The Okun curve is non-linear

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1 Economics Letters 70 (00) locte/ econbse The Okun curve is non-liner Mtti Viren * Deprtment of Economics, 004 University of Turku, Turku, Finlnd Received 5 My 999; ccepted 0 April 000 Abstrct This pper presents cross-country evidence on non-liner Okun curve. The nlysis is bsed on simple error correction model of unemployment. The model is estimted using threshold model estimtor. Evidence from 0 OECD countries for the period provides support for the existence of non-linerities in terms of the output growth effects. Output growth hs strong effect on unemployment when unemployment is low nd output is high, nd vice vers. Thus, in bd times, the effect of output growth on unemployment cn be close to zero. 00 Elsevier Science B.V. All rights reserved. Keywords: Unemployment; Popultion shocks; Threshold models JEL clssifiction: J. Introduction This pper nlyses the reltionship between output growth nd unemployment (i.e. the Okun curve). The im is to find out whether this much debted reltionship is liner especilly in terms of the cyclicl sitution of the economy. The discovery tht the reltionship is non-liner would chnge our thinking in mny respects. First of ll, non-linerities would provide n explntion for the vrying effectiveness of unemployment policies. Second, non-linerities would hve importnt implictions for ggregtion, sy in the context of EMU countries which differ considerbly in terms of their cyclicl sitution. Finlly, if the Okun curve turns out to be non-liner, tht would suggest tht the issue is importnt for other economic reltionships s well. The empiricl nlysis is bsed on simple (non-liner) error correction model for unemployment. The long-run level of unemployment is relted to the working-ge popultion nd to the structure of the lbour mrket, which is proxied by time trends. Thus, this eqution tkes the form: *Bnk of Finlnd, P.O. Box 60, 000 Helsinki, Finlnd. Tel.: ; fx: E-mil ddress: Mtti.Viren@bof.fi (M. Viren) / 0/ $ see front mtter 00 Elsevier Science B.V. All rights reserved. PII: S (00)

2 54 M. Viren / Economics Letters 70 (00) u 5 n t t m, () t 0 n t 3 4 t where u is the log of unemployment U (U is the number of unemployed persons), n5log(n), which is the working ge popultion, nd t is the time trend. The corresponding error correction model is then of the following form: Du 5 b b EC b Dn b Dy b Dy, () t 0 t t 3 t 4 t t where D denotes the first-difference opertor, EC the error correction term (derived from Eq. ()) nd y output. y denotes the vlues of y which correspond to the observtion in which z, z* where z is the threshold vrible nd z* the estimted fixed threshold vlue used in sorting the dt. Accordingly, y is relted to the observtions in which z $ z* (see Grnger nd Tersvirt (993) nd Hnsen (997) for detils of the methodology). The bsic ide of Eq. () is simple: in the short run, unemployment rects to both popultion nd output shocks. The effect of popultion shocks is ssumed to be invrint with respect to the cyclicl sitution (to keep the number of estimted prmeters t resonble level) while the output effect is ssumed to differ in booms nd depressions. This pper does not explin why the output effect differs but simple Keynesin models provide rtionliztion for possible regime shifts. Popultion shocks cn be resonbly well chrcterized s exogenous but output my not hve this property. Given the dt (nd the threshold model), we cnnot relly do very much s regrds this possible simultneity problem.. Empiricl results The dt used in this nlysis re nnul nd cover 0 OECD countries over the period (with minor exceptions). The dt re derived from the recent (December 998) OECD CD (for more detils of the dt, see Kinder nd Viren (998)). The dt cn be chrcterized by the following verge vlues (over time nd ll countries): Du54.9%, Dn50.8%, Dy53.%, U/N53.5%, U/(E U ) 5 5.%, where E is totl employment. Thus, U/(E U ) is the unemployment rte. The following lterntive threshold vribles re experimented in the nlysis: y y*, Dy, u u* nd Du where y* denotes the output trend (constructed by the HP filter) nd u* the equilibrium level of unemployment which ws constructed using Eq. (). For the ske of comprison, Eq. () is lso estimted in liner form nd, moreover, using simple fixed zero threshold for Dy. A summry of estimtion results of Eq. () is presented in Tble. We report comprison of the coefficient estimtes nd the R s for the liner model (which corresponds to the prmeter restriction b35b4 in Eq. ()) nd for different threshold models. Detiled estimtion results re presented in Tble just for one threshold vrible. On the bsis of Tble, we hve chosen the unemployment gp u u* s this representtive threshold vrible. Unit root tests suggest tht the time series of u, e, p, nd y re of I() type. Also the unemployment/popultion rtio turns out to be non-sttionry. For resons of spce, the test results re not reported here but they re vilble upon request from the uthor. Du nd u u* re the best threshold vribles in terms of explntory power. Du, lthough representing the best fit, is, however, in some cses (slightly) non-sttionry, nd obviously using Du we would crete some sort of simultneity problem. Therefore, we report here the detiled results for u u*.

