinson et al. (1984), Lancaster and Nickell (1980) and Narendranathan et al. (1985) study the effect of unemployment benefits on the transition rate to work.

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prior information is available on the shape of the hazard, the empirical analysis based on such assumptions may be unreliable. Elbers and Ridder (1982) show that the MPH model under some regularity assumptions can be non-parametrically identified2. Based on this. we may specify a semi-parametric approach, which specifies the hazard to be constant within predefined duration intervals while it remains flexible between the intervals. We discuss this in section 4.2.1.

The third assumption involves the distribution of unobserved heterogeneity G. Common para-metric specifications are the Gamma or log-normal distribution. However, since the choice of a particular distribution is often arbitrary, it may seriously affect the hazard function (see e.g., Heckman and Singer (1984a)) if the specification of the hazard is misspecified. In addition Heckman and Singer (1984b) show that the maximum likelihood estimator of the unobserved heterogeneity distribution is a discrete distribution. This allows us to model the unobserved heterogeneity distribution by a number of mass points with associated probabil-ities. Althought the underlying true unobserved heterogeneity distribution can be approxi-mated arbitrarily close by an increasing number of points of support, in practice it is difficult to find more than a few mass points. This need not be prejudicial since the information on G is revealed from the inference between t and x in the data, and it may be that a mixing distribution G with a few mass points is able to capture most of this. Heckman and Singer (1984b) gives an empirical proof.

The relevance of unobserved individual specific effects in duration models has been recog-nized in many empirical studies (for surveys, see e.g., Lancaster (1990) and Devine and Kiefer (1991)). In the analysis of unemployment durations special attention lies on distinguishing negative duration dependence from unobserved heterogeneity. For example, for long-term unemployed stigma effects may cause the individual hazard rate to decrease as a function of duration (see e.g. Vishwanath (1989) and Van den Berg (1994)). However, the presence of unobserved heterogeneity causes the hazard rate to decrease as well. This follows from the fact that, on average, high employable people (these are people with the largest hazard rate) leave unemployment first. Althought we consider employment durations, a similar reasoning can be used. Low employable workers may have shorter job durations and transfer to un-employment more easily than their higher employable colleagues. This implies that, as time increases, the hazard rate to unemployment will be based on more and more people that are high employable. If the low (or high) level of employability is due to unobserved individual characteristics it may lead to decrease the hazard rate to unemployment as well.

One of the advantages of the MPH model is that it can be extended to a competing risk framework in which people face multiple exit destinations but only one of them is materi-alized. The observed duration is in fact the observed minimum of two (or more) duration variables. In case of employment durations, which are considered in this paper, one faces not only the risk of unemployment but also of making a transition to employment, i.e. a job rotation. Let Tu be the stochastic variable that describes the employment duration with

exit to unemployment and Tethe employment duration with exit state employment. We only

observe T = min(Tu, Te) and hence, one of the durations is latent. If these two random

pro-cesses have different determinants, the effect of job mobility may be inconsistently measured in a single risk MPH model.

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There is one issue that remains to be discussed. Though it is generally assumed that job mobility is a result of the level of employability, the reversed causality makes the relation be-tween job mobility and employability rather complex. On one hand, job mobility varies with the degree of employability. Good employable workers are able to retain their jobs, change jobs more easily and, in case of unemployment, resume work faster. On the other hand, current level of employability strongly correlates with employability in the past which again affects the level of job mobility. Though the econometric analysis of endogenous variables in non-linear models is similar as in linear models, the empirical applications are usually limited to specific socio-economic experiments on the duration variable. For example, Bijwaard and Ridder (2005) developed a two-stage instrumental variable (IV) estimation technique in or-der to estimate the effect of training on the transition rate out of unemployment, where the compliance to training is selective. Still, finding appropriate IV variables remains difficult. In case panel data is available, another way of dealing with the endogeneity is by using lagged versions of the endogenous variables. Under the assumption that the past level of employa-bility can be captured by observed and unobserved explanatory variables, the current level of employability can not affect the past level of job mobility. We choose this approach to deal with the endogeneity between job mobility and employability.

3 Data description

In this paper we use data of the OSA labour Supply Survey. It consists of periodically (2 year) surveys among a panel listing information on their labour market position, job characteristics and individual characteristics. The main advantage of this dataset is that we can combine peoples’ job history with information on personal motives of labour market movements. In particular, we know whether job transitions were made voluntary or involuntary. This en-ables us to make, beside a regular measure of job mobility, also a measure of voluntary and involuntary job mobility.

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Table 1: Number of participants in the OSA Labour Supply Survey wave 1985 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 1st participation: 1985 4020 2622 1927 1430 1097 858 678 518 298 195 152 109 1986 1493 1012 713 581 472 349 266 127 95 71 53 1988 1525 1042 723 569 451 337 189 141 104 72 1990 1253 882 668 481 336 170 118 84 68 1992 1253 834 564 383 200 144 109 82 1994 1136 736 492 225 157 118 84 1996 1310 864 411 289 206 172 1998 1584 770 544 386 293 2000 1795 1049 704 518 2002 1924 1179 814 2004 1684 960 2006 2338 Total 4020 4115 4464 4438 4536 4537 4569 4780 4185 4656 4797 5563

3.1 OSA labour supply survey

The OSA labour Supply Survey is a 2-year periodically survey with respect to the labour market. This paper uses the surveys of the years 1988, 1990, . . ., 20063. The survey contains retrospective questions about people’s labour market positions. Beside the current labour market position, these questions give information on the labour markets position(s) held within the two years before the survey. By merging the surveys together the panel covers jobs in the full period 1986-2006. The OSA labour Supply survey aims to interview the same panel members each two years. Drop outs are replaced by other respondents, keeping the panel characteristics in tact.

