MODELLING TIME OF UNEMPLOYMENT VIA COX PROPORTIONAL MODEL

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MODELLING TIME OF UNEMPLOYMENT VIA COX
PROPORTIONAL MODEL

• Jan Popelka Department of Statistics and
  Probability University of Economics, Prague

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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

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Previous model

• AGE and AGE2 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

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New model

• LABOR OFFICE IN PRIBRAM
• Subjects registered in 2002
• Follow-up period
• January 2002 July 2004 (30 months)
• 4275 unemployed

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New model

• FACTORS
• Age
• Sex
• Education
• Season of registration by Labor office
• Place of living
• State of health
• Martial status

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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

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New model - Factors

• EDUCATION
• Basic 16 (18)
• Secondary without GCE 48 (50)
• Secondary with GCE 32 (29)
• Tertiary 4 (3)
• (180 subjects)

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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

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Arguments for survival analysis

• 1309 observations is right censored - no exit to
  job or lost to follow up
• Duration of unemployment is positively skewed

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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

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Comparison of alternative models
Model Variable AGE No. of variables AIC
1 AGE, AGE2 Continuous age model 13 44890,9 44916,9
2 AGEM Interval classified age model 19 44873,02 44911,02
Likelihood ratio test
Compared models G Df p-value
2 vs 1 17,88 6 0,007
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Cox proportional model estimation
Variable Parameter estimation Hazard ratio Variable Variable Parameter estimation Hazard ratio
AGE (21-25) 0.32874 1.389 EDU2 EDU2 0.61716 1.854
AGE (26-30) 0.15007 1.162 EDU3 EDU3 0.65555 1.926
AGE (31-35) 0.27294 1.314 EDU4 0.71576 0.71576 2.046
AGE (36-40) 0.24667 1.280 SPRING -0.11240 -0.11240 0.894
AGE (41-45) 0.12471 1.133 SUMMER -0.09577 -0.09577 0.909
AGE (46-50) 0.08754 1.091 AUTUMN -0.12567 -0.12567 0.882
AGE (51-55) -0.33129 0.718 FAMILY 0.00774 0.00774 1.008
AGE (56 gt) -1.16671 0.311 HEALTH2 -0.67898 -0.67898 0.507
MALE 0.20277 1.225 HEALTH3 -1.03489 -1.03489 0.355
TOWN -0.08930 0.915








( Plt0.1, Plt0.05, Plt0.01)
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Survival function estimation
Continuous age model.Female, basic education,
registered in winter, perfect health condition,
village, single. Distinction by age.
Interval classified age model. Estimated
survival function for female, basic education,
registered in winter, perfect health condition,
village, single. Distinction by age.
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Survival function estimation
Interval classified age model. Female, 33 years
old, registered in winter, perfect health
condition, village, single. Distinction by level
of education.
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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.
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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