- Email: [email protected]
The analysis of labor market mobility using panel data
European Economic Review 33 (1989) 530-536. North-Holland
THE ANALYSIS OF LABOR MARKET USING PANEL DATA
MOBILITY
Reinhard H U J E R and Hilmar S C H N E I D E R * J.W. Goethe-Universitdt, D'-6000, Frankfurt/Main, FRG
1. Panel data as a tool to collect event histories
Causal analysis is indivisibly connected with a d y n a m i c perspective. In this sense, changes in explanatory variables (covariates) lead to subsequent changes in variables to be explained. Consequently, the observation of a temporal order of cause and effect requires longitudinal data. The term 'event history data' is used to express the fact that temporal changes of qualitative or quantitative variables on the micro-level take place at certain points in time. Individual income development, for example, will follow a temporal step function rather than a continuous course over time. These steps can be viewed as the focus of interest in d y n a m i c analysis. The main questions are: H o w long does it take for such an event to occur? W h a t are the determinants of duration? W h e n analyzing qualitative variables, one is also interested in the destination state after such an event, while the analysis of quantitative variables is concentrated on the question for the direction and a m o u n t of a change. Although panel data are intended to meet the requirements of causal analysis, practical research has to accept a trade-0ff between the completeness of longitudinal observation and related costs. This trade-off causes some methodological problems which can be listed as follows: - T h e observation takes place in discrete rather than continuous intervals. This results in an inaccurate measurement of the duration between events; *Reinhard Hujer is professor at the Department of Economics of the University of Frankfurt. "As head of the special project B-4 of the Sonderforschungsbereich 3 'Microanalytical Foundations of Social Policy' (Department of Advanced Research supported by the German Science Foundation), he is occupied with methodological aspects of panel analysis. Hilmar Schneider is assistant professor at the Department of Economics of the University of Frankfurt; he also is a member of the special project B-4 and is occupied with rriethodologlcal aspects of panel analysis. The reasearch was supported by the German Science Foundation and the University of Frankfurt. We wish to thank P.B. Spahn for the revision of an earlier draft of this paper. 0014-2921/89/$3.50 © 1989, Elsevier Science Publishers B.V: (North-Holland)
R. Hujer and H. Schneider, The analysisof labor market mobility
531
- Observations can be censored. Censoring means that durations are incompletely recorded due to temporal limitation of the observation period, - Panel mortality gradually reduces the sample size. It is desirable to use analytical methods which are able to utilize information from incomplete observations. In some cases, an attempt has been made to close the gaps between subsequent panel waves by retrospective questioning. This is true, for example, for the German Socio-Economic Panel which is used in our paper to demonstrate some of the issues discussed here. The benefit derived from this procedure, however, is being impaired to some degree by a new problem: Retrospective questioning produces a memory bias. The above listed problems have to be taken into account when using methods of longitudinal analysis based on panel data. This will be illustrated in section 2. In section 3 the presented methods are then applied to the analysis of transitions from unemployment to employment. 2. Longitudinal analysis of qualitative dependent variables Models for qualitative dependent variables based on cross-sectional data are usually restricted to the analysis of stock figures or proportions. From a dynamic perspective, however, stocks or proportions can be decomposed into two components: the duration within a particular original state and the probability of entering a new destination state. To give an example from the FRG: It has been found that the unemployment rate is high for youth (9.8x), low for middle age groups (7.1%) and high again for old employees (10.3%) [Schmid (1987)]. But the high unemployment figures for youth and old employees have to be judged quite differently, when comparing them from a longitudinal view. Youth show a high probability of becoming unemployed while its expected duration is rather short. In contrast, the risk of old employees to become unemployed is relatively low, but, once unemployed, they have to expect a long period of unemployment [Schmid (1987)]. A more sophisticated method for analyzing flows between different states of a qualitative variable can be found in transition rate models. [For more details see Andre8 (1985); Blossfeld-Hamerle-Mayer (1986); DiekmannMitter (1984); Heckman-Singer (1986); Kalbfleisch-Prentice (1980); Lawless (1982); Tuma-Hannan (1984)]. The transition rate r(t) is defined as the limit of the transition probability q between an original state a and a destination state b for an infinitesimal small time interval, where t denotes the random variable duration in the original state a: rJ t) = lim %I&,r + d 0 20, At-00
At
afb.