Table 1 shows the inflow and outflow of panel members. Each wave consists of approximately 4500 individuals. As we can see, the survey starts in 1985 with 4020 people. The second wave starts in 1986 with 2622 people from the first wave and 1493 new respondents. In the last year, 2338 new individuals entered the survey, 960 members participated for the second time, 814 for the third, andsoforth. This means that for a panel member who participated in one survey we know all labour market positions within the two years before the time of survey. Note that this may include job durations longer than two years. For panel members that participated in two surveys we have 4 years of job history, etc. Finally we combine all surveys of the years 1988, 1990, . . ., 2006.

The OSA labour Supply survey discriminates between three labour market positions which are: employed, unemployed and inactive. Inactivity refers to individuals that are not active on the labour market. This group of people do not have a job, but they aren’t looking for one either. This state also includes retirement, full-time education and disability. The state of unemployment refers to the unemployed job-seekers. These are people without a job and seeking for a job. This may include people that do not receive any unemployment benefits. Employment refers to people with a job. For the full dataset we identify when people are employed and whether the job ended in another job, unemployment, inactivity or if they remain on the job. We define this more formally in the next section.

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3.2 Duration variables

In this section we define the job durations. Let e → e denote an employment spell that ends in another job, e → u an employment spell that ends in unemployment, e → u an employment spell that ends in inactivity and e → c an employment spell that is right-censored. Note that for the e → e, e → u and e → i spells we know the duration of employment and the state to which a transition is made. Namely, for the e → e spells we know how long one was employed in the current job and that he or she made a transition to another job. For the e → u, e → i spells we know when the job started and that one makes a transition to unemployment or inactivity. The e → c spells are the so-called right-censored job durations. For these spells we know when the job started but, at the time of observation, one was still employed in the same job. Hence, we don’t know when the job ends and therefore, its duration is unknown. We define te for the duration of a e → e spell, tu for the duration of a e → u and tc for the

duration of a e → c spell.

The employment spells that end in inactivity are included in the estimation of the job mo-bility variable (defined in Section 3.3). Since the number of e → i is rather small we exclude them from the analysis of the effect of job mobility on the unemployment risk.

As mentioned in the previous section, the OSA Labour Supply Survey contains for each indi-vidual two years or more of labour market history. This may include states of employment, unemployment or inactivity. Similarly as for the employment spells, we can define unem-ployment spells or inactivity spells. However, since we want to model the transition rate to unemployment and not the transition rate from unemployment or inactivity to employment, we do not define them formally.

After combining the consecutive surveys, the employment history of an individual can be defined in terms of e → e, e → u, e → i and e → c spells. Figure 1 depict examples of a number of job histories. Person 1 has one long employment spell. At the time of the first survey person 1 was already employed and made no transitions within the two years before the survey. Notice then we know the exact date of the start of the spells and that it may lie before two years of the survey. At the time of the second survey, he or she was still em-ployed in the same job. Person 2 and 4 both start with an unemployment spell. They both switched to employment before the time of the first survey and are still employed at the time of observation. Thereafter, person 2 switched jobs and at the time of the second survey he is unemployed. Individual 4 first made a transition to unemployment, but was already em-ployed during the second survey. The same reasoning can be applied to persons 3 and 5. The duration variables defined in the beginning of this section, are the spells of Figure 1 denoted by a single line. Individual 1 has one job spell with unknown time of completion, which is a e → c spell. Persons 3 and 5 start with a employment spell both ending in unemployment, hence these are e → u spells. Employment spells which are followed by other employment spells are e → e spells.

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Table 2: The total number of job spells in the job mobility panel.

Number of spells e → e e → u e → i e → c Total number of Number of per individual spells (%) spells (%) spells (%) spells (%) Spells individuals

1 2 3 0 95 3521 3521 2 46 4 2 48 2816 1408 3 61 5 2 32 1878 626 4 67 7 2 24 1124 281 5 71 6 3 19 675 135 6 76 7 2 15 312 52 7 74 9 3 14 259 37 8 72 11 5 12 128 16 9 82 7 1 10 72 8 10 70 20 0 10 50 5 > 10 70 17 5 8 100 8 Total 4427 533 152 5823 10935 6097

Note: e → e, e → u and e → c indicate a transition made from employment to, employment, unemployment or right-censoring respectively. The number of spells in this table are the number of spells that results after the data selection.

person 2 did not participated for a second time. In that case his employment spell remains right censored, since we do not know whether he is still employed in the same job, switched jobs or made a transition into unemployment. We only know the duration of the job until the time of the first survey. This makes clear that combining information from each wave is essential in order to construct individuals’ labour market histories.

3.2.1 Data selection: The job mobility panel

Because the measure of job mobility is based on the number of job transitions in the past it is a necessary condition that a long enough job history is available. Consequently, not all panel members can be included after merging the surveys together. If people have only one job spell, no information is available on the level of job mobility at the beginning of the current spell. Therefore, we only include the spells that have at least one job spell prior to the current spell. In Table 2 we show the number of job spells per individual that can be identified after this selection.

