A C T A U N I V E R S I T A T I S L O D Z I E N S I S __________ FOLIA OECONOMICA 182, 2004
Anna M alarska*, Zbigniew Szym c zak *’
S E L E C T E D H A Z A R D M O D E L S IN A P P L IC A T IO N T O A N A L Y S E S O F U N E M P L O Y M E N T
1. In trod u ction
The subject o f the testing is the analysis o f results o f the survey study
carried out i.e. the T esting Econom ic Activity o f Population in Poland. Random and representative control group incorporated in the testing carried out by the Polish C entral Statistical O ffice (G U S) included the group o f m ore than 54 thousand Poles. On the basis o f the available set o f questionnaires, the characteristics o f people out o f wok have been m ade according to the dem ographic and social covariates which statistically have a considerable influence on the tim e o f being unem ployed and able and w illing to work.
T h e aim o f presented analysis is adaptation and em pirical verification o f the
usefulness o f selected statistical tools characteristic o f survival analysis used for the determ inant identification and description o f the situation on the labour market in Poland. In particular, the aim o f the authors is to check the usefulness o f selected D. R. C o x ’s m odels (param etric and non-param etric) for estim ation o f the relationship connected with the risk o f experiencing long-term unem ploym ent.
2. Historical background of Poland and the European Union countries
The biggest social and econom ic problem in Poland at the turn o f the centuries is high unem ploym ent rate. The situation o f perm anent im balance on the labour m arket m anifesting itself in the dom ination o f supply over the
Prof., Chair o f E conom ic and Social Statistics, University o f Lódź.
dem and for w orkplaces occurred in the moment o f reform s. H ow ever, in recent years, the num ber o f unem ployed people, i.e. people out o f work, but actively looking for a jo b and able to work is alarm ingly h ig h 1.
T he synthetic m easure o f the unem ploym ent is unem ploym ent rate. The com parison m ade in 15 m em ber countries o f the EU and in Poland in the years
1993-2002 dem onstrates the follow ing regularities:
■ in the EU countries (excluding Greece) there is a dow nw ard trend o f the phenom enon,
• the fastest decline in the rate o f unem ploym ent is in Ireland,
■ the average rate o f unem ploym ent in the EU countries fluctuates between 2.6% (L uxem bourg) and 15.4% (Spain), the sm allest diversity was noticed in A ustria (0.31% ), w hereas the biggest in Ireland (4.39% ).
■ the tendency o f changes in the unem ploym ent rates in Poland is incom parable with other EU countries. The crucial m om ent for Poland was year 1998 when the dow nw ard trend o f the years 1993-1997 changed into the perm anent upw ard trend. T he achievem ent o f the period o f 1993-1997 was evened up in the follow ing years and continues until today. T he m easurable consequence o f this is higher m iddle year rate o f the unem ploym ent rate rise in the years 1997-2002 (by 0.2% ) in com parison with the average dynam ics of decline betw een 1993-1664 (by 1 . 5 % ) - see Figure 1.
C N C O ^ t n C D I ^ O O O l O - ł - C N I
0 ) 0 ) 0 ) 0 ( 7 ) 0 ) 0 ) 0 ) 0 0 0
0 ) 0 ) 0 ) 0 0 ) 0 ) 0 ) 0 ) 0 0 0 T - v - r - T - f - r - ^ ^ c N C N C N -EU -o-Ireland -»-Germany Greece о Spain -♦-Poland
Fig. I. U nem ploym ent rate in UE countries and Poland in 1 9 9 3 -2 0 0 2 S o u r c e : Own description based on Eurostat Survey.
1 According to recom m endations o f EUR OSTAT the International Work Organisation and European Statistic O ffice, the requirement for classifying a person to the group o f unem ployed is meeting the listed three conditions. The same criterion is applied by the G US In BAEL additionally sp ecifyin g that the unem ployed person can be a person w ho is at least 15 and not older than 74 years old.