532
R. Hujer and H. Sckneider, The analysis of labor market mobility
The main interest is to model individual transition rates. One familiar type of model is the proportional hazard Weibull model which is defined as:
rlob(O = exp(~.dtexP(kb)’exp(/?, + &!@a+ si).
(2)
The individual transition rate r&t) may be understood as the instantaneous propensity of an observation unit i to leave the original state a and entering a new destination state b. The transition rate is inversely related to the expected duration in state a: The higher the transition rate level, the lower the expected duration. The model equation consists of two multiplicatively connected terms. The first part, containing the functional parameter 4, covers endogenous time dependency of the transition rate. A positive value of Q means a transition rate monotonously increasing with duration; a negative value means a monotonously falling transition rate. When 4 is zero the transition rate remains constant over time. The second part of the model equation catches the influence of covariates s1 on the transition rate. The covariate effects are expressed by the parameter vector /3. The fact that covariates can change their values over time induces exogenous time-dependency of the transition rate. The introduction of an individual error term E, is intended to control for unobserved heterogeneity. It has been pointed out by Heckman and Singer (1982a, 1982b, 1984) that disregard of unobserved heterogeneity would induce a spurious endogenous time-dependency of the transition rate. It is assumed that E is uncorrelated with 5 and that E follows a discrete distribution with k different levels Sa, referring to k unobserved probability classes with state probabilities /ik Given the assumption of independence between observation units and between subsequent spells, the likelihood function of this model is found to be:
= fi
:
i=lk=l
Akrti(t)“eXp[ - jr&)dr].
Here, ci acts as a switch variable with ci= 1 for complete observations and ci= 0 for right-censored observations. Complete observations contribute to the likelihood function with the density function f(r), while the contribution of right-censored observations is given by the survival function G(t). The survival function G(t) renders the probability of still being in the original state at time t. Both, the density function as well as the survival function
R. Hujer and H. Schneider, The analysisof labor market mobility
533
may be expressed in terms of the transition rate function, and thus the likelihood function may be expressed solely in terms of the transition rate function. It is important to note, within this framework, panel mortality can be treated as a form of right-censoring. Left-censoring can also be considered in the likelihood function but it requires rather strong assumptions. Leftcensored cases will therefore be ignored in the following. For more details refer to Baydar (1987), Heckman-Singer (1985) and Tuma-Hannan (1984). Considering the methodological problems which arise from left-censoring, it seems to be advisable, however, to design a panel with as little left-censored observations as possible. Strictly speaking, the transition rate approach requires continuous time measurement. To circumvent the problem of panel data being based on discrete time measurement several procedures can be applied. Allison (1982) has suggested to use conditional transition probability models instead of transition rate models. Arminger (1984), Galler (1985) and Hujer-Schneider (1986) suggested transformations of discrete time measurement into quasi continuous-time measurement. We will use our own procedure which seems to be the most appropriate compromise between computational effort and numerical accuracy. With this method the last measured time interval per observation is reduced by half in case of complete observations and it is totally eliminated in case of right-censored observations. 3. The process of transition from unemployment to employment Table 1 contains two rate models for the transition of men from unemployment to employment. The data have been derived from the German Socio Economic Panel. Details about the data base may be taken from Hanefeld (1987). The two models are only differing for the fact that the second one is controlled for unobserved heterogeneity, while the first one is not. Disregard of unobserved heterogeneity in the first model means that this model does not contain an error term. When controlling for unobserved heterogeneity, however, the assumption of three unobserved homogenous subpopulations turned out to be optimal. The corresponding model shows a significant positive endogenous time dependency of the transition rate. This means that the propensity to leave unemployment and become employed again increases with unemployment duration. A comparison of the two 4coefhcients shows that ignorance of unobserved heterogeneity would have led to the wrong conclusion that there is no presence of endogenous time dependency of the transition rate. Similar results can be found in the papers of Heckman-Singer (1982a) and Galler (1987). The already mentioned increase of unemployment duration with age is strikingly expressed in the negative age effect for employees older than 50.