In total we have 6097 people that held 10935 employment positions in the period 1986-2006. 4427 spells end in another job, 533 end in unemployment, 152 end in inactivity and 5823 spells are right-censored. Looking at the distribution of the number of spells held per individual after the selection, we see that for a relatively large number of people we have only one spell available. This may result from the fact that they did participate only once or that they have long job durations. For people that participate more than once or have relative short job durations, we have a larger proportion of e → e and e → u. This implies that for a number people the measure of job mobility is based on a relatively short job history and for others on a quite long job history. A straightforward calculation of peoples’ level of job mobility would lead to a inconsistent measure of job mobility. Therefore we use the job mobility panel to estimate the level of job mobility. This is done in the following section.

3.3 The job mobility variables

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Figure 1: Examples of job history in the OSA survey panel

Note: An arrow indicates a transition and for each node the number of the job- or unemployment transitions in the past can be calculated. A spell not ending with an arrow means that the particular spell is right-censored. Althought not depicted in this figure, notice that spells may have different lengths.

be clear from the previous section, the more people participate the surveys, the more we know about their job history. This implies that the level of job mobility can be more accurately mea-sured for people we observe over a longer horizon. In order to obtain a consistent measure of job mobility, we use a proxy of the true level of job mobility. We explain this in the preceding.

Definition of job mobility: Let τj, j = 1, . . . , J ∈ N denote points on the time axis with

an origin somewhere in the past and arbitrary measurement scale (i.e., days, weeks, months, etc.). Define kiτj, k = 1, 2, 3, . . . to be the k-th completed job spell of individual i = 1, . . . , N

observed at time τj. Let τi0 denote the time at which we start to observe individual i. The

total time of observation liτj of individual i until time τj equals τj − τi0. The level of job

mobility for individual i at time τs is defined by:

yiτs =

Ps

j=1kiτj

liτs

. (1)

This definition implies that the level of job mobility of individual i at time τsis the number of

completed job spells observed at time τs devided by the total time of observation liτs. In case

we choose ‘months’ to be the measurement scale, job mobility is the number of completed job spells per month. One may also interpret job mobility as the number of past job transitions (regardless from the exit state) per month. For example, consider individual 3 in Figure 1. Suppose we start to observe this individual at the beginning of the first spell. Let the time at which this spell starts be denoted by τ0. During this spell we observe no completed job

spells yet and hence, the level of job mobility during the completion of the first spell equals 0/liτs = 0, with τi0≤ τs. During the second spell (which is actually an unemployment spell),

we observe one completed job spell and the level of job mobility now becomes 1/liτs > 0, with

τ1≤ τs, where τ1 denotes the time at which the second spell starts. The level of job mobility

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completed job spell. Finally, during the fourth spell we observe two completed job spells and the level of job mobility becomes 2/liτs > 0, with τ3 ≤ τs.

We choose to measure the level of job mobility using past job transitions because we want to reduce the reversed causality that may exist between job mobility and the unemployment risk. Employability may affect the level of job mobility because high employable workers are usually able to switch jobs more easily and have a lower unemployment risk. We assume that, if we can control for the individual specific level of employability, the current level of employability can not affect the past level of job mobility.

The above definition implies that the level of job mobility decreases during the completion of a spell. During a spell, the time of observation liτs increases and hence the level of job mobility

decreases. However, we assume that the level of job mobility remains constant during a spell and changes relatively to the length of observation at the time another spell arrives. In other words, the level of job mobility is set fixed at the beginning of a spell and enters the model as a time constant variable.

3.3.1 Estimation of job mobility

As we can see from equation 1 the level of job mobility depends on the length of observation. For people we observe a long labour market history, the level of job mobility in the past can be estimated quite well. However for individuals we observe over a short period of time, the level of job mobility is relatively high and inaccurate with respect the individual’s true level of job mobility. For example, consider two identical persons with similar job histories (persons 2 and 5 in figure 1). Both switched jobs only once in the last four years. The correct job mobility equals 1/4. Suppose the first person has been observed only for two years and the other for four years. We now measure a job mobility of 1/2 for the first person and 1/4 for the second person. For this reason we choose to estimate the level of job mobility and correct for the observed differences in observation lengths.

This is done as follows. First, using the panel with full information on people’s job history, we calculate for each individual spell the (unadjusted) level of job mobility. Secondly, we run a regression of the job mobility variable on the observation lengths and other variables4. More formally, we run the following regression by pooled OLS:

yiτ = c + α1liτ + α2l2iτ + x0iτβ + iτ,

where xiτ may contain a set of additional regressors and eiτ is the error term. Note that

we use τ to denote the individual’s τ -th spell and not specifically the beginning of a spell. Assuming that we observe all individuals for l∗ = 52 months, the corrected measure of job mobility can be estimated by:

ˆ

y∗_iτ = ˆα1l∗+ ˆα2l∗2+ x0iτβ + ˆˆ iτ.

We make clear that we only want to correct the measure of job mobility for differences in observation lengths and that it is not our primary interest to build a state of the art model for job mobility. Unexplained variations in the job mobility variable due to model misspecification are substituted back into the equation by the residuals.