There is a heated pre referendum discussion about the direction o f transform ations o f Polish im balanced labour m arket perceived m ost o f all through the prism o f unem ploym ent. The com parison analyses o f unem ploym ent in time line, in the EU m em ber countries indicate that in the past in many of them the rate o f unem ploym ent raised ju st before a co u n try ’s accession and during the first years o f m em bership (N ow ak 2003, pp. 7 -9 ). If this regularity was to take place in Poland, it is justified to identify a European U nion country w hose labour m arket underw ent changes in a sim ilar way in the past.
T he country to which unem ploym ent in Poland is m ost often com pared is Spain. The com parison is ju stified by the convergence in the tendency of changes in unem ploym ent rates in Poland and in Spain having assum ed eight- year-period o f delay - see Fig. 2.
- • - S t o p a bezrobocia Hiszpania 1982-2001 - » - S t o p a bezrobocia Polska 1990-2001
Fig. 2. Unem ploym ent rate in Spain in 1982-2001 and in Poland in 1990 -2 0 0 1 S o u r c e : Burwicz 2002.
The elem ent that m akes the convergence o f unem ploym ent rates in Spain and Poland alike is general tendency o f changes. H ow ever, the detail that clearly differentiates them is the level, incidentally higher for Poland. If the scenario o f the Spanish path o f changes in the unem ploym ent rates proved to be true for Poland (even if slightly delayed in tim e), the essential condition for Poland is the country’s accession to the European Union. And having considered the level reserve and the close perspective o f our accession to the EU , the discussion about hypothetical scenario o f the situation o f changes on the labour m arket in Poland is open. Figure 2 dem onstrates two o f them with a dashed line. On the basis o f the optim istic course o f unem ploym ent rate in Poland in the near future, the assum ption is m ade about dynam ically developing positive changes o f national econom y in Poland and the positive influence o f external conditions.
L
0,0%3. T h eo retica l an a ly sis tools - su rvey m eth od ology
The duration (survival) analysis does not belong to the standard set o f statistical analysis m ethods. It is a special m ethod for perform ing the results of studies based on individual data in conditions o f having incom plete data set. The subject o f interest o f the survival analysis2 is the duration tim e o f the phenom enon, and especially, the length o f transition tim e from one state to another for individuals (that is the changes o f status quo o f an individual, a case or a person). The change in the position (state) o f an individual is known as “death” . So, there are tw o types o f time data: censored and relapsed. O bservation is called censored (by the period o f analysis) if during the tim e o f perform ing survival analysis an object did not change its state. It is relapsed () otherw ise. Uncensored time data, which can occur, is not predicted. The inability to predict the m om ent o f change o f an individual’s state m eans incom plete data set.
T hese statistical m ethods also provide an appropriate analytical fram ew ork for studying the probability o f leaving the state o f definite phenom ena.
Let t j ( i = p , к , • ) m eans three spells o f individual observation over a period o f tim e such as:
t - initial m om ent o f the period o f survival analysis, t k - final m om ent o f the period o f survival analysis,
/ . - m om ent o f the change o f state (status quo) o f an individual.
The crucial point o f censored observation on the tim e axis ( / ) in survival analysis is illustrated in Figure ЗА) and 3B).
A) period o f survival analysis
S---^ --- ~4
1 1-
--t „ t „ t
the term ( / . ) o f th e change of an individua l's state is unknow n
B) period o f survival analysis
--- Г ■ ^ 1 --- 1--- ►
t p t к I щ t
the term ( / . ) of the change of an individual's state lies out of a period of survival analysis
Fig. 3. Censored observation In survival analysis
2 The term survival analysis is known in biom edical scien ce and demography. It is called the duration analysis in econ om ic applications and reliability analysis in engineering applications.