Table I
0.0629
0.1954 0.0269 0.577 I -0.1756 -0.1419 - 1.2790 0.0951 - 1.5072 - 0.6700 0.6140 0.333 1 0.5622 -0.2174 1.1889
1.0649
1.2157 I .0273 1.7808 0.8390 0.8677 0.2783 1.0997 0.2215 0.51 I7 1.8477 I .3953 1.7545 0.8046 3.2836
0.0903 0.8585 0.0001 0.1888 0.3383 0.0000 0.4989 0.0030 0.0009 O.tXKtl 0.0850 O.tXNIl 0.2762 0.0000
0.1217
O.oooO
0.1309 601 380
1.1895 1.0204 1.7522 0.8556 0.8825 0.2880 1.0813 0.2437 0.5298 1.8969 1.3996 1.7867 0.8153 3.3773
0.2822 0.1073 0.0528 1.1551
- 1068.4669 168.1341(19)
0.1735 0.0202 0.5609 -0.1560 -0.1250 - 1.2447 0.0782 - 1.4120 -0.6352 0.6402 0.3362 0.5804 -0.2042 I.2171
0.0665 0.4219 0.51 I6 - 1.2652 -2.2320 - 2.9407 0.1442 0.1215 0.8912 O.OoI 0.2313 0.3855 O.oooO 0.5693 0.0038 0.0011 O.OCNKl 0.0740 O.OtKtO 0.2944 O.OtXlO
0.0000 O.oooO O.OWO i 00002
Sign. lev.
Log-likelihood Global x2 (d.f.) Rate of null model Number of cases Number of transitions
Nationality RealschulabschluD (Fach-)Abitur Age between 30 and 40 Age between 40 and 50 Age over 50 Ent. to AL-Geld End of AL-Geld Ant. to AL-Hilfe February/March/April March July/August/September September December
parameter)
(Support points)
F(Weibull
(state probabilities)
As A3 Q, Q,
Al
Variable name
-___ ___Dcjlttirions oj coucrrirttes: Nationality: (I =German/O=else); Realschulabschlutk (I =middle school Ievel/O=else); (Fach-)Abitur: (I =educutional degrees which entitle entrance to university or senior technical college); Age: (I/O=dummies for the given age periods); Ent. to AL-Geld: (I =pcriod of existing entitlement to Arbeitslosengeld/O=else); End of AL-Geld (1 =period of last two months of existing entitlement to Arbeitslosengeld); Ent. to ALHilfe: (I = period of existing entitlement to Arbeitslosenhilfe/O=else); February/March/April to December: (I/O=dummies for the given seasonal periods).
- 1068.9974 167.0732 ( 15)
- 2.4302
0.0880
l.oooo
exp(@
C+
Sign. lev.
&
exp@)
Parameter estimates B (model controlled for unobserved heterogeneity)
Parameter estimates 6 (model not controlled for unobserved heterogeneity)
Weibull model for the transition of men from unemployment to employment (Source: The socio economic panel. waves 1-3. observation period: 19831985).
