1. MODELLING TIME OF UNEMPLOYMENT VIA COX PROPORTIONAL MODEL Jan Popelka Department of Statistics and Probability University of Economics, Prague

2. Applied Statistics 2005 Previous model LABOR OFFICE IN PRIBRAM ► Subjects registered in January 2002 ► Follow-up period: from January 2002 to June 2003 (18 months) ► 597 unemployed (175 right censored) FACTORS ► age, sex, education

3. Applied Statistics 2005 Previous model ► AGE and AGE^2 variables (continuous) DISPUTABLE CONCLUSIONS: ► No relationship between sex and the probability of exiting to a job ► No difference between subjects with tertiary and basic education

4. Applied Statistics 2005 New model LABOR OFFICE IN PRIBRAM ► Subjects registered in 2002 ► Follow-up period: January 2002 – July 2004 (30 months) ► 4275 unemployed

5. Applied Statistics 2005 New model FACTORS ► Age ► Sex ► Education ► Season of registration by Labor office ► Place of living ► State of health ► Martial status

6. Applied Statistics 2005 New model - Factors AGE ► Minimum 15 years ► Maximum 61 years ► Mean 33 years ► Median 30 years SEX ► Females 51% (52%) ► Males 49% (48%) PLACE OF LIVING ► Towns 58% ► Villages 42%

7. Applied Statistics 2005 New model - Factors EDUCATION ► Basic 16% (18%) ► Secondary without GCE 48% (50%) ► Secondary with GCE 32% (29%) ► Tertiary 4% (3%) (180 subjects)

8. Applied Statistics 2005 New model - Factors SEASON OF REGISTRATION ► Spring 20% ► Summer 28% ► Autumn 35% ► Winter 17% MARTIAL STATUS ► Single, divorced or widowed 56% ► Married or common-law marriage 44% STATE OF HEALTH ► Perfect 89% ► Disabled 4% ► Full or partial disability pension 7%

9. Applied Statistics 2005 Arguments for survival analysis ► 1309 observations is right censored - no exit to job or lost to follow up ► Duration of unemployment is positively skewed

10. Applied Statistics 2005 Cox proportional model ► Distribution of duration of unemployment and error components is not known ► Cox proportional hazard model ► Estimated hazard ratios are easy to explain

11. Applied Statistics 2005 Comparison of alternative models ModelVariable AGENo. of variablesAIC 1AGE, AGE^2 Continuous age model 1344890,944916,9 2AGEM Interval classified age model 19 44873,02 44911,02 Compared modelsGDfp-value 2 vs 117,8860,007 Likelihood ratio test

12. Applied Statistics 2005 Cox proportional model estimation VariableParameter estimation Hazard ratio VariableParameter estimation Hazard ratio AGE (21-25)0.32874***1.389EDU20.61716***1.854 AGE (26-30)0.15007**1.162EDU30.65555***1.926 AGE (31-35)0.27294***1.314EDU40.71576***2.046 AGE (36-40)0.24667***1.280SPRING-0.11240**0.894 AGE (41-45)0.124711.133SUMMER-0.09577*0.909 AGE (46-50)0.087541.091AUTUMN-0.12567**0.882 AGE (51-55)-0.33129***0.718FAMILY0.007741.008 AGE (56 >)-1.16671***0.311HEALTH2-0.67898***0.507 MALE0.20277***1.225HEALTH3-1.03489***0.355 TOWN-0.08930**0.915 (* P<0.1, ** P<0.05, *** P<0.01)

13. Applied Statistics 2005 Survival function estimation Interval classified age model. Estimated survival function for female, basic education, registered in winter, perfect health condition, village, single. Distinction by age. Continuous age model. Female, basic education, registered in winter, perfect health condition, village, single. Distinction by age.

14. Applied Statistics 2005 Survival function estimation Interval classified age model. Female, 33 years old, registered in winter, perfect health condition, village, single. Distinction by level of education.

15. Applied Statistics 2005 Survival function estimation Interval classified age model. Male, 33 years old, secondary education with GCE, registered in winter, village, single. Distinction by state of health.

16. Applied Statistics 2005 Next research ► Orientation on the Czech Republic as a complex ► Influence of regional diversification should be examined ► Influence of other factors ► Relationship between the length of unemployment and the age of subjects