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Figure 2 presents histograms of the unadjusted and adjusted job mobility variable. The adjustment to the job mobility variable for the differences in observation lengths result in a smaller variance. This is an immediate result from reducing the variance of the observation length by assuming that we observe all individuals for 52 months. The unadjusted measure of job mobility has an average of 1.06 job transitions per year and a variance of 2.58, which are both rather large. The adjusted measure of job mobility indicate at a lower average of 0.68 job transitions per year and a variance of 0.38. We also present the distribution of the job mobility variables for people we observe less than (and equals to), or more than 12 months (denoted by A2, A3 and B2, B3). Though we explain the rationale of this in the next section, it is important to realize that, by definition, the average level of job mobility is relatively large for people we observe less than 12 months as job mobility is a nonlinear decreasing function in liτ.

3.3.2 Long and short job histories

In the empirical analysis we make a distinction between people we have observed less than (or equal to) 12 months and more than 12 months at time a spell starts. This distinction is important, as both variables indicate a different type of job mobility. According to the job matching theory, changing jobs is considered to be a movement toward a more optimal job match, which should reduce the need for separation. This type of job change is negatively correlated with the need for another job change in the short run.

Since the job mobility variable is a nonlinear (decreasing) function, the average job mobility for people we observe less than 12 months is, by definition, significantly higher than for those we observe longer than 12 months (see Figure 2). For example, consider the first spell of an individual in the job mobility panel. At time this spell starts, the observation length is shortest, say 6 months. The selection criterion we used for the job mobility panel implies that there was as at least one job spell before the current spell. This implies that there was 1 job spell before the first spell and hence in this case the level of job mobility equals 1/6 or 2 job transitions per year. Because of the different type of job mobility, this suggest that a relative high level of job mobility due to a short observation period is negatively related with the unemployment risk. This affects the inference of job mobility with the unemployment risk for people we observe over a longer horizon. Therefore, instead of using one measure of job mobility (i.e., in which all individual levels of job mobility are present) we use two measures of job mobility that discriminates between people we observe less than 12 months and more than 12 months. This can be easily done by specifying:

y1,iτs = yiτs if liτs > 12 0 if liτs ≤ 12 y2,iτs = yiτs if liτs ≤ 12 0 if liτs > 12

where y1,iτs denotes the job mobility measured for people that have been observed for more

than 12 months and y2,iτs for people less than or equal to 12 months. In the following we

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Figure 2: Histograms of the unadjusted and adjusted measure of job mobility.

Note: Figures A1, A2 and A3 are histograms of the unadjusted measures of job mobility, with 1 indicating to the overall measure of job mobility in the sample, 2 to the measure of job mobility for people we observe for less than 12 months and 3 to the measure of job mobility for people observed longer than 12 months. Similarly, B1, B2 and B3 refer to the adjusted measure of job mobility. The measurement scale is number of job rotations per year.

3.3.3 Voluntary and involuntary job mobility

Beside the effect of job mobility on the unemployment risk we are also interested in the effects of voluntary and involuntary job mobility. Though the measures of voluntary and involuntary job mobility can be estimated similar to the regular measure of job mobility we first define what we consider to be voluntary and involuntary.

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the nominator of equation (1) for yv,iτ all have a voluntary exit. Similar reasoning can be

applied for involuntary job mobility. Assuming that there is no relation between whether transitions were made (in)voluntary and the observation lengths, the adjusted measure of (in)voluntary job mobility can be estimated according to,

b y∗_v,iτ = by ∗ iτ yiτ yv,iτ, by ∗ wiτ = b y_iτ∗ yiτyw,iτ. (2)

Althought not presented in this paper, the adjustment had similar impact as to the regular job mobility variable.

3.4 The estimation sample

In this section we define the estimation sample. The data used for the estimation of the job mobility variables involves multiple spells per individual. Some people switch jobs more often and therefore have a relative large number of e → e spells. On the other hand, other people frequently fall into unemployment and therefore have a relative large number of e → u spells. This implies that spells within individuals are dependent, which mechanically reduce the standard errors of the model coefficients. On the other hand, as job mobility is based on the number of past employment spells the endogenous relation with the unemployment risk becomes more entangled and harder to identify. Therefore, to correctly estimate the effect of job mobility on the unemployment risk we randomly select one spell per individual.

Table 3 presents summary statistics for the estimation sample on the number of job spells, average durations and job mobility. We present the statistics for people we observed less than 12 months and more than 12 months, prior to the current spell. Notice that the number of spells now equal the number of individuals in the sample, which are in fact 6097 individuals. 1433 people (24% of the total number of people) have been observed less than 12 months before the current spell and 4664 (76% of the total number of people) individuals more than 12 months. Notice that we are interested in the effect of job mobility for people we observe more than 12 months, which covers about 76% of the sample.

Turning to the fraction of different types of spells relative to the total number of spells within the two groups, we see that they are approximately equally distributed. Only the right-censored spells is somewhat higher in the group of people we observe more than 12 months. The average duration of the e → u spells is shorter than the average duration of the e → e spells. This difference is reasonable since labour contracts are usually signed for one year with possible extensions of another year. Within this period it is easier for the employer to dissolve the contract which increases the probability of unemployment and shortens the job duration. In contrast, e → e may indicate that the employer was satisfied about the productivity of the employee and that there was no need to dissolve the contract. The average duration of e → c spells for people we observe less than 12 months is higher than the average duration of e → c spells for people we observe more than 12 months. This is mainly due to the fact that people we observed more than twelve months have changed jobs relatively recent compared to individuals we observed less than twelve months. Table 3 also presents the average level of job mobility before and after the correction which decrease the mean and standard deviation of job mobility.