P
!z
R. Hujer and H. Schneider, The analysis of labor market mobility
535
Their transition rate level is only about 28% of that for the reference group consisting of unemployed youth up to age 30. Special interest should be paid to the effect of unemployment compensation. The German system of unemployment compensation knows two categories of support payments. During the first phase of unemployment eligible persons will receive the so-called Arbeitslosengeld, which covers 63% of the previous net income (67% for persons with children in their household). After expiration of Arbeitslosengeld, which usually takes place after 12 months of unemployment, recipients are supported by Arbeitslosenhi&. In practice, the level of Arbeitslosenhilfe lies approximately 10 to 20% below the level of Arbeitslosengeld. Under statistical criteria, the transition rate of persons eligible to Arbeitslosengeld does not differ from that of other persons, according to the model parameters. More surprisingly, the transition rate of persons receiving Arbeitslosenhilfe is significantly lower than that of other persons. This result is not in accordance with search theoretical argumentation [Lippman-McCall (1976)]. In the present case it has to be assumed that the fact of receiving Arbeitslosenhilfe is at the same time an indicator of placement difficulties which are not adequately enough covered by the included covariates. Presumably they dominate the effect of a change in the replacement ratio. The two models are also containing an example for the treatment of memory effects. Related problems have been discussed in detail by AkerlofYellen (1985), Poterba-Summers (1984) and Sikkel (1985). Our computed durations are based on retrospective calendars. Interviewees are asked to report their occupational statuses during the months of the last calendar year. Problems arise when putting together consecutive calendars. Therefore, we find an overproportionate number of transitions from December to January of each year, which has no real background. We have tried to control possible interaction with other covariates by introducing a separate December effect. Its value, however, is of no substantial interest. 4. Conclusions The present analysis of unemployment duration gives a good impression of the usefulness of panel data for the analysis of labor market mobility. Natural deficiencies of panel data can be compensated sufficiently through particular consideration within the methodological framework. In any case, however, it seems to be worth mentioning that efforts regarding the preparation of data may reach timely dimensions unknown in cross-sectional analysis. Implementing costs and time required for the analysis are therefore the decisive restrictions which have to be taken into account when carrying out a panel survey.
536
R. Hujer and H. Schneider, The analysisof labor marker mobility
References Akerlof. GA. and J.C. Yellen, 1985, Unemployment through the filter of memory, Quarterly Journal of Economics C3,747-773. Allison, P.D., 1982. Discrete-time methods for the analysis of event histories, in: S. Leinhardt, ed., Sociological methodology (Bass, San Francisco) 61-97. Andre& H.-J., 1985, Multivariate Analyse von Verlaufsdaten (Mannheim). Arminger, Cr., 1984, Modelltheoretische und Methodische Probleme bei der Analyse von Paneldaten mit qualitativen Variablen. Vierteljahreshefte zur Wirtschaftsforschung 4, 470-480. Baydar. N., 1987, What can backward recurrena time data tell us: An application to residential mobility in the U.S., in: K.U. Mayer and N.B. Turna, eds, Applications of event history analysis (Max-Planck-Institut, Berlin) 561-600. Blossfeld, H.-P., A. Hamerle A. and K.U. Mayer, 1986, Ereignisanalyse-Statistische Theorie und Anwendung in den Wirtschafts- und Sozialwissenschaften (Campus, Frankfurt, New York). Diekmann, A. and P. Mitter, 1984, Methoden zur Analyse von ZeitverlPufcn (Teubner, Stuttgart). Galler, H.P., 1985, Ubergangsratenmodelle bei intervalldatierten Ereignissen, Sfb-3-Working paper no. 164 (Sib 3, Frankfurt, Mannheim). Galler, H.P. and U. PBtter, 1987, Unobserved heterogeneity in models of unemployment duration, in: K.U. Mayer and N.B. Tuma, eds., Applications of event history analysis in life course research (Max-Planck-Institut, Berlin) 628-650. Hanefeld, U., 1987, Das Sozio-iikonomische Panel - Grundlagen und Konzeption (Campus, Frankfurt, New York). Heckman, JJ. and B. Singer, 1982a. The identification problem in econometric models for duration data, in: W. Hildenbrand, ed.. Advances