Labour mobility of unemployed workers

Regional Science and Urban Economics 32 (2002) 359–380 www.elsevier.com / locate / econbase

Labour mobility of unemployed workers Juha Kettunen* ¨ Turku Polytechnic, Sepankatu 3, FIN-20700 Turku, Finland Received 4 June 1999; received in revised form 17 April 2001; accepted 13 June 2001

Abstract In this study the mover–stayer models of transition intensities and labour mobility are examined using Finnish microeconomic data on unemployment durations. Duration models are used to analyse the probabilities of transition. The probabilities of becoming employed, moving to another region and changing occupations are estimated using censored data on unemployment durations. The models are based on a Gompertz distribution, which yields estimates of the proportion of unemployed persons who become employed, move or change occupations. Allowance for neglected heterogeneity is made assuming that the effect of omitted variables has a gamma distribution across persons.  2002 Elsevier Science B.V. All rights reserved. Keywords: Labour; Mobility; Unemployment JEL classification: J64

1. Introduction This study is concerned with the estimation of transition intensities in the labour market using microeconomic data. The work is motivated by the study of Theeuwes et al. (1990), who estimated the transition intensities between three basic labour market states: not in the labour force (non-participation), employment and unemployment. Each of these states has two transitions. Using Dutch data, *Corresponding author. Fax: 1358-10-553-5791. E-mail address: [email protected] (J. Kettunen). 0166-0462 / 02 / $ – see front matter  2002 Elsevier Science B.V. All rights reserved. PII: S0166-0462( 01 )00083-7

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Theeuwes et al. estimated six models of transitions between these states and one model allowing for transitions between different jobs. The problem with estimating models for all these transitions is that some transitions are observed only a few times or not observed at all. Discrete choice models of leaving a state have often been used to analyse transition intensities. The choice between non-participation and participation in the labour market is the basis for studies of the supply of labour. The two-state estimation procedure is usually used to model the supply of labour. The first stage is discrete choice estimation of the probability of entering the labour force. The second stage is estimation of working hours using the model of ordinary least squares (Heckman, 1976, 1979). Models of becoming employed have been widely studied in the literature on job search theory. Atkinson and Micklewright (1991) argue that the state of nonparticipation should be incorporated in models of the labour market. However, not many studies have dealt with the well-known and important feature of unemployment that some persons will not return to work. Some of these may be discouraged workers who have stopped looking for a job. There are many ways out of formal unemployment, including early retirement, disability, maternity leave and training programmes. Van den Berg (1990) has allowed for transitions from unemployment to non-participation. He has estimated a model of unemployment duration using information on non-participation. Such data are not, however, available for this study. The procedure presented in this paper differs from earlier attempts. This study shows that complete information on the state of destination is not necessarily needed and it provides alternative models to estimate transition intensities from unemployment to employment and non-participation. Models of unemployment duration are used here because exact durations contain more information than 0–1-valued indicators. The proportions of the persons who become employed, move and change occupations are estimated from data in which the information on the length of unemployment is censored. This procedure differs from traditional competing risk models. Re-employment with regional and occupational mobility has four distinct alternatives: to accept a job within the same region and occupation, to move keeping the previous occupation, to switch to a different occupation within the same region, or to switch to a job in a different occupation and region. In principle, the traditional competing risk models can be applied. The last alternative is so rare in practice that very large data sets are needed to get enough observations and reasonable results. However, such a large data set is not available in this study. The censoring indicators are defined in the three different models to indicate persons who became employed, persons who moved to get a job and persons who changed their occupations to get a job. If some unemployed persons never return to work, there are some technical requirements for the distribution of unemployment durations. The distribution

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should allow for the probability of becoming employed to be low enough for some of the individuals that they will never become employed. It means that the survivor function should allow the possibility of its asymptotically decreasing to a positive value instead of to zero. Defective distributions give estimates for the proportion of persons who become employed, move or change their occupations. A Gompertz distribution allows for the defectiveness, which is not assumed a priori. In mover–stayer terminology, movers become employed but stayers will not find acceptable offers. The hazard rate is low enough for the stayers so that they get trapped and will never become employed, move or change occupations. Models of unemployment duration and regional and occupational mobility are estimated using Finnish microeconomic data. The same mover–stayer model is applied to an empirical study of different situations of moving and staying. The time between the dates of becoming unemployed and employed is the duration variable of interest in the model of unemployment duration. The time between the date of becoming unemployed and the dates of exit from unemployment by moving and changing occupations to become employed are the duration variables of interest in models of regional and occupational mobility, respectively. Analogously to biological studies the Weibull model has been used for modelling total mortality (e.g. Burch et al., 1973) and the Gompertz model for cause-specific mortality (e.g. Dix et al., 1980). The analogy is obvious, because some unemployed workers move or change occupations in order to become employed. This study is organised as follows. Section 2 presents a job search model with labour mobility. In Section 3 the properties of the Gompertz distribution are discussed. In addition, the log-likelihood functions are derived assuming that the effect of omitted variables has a gamma distribution across persons. In Section 4 the data of this study and the results of estimations are presented. Finally, Section 5 summarises and concludes the study.

