MODELLING TIME OF UNEMPLOYMENT VIA COX PROPORTIONAL MODEL

MODELLING TIME MODELLING TIME OF OF

UNEMPLOYMENT UNEMPLOYMENT VIA COX VIA COX

PROPORTIONAL PROPORTIONAL MODELMODEL

Jan Popelka Jan Popelka Department of Statistics and Department of Statistics and

Probability University of EconomicsProbability University of Economics,, PraguePrague

Applied Statistics 2005

Previous Previous modelmodel

LABOR OFFICE IN PRIBRAMLABOR OFFICE IN PRIBRAM►Subjects registered in January 2002Subjects registered in January 2002►Follow-up period: Follow-up period:

from January 2002 to June 2003 from January 2002 to June 2003 (18 (18 months)months)

►597 unemployed597 unemployed(175 right censored)(175 right censored)

FACTORSFACTORS►age, sex, educationage, sex, education


Previous Previous modelmodel

►AGE and AGE^2 variables (continuous)AGE and AGE^2 variables (continuous)

DISPUTABLEDISPUTABLE CONCLUSIONS: CONCLUSIONS:►No relationship between sex and the No relationship between sex and the

probability of exiting to a job probability of exiting to a job ►No difference between subjects with No difference between subjects with

tertiary and basic educationtertiary and basic education


NewNew model model

LABOR OFFICE IN PRIBRAMLABOR OFFICE IN PRIBRAM►Subjects registered in Subjects registered in 20022002►Follow-up period: Follow-up period:

January 2002 – July 2004 (30 months)January 2002 – July 2004 (30 months)►4275 unemployed4275 unemployed


New modelNew model

FACTORSFACTORS►AgeAge►SexSex►EducationEducation►Season of registration by Season of registration by LLabor officeabor office►Place of livingPlace of living►State of healthState of health►Martial statusMartial status


New model - New model - FFactorsactors

AGEAGE►MMinimum 15 inimum 15

yearsyears►MMaximum 61 aximum 61

yearsyears►MMean 33 yearsean 33 years►MMedian 30 yearsedian 30 years

SEXSEX►Females 51% Females 51% (52%)(52%)

►MMales 49% ales 49% (48%)(48%)

PLACE OF LIVINGPLACE OF LIVING►TTowns 58%owns 58%►Villages 42%Villages 42%



EDUCATIONEDUCATION►Basic 16% Basic 16% (18%)(18%)

►Secondary without GCE 48% Secondary without GCE 48% (50%)(50%)

►Secondary with GCE 32% Secondary with GCE 32% (29%)(29%)

►Tertiary 4% Tertiary 4% (3%)(3%) (180 subjects)(180 subjects)



SEASON OF REGISTRATIONSEASON OF REGISTRATION► Spring 20%Spring 20%► Summer 28%Summer 28%► Autumn 35%Autumn 35%►Winter 17%Winter 17%

MARTIAL STATUSMARTIAL STATUS► SSingle, divorced or widowedingle, divorced or widowed 56% 56% ►Married or common-law marriage 44% Married or common-law marriage 44%

STATE OF HEALTHSTATE OF HEALTH► Perfect 89%Perfect 89%►Disabled 4%Disabled 4%► Full or partial disability Full or partial disability

pension 7%pension 7%


Arguments for survival Arguments for survival analysisanalysis

► 1309 observations is right censored - no exit to 1309 observations is right censored - no exit to job or lost to follow upjob or lost to follow up

►Duration of unemployment is positively skewedDuration of unemployment is positively skewed

0

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0-100 101-200 201-300 301-400 401-500 501-600 601-700 701-800 801-900

Time of unemployment (days)

Fre

qu

en

cy


Cox proportional modelCox proportional model

►Distribution of duration of Distribution of duration of unemployment and error components unemployment and error components is not knownis not known

►Cox proportional hazard modelCox proportional hazard modelT

0( , , ) ( ) exp( )h t h tx β x β

T

1 0 1 0( , , ) exp[( ) ]t x x x x β

►Estimated hazard ratios are easy to explainEstimated hazard ratios are easy to explain


Comparison of alternative Comparison of alternative modelsmodels

Model Variable AGE No. of variables AIC

1 AGE, AGE^2Continuous age model

13 44890,9 44916,9

2 AGEMInterval classified age model

19 44873,02 44911,02

Compared models G Df p-value

2 vs 1 17,88 6 0,007

ˆ2 log L

Likelihood ratio test


Cox proportional model Cox proportional model estimation estimation

Variable Parameter estimation

Hazard ratio

Variable Parameter estimation

Hazard ratio

AGE (21-25) 0.32874*** 1.389 EDU2 0.61716*** 1.854

AGE (26-30) 0.15007** 1.162 EDU3 0.65555*** 1.926

AGE (31-35) 0.27294*** 1.314 EDU4 0.71576*** 2.046

AGE (36-40) 0.24667*** 1.280 SPRING -0.11240** 0.894

AGE (41-45) 0.12471 1.133 SUMMER -0.09577* 0.909

AGE (46-50) 0.08754 1.091 AUTUMN -0.12567** 0.882

AGE (51-55) -0.33129*** 0.718 FAMILY 0.00774 1.008

AGE (56 >) -1.16671*** 0.311 HEALTH2 -0.67898*** 0.507

MALE 0.20277*** 1.225 HEALTH3 -1.03489*** 0.355

TOWN -0.08930** 0.915

(* P<0.1, ** P<0.05, *** P<0.01)


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Est

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Age 21 - 25

Age 31 - 35

Age 51 - 55

Baseline survivalfunction (age 15 - 20)

Survival function estimationSurvival 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.

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Esti

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Age 21

Age 33

Age 54

Baseline survivalfunction (age 0)



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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Basic education

Secondary educationwithout GCE

Secondary education withGCE

Tertiary education



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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Perfect

Disabled

Full or partial disability pension


Next researchNext research

►Orientation on the Czech Republic as a Orientation on the Czech Republic as a complexcomplex

► Influence of regional diversification Influence of regional diversification should be examined should be examined

► Influence of other factorsInfluence of other factors►Relationship between the length of Relationship between the length of

unemployment and the age of subjectsunemployment and the age of subjects

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MODELLING TIME OF UNEMPLOYMENT VIA COX PROPORTIONAL MODEL