in econometrics (Cambridge University Press, Cambridge) 39-77. Heckman, J.J. and B. Singer, 19824 Population heterogeneity in demographic models, in: K.C. Land and A. Rogers, eds.. Multidimensional mathematical demography (Academic Press, New York) 567-599. Heckman. J.J. and B. Singer, 1984, Econometric duration analysis, Journal of Econometrics 24, 63-132. Heckman, J.J. and B. Singer, 1985, Social science duration analysis, in: JJ. Heckman and B. Singer, eds., Longitudinal analysis of labor market data (Cambridge University Press, Cambridge, London, New York, New Rochelle, Melbourne, Sydney) 39-l 10. Heckman, J.J. and B. Singer, 1986, Econometric analysis of longitudinal data, in: Z. Griliches and M.D. Intriligator, eds., Handbook of econometrics, Vol. 3 (Elsevier, New York, Oxford, Tokyo) 1689-1763. Hujer, R. and H. Schneider, 1986, Semiparametrische und parametrische Ratenmodelle - Eine Anwendungsbezogene Einfrihrung in die statist&hen Grundlagen mit Programmbeispielen, Sfb-3-Working paper no. 200 (Sib 3, Frankfurt, Mannheim). Kalbfleisch. J.D. and R.L. Prentice, 1980, The statistical analysis of failure time data (Wiley, New York, Chichester, Brisbane, Toronto). Lawless, J.F., 1982, Statistical models and methods for lifetime data (Wiley, New York, Chichester, Brisbane, Toronto, Singapore). Lippman, S.A. and J.J. McCall. 1976, The economics of job search: A survey, in: Economic Inquiry 14, 155-189. Poterba, J.M. and L.H. Summers, 1986, Reporting errors and labor market dynamics, Econometrica 54, 1319-1338. Schmid, G., 1987, Arbeitsmarktpolitik im Wandel - Entwicklungstendenzen des Arbeitsmarktes und Wirksamkeit der Arbeitsmarkpolitik in der Bundesrepublik Deutschland. WZBarbeitspapier IIM/LMP 87-17. Sikkel. D., 1985, Models for memory effects, Journal of the American Statistical Association 80, 835-841. Tuma. N.B. and M.T. Hannan, 1984, Social dynamics: Models and Methods (Academic Press, Orlando, San Diego, San Francisco, New York, London, Toronto, Montreal, Sydney, Tokyo).
THE ANALYSIS OF LABOR MARKET USING PANEL DATA
MOBILITY
Reinhard H U J E R and Hilmar S C H N E I D E R * J.W. Goethe-Universitdt, D'-6000, Frankfurt/Main, FRG
1. Panel data as a tool to collect event histories
Causal analysis is indivisibly connected with a d y n a m i c perspective. In this sense, changes in explanatory variables (covariates) lead to subsequent changes in variables to be explained. Consequently, the observation of a temporal order of cause and effect requires longitudinal data. The term 'event history data' is used to express the fact that temporal changes of qualitative or quantitative variables on the micro-level take place at certain points in time. Individual income development, for example, will follow a temporal step function rather than a continuous course over time. These steps can be viewed as the focus of interest in d y n a m i c analysis. The main questions are: H o w long does it take for such an event to occur? W h a t are the determinants of duration? W h e n analyzing qualitative variables, one is also interested in the destination state after such an event, while the analysis of quantitative variables is concentrated on the question for the direction and a m o u n t of a change. Although panel data are intended to meet the requirements of causal analysis, practical research has to accept a trade-0ff between the completeness of longitudinal observation and related costs. This trade-off causes some methodological problems which can be listed as follows: - T h e observation takes place in discrete rather than continuous intervals. This results in an inaccurate measurement of the duration between events; *Reinhard Hujer is professor at the Department of Economics of the University of Frankfurt. "As head of the special project B-4 of the Sonderforschungsbereich 3 'Microanalytical Foundations of Social Policy' (Department of Advanced Research supported by the German Science Foundation), he is occupied with methodological aspects of panel analysis. Hilmar Schneider is assistant professor at the Department of Economics of the University of Frankfurt; he also is a member of the special project B-4 and is occupied with rriethodologlcal aspects of panel analysis. The reasearch was supported by the German Science Foundation and the University of Frankfurt. We wish to thank P.B. Spahn for the revision of an earlier draft of this paper. 0014-2921/89/$3.50 © 1989, Elsevier Science Publishers B.V: (North-Holland)
R. Hujer and H. Schneider, The analysisof labor market mobility