2. Job search with labour mobility Assume that an unemployed person gets utility from consumption C and leisure L and that there is no saving. The utility of an unemployed person is u 0 (C, L), where C consists of unemployment insurance (UI) benefits b minus the costs of search. Leisure is the time not spent in job search so that L 5 1 2 s, where s is the search intensity. If an individual is unable to find a job within the local labour market area, a suitable job may be found elsewhere; or if he is unable to find a job within his occupation, he may change it. The arrival rate of job offers from area i and occupation j is assumed to follow a Poisson process with intensity a ij (s), which is a function of time spent on search. It is assumed that a ij (0) 5 0, ≠a ij / ≠s . 0 and ≠ 2 a ij / ≠s ≠s # 0. Moving from an area of declining industries and high unemployment to a region

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with growing employment or changing occupations will involve costs. These costs are measured in utility terms. It is assumed that the model includes the searching costs c, the visiting costs c i to an area i, the permanent cost of becoming employed c j and the moving costs c mi . The cost c j is a permanent loss in utility of a person who changes his occupation. The cost c is deterministic whereas c i , c j and c im are probabilistic. The costs are of the flow type, apart from c im , which is of the lump-sum type. For simplicity infinite search horizon is assumed. The value function can be written as follows: u¯

5

V 5 u 0 (b 2 c 2 SS a ij c i , 1 2 s) 1 SS a ij

E [(u 2 c ) /r 2 c j

m i

6Y

2V ] dF(u)

u ij

r,

(1) where u ij is the reservation utility of occupation j in area i, u¯ is the maximum attainable utility, r is the subjective rate of time preference and F(u) is the distribution function of utility. The offers that are at least u ij are acceptable. The necessary condition for the optimal u ij can be solved by setting ≠V/ ≠u ij 5 0, which gives V 5 (u ij 2 c j ) /r 2 c im .

(2)

Thus the expected value of continuing the search, i.e. the value function, is equal to the utility of an acceptable offer minus the permanent cost discounted over the search horizon net of the moving cost. The fundamental equation for the reservation utility is solved by inserting Eq. (2) into Eq. (1), which gives u¯

m i

u ij 5 u 0 (b 2 c 2 SS a ij c i , 1 2 s) 1 c j 1 rc 1 SS a ij

E (u 2 u ) dF(u) /r, ij

(3)

u ij

where the comparative static results can be solved. Summarizing the comparative static properties of the reservation utility, the following results are obvious. The reservation utility u ij is (a) a decreasing function of the searching cost c and visiting cost c i , (b) an increasing function of the unemployment insurance (UI) benefits b, arrival rate of job offers a ij , permanent cost of re-employment c j and moving cost c mi , improvement of offer distribution and uncertainty of job offers. The effect of the subjective rate of time preference r is generally ambiguous, but numerical simulations show that the reservation utility is nearly always a decreasing function of r (Kettunen, 1992). Another decision variable of the model is the search intensity s. An unemployed person’s objective is to maximize the expected discounted utility by choosing a

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search intensity relative to the acceptance rule of job offers. The necessary condition for the optimal search intensity is obtained by differentiating V in Eq. (1) with respect to the search intensity. The derivation of the comparative static results is complicated by the fact that the necessary conditions involve not only endogenous and exogenous variables but also the value function. The endogenous variables are affected by exogenous variables directly and indirectly via the change in the value function. The results can be solved by implicit differentiation. The following results are obvious. The search intensity is (a) a decreasing function of the UI benefits b, the permanent cost of reemployment c j , the moving cost c mi and the subjective rate of time preference r, (b) an increasing function of searching cost c, arrival rate of job offers a ij , improvement of offer distribution and uncertainty of job offers. The effect of the visiting cost c i is generally ambiguous (Kettunen, 1992). The hazard function is a product of the arrival rate and the probability that an offer is acceptable h 5 SS a ij (s)(1 2 F(u ij )).

(4)

The hazard of moving is obtained by assuming that the moving cost c mi is positive. Correspondingly if the cost of changing occupations c j is positive, h defines the hazard of changing occupations. The hazard function is affected by two endogenous variables; the reservation utility and search intensity. Both of them have to be taken into account when examining the effects of exogenous variables on the hazard function. Summarizing the effects of exogenous variables on the hazard function, the following results are obvious. The hazard function is (a) a decreasing function of the UI benefits b, permanent cost of re-employment c j and moving cost c im , (b) an increasing function of the searching cost c. The effects of the arrival rate of job offers a ij , visiting cost c i , subjective rate of time preference r, and improvement and uncertainty of job offers on the hazard function are generally ambiguous (Kettunen, 1992). It is reasonable to assume that the permanent loss of utility of a person who changes his occupation c j is small in similar occupations. If the occupations differ much from each other we could expect that people change occupations more seldom. This hypothesis is investigated in the empirical analysis. Using a search model with a finite search horizon it can be argued that the hazard function decreases during the last years due to the lump sum type of moving costs. The moving costs may be so large that the expected income cannot compensate for them. Hence if the moving costs are significant we could expect that the age of an unemployed person has a negative effect on the re-employment probability.

