A multivariate labour market model in the Czech Republic 1. Jana Hanclová Faculty of Economics, VŠB-Technical University Ostrava

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1 A mulivariae labour marke model in he Czech Republic Jana Hanclová Faculy of Economics, VŠB-Technical Universiy Osrava Absrac: The paper deals wih an exisence of an equilibrium unemploymen-vacancy rae relaionship in he Czech Republic. We formulae a basic disequilibrium growh model of employmen. Furhermore we sudy a long-run seady sae of his bivariae labour marke model and we ry o inroduce a random disurbance erm. The nex exension of his model makes (un)employmen flows endogenously using macroeconomic cyclical variables as well as variables associaed wih he composiion of he unemploymen. We ry o show an empirical sudy wih monhly ime series over he period for he Czech labour marke. Keywords : Unemploymen-vacancies relaionship, coinegraing analysis, equilibrium models, labour marke model. Inroducion Many economic sudies deal wih he inverse relaionship beween he unemploymen rae and vacancy rae (uv). The basic bivariae labour marke model proposed by Beveridge is possible o exend by inroducing endogeneiy in employmen search. This modificaion gives rise o sudy a mulivariae framework of he (dis)equilibrium relaionship. The objecive of his sudy is o examine he exisence of he uv relaionship in he Czech Republic using more recen daa, from January 993 o December 999. We use appropriae economeric ime series mehods o synhesize pas sudies wih an equilibrium or disequilibrium approach. Cyclical macroeconomic variables and variables associaed wih he composiion of he unemploymen pool are examined wheher hey are relaed wih u and v in he long run using coinegraion analysis. The paper is suppored by he Gran Agency of he Czech Republic gran. No. 42//65 and corresponds o he research programme of he Faculy of Economics VŠB-Technical Universiy no. CEZ:J7/98:2755

2 A mulivariae labour marke model in he Czech Republic The basic and expanded (dis)equilibrium models consruced: A disequilibrium model of ouflows from and inflows o employmen can be E = E E H Q (E) where H hires a period, Q quis lay-offs a period. A hiring funcion can be specified by he Cobb-Douglas funcion wih consan reurns o scale. The flow of he number of hires and rehires a period depends on he socks of unemployed people (U) and vacancies (V) a he end of period (-), and he consan rae job search parameer β according o a following equaion: α α H β [ U V ], (E2) where = β describes he efficiency of job search behaviour. Hiring funcion H is assumed o be homogeneous of degree one in U and V. I is also assumed ha he urnover (qui) rae is proporional o he level of employmen wih he consan rae δ. The ne change in employmen can be expressed using a basic disequilibrium labour marke model: or E = β α α [ U V ] δ E α α [ ue ve ], (E3) e = β δ (E4) where e = E / E ue = U / E ve = V / E. (E5) In a long-run equilibrium labour marke model he job sock and labour force are consan and here is equaliy beween he flows of accessions and separaions on he labour marke (i.e. e = ) : α α [ ve ] = ( α ) β ue δ or ln( ue ) = ln( ve ) + ln( δ / β ), (E6) α α