531
- Observations can be censored. Censoring means that durations are incompletely recorded due to temporal limitation of the observation period, - Panel mortality gradually reduces the sample size. It is desirable to use analytical methods which are able to utilize information from incomplete observations. In some cases, an attempt has been made to close the gaps between subsequent panel waves by retrospective questioning. This is true, for example, for the German Socio-Economic Panel which is used in our paper to demonstrate some of the issues discussed here. The benefit derived from this procedure, however, is being impaired to some degree by a new problem: Retrospective questioning produces a memory bias. The above listed problems have to be taken into account when using methods of longitudinal analysis based on panel data. This will be illustrated in section 2. In section 3 the presented methods are then applied to the analysis of transitions from unemployment to employment. 2. Longitudinal analysis of qualitative dependent variables Models for qualitative dependent variables based on cross-sectional data are usually restricted to the analysis of stock figures or proportions. From a dynamic perspective, however, stocks or proportions can be decomposed into two components: the duration within a particular original state and the probability of entering a new destination state. To give an example from the FRG: It has been found that the unemployment rate is high for youth (9.8x), low for middle age groups (7.1%) and high again for old employees (10.3%) [Schmid (1987)]. But the high unemployment figures for youth and old employees have to be judged quite differently, when comparing them from a longitudinal view. Youth show a high probability of becoming unemployed while its expected duration is rather short. In contrast, the risk of old employees to become unemployed is relatively low, but, once unemployed, they have to expect a long period of unemployment [Schmid (1987)]. A more sophisticated method for analyzing flows between different states of a qualitative variable can be found in transition rate models. [For more details see Andre8 (1985); Blossfeld-Hamerle-Mayer (1986); DiekmannMitter (1984); Heckman-Singer (1986); Kalbfleisch-Prentice (1980); Lawless (1982); Tuma-Hannan (1984)]. The transition rate r(t) is defined as the limit of the transition probability q between an original state a and a destination state b for an infinitesimal small time interval, where t denotes the random variable duration in the original state a: rJ t) = lim %I&,r + d 0 20, At-00
At
afb.
532
R. Hujer and H. Sckneider, The analysis of labor market mobility
The main interest is to model individual transition rates. One familiar type of model is the proportional hazard Weibull model which is defined as:
rlob(O = exp(~.dtexP(kb)’exp(/?, + &!@a+ si).
(2)
The individual transition rate r&t) may be understood as the instantaneous propensity of an observation unit i to leave the original state a and entering a new destination state b. The transition rate is inversely related to the expected duration in state a: The higher the transition rate level, the lower the expected duration. The model equation consists of two multiplicatively connected terms. The first part, containing the functional parameter 4, covers endogenous time dependency of the transition rate. A positive value of Q means a transition rate monotonously increasing with duration; a negative value means a monotonously falling transition rate. When 4 is zero the transition rate remains constant over time. The second part of the model equation catches the influence of covariates s1 on the transition rate. The covariate effects are expressed by the parameter vector /3. The fact that covariates can change their values over time induces exogenous time-dependency of the transition rate. The introduction of an individual error term E, is intended to control for unobserved heterogeneity. It has been pointed out by Heckman and Singer (1982a, 1982b, 1984) that disregard of unobserved heterogeneity would induce a spurious endogenous time-dependency of the transition rate. It is assumed that E is uncorrelated with 5 and that E follows a discrete distribution with k different levels Sa, referring to k unobserved probability classes with state probabilities /ik Given the assumption of independence between observation units and between subsequent spells, the likelihood function of this model is found to be:
= fi
:
i=lk=l
Akrti(t)“eXp[ - jr&)dr].
