ISSN 1414-6509 The Phillips Curve in Ialy Agosinho Silvesre Rosa Universidade de Évora (PORTUGAL) Endereço para conao Deparameno de Economia, Universidade de Évora, Largo dos Colegiais 2 - Évora - Porugal. Telephone: (351) 266 740 894, Fax: (351) 266 742 494. CEP: 7000-803 - E-mail: arosa@uevora.p Recebido em 30 de agoso de 2014. Aceio em 18 de dezembro de 2014. ABSTRACT The esimaion of he Phillips curve in Ialy, using he wage inflaion rae as a dependen variable, based on annual daa from he period 1961-2012, using he Johansen Mehod, allows us o conclude wo hings. Firsly, in he long erm, here are wo long-erm relaionships: he wage inflaion rae relaes posiively o he inflaion rae, negaively o he unemploymen rae and posiively o he average labour produciviy growh index, as was expeced; he inflaion rae relaes posiively o he wage inflaion rae, negaively o he unemploymen rae and posiively o he average labour produciviy growh index, as was expeced. Secondly, in he shor erm, he variaion of he wage inflaion rae relaes posiively and significanly o he error correcion mechanism of he firs long-erm relaionship; herefore, here is a significan response o he equilibrium error beween he wage inflaion rae and is deerminans (inflaion rae, unemploymen rae, labour produciviy growh index). Besides his adjusmen, he variaion of wage inflaion rae responds significanly and negaively o he variaion in unemploymen rae and significanly and posiively o he average labour produciviy growh. JEL Classificaion: C12, C32, E24, E31 Key Words: Wage Inflaion, Phillips curve, Coinegraion
The Phillips Curve in Ialy 75 1. Inroducion The original Phillips curve describes an empirical relaionship beween wage inflaion and unemploymen in accordance wih Phillips (1958). Lipsey (1960) inroduces he heoreical fundamens of ha curve and Samuelson and Solow (1960) apply he more used modificaion: he relaion beween he inflaion rae and he unemploymen rae. This relaionship was grealy used in he 1960s by policy-makers. The rade-off beween inflaion and unemploymen was recommended o economic policy makers as an insrumen ha would allow hem o formulae policy programmes wih alernaive combinaions of unemploymen and inflaion rae. The Oil Shock in he 1970s raised problems in relaion o ha heory, because here was unemploymen ogeher wih increasing inflaion. Friedman (1968) and Phelps (1967) inroduced expecaions in he original Phillips curve o ake accoun of expeced inflaion. The firs expecaions inroduced were adapive expecaions: e W f U, P [1] where W is he money wage rae, U he unemploymen rae, e P he inflaion expecaions. Friedman (1977) disinguished hree sages of he Phillips curve: firs, a sable rade-off beween inflaion and unemploymen; second, he disincion beween shor and long run: in he long run, he Phillips curve was verical; hird, a posiively sloped Phillips curve. Today, he mos acceped is he second sage, bu he new classical school (see Lucas (1973)) wih he inroducion of raional expecaions and marke clearing, admis ha he Phillips curve is almos verical, even in he shor run. However, he new Keynesian school do no believe ha markes clear all he ime, so sicky wages and prices imply ha he Phillips curve is no verical in he shor run. 1 According o Robers (1995), he New Keynesian Phillips curve is: P E P c y 0 [2] 1 0 where P is he log of acual price a ime, E are he raional expecaions a ime, y is he percen deviaion of aggregae oupu from is rend, γ is a posiive consan, and ε is is a residual error erm. This equaion is similar o ha of Friedman and Phelps, bu he New Keynesian models emphasize he role of explici nominal rigidiies in inerpreing model (Robers, 1995, p. 980), his equaion is also similar o ha of Lucas (1973), excep his equaion includes expecaions do nex period s inflaion, whereas Lucas s supply curve incorporaes expecaions of curren inflaion. The reason fuure inflaion maers in he New Keynesian model is ha prices are sicky. (Robers, 1995, p. 980). Remembering he Okun Law we can have he equaion: P E P c U 0 [3] 1 0 where U is he unemploymen rae. According o Galí and Gerler (1999) we can have a hybrid version of he New Keynesinan Phillips curve: * y 0 1 1 E 1 1 y [4] 1 See Ball, Mankiw and Romer (1988) and Robers (1995).
76 Agosinho Silvesre Rosa where π is he inflaion rae a ime, y-y * is he oupu gap. Therefore inflaion depends on he oupu gap, expeced fuure inflaion and lagged inflaion. Bu he difficul wih using he oupu gap le he economiss o use measures of real marginal cos, and he hybrid Phillips curve becomes: 2 mc f E1 b 1 [5] where mc is a measure of aggregae marginal cos. 3 Bu remembering he Okun Law we can have he equaion: U U * E [6] f 1 b 1 where U is he unemploymen rae. So he inflaion rae depends on he unemploymen rae, expeced fuure inflaion and lagged inflaion. Mazumder (2012) finds here is evidence o his day ha he Phillips Curve remains highly robus beween differen moneary policy regimes, conrary o he claims of Lucas (1976) in his sudy for he Unied Saes, so he radiional Phillips curve is alive. We can say ha he hree main facors influencing wage negoiaion and driving he rae of growh of nominal wages are core inflaion, produciviy growh and he sae of demand in he labour marke. The core or underlying rae of inflaion has one backward-looking componen and one forward-looking componen, bu in low-inflaion periods here is lile difference beween core and acual inflaion. In our model, we can refer o i as expecaion of inflaion. The produciviy gains means ha wages can rise wihou any increase in uni labour cos, so wihou impac on he inflaion rae. In our model, we can expec a posiive impac of produciviy growh on wages. The sae of demand in he labour marke can be measured by he unemploymen rae. When he unemploymen rae is above he equilibrium rae of unemploymen (NAIRU in economic erms), wages end o slow down, and vice-versa. In our model, we can expec a negaive relaionship beween he rae of growh of nominal wages and he unemploymen rae, where Q is he average labour produciviy growh: ( ) ( ) ( ) W f U, P e, Q [7] 2. Daa We use annual daa whose jusificaion in heoreical erms is given by Campbell and Perron (1991, p. 153), where eiher due saionariy analysis needs a long-erm period, or because seasonal adjusmen procedures ofen creae a bias oward nonrejecion of a uni roo hypohesis (Campbell and Perron, 1991, p. 153). As saed previously, we formulaed he model on he basis of raes of change, so we oped o ransform he available annual daa ino raes of change. Thus we seleced four annual variables for he period 1961-2012: W, money wages rae; P, inflaion rae; U, unemploymen rae ; Q, average labour produciviy growh. The daa source is AMECO. 2 See Andreas Hornsein (2008). 3 See also Russel and Chowdhury (2013) abou modern heories of he Phillips curve and Nason and Smih (2008) abou he applicaion of he New Keynesian Phillips curve o he USA.