3 A mulivariae labour marke model in he Czech Republic 54 which is he hyperbolic uv relaionship. Anhony (999) inroduced a random disurbance erm ( ε ) ino E3 as a muliplicaive erm in boh he hiring and qui funcion. In his case we can express he equaion E3 as follows: E or α α µ [ U V ]{ e ν } δ { e } E = β (E7) α = ε (E8) α α α ln( ue ) ln( ve ) + ln( δ / β ) + where 2 2 ε = ν µ, µ ~ N(, σ ) ν ~ N(, ) (E9) µ σ ν This framework allows coinegraion ess o be conduced using he disurbance erm in equaion E8. If i can be shown ha logged ue and ve are I() and ε is I(), hen ue and ve are coinegraed and here is long-run equilibrium. The bivariae labour marke model is resricive as β and δ were specified as fixed parameers, implying ha un(employmen) flows are exogenous. As a consequence, his model will fail o idenify an equilibrium relaionship if addiional variables consiue par of he long-run relaionship. Therefore we modify our model by allowing (un)employmen flows o be endogenously deermined. These flows can be dependen on cyclical macroeconomic variables as well as facors associaed wih srucural unemploymen. Nex we can es wheher his mulivariae specificaion of he Beveridge Curve does in fac represen a long-run or coinegraion relaionship using our daa sample in he Czech Republic. We ry o inroduce following cyclical macroeconomic variables : i ineres rae (PRIBOR 3M) during monh, rwi real wages in indusry during monh, subsr replacemen raio for period [=*(unemploymen benefis/nominal wages in indusry)]. Facors associaed wih he srucural composiion of unemploymen may also be relevan in influencing uv as hey would parially capure coss of labour search. We consider o inroduce: l - number of long-erm unemployed people (> year) a he period, f - number of unemployed females a he period.

4 A mulivariae labour marke model in he Czech Republic 55 The variables o be expressed as funcions of unemploymen rae and vacancy rae in he long run. If we he qui rae is defined as ν ϕ λ i δ = δ rwi subsr e (E) hen a mulivariae disequilibrium labour marke model can be expressed: E β β2 α α µ γ ϕ λ i ν [ U V ]{ e } δ rwi subsr e { e } E = β l f (E) and a mulivariae long-run equilibrium model is ln ue = where ( ) α γ ϕ λ β β2 δ ln ve + ln rwi + ln subsr + i ln le ln fe + ln + ε α α α α α α α β α (E2) l f ε = ν µ, β + β2 =, le =, fe =, λ, ϕ > (E3) E E Equaion E2 provides a richer model srucure han he convenional model E8. 3. Empirical sudy 3.. Time series daa Monhly ime series daa are used for our empirical sudy in he Czech labour marke from he January 993 o he December 999 (i.e. 84 observaions excluding lags in modelling). All series are seasonally adjused wih he excepion of ineres raes and unemploymen benefis. Where quarerly series are available, monhly series are obained by linear inerpolaion. Unemploymen rae (ue ) and vacancy rae (ve ) are shown in Fig UE VE Fig. : Unemploymen rae and vacancy rae developmen

5 A mulivariae labour marke model in he Czech Republic 56 In deerminig he (non)saionariy properies of he daa we esed on a runcaed sample beween January 994 and December 999 o allow for possible leads and lags esimaion. We used he PP (Phillips Perron) ess for uni roos wih resuls repored in he Table. Tes resuls for he logged unemploymen rae and vacancy rae are marginal ye indicaive of nonsacionariy for PP ess suppor he same resuls. The PP es makes a correcion o he -saisic of he coefficien of ln(variable) - o accoun for serial correlaion in random erm. Furhemore PP ess indicae ha employmen growh and marginal real wages in indusry are saionary or I(). All oher daa series (yue, yve, ysubsr, yle, yfe) are nonsaionary or I().. Supplemenary esing on he I() series fond none of hem o be I(2). Logged ineres rae daa series was I(). Since he unemploymen rae and vacancy rae are found o exhibi nonsaionary behaviour using PP ess, i seems appropriae o model he uv relaionship using coinegraing analysis. Variable Descripion PPsaisics Lag lenghs e Employmen growh -8,76 * yue ln(unemploymen rae),495 yve ln(vacancy rae) 2,224 * i ineres rae -2,69 * ysrwi ln(real wage) -4,72 * ysubsr ln(replacemen rae) -,97 * yle ln(long-erm unemploymen rae) -,8 yfe ln(female unemploymen rae),76 due yue -5,357 * dve uve -5,263 * di i -7,4 * dsubsr subsr -3,92 * dle l -5,585 * dfe f -8,773 * = difference of variable Criical values (including inercep and rend) % (-4.85) 5% (-3.47) %(-3.62) Table : Tess for he null of nonsaionariy and saionariy