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3. Parametric models of unemployment duration

3.1. Gompertz distribution Let us consider independent pairs of independent random variables T and Z, where T is the duration variable of primary interest and Z is a censoring variable. The duration of unemployment is defined as the difference between the date of entry into unemployment and the date of becoming employed. A duration or a censoring time is observed, t 5 min(T, Z), with c being an indicator of complete periods of unemployment. If T , Z, then c 5 1 and otherwise c 5 0. In the cases of regional and occupational mobility the random variable T is defined as the duration of unemployment between the date of entry into unemployment and the date of exit due to moving or changing occupations in order to get a job. The models of transition intensities are specified in terms of the hazard function. A generic form for the likelihood contribution of parametric duration models with censored data is written as l(t) 5 h(t)c exp[2I(t)], where h(t) is the hazard and I(t) is the integrated hazard. A commonly applied specification is the proportional hazards model, where the hazard function factors into the product of a function of duration t and a function of the regressors x. The hazard is written as h(t) 5 h 0 (t)h 1 (x), where h 0 (t) is called the baseline hazard. The baseline hazard of a Gompertz distribution is h 0 (t) 5 exp(tu ). The hazard function of the two-parameter Gompertz distribution can be written as follows h(t) 5 j e tu .

(5)

The hazard function varies as an exponential function of time starting from j . The explanatory variables x are introduced into the model in log-linear form j 5 exp(xb ), where b is a vector of the structural parameters. The integrated hazard of the Gompertz distribution can be written as follows I(t) 5 e x b (e tu 2 1) /u.

(6)

The survivor, density and hazard functions can then be written as follows S(t) 5 e 2e

x b (e tu 21) / u

f(t) 5 e x b 1tu 2e h(t) 5 e x b 1tu .

x b (e tu 21) / u

(7)

(8)

(9)

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The shape of the survivor function of the Gompertz model is investigated by considering its limits as duration approaches infinity: xb If u , 0, then lim t →` S(t) 5 e e / u If u . 0, then lim t →` S(t) 5 0. These limits give the estimates for the proportion of individuals who will never become employed, move or change occupations in order to get a job. To write the likelihood functions and estimate the unknown parameters, the hazard functions and integrated hazards of the two models presented are substituted for the log-likelihood contribution. The log-likelihood function of the Gompertz model can be written as

O [c (x b 1 t u ) 2 e N

L(u, b ) 5

i

i

i

xi b

(e t iu 2 1) /u ],

(10)

i 51

where N is the number of individuals in the sample. L(u, b ) is maximised with respect to the unknown parameters u and b. The data consist of the duration of unemployment measured in weeks t i , indicators c i and explanatory variables x i , i 5 1, . . . ,N.

3.2. Gamma mixing distribution Unobserved heterogeneity has been widely discussed in the econometric literature following the pioneering study of Lancaster (1979). He found that the estimated parameters are biased towards zero if the unobserved heterogeneity is not controlled for, and he assumed a parametric functional form for the pattern of unobserved heterogeneity. The method of correcting for omitted variables using the gamma mixing distribution has been widely used with exponential and Weibull duration distributions (e.g. Kooreman and Ridder, 1983; Newman and McCulloch, 1984; Narendranathan et al., 1985). An advantage of the gamma mixing distribution is that the log-likelihood function can be expressed in a closed form. In this study the assumption of gamma distributed unobserved heterogeneity has been extended to the Gompertz distribution. Heckman and Singer (1984a,b) have shown that estimates of structural parameters may be sensitive with respect to the parametric forms assumed for heterogeneity. They proposed a discrete pattern of heterogeneity for the incorporation of unobserved heterogeneity into duration models. This approach was successfully applied with the Weibull distribution (Kettunen, 1996b). The parameter estimates of the Weibull model with the gamma mixing distribution and the discrete mixing distribution lead to rather similar results. The approach of the discrete mixing distribution was not successful with the Gomperz distribution. The problem seems to be that one mass point approaches infinity, leading to numerical overflows in the estimation.

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The survivor, density and hazard functions with the gamma mixing distribution can be written as 1 Sg (t) 5 [1 1 s 2 I(t)] 21 / s

2

(11)

fg (t) 5 h(t)[1 1 s 2 I(t)] 21 / s

2 21

(12)

21

2

h g (t) 5 h(t)[1 1 s I(t)] ,

(13)

where I(t) is the integrated hazard of the original Gompertz distribution (6). After allowing for gamma heterogeneity, the limits of the survivor functions can be written as follows: 2 If u ,0, then lim t →` Sg (t) 5 [1 2 s 2 e x b /u ] 21 / s . If u .0, then lim t →` Sg (t) 5 0. These limits give the final estimates for the proportion of individuals who will never become employed, move or change occupations to get a job. The log-likelihood function of the Gompertz model with gamma heterogeneity can be written as

O hc (x b 1 t u ) 2 (c 1 1 /s ) log[1 1 s N

2

L(u, b, s ) 5

i

i

i

i

2

e x i b (e t iu 2 1) /u ]j,

i 51

2

which is maximised with respect to the unknown parameters u, s and b.