3 M. Viren / Economics Letters 70 (00) Tble Summry of estimtion results for ll countries Constnt ECt Dn Dy Dy R None Dy y y* Dy u u* Du Numbers re verge vlues for coefficient estimtes nd R s for ll countries. The results re qulittively very similr for ll threshold vrible specifictions. Thus, popultion shocks increse nd output shocks decrese unemployment. The coefficient of the error correction terms suggest tht it tkes bout three yers to rech the equilibrium level of unemployment. The importnt point is, however, the fct tht lthough the explntory power of the lterntive specifictions differs somewht, s cn be seen from Tble, threshold models clerly outperform liner specifiction in ll cses. Thus, for most countries, there ppers to be sttisticlly significnt regime shift in the output effect of our Okun curve specifiction Eq. (). In the cse of the u u* threshold vrible (Tble ), only in the cse of Finlnd nd Icelnd cn we not reject the hypothesis 3 of no-threshold t the conventionl 5% level of significnce when the bootstrpped P-vlues re used. This shift cn be chrcterized in the following wy: output growth hs negtive effect on unemployment (growth) when output is high (bove the long-run trend) or unemployment is low (gin, reltive to the nturl level ). By contrst, in the cse of depression, the mgnitude of the 4 output effect is much smller or completely negligible (see Tble ). The coefficient estimted for different threshold vribles (sy, between Dy nd y y*, nd similrly between Du nd u u*) differ somewht but tht is not prticulrly surprising becuse these vribles re fr from perfectly 5 correlted with ech other (reflecting slightly different cyclicl situtions). The results re nevertheless so cler nd systemtic tht we should py more ttention to this non-linerity (regime shift) possibility both when modelling unemployment policy nd crrying out econometric nlysis in this re. 3 In ddition to the 0 countries mentioned bove we hd lso dt for Germny. Unfortuntely, becuse of unifiction, the smple size ws so smll tht threshold estimtion did not mke sense. If, however, more strightforwrd methodology with fixed zero threshold for Dy is used, the results turn out to be very similr to those in other countries. Thus, the following prmeter estimtes re obtined for b3 4.0 nd b If we look t the unemployment rte effects insted of the unemployment growth effects, we could sy tht (on n verge) % increse in output growth lowers the unemployment rte from, sy, 5% to depending on the cyclicl sitution. A % increse in working-ge popultion growth would increse the unemployment rte to 5.5% (i.e. one-third of dditionl popultion would be unemployed in the short-run). 5 The following verge vlues of correltion coefficients cn be computed for the smple period: hy y*, Dyj 0.4, hy y*, u u*j 0.60, hy y*, Duj 0.53 hdy, u u*j 0.8 hdy, Duj 0.55 nd hu u*, Duj 0.36.

4 56 M. Viren / Economics Letters 70 (00) Tble Estimtion results for the u u* threshold model Country Constnt ECt Dnt Dy Dy R / SEE dw/lm F/( p) z* Austrli (.7) (.49) (0.80) (5.6) (.6) (0.00) Austri (3.) (4.99) (.87) (6.67) (.78) (0.00) Belgium (.07) (5.0) (6.3) (7.94) (.6) (0.000) Cnd (0.68) (.45) (4.66) (7.47) (3.67) (0.00) Denmrk (3.46) (.06) (0.79) (4.58) (.6) (0.06) Finlnd (4.8) (0.78) (.05) (6.36) (5.39) (0.084) Frnce (.6) (5.03) (.56) (4.4) (0.60) (0.000) Greece (0.36) (5.65) (.3) (4.73) (0.33) (0.03) Icelnd (.9) (3.0) (.55) (6.03) (6.3) (0.00) Irelnd (.09) (3.50) (.49) (4.96) (0.43) (.84) (0.004) Itly (.64) (3.5) (.66) (5.8) (.75) (0.00) Jpn (3.40) (4.76) (3.0) (0.38) (3.0) (0.000) Netherlnds (0.0) (.73) (.3) (.97) (0.45) (0.00) New Zelnd (.3) (.74) (0.54) (3.7) (0.76) (0.00) Norwy (.8) (4.7) (0.79) (4.3) (0.33) (0.00) Portugl (0.9) (5.7) (0.84) (.4) (.07) (0.008) Spin (3.00) (7.7) (7.95) (8.09) (0.7) (0.000) Sweden (3.79) (.83) (.80) (6.53) (3.63) (0.00) UK (.4) (4.55) (.5) (.87) (.97) (0.000) USA (.65) (0.93) (4.3) (.03) (5.58) (0.030) Numbers inside prentheses under coefficient estimtes re t-rtios. LM is test sttistic for first order utocorreltion (with x distribution under H 0), F denotes test sttistic for the hypothesis of no threshold. Numbers inside prentheses re bootstrpped probbility vlues (000 replictions re used). z* is the threshold vlue of u u*. When computing the LM test we utilized Chn (993) in which it is shown tht the threshold prmeter is superconsistent nd thus cn be treted s known prmeter.

5 M. Viren / Economics Letters 70 (00) Acknowledgements Finncil support from the Yrjo Jhnsson Foundtion is grtefully cknowledged. References Chn, K., 993. Consistency nd limiting distribution of the lest squres estimtor of threshold utoregressive model. Annls of Sttistics, Grnger, C., Tersvirt, T., 993. Modelling Non-liner Reltionships. Oxford University Press. Hnsen, B., 997. Smple Splitting nd Threshold Estimtion. Working Pper. Boston College. Kinder, J., Viren, M., 998. Employment Growth nd Lbour Mrket Flexibility in OECD Countries. VATT Discussion Ppers 84.