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Table 3: Summary statistics for the estimation sample: Spells, durations and job mobility

Number of spells Mean duration Spells (l ≤ 12) (l > 12) (l ≤ 12) (l > 12)

e → e 392 1124 23.44 24.59

e → u 64 188 16.24 17.52

e → c 977 3352 36.12 27.64

Total 1433 4664

Mean Std.Err. Mean Std.Err. Job mobility variables (l ≤ 12) (l > 12) Before correction: Job mobility 2.90 2.84 0.52 0.35 Voluntary 2.84 2.80 0.46 0.30 Involuntary 1.06 2.20 0.20 0.29 Unknown 2.97 2.90 1.13 0.42 After correction: Job mobility 1.14 1.01 0.42 0.26 Voluntary 1.11 1.00 0.37 0.20 Involuntary 0.42 0.81 0.33 0.14 Unknown 1.16 1.03 0.32 0.13

Unemployment periods per year 1.90 1.39 0.42 0.31 Note: l ≤ 12 refers to the group of people we observed less than (and equal to) 12 months prior to the current spell and l > 12 to the group of people we observed more than 12 months. e → e, e → u and e → c denote job spells with exit destinations employment, unemployment and right-censoring respectively.

3 in which we depict the empirical hazard rates for the probability of making a transition to employment and unemployment5 _{We see that the probability of job change is highest after}

12, 24 and 36 months of employment. This may be due to the type of labour contract that is based in most cases on fixed durations. This pattern is less clear for the transition rate to unemployment, but it seems that most people loose their job within the first year. We see a slight peak at 6 and 12 months which is very much likely considering legal dismissal procedures.

3.5 Control variables

This section presents the control variables that are included in the model. The main reason of including these variables is that the observed differences in the exit rates to unemployment (and employment) can be explained by individual characteristics. In other words, to correctly estimate the effect of job mobility we have to take into account the individual specific level of employability. We also refer to this as the worker’s productivity profile. Table 4 contains the summary statistics on all control variables of the estimation sample. For each spell we have several underlying explanatory variables that can be categorized into individual charac-teristics, job characteristics and personal characteristics related to job changes. Notice that in the estimation sample the number of spells equals the number of individuals.

To begin with, the first column of Table 4 describes the individual characteristics. About

5_{Instead of the exit rates one could also depict the survival function. However, we choose the hazard rates}

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Figure 3: The hazard rate for making a transition from employment to unemployment or to another job.

53% of the panel is male and 47% female. The marital status is 58% married and 23% sin-gle. Married people are often older (average age is 34) and have higher requirements (wage, contract type etc.) to new jobs and possibly switch less often than (younger) singles. This is partly due to the fact that married couples also have higher financial responsibilities which are at risk when they change jobs. Therefore they may be considered to be relatively more motivated to avoid unemployment than younger singles. For the same reason, the number of children may as well affect the unemployment risk. 42% of the panel members have one child or more against 31% without children. Also, the level of education may affect the employment risk or unemployment risk. High educated people are often high employable and switch jobs rather easily without intermediate periods of unemployment. The fraction of people with a university or higher vocational degree is 26%. Most people (68%) in the panel have had primary education or a lower vocational degree. Furthermore, we have information on the residence and etnicity of the respondents. People from the South of the Netherlands form the biggest group in the sample (47%). West and East are almost equally balanced (20%, 24% respectively) while only a small number of people from the North are represented in the panel. For the Netherlands most economic activity take place in the West and consequently provide more jobs. Finding a new job will be easier in the West as opposed to other parts of the country.

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peo-ple long term income security. Other labour contracts are pre-fixed, flexible and temporary labour contracts. About 10% of the jobs are contracted with a pre-fixed labour contract. These contracts are in most cases signed for one year, with possible extension to a fixed term contract. 6% to 7% of the jobs have a flexible or temporary labour contract. For employers it is relatively easy to end these kind of contracts within short notice. Therefore, the risk of unemployment is highest for these contract types.

Another job characteristic is firm size. Approximately, the number of individuals working within companies ranging from less than 10 employees to 500 employees or more are equally distributed. Except from firms with 50-100 employees and firms with more than 500 employ-ees, about 20% of the panel is working for a company that employs less than 10, 10-50 or 100-500 people. Large firms may be better able to offer internal career opportunities by which switching jobs (and avoid unemployment) becomes more easily. To capture sectoral effects on the risk of unemployment, we include sector variables as well. As we can see in Table 4, the number of individuals are approximately equally distributed over the different sectors. In this paper we include the following sectors6_{: (1) Business Services and other Services, (2)}

Government, Education and Health Care, (3) Trade, Transport, Communication and Cater-ing Services and (4) Agriculture, Industry and Construction.

We also include variables that represent whether the last labour market transition was made voluntary or involuntary and internal or external. This is important since these variables capture the individual specific motive of making a transition to the current spell. and it may reflect how long they will stay in this job. One may argue that, in case the last job transition was made voluntary, the current job is in some way better than the previous one, which makes future job switching less likely and reduce the unemployment risk. If the current job resulted from an involuntary job transition, the job is more likely not to last forever and end in unemployment or a better job. From Table 4 we see that 62% of the jobs are a result of a voluntary transition, 16% of an involuntary transition and for 22% we don not know the underlying personal motive of transition. Furthermore, we also know whether the job resulted from an internal or external job transition. Though the effect on the unemployment risk is less clear, internal transitions may indicate at higher employable people since the employer offered them job opportunities within the firm. Nevertheless, external job transitions may also indicate at well employable people. External job transitions may indicate at a relative high level of search capital. Apparently, the individual managed to find another job that according to the job search theory is most likely a better match.