1 Unobserved heterogeneity is characterised by an unobserved component v. The hazard function conditional on v is h(tuv) 5 vh(t). Appropriate marginal functions are needed. A simple procedure is to first derive the survivor function marginal with respect to v. It can be written as follows `

Sg (t)5

Ee

2vI(t )

g(v) dv,

2`

where it is assumed that v has a gamma density

cm g(v)5 ]] v m 21 e 2 c v G( m)

`

E

with G ( m )5 w m 21 e 2w dw. 0

It is natural to normalise the expected value E(v) 5 m /c to one. This is done simply by setting c 5 m. A change of variables w 5 v[ m 1 I(t)] can be used in the integration. Differentiation of the marginal survivor function gives the needed density function. The marginal hazard function is obtained as a ratio of the density function and the survivor function. The variance of the unobserved heterogeneity, s 2 5 1 /m, is estimated.

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4. Transition intensities from unemployment

4.1. Description of the data on unemployment durations Finnish data on 2077 unemployed persons were used to analyse the transition intensities to employment and labour mobility. The data were compiled for this study from the administrative files of the Ministry of Labour. The duration of unemployment was calculated in weeks as the difference between the date of entry into unemployment and the date of becoming employed. Every hundredth worker was picked from those who became unemployed during 1985. These individuals were followed until the end of their unemployment but no later than the end of 1986. The data include 40% censored observations. The information on the unemployment benefits paid out during the periods of unemployment was obtained from the files of the Social Insurance Institution and Postipankki (the state-owned postal bank). The information on taxable assets and income was compiled from the administrative tax register. The data were also used to analyse the effects of unemployment benefits (Kettunen, 1993, 1994a,b, 1996a) and the effects of education on the duration of unemployment (Kettunen, 1994a, 1996b). Unfortunately there is no information on the reasons why some persons did not become employed, move or change occupations. Nor is there any information on the search activity of these persons. There are two systems and therefore two kinds of unemployment benefits in Finland. The basic unemployment allowance is financed wholly by the state and paid by the Social Insurance Institution. It is means tested. Persons who are in need of financial assistance are eligible for the allowance. The earnings-related unemployment allowance exists for workers in all industries and is paid by UI funds, which are administered mainly by labour unions. The UI funds and hence the earnings-related unemployment allowance is available to non-trade union members. The earnings-related unemployment allowance is financed by the state, employers and employees. It is paid to unemployed persons who have been members of UI funds for at least 6 months and who have been working during that time. The rules of the system imply that unemployed persons without work experience or who wish to return to the labour force from housework are not eligible to receive this allowance. Nearby all the UI funds pay the allowance through the Postipankki, which gave the information for the research on the earnings-related unemployment allowances during the unemployment periods. Table 1 presents descriptive statistics of the data on unemployed workers. Means, standard deviations, minimums and maximums of the data have been calculated in order to get a preliminary overview of the data. Unfortunately the sample statistics and those of the population cannot be compared, because there are no aggregate inflow data available in Finland. The replacement ratio for each worker was calculated as an average of the period of unemployment. The average in Table 1 was calculated for individuals.

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Table 1 Descriptive statistics of the data on unemployed workers

Unemployment duration, weeks Replacement ratio of UI benefits Member of UI fund, 15yes Number of children Married, 15yes Sex, 15male Age, years Education, 15at least 12 years Training for employment, 15yes Came from schooling, 15yes Came from housework, 15yes Regional demand, V/ U ratio Occupational demand, V/ U ratio Taxable assets, millions of FIM

Mean

S.D.

Minimum

Maximum

15.06 0.16 0.42 0.23 0.37 0.53 31.14 0.45 0.15 0.14 0.07 0.11 0.12 0.01

18.05 0.21 0.49 0.62 0.48 0.50 11.94 0.50 0.36 0.34 0.26 0.13 0.05 0.03

0.14 0.00 0.00 0.00 0.00 0.00 14.00 0.00 0.00 0.00 0.00 0.02 0.07 0.00

104.23 0.90 1.00 5.00 1.00 1.00 64.00 1.00 1.00 1.00 1.00 0.42 0.23 0.54

The number of observations is 2077.

The replacement ratio is rather low. One reason is that about 42% of the persons did not get any benefits. Some of these did not get any benefits because the basic unemployment allowance is means tested. It is suspected that some persons did not even apply for the benefits, because they were not eligible for them. Unfortunately the data set does not have information about that. Another reason for the low replacement ratio is that some of the workers became employed during the first few weeks of unemployment including the 5-day waiting period of benefits. About 42% of the workers were members of UI funds. Membership in a UI fund is one requirement for the earnings-related unemployment allowance. The rest of the workers are eligible for the basic unemployment allowance if they fulfil the stipulated requirements. According to the figures the unemployed workers were most often single men and had rather few children to take care of. Usually unemployed workers were rather young. Their average age was about 31 years. The indicator of the level of education in the data corresponds to the compulsory basic education and the secondary education, which Finnish children complete at age 18–19. Most of the workers had a rather low education, because only 45% of them had not the criterion level chosen for the indicator. About 15% of the workers had received training for further employment before their unemployment. It is not known from the data when they got this training. About 14% of the unemployed workers came from schooling and 7% came from housework. Regional and occupational demand are measured using the unemployment / vacancy ratios (U / V-ratios) in the 12 major labour districts of Finland defined by the Ministry of Labour. They measure the tightness of the labour market.