It happens that the change o f an individual state takes place in the period o f survival analysis. Such observation is called relapsed (uncensored), and it is illustrated in Figure 4.
period o f survi val analysis
1 ---
1---t-t p t» t к
s. ---- v--- ^ I
state 1 state 2
Fig. 4. Relapsed observation in survival analysis
T he pioneers o f survival analysis are: D.R. Cox and D. O akes. T heir m onograph entitled Analysis o f survival data published in 1984 greatly contributed to the theory and practice o f this testing m ethod.
O ne o f survival analysis m ethods is causal m odels. They are built sim ilarly to classical regression equations. N evertheless, in order to characterise the relationships betw een the risks o f long term period o f being in a definite state, it is unfounded to use sim ple m ethods o f m ultiple regression for the follow ing reasons:
• the com plexity o f distribution o f dependent variable which is the tim e of duration (m ost often undergoes exponential or W eibull distribution),
• occurrence o f censored observations.
The reasonable tool is Cox regression being the m ethod for m odeling time- to-event data in the presence o f censored cases.
P a r a m e t r i c causal m odels used in time data analysis (for cases being in
a definite state) are (Stanisz 2000, p. 349):
- model o f linear regression: i = + (1)
j=i
- log-norm al regression model: ln( t ) = a0 + £ üjXj + e , (2) J=!
( " "1 -e x p o n e n tia l m odel: S( 1 ) - e x p a 0 + ' Z a j x j + e ,
I j=l
however, п о п - p a r a m e t r i c group com prises of:
- C ox’s proportional hazard model: h ( t ) = h 0( t )- e x p
(3)
\
t a j X j
j=i
- C o x ’s proportional hazard model with explanatory variables depended on time:
In form ulas (1)—(5) the argum ent o f a hazard function Xj (xk ) indicates
j - t h ( к - th ) case o f determ inant A" (factor, explanatory variable) o f being
an individual in invariable state.
In the first tw o m odels, it is assum ed that the survival tim e (or log survival tim es) com es from a normal distribution. If lognorm al regression is requested,
i is replaced by its natural logarithm. The estim ators are com puted by using
a very efficient m ethod, the so-called expectation m axim ization (EM ) algorithm , for obtaining the m axim um likelihood estim ates for this m odel. In exponential model (3), it is assum ed that the distribution o f dependent variable is exponential. T he usual method to estim ate the structural param eters of param etric m odels is by m axim um likelihood (ML).
C o x’s non-param etric model ((4) and (5)) - contrary to param etric models - is focused on the changes o f the hazard function factored by a function o f elapsed duration / and the function o f explanatory X variable. The proportional hazard model (4) is the most general o f the regression models. It does not make any assum ptions about the nature or shape o f the underlying survival distribution. The model assum es that the underlying hazard rate3 (rather than survival time) is a function o f the independent variables (covariates); thus, in a sense, C ox’s regression model may be considered to be a nonparam etric method. M odel № (4) only assum es that the risk o f failure the state over time depends on:
♦ changes o f contingent on the particular covariate vector X (independent variables),
♦ the so-called base-line hazard li0(t) (referred also as the zero hazard line when the values for all independent variables (i.e., in A") are equal to zero) with unknown form o f a function.
In this model only base-line hazard function depends on tim e t. O ther explanatory factors, w hich are com prised in the log-linear function, are not correlated w ith tim e t. Thus, another assum ption called p r o p o r t i o n a l i t y is made. T his is, therefore, assum ed that the proportion o f hazard assigned for two different m om ents does not depend on tim e t and is specified as:
3 The hazard rate is defined as the probability per time unit that a case that has survived to the beginning o f the respective interval will fail in that interval. Sp ecifically, it is com puted as the number o f failures per time units in the respective interval, divided by the average number o f surviving cases at the m id-point o f the interval.
h ( t , x , , x 2, - , x n ) 1
— 1--- — ---1 = exp
h \ t , x\,x'2...x'J Í a j ( x j - x ) ) (6)
I he aim of these exploratory analyses is to identify the determ inants o f the changes o f phenom ena in time. It im plies the necessity o f dividing (stratification) o f sam pling (control group). If in every separated stratum (sub set) different hazard functions occur, then the s t r a t u m a n a l y s i s is likely to occur in C o x ’s proportional hazard models. It is useful for:
♦ discovering com plex and unknown (therefore difficult to identify) interactions betw een explanatory variables and time o f survival o f every stratum ,
♦ verification o f diversification for the dependence in every stratum .