Here, ci acts as a switch variable with ci= 1 for complete observations and ci= 0 for right-censored observations. Complete observations contribute to the likelihood function with the density function f(r), while the contribution of right-censored observations is given by the survival function G(t). The survival function G(t) renders the probability of still being in the original state at time t. Both, the density function as well as the survival function
R. Hujer and H. Schneider, The analysisof labor market mobility
533
may be expressed in terms of the transition rate function, and thus the likelihood function may be expressed solely in terms of the transition rate function. It is important to note, within this framework, panel mortality can be treated as a form of right-censoring. Left-censoring can also be considered in the likelihood function but it requires rather strong assumptions. Leftcensored cases will therefore be ignored in the following. For more details refer to Baydar (1987), Heckman-Singer (1985) and Tuma-Hannan (1984). Considering the methodological problems which arise from left-censoring, it seems to be advisable, however, to design a panel with as little left-censored observations as possible. Strictly speaking, the transition rate approach requires continuous time measurement. To circumvent the problem of panel data being based on discrete time measurement several procedures can be applied. Allison (1982) has suggested to use conditional transition probability models instead of transition rate models. Arminger (1984), Galler (1985) and Hujer-Schneider (1986) suggested transformations of discrete time measurement into quasi continuous-time measurement. We will use our own procedure which seems to be the most appropriate compromise between computational effort and numerical accuracy. With this method the last measured time interval per observation is reduced by half in case of complete observations and it is totally eliminated in case of right-censored observations. 3. The process of transition from unemployment to employment Table 1 contains two rate models for the transition of men from unemployment to employment. The data have been derived from the German Socio Economic Panel. Details about the data base may be taken from Hanefeld (1987). The two models are only differing for the fact that the second one is controlled for unobserved heterogeneity, while the first one is not. Disregard of unobserved heterogeneity in the first model means that this model does not contain an error term. When controlling for unobserved heterogeneity, however, the assumption of three unobserved homogenous subpopulations turned out to be optimal. The corresponding model shows a significant positive endogenous time dependency of the transition rate. This means that the propensity to leave unemployment and become employed again increases with unemployment duration. A comparison of the two 4coefhcients shows that ignorance of unobserved heterogeneity would have led to the wrong conclusion that there is no presence of endogenous time dependency of the transition rate. Similar results can be found in the papers of Heckman-Singer (1982a) and Galler (1987). The already mentioned increase of unemployment duration with age is strikingly expressed in the negative age effect for employees older than 50.
Table I
0.0629
0.1954 0.0269 0.577 I -0.1756 -0.1419 - 1.2790 0.0951 - 1.5072 - 0.6700 0.6140 0.333 1 0.5622 -0.2174 1.1889
1.0649
1.2157 I .0273 1.7808 0.8390 0.8677 0.2783 1.0997 0.2215 0.51 I7 1.8477 I .3953 1.7545 0.8046 3.2836
0.0903 0.8585 0.0001 0.1888 0.3383 0.0000 0.4989 0.0030 0.0009 O.tXKtl 0.0850 O.tXNIl 0.2762 0.0000
0.1217
O.oooO
0.1309 601 380
1.1895 1.0204 1.7522 0.8556 0.8825 0.2880 1.0813 0.2437 0.5298 1.8969 1.3996 1.7867 0.8153 3.3773
0.2822 0.1073 0.0528 1.1551
- 1068.4669 168.1341(19)
0.1735 0.0202 0.5609 -0.1560 -0.1250 - 1.2447 0.0782 - 1.4120 -0.6352 0.6402 0.3362 0.5804 -0.2042 I.2171
0.0665 0.4219 0.51 I6 - 1.2652 -2.2320 - 2.9407 0.1442 0.1215 0.8912 O.OoI 0.2313 0.3855 O.oooO 0.5693 0.0038 0.0011 O.OCNKl 0.0740 O.OtKtO 0.2944 O.OtXlO
0.0000 O.oooO O.OWO i 00002
Sign. lev.