6 A mulivariae labour marke model in he Czech Republic Coinegraing analysis for he basic model_ (yue, yve) Then we ry o es for coinegraion ( i.e. ha linear combinaion of nonsacionary ime series yue and yve is I()). If an long-run equilibrium relaionship exiss we esimae he coinegraion equaion. We applied 3 coinegraion ess for model_ (yue, yve): a) Linear regression_ of ln(ue ) on ln(ve ) and esing for nonsaionariy of residua ime series (wihou rend and inercep) and also linear reggresion_2 of ln(ve ) on ln(ue ) and esing for nonsaionariy of he second residua ime series, b) Engle-Granger es, c) Johansen es. Resuls are repored in Table 2. ADF (Augmened Dickey-Fuller) ess for residua_ and residua_2 esimaed by OLS mehod (since resuls can vary wih he ordering of variables in regression) indicaed coinegraion yue and yve bu wih slow DW value for he model esimaing residua. The Granger(969) approach is o see how much he curren yue can be explained by pas values of yue and hen o see wheher adding lagged values of yve can improve he explanaion (and vice versa). The null hypohesis is herefore ha yve does no Granger-cause yve in he firs regression and ha yue does no Granger-cause yve in he second regression. For our resuls we canno rejec he hypohesis ha yve does no Granger cause yue bu we do rejec he hypohesis ha yue does no Granger cause yve on 5% level of significance. a) Tes for coinegraion Resuls OLS: * E ( yue) = *,964 yve 2 R * =.64 DW =.9 sign. F =. Resid_: Observed ADF saisic =-2,582 * Criical value(5%)=-,946 Resid_ ~ I() OLS: * E ( yve) = *,635 yue 2 R =.62 DW =.33 sign. F =. Resid_2: Observed ADF saisic =-2,296 * Criical value(5%)=-,946 Resid_2 ~ I() Coinegraion yue, yve

7 A mulivariae labour marke model in he Czech Republic 58 Engle-Granger (76 obs.): Null hypohesis: F-Saisic Probabiliy b) YVE does no Granger Cause YUE yue -> yve YUE does no Granger Cause YVE

8 A mulivariae labour marke model in he Czech Republic 59 Johansen es: Tes assumpion: Linear deerminisic rend in he daa Series: YUE YVE c) Eigenvalue Likelihood Raio 5 % Criical Value % Criical Value Hypohesized No. of CE(s) > None * < A mos * (**) denoes rejecion of he hypohesis a 5% (%) significance level L.R. es indicaes coinegraing equaion a 5% Normalized Coinegraing Coefficiens: Coinegraing Equaion YUE C Coinegraing equaion a 5% significance level Table 2: Various ess for coinegraion for model_ (yue, yve)

9 A mulivariae labour marke model in he Czech Republic 6,24,9,4,9,4 -, 993: 993:4 993:7 993: 994: 994:4 994:7 994: 995: 995:4 995:7 995: 996: 996:4 996:7 996: 997: 997:4 997:7 997: 998: 998:4 998:7 998: 999: 999:4 Figure : Normalized coinegraing equaion for model_ (yve,yue) Johansen (99, 995) developed he mehodology for implemenaion VAR-based coinegraion ess. Johansen s mehod is o es he resricions imposed by coinegraion on he unrescriced VAR involving he series. In he second column (Likelihood Raio) gives race saisic. To deermine he number of coinegraing relaions (k), we proceeded sequenially from k= o (number of non-saionary variables - ) unil we fail o rejec hypohesis. For our model_ (yue,yve) Johansen s es indicaed coinegraing eaquaion a 5% significance level. The figure shows normalized coinegraing equaions for model_ - (yve,yue). 3.3 Coinegraing analysis for exended mulivariae models Furhermore we applied coinegraion analysis for oher 3 models using hree abovemenioned mehods: Model_2 (yue, yve, i), Model_3 (yue, yve, ysubsr), Model_4 (yue, yve, i, ysubsr). The Table 3 includes resuls only for Johansen s es. Johansen s race saisic deeced: 2 coinegraing equaion a 5% significance level for model_2 (yue, yve, i), 2 coinegraing equaions a 5% significance level for model_3 (yue, yve, ysubsr), 3 coinegraing equaions a 5 % significance level for model_4 (yue, yve, ysubsr, i).