People’s motivation to stay in the current job is measured by job satisfaction. The figures in Table 4 show that the fast majority of people (about 80%) is satisfied or highly satisfied with their current job. A high job satisfaction indicates that people are (more than) satisfied in their current job and probably they are eager to keep their job. It may also indicate at high employable workers that employers will not quickly dismiss.

Finally, more refined measures of employability are the variables that indicate whether one has a weak relation between job and former education and whether one is well employable in another function. 13% of the panel members answer that their current job is weakly related to their education. This may work both ways. One explanation is that the job in which they

6

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are currently employed is well suited and the former education was in some way a wrong choice. The other one is that the current job is just temporary and in the meanwhile, they maybe are looking for a better match. Despite the fact that we do not have this information it may be argued that a weak relation between job and education indicates at higher unem-ployment risk and employability risk. In case the variable measures the first effect, people with a strong relation between work and education should be considered more employable than people with a weak relation between job and education. In case of the second possibility, the variable indicates that the current job is temporary and, in some way, is more likely to end in unemployment or in another job. The other employability variable measures whether one is well employable in another function. These people should be better in finding another job and hence become less frequently unemployed. About 31% op the panel answer that they are well employable in another function.

One final remark concerns the way in which the variables enter the empirical model. All cat-egorical variables enter the model as a time constant dummy variable. For each catcat-egorical variable we define a category ’unknown’ in order to maintain as much observations as possi-ble. Other variables, such as the job mobility variables, age, wage rate and macro economic variables, enter the model as a time constant variable, measured at the beginning of the spell.

4 Modeling approach

This section presents the empirical model. In Section 2.2 we already made clear that the model we use is a member of the class of MPH models. We refer to Lancaster (1990) for an excellent introduction to duration analysis and MPH models. More advanced topics are covered in Van den Berg (2001).

This section gives a more detailed formulation of the MPH model used in this paper. First, in Section 4.1 we explain the basic concept of duration analysis. In Section 4.1.1 we explain how we model competing risks. In Section 4.2 we show how unobserved heterogeneity enter the model. Finally, in Section 4.2.1 we present the assumptions made on the parametrization of the model.

4.1 Basic concepts

A good way to introduce the model is to start with its most simplest form. Consider an employment spell with its duration to be stochastic and denoted by T . Assume, for the time being, that only a transition can be made to unemployment, or otherwise, stay employed. The probability that a person who was employed for a time t makes a transition to unemployment in the short interval of length dt after t equals P (t ≤ T < t + dt|T ≥ t). The conditioning event T ≥ t implies that this person is still employed at time t. If we divide this probability by dt and let dt → 0, we get the average probability of unemployment at time t over a short time period after t:

θ(t) = lim

dt→0

P (t ≤ T < t + dt|T ≥ t)

dt ,

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Table 4: Panel characteristics of the estimation sample

Individual characteristics % Job characteristics % Personal motives % Gender Labour contract Last transition voluntary

male 53 fixed 63 yes 62

pre-fixed 10

Marital status flexible 6 Last transition internal

married 58 temporary 7 yes 34

single 23 unknown 13

living with partner 14 Job satisfaction

divorced 3 Firm size very high 35

widow 1 [1, 10) 18 high 44

[10, 50) 23 low 7

Number of children [50, 100) 10 very low 1 no children 31 [100, 500) 19 unknown 13

1 child 13 [500, ∞) 11

2 children 21 unkown 18 Weak relation between work and education

3 children 7 yes 13

4 children 1 Self-employed

5 children or more − without employees 3 Well employable in other function

unknown 26 with employees 1 yes 31

manager 26 Education primary 37 lower vocational 30 higher vocational 19 university 7 secundary education 6 unknown 1 Region South 47 West 24 East 20 North 9 Etnicity Dutch 62 unknown 31 Western immigrant 6 non-Western immigrant 2

Other control variables Mean Std. error

Age 34 10

Hourly wage 23 19

GDP 2.76 1.25

Unemployment rate 5.12 1.25

N 6097

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(cdf) of T :

θ(t) = f (t)

S(t) (3)

with S(t) ≡ 1 − F (t) called the survival function, since it denotes the probability of staying employed until and including time t. The relation in equation 3 connects the three major building blocks in duration analysis: the hazard function, survival function and the pdf of the duration variable T . Since f (t) = −dS(t)/dt, equation 3 is a differential equation in t. The solution of this differential equation, subject to the initial condition S(0) = 1 is

S(t) = exp − Z t 0 θ(s)ds . (4)

From equation 3 and 4 the density of T can be written as f (t) = θ(t) exp − Z t 0 θ(s)ds . (5)

Note that the hazard fully characterize the distribution of T . The most simple parametric form for the pdf of T is the Exponential distribution. As already mentioned in Section 2.2, the Exponential distribution is often too restrictive on the shape of the hazard as the hazard is assumed to be a constant γ that does not vary with t. From equation 4 it follows that S(t) = exp(−γt) and f (t) = γ exp(−γt).