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According to the figures there were on average about ten unemployed workers for each vacancy in the employment offices. Their taxable assets were rather low. One reason for this is that the unemployed persons were rather young.

4.2. Re-employment The results of estimations regarding the model of unemployment duration are presented in Table 2. The replacement ratio of UI benefits significantly decreases the probability of re-employment. The result gives support to the disincentive Table 2 Gompertz models of unemployment duration (A) Constant Replacement ratio of UI benefits Member of UI fund, 15yes Number of children Married, 15yes Sex, 15male Age, years Education, 15at least 12 years Training for employment, 15yes Came from schooling, 15yes Came from housework, 15yes Regional demand, V/ U ratio Occupational demand, V/ U ratio Taxable assets, millions of FIM

u

(B) 21.639 (0.132) 21.232 (0.157) 0.208 (0.064) 20.001 (0.054) 0.147 (0.069) 20.011 (0.060) 20.039 (0.003) 0.044 (0.062) 0.183 (0.077) 0.278 (0.082) 20.649 (0.135) 0.113 (0.242) 0.563 (0.627) 0.765 (1.115) 20.023 (0.002)

s2 Log-likelihood

24931.8

21.363 (0.181) 21.533 (0.197) 0.258 (0.078) 20.005 (0.063) 0.148 (0.082) 20.031 (0.072) 20.046 (0.005) 0.051 (0.075) 0.226 (0.094) 0.300 (0.101) 20.742 (0.154) 0.155 (0.278) 20.352 (0.761) 0.791 (1.240) 20.010 (0.005) 0.332 (0.127) 24927.4

(A) Gompertz model, (B) Gompertz model with gamma heterogeneity. Standard errors are given in parentheses.

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effects of benefits based on search theory. According to the search models generous UI benefits reduce the probability of becoming employed by increasing the selectivity and reducing the search activity of unemployed persons. There is unaminity in the qualitative impacts of UI benefits on the probability of becoming employed. Similar results have been obtained by Lancaster (1979), Nickell (1979), Atkinson et al. (1984) and Narendranathan et al. (1985). Members of the UI funds become employed earlier than non-members. Similar results have been obtained for Finland by Lilja (1993) using data from the Labour Force Surveys. Members of the UI funds and labour unions have more incentives to become employed. According to the well-known results of search models by Mortensen (1977), Hamermesh (1979) and Burdett (1979) members of labour unions find unemployment more attractive than the non-members when jobs are of uncertain duration. Members’ earnings-related unemployment allowances create a higher value of search and hence a closer attachment to the labour market because the earnings-related unemployment allowance is higher than the basic unemployment allowance. An important characteristic of the system is that the unemployed workers who are eligible for earnings-related unemployment allowance have a reduction of their benefits after the hundredth day of unemployment. It has been shown that the reductions increase the probability of re-employment (Kettunen, 1996a). The higher earnings-related unemployment allowance also creates incentives for joining a trade union. Actually, with the increase in benefits in Finland since the 1960’s, the degree of unionisation has risen markedly. The coefficient of the number of children is statistically insignificant. Married persons seem to become employed earlier than single persons. The effect of sex is statistically insignificant. Older people are more apt to encounter problems in finding jobs, as is anticipated by search theory. Level of basic education does not have a statistically significant effect, but training for further employment has a positive effect on the probability of re-employment. Those having completed school and those having completed military service definitely find acceptable jobs earlier than the others. The persons who have come from housework have low re-employment probabilities. Most persons who come from housework are female, which partly accounts for the insignificant result for gender. The explanatory variables for the regional and occupational demand have insignificant coefficients. A similar result was obtained by Lilja (1993). Accordingly, the re-employment of unemployed workers does not depend notably on the number of unemployed workers and vacancies. It may, however, have effects on labour mobility, which is examined later in this study. The parameter estimate of the duration dependence u is negative, indicating that the hazard function decreases and that the survivor function asymptotically decreases to a positive value. Hence some persons will never become employed. When gamma heterogeneity is introduced into the model, the negative duration dependence decreases. Another implication of the negative u is that the expected

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value of the unemployment duration is not defined, for some persons do not become employed again. This fact can be seen, for example, in Broadbent (1958) and Lee (1980). The technical reason is that the integral of the survivor function from zero to infinity does not converge. The constant of the model, in which the effect of omitted variables is captured, decreases, and the absolute values of the statistically significant parameter estimates increase when gamma heterogeneity is introduced into the model, as expected.