10 A mulivariae labour marke model in he Czech Republic 6 Model Model_2 (yue,yve,i) Model_3 (yue, yve, ysubsr) Johansen coinegraing ess Series: YUE YVE I (Tes assumpion: No deerminisic rend in he daa) Likelihood 5 Percen Percen Hypohesized Eigenvalue Raio Criical Value Criical Value No. of CE(s) > None ** > A mos * < A mos 2 L.R. es indicaes 2 coinegraing equaion(s) a 5% significance level Series: YUE YVE YSUBSR (Tes assumpion: No deerminisic rend in he daa) Likelihood 5 Percen Percen Hypohesized Eigenvalue Raio Criical Value Criical Value No. of CE(s)

11 A mulivariae labour marke model in he Czech Republic 62 Model_4 (yue, yve, i, ysubsr) > None ** > A mos * < A mos 2 L.R. es indicaes 2 coinegraing equaion(s) a 5% significance level Series: YUE YVE YSUBSR I (Tes assumpion: No deerminisic rend in he daa) Likelihood 5 Percen Percen Hypohesized Eigenvalue Raio Criical Value Criical Value No. of CE(s) > None ** > A mos **

12 A mulivariae labour marke model in he Czech Republic 63 > A mos 2 * 2.55E-5.92 < A mos 3 L.R. es indicaes 3 coinegraing equaion(s) a 5% significance level Table 3: Resuls for Johansen s coinegraing es ( *[**] denoes rejecion of he hypohesis a 5%[%] significance level) 4. Summary and conclusions The aim of his paper was o invesigae exisence of he uv relaionship for he labour marke in he Czech Republic using coinegraing analysis. Coinegraing es resuls sugges ha bivariae long-run uv relaionship exiss ( model_) and i is depiced in Fig.. These resuls suppor he basic labour marke search model which assumes exogeniy of (un)employmen flows. A modified Beveridge curve was used o examine he exisence mulivariae equilibrium relaionship. This was achieved by making (un)emloymen flows endogenously deermined by macroeconomic cyclical variables ( i, subsr ). The Johansen s coinegraing ess indicaed he exisence of equilibrium relaionship beween unemploymen, vacancies and he replacemen raio and ineres rae. This suggess ha cyclical variables are influenial in deermining he sabiliy of Beveridge curve. The empirical resuls show ha unemploymen rises when he raio of uneploymen benefis increases o work income. Also he ineres rae was coinegraed wih unemploymen and vacancies rae and move posiively wih unemploymen. References. Anhony J.D.F. (999): The relaionship beween unemploymen and vacancies in Ausralia. Applied Economics, No. 3, pp Eviews User s Guide (998). Quaniaive Micro Sofware.

13 A mulivariae labour marke model in he Czech Republic Granger,C.W.J (969): Invesigaing causal relaions by economeric models and crossspecral mehods. Economerica, No. 37, pp Jablonský,J. (993).: Mulicrieria evaluaions of urban regions in he Czech Republic. In: Applying Mulicrieria Mehods for Environmenal Managemen. Ispra 993, s Johansen,S.(99): Esimaion and Hypohesis Tesing of Coinegraion Vecors in Gaussian Vecor Auoregressive Models. Economerica, No. 59, pp Johansen,S.(995): Likelihood-based Inference in Coinegraed Vecor Auoregressive Models. Oxford Universiy Press. Jana Hanclová, Faculy of Economics VŠB- Technical Universiy Osrava, Czech Republic