The class of proportional hazard (PH) models model the hazard rate proportional to a baseline hazard. The variations in the individual transition probabilities can be explained by the elapsed duration and by individuals’ characteristics x. More formally,

θ(t|x) = λ(t) exp(x0β) (6)

where λ(t) is the so-called baseline hazard with scale factor exp(x0β), β is a vector of param-eters and x a set of regressors. This specification of the hazard is called a PH model because exp(x0β) has a multiplicative effect on the baseline hazard and is not an explicit function of t. This implies that the shape of the hazard is the same for each individual, while the level of the hazard may vary between individuals.

The model in equation 6 is the corner stone in many empirical analysis of durations. Many different distributional assumptions on the shape of the hazard have been studied (we already discussed this in section 2.2). In general, there is no clear preference for the type of distribu-tion unless one has specific prior informadistribu-tion on the shape of the hazard. Moreover, in case we consider the durations to have multiple exit destinations, the corresponding hazards may all have a different underlying distributions. Since we only observe realizations of the joint distribution, the marginals are almost impossible to identify. A good alternative is to use a semi-parametric approach in which the hazards are assumed to be constant within predefined intervals and model the dependence structure between the marginals by means of a unob-served heterogeneity distribution. Before explaining this further, we first show how to model durations with multiple exit destinations.

4.1.1 Competing risks

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variables is latent. For example, in the above we assumed that only a transition can be made from employment to unemployment. However, beside of the risk of unemployment one also faces the risk of making a transition to employment and possibly avoid unemployment, see also Section 2.2. More formally, consider the destination states e (employment) and u (unemployment). We define the random variables Te and Tu for the time being employed

and exit to e or u respectively. Only T = min{Te, Tu} is observed. Let θe(t|x) be the

hazard of Te and θu(t|x) be the hazard of Tu and assume that Teand Tu are independent (an

assumption that will be relaxed later on). The probability that a person makes a transition to unemployment in the short interval of length dt after t equals

P (t ≤ Tu < t + dt, Te≥ t + dt|x) = θu(t|x) exp − Z t 0 θu(s|x)ds − Z t 0 θe(s|x)ds dt. Let de be a dummy variable with de= 1 if a transition is made to employment and du = 1 if

a transition is made to unemployment. Then we may write the joint pdf of T in terms of the dummy variates de, du and T :

Suppose we observe mu spells that exit to u and me spells that exit to e. Let k denote the

spell under consideration. Then the log likelihood can be expressed as

mu X k=1 dulog θu(tk|x) + log Su(tk|x) + me X k=1 delog θe(tk|x) + log Se(tk|x). (8)

Note that if du = de = 0 the corresponding duration is right-censored but contribute to the

log-likelihood through both survival functions. The log-likelihood is a function of the unknown θi functions and the β vector of unknown parameters. Also note that the log-likelihood can

be written in two separate log-likelihood functions, one for each destination state. This is a result of the assumption of independence between Te and Tu. We relax this assumption in

the next section.

4.2 The empirical model

In the previous section we explained the basic PH model and how to model competing risks. In this section we present the empirical model which is used to estimate the effects of job mobility on the unemployment risk. The PH model with competing risk can be extended to allow for measurement errors in the dependent variables as well as omitted unobserved covariates by including unobserved heterogeneity, (see Lancaster (1990)). This is the class of the so-called mixed proportional hazard (MPH) models.

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for each destination state with unobserved heterogeneity distribution G(vu, ve).

Let the transition rate from employment to u or e at t conditional on x and v to be denoted by θu(t|x, vu) and θe(t|x, ve) respectively. As in section 4.1, we assume the hazard functions

of Te and Tu to satisfy the following condition:

θi(t|x, vi) = λi(t) exp(x0β)vi, i = e, u. (9)

This is called the Mixed Proportional Hazard model (MPH). Recall from Section 4.1.1 that we observe T = min(Tu, Te) which are realizations of the joint distribution of Tu and Te. Let

fu and fe denote the pdf of Tu and Te respectively. We can write the (conditional) joint pdf

of T in terms of fu and fe using the indicator variables du and de that indicate whether a

transition was made at t to unemployment or employment. Assuming that Tu and Te are

independent conditional on x, ve and vu the joint pdf of T conditional on x and v can be

between the hazards θu and θe is by way vu and ve are related. In other words, if vu and ve

are dependent, Tu and Te are dependent conditional on x. In case of independence of vu and

ve, the MPH model reduces to two unrelated MPH models, one for each destination state

u, e. In order to construct the log-likelihood function, we derive the joint pdf of T conditional on x by integrating over the mixing distribution G(vu, ve):

f (t|x) = Z vu Z ve fu(t|x, vu)dufe(t|x, ve)dedG(vu, ve). (11)

Suppose we observe mu spells that exit to u and me spells that exit to e. Let k denote the

spell under consideration. The log-likelihood can now be written as:

LN = Z vu Z ve (_m u X k=1 dulog θu(tk|x, vu) + log Su(tk|x, vu)+ me X k=1 delog θe(tk|x, ve) + log Se(tk|x, ve) ) dG(vu, ve). (12)

In order to estimate the log-likelihood function we have to decide upon a functional form for the hazards θu, θe and the mixing distribution G. We discuss this in the following section.

4.2.1 Parametrization

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numbered κ = 1, 2, . . ., with a parameter λtκ assigned to each interval such that the baseline hazards in θi, i = e, u are: λi(t) = X κ=1,2,... λiκIκ(t) (13)

where t denotes the elapsed duration and Iκ(t) is an indicator function that equals 1 when

t lies in the interval κ and zero elsewhere. Notice that this approach requires to estimate twice the number of κ parameters since we consider two hazards functions. By examining the Kaplan Meier estimates in Figure 3 we choose 6-monthly intervals: 0-6, 6-12, 12-18, 18-24, 24-30, 30-36, 36-42, 42-48, 48-54, 54+.