4.3. Regional mobility This section is concerned with the estimation of the models of regional mobility in the labour market. The models of becoming employed have been widely studied in the search theoretical and microeconometric literature, but the important feature of becoming employed by moving to another area of residence has not, however, received notable attention. The probability of becoming employed by moving is so low for many people, that they do not move. The proportion of the people who move to get a job is estimated from the data, where the completed periods of unemployment are not noted for all observations. The region is defined by the UI Act as an area of residence where a person normally goes to work. The regions have been defined by the Ministry of Labour so that for each person it is the municipality where the person resides and usually some other defined municipalities nearby. Regional unemployment disparities have been high and fairly persistent in Finland. Unemployment has traditionally been high in the northern and eastern regions of Finland where net internal migration has been negative. Most people live in southern Finland, which is prosperous and where unemployment has been low. Regional mobility is defined in the data set as taking place if a worker moves from one area of residence to another to get a job. Some people may move due to family reasons but do not find a job. Some persons may find a job in another region and commute. Such cases are not included in regional mobility statistics. These observations have not been omitted from the sample but classified as censored observations in the econometric analysis. The data set does not indicate whether the family status or homeownership status of the respondent has changed during the observation period, nor does it include information about the distance between the old and new domiciles. There are many empirical studies on the probability of regional mobility. Usually discrete choice models are used to analyse the determinants of mobility (e.g. Borjas, 1987; Falaris, 1987; Hughes and McCormick, 1987; Molho, 1987; Boots and Kanaroglou, 1988; Pissarides and Wadsworth, 1989). Our study extends previous research by analysing the regional mobility of unemployed persons who move to get a job. Re-employment by moving, a rather rare phenomenon, is analysed using data on 2077 unemployed persons. About 97% of the observations are right censored. In

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censored cases the complete periods of unemployment until the date of moving were not recorded. Some of the persons leave unemployment by staying in their area of residence and some of them are lost in the follow-up. In the latter case it is not known whether the persons moved or not. Therefore a discrete choice model would clearly be inappropriate. When the degree of censoring is high, it is reasonable to estimate only rather parsimonious models. Table 3 presents the results of estimations. According to the search models the UI benefits have a negative effect on re-employment probability and labour mobility. The parameter estimate of the replacement ratio takes a negative sign, as expected, and the effect is rather strong and statistically significant. From a policy viewpoint it is interesting to note the economic importance of the UI benefits. According to the model the increase of the replacement ratio of an average person by 1% will decrease the probability of moving by 0.88 and 0.97% in these two models. Members of the UI funds, who are usually members of labour unions, do not move as often as non-members. One explanation given by search theory is that members’ generous earnings-related UI benefits create a higher value of search for employment and therefore a closer attachment to the labour market (e.g. Mortensen, 1977). As a result, they have more work experience and skill than non-members. Hence members are not as likely as non-members to accept an offer outside their area of residence. Age is a statistically significant factor. Older persons are less flexible in leaving Table 3 Gompertz models of regional mobility (A) Constant Replacement ratio of UI benefits Member of UI fund, 15yes Age, years Regional demand, V/ U ratio Occupational demand, V/ U ratio Duration dependence, u

23.540 (0.537) 25.185 (0.959) 21.378 (0.461) 20.053 (0.022) 21.941 (1.446) 2.761 (3.111) 20.024 (0.013)

Variance of the heterogeneity, s 2 Log-likelihood

2333.3

(B) 23.353 (0.698) 25.731 (1.025) 21.515 (0.494) 20.059 (0.026) 22.387 (1.637) 3.692 (3.449) 20.010 (0.018) 4.116 (5.007) 2332.9

(A) Gompertz model, (B) Gompertz model with gamma heterogeneity. Standard errors are given in parentheses.

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their area of residence. With substantial amounts of human capital older workers will have a narrow choice set of alternative jobs available. The incentives for moving may also be quite restricted because older people may have larger moving costs. The demand for labour in the area of residence of unemployed persons seems to decrease the probability of moving. In addition, the occupational demand in the whole country seems to increase the probability of moving. The demand effects are not, however, statistically significant in these models. The parameter estimate of the duration dependence u is negative indicating a fall in the hazard function and a survivor function that decreases asymptotically to a positive value. Hence some of the persons will not move to get a job. When gamma heterogeneity is introduced into the model, the negative duration dependence decreases. The variance of the unobserved heterogeneity is, however, statistically insignificant. Therefore the model which neglects the unobserved heterogeneity can be accepted.

4.4. Occupational mobility This section is concerned with the estimation of occupational mobility. Occupations in the data are measured on a very detailed level. The most accurate definition of occupations includes 1320 occupations. The models of becoming employed have been widely studied in the search theoretical and econometric literature, but the important feature of becoming employed by changing occupations has not, however, received notable attention. There are some empirical studies on educational and occupational choices, which may be regarded as investment decisions. Willis and Rosen (1979) tested the human-capital maximising hypothesis in the context of the educational choices of a panel of individuals in the United States. Similar work was done by Pissarides (1981, 1982) for the United Kingdom. Applications to occupational upgrading have been made by Grimes (1986) and to occupational choice decisions by Boskin (1974) and Schmidt and Strauss (1975). Stone (1982) has studied the decision to change occupations using binary logit models with duration of unemployment as an explanatory variable. Robertson and Symons (1990) follow these studies by estimating a logit model for the rough classification of occupations: professional, skilled and unskilled. Our study extends this approach by focusing on the occupational mobility of unemployed persons and the effect of earnings and training for further employment with other factors in that decision. The complete periods of unemployment until the date of becoming employed by changing occupation are not recorded for all the observations, because some persons become employed in their previous occupations, some of them are lost in the follow-up and some of them do not return to work. In some cases the previous occupation was not known. The duration variable of primary interest was not recorded in full if the person became unemployed after leaving school or military