T he assum ption of proportionality is disproved in other non-param etric hazard m odels (5) since in many cases it is not possible to m ake an unconditional assum ption o f independence o f tim e and explanatory variables. M ethods o f the evaluation o f the dependence o f explanatory variable to tim e are:
- analysis o f hazard function figures prepared for tw o or several sub-sets o f this variable (they should not cross) and
- verification o f the hypothesis o f statistical significance o f a variable which is considered to be dependant on time, after having previously developed the model described by equation (4) to the form o f model (5).
The estim ation m ethod o f the param eters o f both non-param etric hazard m odels (after having transform ed them into a m ore sim ple form ) is by the m axim um likelihood with incom plete data set. T he goodness-of-fit m easure is com puted as usual, that is, as a function o f the log-likelihood for the model with all covariates, and the log-likelihood o f the model in which all covariates are forced to 0. The significant value of chi-square (^ 2) - statistics obtained in increm ent test4 - proves the hypothesis stating that the independent variables have significant influence on the time o f survival o f individuals (cases). The results spreadsheet with the param eter estim ates for the Cox non-param etric hazard regression model includes the so-called W ald statistic, and the p -level for that statistic. T his statistic is based on the asym ptotic norm ality property o f m axim um likelihood estim ates. The W ald statistic is tested against the chi- square distribution. T he estim ators o f non-param etric C o x ’s m odels are interpreted as hazard ratios. They show the scale o f increasing risk leaving the definite state by e /!' -1 100% if the X j determ inant rises by one unit.
4 The value o f test is equal to doubled difference o f the logarithm o f lik elihood function for model together with all explanatory variables and the logarithm o f lik elihood function for the model in which independent variables were replaced with zeros.
4. C h a ra cteristics o f B A E L control group
4.1. Principles of rotation and selection of individuals for the test
The survey o f econom ic activity o f population (BAEL) in Poland has been carried out by GUS since M ay 1992. Until the fourth quarter o f 1999 it took place in specifically determ ined periods of time. In fixed in advance and always in the same week o f February, May, August and November m embers o f approxim ately 20 thousand households, randomly chosen, having considered the representative factor o f the control group, gave answers about their professional status. At present, the survey is carried out all year round with the so called m ovable survey week. This m eans that every week (it is assumed that there are 13 weeks in a quarter) m embers o f the households which were drawn from the quarterly control group are surveyed and constitute thirteenth part. Invariably since the second quarter o f 1993, quarterly control groups are selected rotationally. Every time the quarterly control group in the num ber o f 24440 flats is divided into 4 subgroups, and every quarter two o f them are changed. One o f them is totally new and the other one is the one which was surveyed in exactly the same quarter o f the previous year. Individuals o f particular subgroups are selected random ly and independently from the results o f the drawing to other subgroups. In the “lifetim e” o f every established subgroup, the group is observed for two subsequent quartets of the year. The survey period is suspended for half a year, and then again reactivated only for a half-a-year period, and then the group comes to an end o f its life.
Individual tim e data sets, which are a subject to this analysis, com e from the control group num ber 12, i.e. surveyed in February 1995. In the initial period of the labour m arket research (until M ay 1999), GUS m ade observations with quarterly frequency and alw ays in the m iddle month o f every quarter.
4.2. Demographic and social structure of the control group
The structure o f B A EL control group being a subject to em pirical analysis in several selected dem ographic and social sections is presented in Figure 5 -7 .