Log-likelihood Global x2 (d.f.) Rate of null model Number of cases Number of transitions
Nationality RealschulabschluD (Fach-)Abitur Age between 30 and 40 Age between 40 and 50 Age over 50 Ent. to AL-Geld End of AL-Geld Ant. to AL-Hilfe February/March/April March July/August/September September December
parameter)
(Support points)
F(Weibull
(state probabilities)
As A3 Q, Q,
Al
Variable name
-___ ___Dcjlttirions oj coucrrirttes: Nationality: (I =German/O=else); Realschulabschlutk (I =middle school Ievel/O=else); (Fach-)Abitur: (I =educutional degrees which entitle entrance to university or senior technical college); Age: (I/O=dummies for the given age periods); Ent. to AL-Geld: (I =pcriod of existing entitlement to Arbeitslosengeld/O=else); End of AL-Geld (1 =period of last two months of existing entitlement to Arbeitslosengeld); Ent. to ALHilfe: (I = period of existing entitlement to Arbeitslosenhilfe/O=else); February/March/April to December: (I/O=dummies for the given seasonal periods).
- 1068.9974 167.0732 ( 15)
- 2.4302
0.0880
l.oooo
exp(@
C+
Sign. lev.
&
exp@)
Parameter estimates B (model controlled for unobserved heterogeneity)
Parameter estimates 6 (model not controlled for unobserved heterogeneity)
Weibull model for the transition of men from unemployment to employment (Source: The socio economic panel. waves 1-3. observation period: 19831985).
P
!z
R. Hujer and H. Schneider, The analysis of labor market mobility
535
Their transition rate level is only about 28% of that for the reference group consisting of unemployed youth up to age 30. Special interest should be paid to the effect of unemployment compensation. The German system of unemployment compensation knows two categories of support payments. During the first phase of unemployment eligible persons will receive the so-called Arbeitslosengeld, which covers 63% of the previous net income (67% for persons with children in their household). After expiration of Arbeitslosengeld, which usually takes place after 12 months of unemployment, recipients are supported by Arbeitslosenhi&. In practice, the level of Arbeitslosenhilfe lies approximately 10 to 20% below the level of Arbeitslosengeld. Under statistical criteria, the transition rate of persons eligible to Arbeitslosengeld does not differ from that of other persons, according to the model parameters. More surprisingly, the transition rate of persons receiving Arbeitslosenhilfe is significantly lower than that of other persons. This result is not in accordance with search theoretical argumentation [Lippman-McCall (1976)]. In the present case it has to be assumed that the fact of receiving Arbeitslosenhilfe is at the same time an indicator of placement difficulties which are not adequately enough covered by the included covariates. Presumably they dominate the effect of a change in the replacement ratio. The two models are also containing an example for the treatment of memory effects. Related problems have been discussed in detail by AkerlofYellen (1985), Poterba-Summers (1984) and Sikkel (1985). Our computed durations are based on retrospective calendars. Interviewees are asked to report their occupational statuses during the months of the last calendar year. Problems arise when putting together consecutive calendars. Therefore, we find an overproportionate number of transitions from December to January of each year, which has no real background. We have tried to control possible interaction with other covariates by introducing a separate December effect. Its value, however, is of no substantial interest. 4. Conclusions The present analysis of unemployment duration gives a good impression of the usefulness of panel data for the analysis of labor market mobility. Natural deficiencies of panel data can be compensated sufficiently through particular consideration within the methodological framework. In any case, however, it seems to be worth mentioning that efforts regarding the preparation of data may reach timely dimensions unknown in cross-sectional analysis. Implementing costs and time required for the analysis are therefore the decisive restrictions which have to be taken into account when carrying out a panel survey.
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