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service because they did not have the chance to choose their first occupation. These kinds of observations are censored observations where the complete period of unemployment was not recorded. Each occupation is measured using a 5-digit code in the Nordic Occupational Classification. The classification is such that similar occupations form subgroups. These are categorized into groups, which in turn are placed into main groups. The first, 1–2, 1–3 and 1–5 digits classify 10, 84, 305 and 1320 groups or occupations, respectively. On the different levels there are 103, 142, 161 and 202 completed periods whose duration between the date of becoming unemployed and the date of changing one’s occupation was recorded. The rest of the observations are censored. People change their occupations most often on the most accurate 5-digit level, where the occupations do not differ very much from each other. It is an empirical matter on which level occupational mobility is examined. In practice, as occupations are defined very narrowly in the employment offices, the 5-digit level is the most appropriate. An unemployed person can apply for jobs in several different occupations. There are, however, regulations that certain degrees and certificates are needed to work in specific occupations in Finland. The companies receiving the applications are more likely to offer the job to an applicant with the requisite training, work experience and skill, less likely otherwise. Therefore, the probability that the unemployed person will be offered a job in his prior occupational group is higher than the probability that the person will be offered a job in some more distant occupational group. Tables 4 and 5 present the results of estimations. The characteristics that are negatively related to the probability of changing occupations are those that make the unemployed person’s skills occupation-specific. According to the search models the UI benefits increase the probability that workers will seek job opportunities within their previous occupations rather than jobs associated with alternative, lower-paying occupations. The parameter estimates of the replacement ratio of UI benefits take negative signs, as expected. The effect of the replacement ratio is statistically significant after allowing for gamma heterogeneity. The estimates for the elasticities of the replacement ratio on the probability of changing occupations vary between 20.15 and 20.23, depending on the level of occupations. As members of UI funds are often skilled and motivated, they are more prone than non-members to change occupations. Many other explanatory variables have significant effects on the probability of changing occupations. Age is a statistically significant factor, for older persons are not very flexible in changing occupations. They have accumulated occupation-specific human capital. Education can be regarded as an investment decision on the part of the individual, as noted by Becker (1964). Furthermore, it can be argued that job opportunities increase with the length of schooling, because one can accept a job

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Table 4 Gompertz models of occupational mobility Level of classification of occupations:

1

2

3

5

Constant

24.030 (0.476) 20.743 (0.493) 0.273 (0.223) 20.027 (0.013) 0.497 (0.243) 0.245 (0.280) 20.122 (0.342) 0.163 (0.341) 0.717 (0.862) 25.466 (2.466) 21.643 (0.721) 20.027 (0.009) 2658.6

23.635 (0.431) 20.743 (0.407) 0.253 (0.188) 20.025 (0.011) 0.262 (0.205) 0.241 (0.233) 0.076 (0.285) 0.270 (0.277) 1.108 (0.687) 26.064 (2.086) 21.453 (0.632) 20.026 (0.007) 2867.3

23.661 (0.400) 20.420 (0.366) 0.350 (0.176) 20.030 (0.010) 0.290 (0.194) 0.241 (0.222) 0.065 (0.271) 0.207 (0.265) 1.298 (0.637) 24.861 (1.849) 20.610 (0.366) 20.027 (0.007) 2966.8

23.448 (0.369) 20.468 (0.333) 0.371 (0.154) 20.035 (0.009) 0.299 (0.173) 0.340 (0.188) 20.029 (0.247) 0.079 (0.248) 1.129 (0.569) 23.538 (1.623) 20.404 (0.328) 20.027 (0.006) 21165.2

Replacement ratio of UI benefits Member of UI fund, 15yes Age, years Education, 15at least 12 years Training for employment, 15yes Came from schooling, 15yes Came from housework, 15yes Regional demand, V/ U ratio Occupational demand, V/ U ratio Taxable assets, millions of FIM

u Log-likelihood

Standard errors are given in parentheses.

below one’s educational level, but will generally not receive a job offer above it. The results of estimations give support to these arguments. Training for further employment provided by the government seems to have a positive effect on the probability of changing occupations. The result is as expected, since the purpose of the training is to promote the matching of workers with available jobs by providing skills needed in them. Those leaving school or the army do not differ in this respect from other persons. The demand for labour in the area of residence of unemployed persons is positively related to the probability of changing occupations. According to the results for regarding the regional mobility, rather few people move to get a job. As a result, it is reasonable to argue that disinclination to move is reflected in the probability of changing occupations so as to remain in the area where the unemployed workers live. On the other hand, the occupational demand in the whole country has a strong negative effect on the probability of changing