B A EL control group com prises of males in 47.5% . R egardless o f sex, the most num erous is the group o f econom ically active people (48.6% ). 8.4% out o f the w hole population surveyed are unem ployed persons - see Figure 5a and 5b.
In the survey GUS distinguishes seven education categories, i.e. tertiary (university), post secondary, secondary vocational, general secondary, basic vocational, prim ary and incom plete primary. The biggest group is represented by the population with prim ary education (19.2 thousand) , in the next place with basic vocational (14.0 thousand). The sm allest group is represented by the population with post secondary education (1.2 thousand). In the light o f the
distinguished professional activity categories, the w idest diversity is am ong population with general secondary education, and in the second place basic vocational, how ever the least diverse is the population with incom plete elem entary education - see Figure 6.a-6.d.
W omen i oonomfa My nm nyi i mptoytd S ', 9 4 III.I, tiv r Employed Unemployed 7. 9 % ■v: г a) b)
Fig. 5. E conom ic activity o f the population In Poland by sex S o u r c e : Own schem e based on BAEL data In February 1995.
E ducation level te rtia ry
Economically inactive
19 8%
Employed 65 9 %
Education level: secondary vocational
Economically inactive
24 4%
a)
b)
E ducation level: general secondary
Economically 45 5%
E m p lo y e d U nem ployed
A 4% 4 о fv ,
E ducation level: g ram m ar school and low er
Fmnlnvori
EooiKHnlHwy
d)
Fig. 6. E conom ic activity o f the population In Poland by the level o f education S o u r c e: A s same as Fig. 5.
The structure o f professional activity o f the population surveyed according to the place o f residence and considering the division into urban and rural as it is illustrated in Figure 7a-7 b .
Residence: ur'ban Economically inactive 44 t% Employed 47 1% Employed 50 8% Residente: ru ra l Economically inn. tiv r 4 1 3% a) b)
Fig. 7. E conom ic activity o f the population In Poland by place o f residence S o u r с e: A s same as Fig. 5.
P o p u latio n o f cities over 100 thous. Economically
inactive 44 8%
P opulation o f cities un d er 5 thous Lco no m n ully ... Ii.r 4‘, 0" .. E m p lo ye d 44 1% b)
population In Poland by urban residence
Employed 47 9%
a)
Fig. 8. Econom ic activity o f the S o u r c e : As same as F’ig. 5.
T he category “ urban” in B A EL control group is desegregated into 7 variants distinguished by the num ber o f inhabitants. The biggest num ber o f the population surveyed lives in cities o f over 100 thousand population and the sm allest num ber in those below 5 thousand (also below 2 thousand). From the point o f view o f distinguished professional activity categories, the m ost diverse is the population o f the biggest cities, and next o f the cities with a population o f between 5 and 9.999 thousand inhabitants. The least diverse is the population o f the sm allest cities.
4.3. Technology o f filtering the control group
M ethodology o f survival analysis in the aspect o f identification o f social and econom ic determ inants with respect to the periods o f unem ploym ent requires the division o f statistical control group into tw o separate groups. First o f them consists o f persons who were out o f work in the past, yet, once they got the job, they belonged to S labour forces . The other group is m ade up o f other
individuals w ho (•) eith er despite the efforts they m ade rem ained in
S unem ployed or (•) are ^ econom ically inactive |. U sing the term inology
characteristic o f survival analysis they are respectively: - persons about whom an analyst has com plete data set, - persons about whom an analyst has incom plete data set, - persons passed over the analysis.
Schem e 1. Technology o f filtering BA EL’s control group
S o u r c e : Own schem e based on BAEL survey.
The aim o f the algorithm o f BAEL control group filtration is the selection o f individuals affected by unemployment in the real time o f the survey (for the critical
moment o f the observation) or not in the distant past. Classification algorithm of the selection o f persons in BA EL’s control group is presented in Schem e I.