For the mixing distribution G we specify a discrete distribution with a finite number of mass points. Let ve1 and ve2 be the points of support of veand vu1and vu2be the points of support

of vu, with probabilities pe1u1, pe1u2, pe2u1 and pe2u2 according to:

pu1e1 = P (vu= vu1, ve= ve1)

pu2e2 = P (vu= vu2, ve= ve2).

In case there are no unobserved individual specific effects that can be related to the observed differences in the transition rates to unemployment or employment, the model reduces to two unrelated MPH models (see also the previous section or Van den Berg et al. (1996)). In fact, we have that vu1 = vu2 and ve1 = ve2. This implies that (for single spell data) individual

specific effects can only be identified if the exit rates are dependent. The dependence between the exit rates is induced by the covariance matrix of v:

Cov(vu, ve) = (pu1e1pu2e2− pu2e1pu1e2)(vu1 − vu2)(ve1− ve2).

Notice that this is a less restrictive assumption than we made in section 4.1.1 in which we assumed that Teand Tuare independent conditionally on x. In the current setting we allow the

hazards to be dependent by means of their heterogeneity distribution. In other words, θu and

θe are independent if and only if vu and ve are independent, which implies Cov(vu, ve) = 0

or pu1e1pu2e2 = pu2e1pu1e2. Similarly we have that θu and θe are dependent if and only if

Cov(vu, ve) 6= 0.

In the maximum likelihood procedure we prevent the hazard to be negative by restricting the location parameters ve and vu by replacing them with exp(ve) and exp(vu). Further, to

prevent the associated probabilities to lie in the unit interval we specify, pe1u1 = exp(γ1)/[1 + exp(γ1) + exp(γ2) + exp(γ3)]

pe1u2 = exp(γ2)/[1 + exp(γ1) + exp(γ2) + exp(γ3)]

pe2u1 = exp(γ3)/[1 + exp(γ1) + exp(γ2) + exp(γ3)]

pe2u2 = 1 − pe1u1pe1u2 − pe2u1,

where γ1, γ2 and γ3 may vary form −∞ to +∞. The maximization of the log-likelihood

can be done numerically. We included a Stata code for the maximum likelihood procedure in Appendix C. The standard errors of pe1u1, pe1u2, pe2u1, pe2u2 and Cov(vu, ve) can be calculated

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5 Estimation results

This section presents the estimation results. We use the competing risk model presented in section 4.2 and parametrized according to section 4.2.1. As part of a sensitivity analysis, we compare the results with estimates found in case we do not control for unobserved hetero-geneity. This model is referred to as model 1. The model that does control for unobserved heterogeneity is denoted by model 2. First, we specify both models by including the control variables x and the regular (adjusted) job mobility variables (specification A). We expect that job mobility is positively related with employability, meaning that individuals with a high level of job mobility have a lower probability of making a transition to unemployment and are more likely to switch jobs. This means that the sign of the coefficient of job mobility is expected to be negative. Secondly, we investigate whether the effects of job mobility can be related to voluntary and involuntary job mobility. Instead of using the regular (adjusted) measure of job mobility we use the measure of job mobility that discriminates between vol-untary and involvol-untary job mobility (specification B ). We expect that volvol-untary job mobility and employability are positively related, whereas involuntary job mobility is more likely to tear down human capital and increase the unemployment risk.

Before we present the estimation results, we comment on the following. We comment on the results in terms of the model coefficients. We could however also comment in terms of the marginal effects of one of the underlying regressors (i.e. job mobility) on the probability of unemployment or on the mean duration of an ‘average individual’. Since we are mainly interested whether there exist a significant effect of job mobility on the unemployment risk we interpret the results by the model coefficients. Secondly, in total we use a 48 control variables, which implies that for model 1A the total number of unknown parameters equals 122 (for each risk we have 48 control variables, a constant, 10 hazard parameters and two job mobility variables7) and for model 2A we have 131 unknown parameters (instead of the constants we have four mass points and three associated probabilities). For the models with the measure of voluntary and involuntary job mobility, we have instead of one job mobility variable three job mobility variables (voluntary, involuntary and unknown). The total unknown parameters then amounts to 126 for model 1 and 135 for model 2. In order to maintain readability we present the results in five separate tables.

This section is organized as follows. First, we present the main results in section 5.1, which are the effects of job mobility and the effects of (in)voluntary job mobility. We comment on the estimates of the model parametrization in section 5.2. At the end of this section we present the estimates of the control variables.

5.1 Effects of job mobility on the unemployment and employment risk

Table 5 presents the estimation results. First we estimate the effects of job mobility on the unemployment risk and employment risk (specification A). Thereafter, we estimate the effect of voluntary and involuntary job mobility (specification B). We use the same set of control variables in each estimation.

We find that job mobility (l > 12 months) has a positive effect on the unemployment risk. In other words, people with a high level of job mobility have a higher probability to make a transition to unemployment than people with a low level of job mobility (model 1,

Eﬀects of job mobility on the unemployment risk

Effects of job mobility on the unemployment risk

Acknowledgments

Contents

1

Introduction

2

Theoretical framework

3

Data description

4

Modeling approach

5

Estimation results