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Table 5 Gompertz models of occupational mobility allowing for gamma heterogeneity Level of classification of occupations:

1

2

3

5

Constant

23.460 (0.674) 21.065 (0.674) 0.383 (0.318) 20.034 (0.018) 0.634 (0.350) 0.172 (0.408) 20.246 (0.459) 0.389 (0.460) 0.985 (1.140) 28.099 (3.366) 22.025 (0.824) 20.003 (0.018) 7.720 (5.393) 2657.3

23.011 (0.661) 21.331 (0.604) 0.394 (0.280) 20.033 (0.016) 0.296 (0.306) 0.270 (0.354) 20.039 (0.416) 0.511 (0.417) 1.844 (0.966) 28.769 (2.957) 21.920 (0.784) 20.004 (0.017) 7.291 (3.862) 2864.6

23.103 (0.602) 20.888 (0.340) 0.528 (0.258) 20.041 (0.015) 0.361 (0.282) 0.267 (0.331) 20.046 (0.388) 0.404 (0.392) 2.141 (0.874) 26.824 (2.505) 20.727 (0.431) 20.002 (0.016) 6.115 (3.306) 2964.1

22.905 (0.536) 20.971 (0.472) 0.531 (0.220) 20.047 (0.013) 0.334 (0.243) 0.446 (0.274) 20.186 (0.340) 0.131 (0.350) 1.705 (0.747) 24.600 (2.167) 25.266 (3.992) 20.002 (0.014) 4.346 (2.305) 21162.8

Replacement ratio of UI benefits Member of UI fund, 15yes Age, years Education, 15at least 12 years Training for employment, 15yes Came from schooling, 15yes Came from housework, 15yes Regional demand, V/ U ratio Occupational demand, V/ U ratio Taxable assets, millions of FIM

u s2 Log-likelihood

Standard errors are given in parentheses.

occupations. The assets of unemployed persons are negatively related to the probability of changing occupations. The parameter estimates of duration dependence u are statistically significant and negative, indicating that the hazard function is decreasing and that the survivor function decreases asymptotically to a positive value. Hence some of the persons will never change occupations. When gamma heterogeneity was introduced into the model the negative duration dependence decreases, as expected.

4.5. Proportions of re-employment and labour mobility Table 6 includes the estimates of proportions of the unemployed persons who become employed, move or change occupations. The distribution function, which is one minus the survivor function, approaches these proportions as the duration of

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Table 6 Proportions of unemployed persons who become employed, move or change occupations Years of unemployment

2

5

`

Re-employment Regional mobility Occupational mobility: least accurate level of classification most accurate level of classification

0.92 0.07 0.25 0.48

0.96 0.09 0.28 0.51

0.97 0.10 0.29 0.52

unemployment approaches infinity. The proportions have been calculated using the average characteristics of the persons in the sample for 2 and 5 years of unemployment and for infinity. The estimates of the probabilities of becoming employed given by the Gompertz model with gamma mixing distribution are 0.92, 0.96 and 0.97, respectively. According to the aggregate statistics of the Ministry of Labour the estimates seem to be reasonable. As a final estimate it can be said that only about 3% of the persons who became unemployed during 1985 will never be re-employed. The estimate of the proportion of persons who move to obtain employment is 0.10. Tervo (1997) has estimated that the percentage of unemployed workers who migrated in Finland was 8.2 in 1985–1990. The proportion of regional mobility given by Gompertz model seems to be reasonable in size, because the two different estimates are comparable in size. The estimates of the proportion of persons who do not change occupations vary between 0.29 and 0.52 depending on how accurately the level of occupation is measured. If the occupations differ much from each other the unemployed persons more seldom change their occupations to become employed. This result gives support to the search theory.

5. Conclusions Gompertz models of unemployment duration and labour mobility were estimated using Finnish microeconomic data collected from various administrative files. Completed periods of unemployment were not recorded for all the observations in the data. The models take into account the fact that some of the persons will never become employed, move or change their occupations to get a job. Even though the data are rich in explanatory variables and are more reliable than the data based on interviews, it might be argued that relevant variables have been omitted from the model. Neglected heterogeneity across individuals was taken into account in estimation. A Gompertz model allowing for unobserved heterogeneity was derived and estimated, assuming that the effect of omitted variables has a gamma distribution across individuals.

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Comparing the results of the two models shows that the model which does not correct for unobserved heterogeneity gives lower estimates of parameters. The absolute values of parameters increase when heterogeneity is introduced into the model. In addition, the Gompertz model gives estimates for the hazard function that are too low. Consequently, the survivor functions of the models with gamma distributed unobserved heterogeneity are lower. It can be concluded that, when correcting for omitted variables, the estimate of the proportion of persons who will become employed again is 97%. The corresponding estimates for the persons who will move or change their occupations to get a job are 10 and 29–52%, depending on the accuracy of measuring occupations.

Acknowledgements I wish to thank Professor Andrew Chesher and two anonymous referees for their helpful comments.

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