5. E m p irical hazard m od els
T his study includes estim ations o f selected hazard m odels where the follow ing sym bols are used:
- explicate variable - /: time o f being unem ployed (given in m onths), -e x p la n a to ry v a ria b le - p r a c t i c e (job seniority): total period o f w orking in the last place o f work in case o f unem ployed persons or jo b seniority in the present w orkplace in case o f em ployed persons,
- explanatory variable - a g e : age o f a person surveyed in the B A EL survey. T he first result breakdow n presents estim ations o f param etric hazard m odels in their general form ula - see T able 1.
T he high form al, content-related and m ethodological note o f estim ations of hazard m odels given in the m axim um likelihood estim ation m ethod consists of:
1° correctness o f algebra sym bols referring to respected explanatory variables. T he increase o f practice o f an unem ployed is accom panied by shorter duration o f unem ploym ent and along with an unem ployed p erso n ’s age the duration is extended. T his regularity show s the paradox o f P olish labour m arket in a sense that the chances o f finding a jo b by an unem ployed person are the bigger, the m ore experienced and younger he or she is. A P olish em ployer therefore offers a jo b to an unem ployed person w ith con siderab le work experience but young. T his m eans that the risk o f being unem ployed affects in m ajority older and m ost o f all w orse qualified persons,
2° the quality o f param eters o f stochastic structure o f m odels is com prised of: - absolutely small values o f standard errors in relation to estim ations o f relevant param eters,
- high values o f /-Student statistics testing the significance o f every explanatory variable. T he test shows that at any low (bordering on reliability: p = 0.000) level o f significance the true hypothesis is the one concerning the influence o f jo b seniority and age on the duration o f unem ploym ent,
3° goodness-of-fit o f every model manifested in both the level o f the measure o f fitting analytical form to empirical data and the accuracy evaluation as for the choice o f explanatory variables. In case o f hazard m odels estim ated by the m aximum likelihood estim ation method, this evaluation is m ade in aggregate by the x 2 statistics. This test shows that at any low level o f significance (nearly reliable: p ~ 0.000) the statem ent that the distinctness o f quotation with specified explanatory variables in relation to the hypothetical model where these variables were not included is true.
Table 1. Estim ates and statistical characteristics o f the parametric m odels o f survival analysis
variable beta standard
error t-St P variable beta
standard
erro r t-St P variable beta
standard
error t-St P normal model" log-norm al m odel exponential m odel
pra ctice -2 .1 5 4 0.054 -3 9 .5 4 3 0.000 pra ctice -0 .1 4 2 0.004 -3 5 .0 7 1 0.000 p ractice -0 .1 7 5 0.005 -3 7 .0 7 3 0.000
age 1.749 0.051 34.429 0.000 age 0.114 0.004 30.129 0.000 age 0.145 0.005 30.022 0.000
constant -1 1 .8 0 0 1.227 -9 .5 8 9 0.000 constant 0.704 0.091 7.734 0.000 constant 0.466 0.115 4.063 0.000 3^= 2152.33; df = 2; p = 0.000 X2= 1814.49; d f = 2; p = 0.000 XJ= 2073.69; df = 2; p = 0.000
“ Broadening o f practice (m easured by the total jo b seniority) for the period o f one year results in shortening the time o f searching for a jo b by slightly longer than 2 m onths on average having assum ed ceteris paribus. On the same prem ise, it is expected that the duration o f unem ploym ent is extended by nearly 2 m onths together w ith another year o f the unem ployed goin g by.
S o u r c e : Own calculation based on B A E L ’s survey.
-J Scl cclcd H a/. ar d Mod els in Appl ica ti on to A n a ly s e s ...
T o recoup: the attributes o f presented m odels are both (• ) statistical significance o f data which brings in respected independent variables to the description o f dependant variable and (•) an adequately good description o f the analysed phenom enon (in statistical meaning). Both explanatory variables appear to be “essential” predictors o f time during w hich an unem ployed can search for a jo b and every model “explains” the analysed phenom enon to a satisfactory extent (adequately well).
F urther em pirical action o f the above m entioned hazard model is enriched with an elem ent o f quality (factor) diversifying the control group into groups called strata. In the survey, the stratification factors o f the control group are sex, place o f residence or level o f education. This group o f C o x ’s hazard m odels, called m odels with stratification, enables carrying out tests to check the consistency o f at least tw o em pirical distributions o f explanatory variable (duration o f unem ploym ent) extracted on the basis o f variants o f stratification factor. T he discrim inant o f stratification model is separate m atching the hazard function for every partial group described by the variants o f the respected factor and including the possibility o f making an assum ption that there are different forms o f hazard functions within the stratum. The aim o f analysis with stratum is to discover the significant distinctions between distributions o f selected groups.
The results o f consistency o f param etric estim ations o f hazard m odels within and without the stratum form ula are presented in T able 2.
Table 2. Estimates o f hazard m odels with stratification and w ith o u t"
Model log-likelih ood - total log-likelihood by groups ľ d f V stratification by gender exponential -1 0 7 2 9 .7 0 -1 0 7 1 9 .8 0 19.726 3 0 .0 0 0 1 9 4 log-normal -5 3 2 7 .2 9 -5 3 1 5 .4 2 23.752 4 0 .0 0 0 0 9 0 normal - 1 1 9 0 0 .3 0 - 1 1 8 6 5 .2 0 70.178 4 0 .0 0 0 0 0 0
stratification by place o f residence
exponential -1 0 7 2 9 .7 0 - 1 0 6 9 9 .9 0 5 9.644 21 0.0 0 0 0 1 5
log-normal -5 3 2 7 .2 9 - 5 2 7 9 .4 7 95.652 28 0 .0 0 0 0 0 0
normal -1 1 9 0 0 .3 0 -1 1 8 4 4 .5 0 111.490 28 0 .0 0 0 0 0 0
stratification by educational level
exponential - 1 0 7 2 1 .3 0 -1 0 5 6 7 .5 0 307.475 15 0 .0 0 0 0 0 0
log-normal - 5 3 2 2 .3 9 -5 1 5 1 .8 3 341.134 20 0 .0 0 0 0 0 0
normal -1 1 8 8 9 .8 0 -1 1 6 8 5 .4 0 408.908 20 0 .0 0 0 0 0 0
“ Every presented model describes the reality in a better way in the variant with stratification rather than without it. The value o f chi-squared statistics o f accretion test informs to what extent the model with distinguished strata differs from the model without stratification. The underpinning o f hypothesis about the existence o f distinctions in the quality o f compared m odels is justified at any low level o f significance (p).
The results o f the analysis prove that the introduction o f factors diversifying unem ployed persons according to sex, place o f residence or education, im proves the Figure o f the model phenom enon and the precision o f its description. The position o f an unem ployed person looking for a source o f incom e to the great extent depends on what sex he or she is, where he or she lives and what his or her professional qualifications are. This means that the personalized features o f an individual statistically diversify his or her chances o f exiting unem ployed resources.
A nother result breakdow n (see T able 3) includes the effect o f estim ation of C ox’s proportional hazard model in general form ula (in case o f the control group in aggregate).
Table 3. Estimates and statistical characteristics o f the C o x ’s model
va ria b le beta sta n d a rd erro r t-St exp(beta) P p ra c tic e 0 .172 0.005 35.925 1. 188 0 .000
a g e -0 .1 4 4 0 .005 - 2 9 .2 7 5 0 .8 6 6 0 .000 X2= 1951.23; < //= 2 ;/> = 0 .000
S o u r c e : As same as Tab. 1.
The estim ated param eters o f C ox’s model are the risk coefficients which in survival term inology mean occurrence o f failure. W ith respect to the peculiarity o f analysed phenom enon, it is a desired state identified with the exit from the unem ployed resources to the group em ployed persons. A ccording to the presented hazard model o f duration of unem ploym ent, the chance o f changing status quo o f an unem ployed rises by approxim ately 18.8% in the circum stances when professional practice improves over 1 year, and every additional year of unem ployed p erso n ’s life has a negative influence on the position on the labour market reducing his or her chance by o f getting a jo b about 13.4%.
Both explanatory variables describing the risk o f changing the state o f an unem ployed (from unem ploym ent to em ploym ent) determ ine it to the great extent and the characteristics o f content-related evaluation o f the model along with the quality evaluation are fully satisfactory.
7. S u m m ary - ev a lu a tio n o f u sefu ln ess o f hazard m od els in the a n a ly sis o f u n em p lo ym en t
Presented application o f the unusual statistic m ethod to the phenom enon of unem ploym ent in Poland brought positive results from the cognitive point of view. H azard m odels, w hich belong to the category o f endurance analysis
m ethods, appeared to be an invaluable tool in discovering the nature and identification o f time determ inants o f searching for a jo b by an unem ployed person in conditions o f highly unstable labour m arket. The situation o f an unem ployed in Poland is highly unfavourable. T he reasons for this can be seen, am ong others, in constantly extending time of being unem ployed which results in the lack o f financial source o f income. From the sociological research it com es out that the poverty and declassification o f unem ployed are spreading w ider and wider.
Some quantitative statistical analyses support sociological research enabling not only identification but also enum eration o f determ inants o f social inequalities caused by bed situation on the labour m arket. Survival analysis m ethods represented in the test are superior to standard m ethods in the sense that they find an application in case when they do not m eet basic m ethodological principles characteristic o f popular m ethods and techniques that model quantitative phenom ena. Formal correctness and thorough content-related evaluation o f results surpasses the perform ed analysis, which from the point o f view o f the objective set in the survey, provides high note o f em pirical usefulness o f m odeling techniques and description o f such an im portant social phenom enon like unem ploym ent.
R eferen ces
B u r w i c z P. (2 0 0 2 ), W ykorzystanie do św ia d czeń H iszpan ii w zw a lcza n iu b ezro b o cia w a n a
lizach sym ulacyjn ych rozw oju rynku p ra c y w P olsce, praca magisterska obroniona na
W ydziale Ek-Soc. UL, Łódź.
G o r t e r C. (1 9 9 1 ), The D ynam ics o f U nem ploym ent a n d V acancies on R egion al L abour
M arkets, Amsterdam.
K u c h a r s k i L. (2 0 0 2 ), P rze p ływ sily ro b o czej w P olsce w latach d ziew ięćdziesiątych .
N o w a k P. Z. (2 0 0 3 ), P olskie b ezro b o c ie w unijnych realiach, „N o w e Ż ycie G ospodarcze”, nr 7, pp. 7 -9 .
S t a n i s z A. (2 0 0 0 ), P rzy stęp n y kurs sta tystyk i z w ykorzystaniem p ro g ra m u STATIST1CA PL na
Anna Mularska, Zbigniew Szymczak
W Y B R A N E M O D E L E H A Z A R D U W Z A S T O S O W A N I U D O A N A L IZ Y B E Z R O B O C IA
Przedmiotem artykułu jest analiza w yników opracowania ankiet pochodzących z Badania A ktyw ności Ekonom icznej Ludności w Polsce. W oparciu o dostępny zbiór ankiet dokonano charakterystyki osób pozostających bez pracy w edług tych cech dem ograficzn o-spolecznych, które statystycznie istotnie oddziałują na czas pozostaw ania w zasobie bezrobotnych osób mogących i chcących pracować. Spraw dzono użyteczność wybranych m odeli D. R. C oxa do szacow ania zależności zw iązanych z ryzykiem długotrwałego pozostaw ania w zasobie bezrobotnych. Zastosow ane w badaniu m etody okazały się cennym narzędziem poznania natury i identyfikacji determinant czasu poszukiw ania pracy przez bezrobotnego w warunkach w ysoce niezrów now ażonego rynku pracy.