The Phillips Curve in Ialy 77 3. Saionariy of he daa The Dickey-Panula (1987) es allows us o rejec he null hypohesis of I(2) agains I(1) in all variables sudied. Wih he ADF es, we can say he variablesw, U, P are I(1), and he variable Q is I(0). Using he Perron and Vogelsang (1992) es o inquire for a uni roo in imes series under srucural change wih endogenous choice of he break poin (Tb), wih he procedure of endogenous selecion of k described by Perron (1997, p. 359), we can reach he same conclusion. 4. Esimaion of he Phillips curve model We use he Johansen mehod as being he one ha allows he deecion of he presence of more han one coinegraing vecor among variables in he sudy. There are saionary regressors in he VAR model, so we canno use he criical values of Johansen (1996). Therefore, we follow he mehodology of Rahbek and Mosconi(1999), which consiss of adding o he VAR he cumulaed explanaory I(0) variables as I(1) exogenous variables, and hus he criical values of he race or eigenvalue ess of, among oher auhors, Pesaran, Shin and Smih(2000) can be used. 4 Firs, as we have exogenous variables, he coinegraed VAR model o use corresponds o he condiional model: 5 Y c c k1 i X i y X 1 i1 Z where X is a N1 vecor of I(1) variables, which we can divide ino N y endogenous I(1) variables (Y ) and N z exogenous I(1) variables (Z ), such ha N y + N z = N. y is he long-run muliplier marix of order (N y N) given by y = y ', where y is a (N y r) marix and a (Nr) marix of r coinegraning vecors. The null hypohesis of he coinegraion rank (exisence of r coinegraing vecors) is wrien: Hr: R [ y ] = r, r = 0,..., N y ; [9] where "R" is he rank of he marix. In he esimaion of he condiional model (8), we can consider 5 cases (or models) consonan wih he resricions imposed on he deerminisic erms, in accordance wih PSS(2000). 4.1 Esimaion of he Long-Term Model A he beginning we have a model wih hree endogenous I(1) variables (W, U, P ), and one exogenous I(0) variable ( Q ). In erms of k order of he VAR, we seleced VAR(3), using eiher mulivaried saisics, or univaried saisics, so ha he esimaed residuals have no serial correlaion (LM es), no c [8] 4 Referred o as PSS(2000), aferwards. 5 We assume ha he Z variables are weakly exogenous and hey are no coinegraed beween hem, which implies ha we can efficienly deermine and es he parameers of long erm ( and ), bu wih resource o he condiional model [see PSS(2000)].
78 Agosinho Silvesre Rosa auoregressive condiional heeroscedasiciy (ARCH es) and hey do no deviae oo much from normaliy (BJ es), as Johansen (1996, p. 20) recommends. Wih k=3, whaever he model of he Johansen mehod is in relaion o he deerminisic erms, we canno rejec he exisence of wo coinegraning vecors by he Trace es. We canno rejec he weak exogeneiy of he unemploymen rae (U) in he models II o IV, 6 on a significance level of 5% (Table 1). Table 1 - Weak exogeneiy es 7 of unemploymen rae (U) Model Model II Model III Model IV LR es 2 (2)= 0.26 [0.88] 2 (2)= 0.66 [0.72] 2 (2) = 0.11 [0.95] Noe: The null hypohesis is H0: U = 0. Source: Calculaions were performed by he auhor. We esimaed he model wih wo endogenous I(1) variables (W and P ), one I(1) exogenous variable (U), one I(0) variable ( Q ). in accordance wih he Rahbek and Mosconi(1999) mehodology: W P ; U csum Q & U Q We confirm he k order of he VAR wih exogenous U, as a VAR(3) and he mehodology of PSS(2000) leads us o choose model IV. Given VAR(3) and model IV, one can confirm ha he exisence of wo coinegraning vecors canno be rejeced, eiher by he race es, or by he maximum eigenvalue es (Table 2). Eigenvalue Table 2 Coinegraion ess Trace es Maximum eigenvalue es H0 Ha Trace H0 Ha max 0.47811 r = 0 r 1 51.3219 a r = 0 r = 1 31.8642 a 0.32773 r 1 r = 2 19.4577 a r 1 r = 2 19.4577 a a = he null hypohesis (H0) is rejeced agains he alernaive hypohesis (Ha). Source: Calculaions were performed by he auhor. The AIC, SBC and HQC crierions also selec he model wih r=2. The vecor 1 normalized in relaion o W wihou resricions wih X' = [W P U csumq Trend] is given by: ' 1 1 0.707 1.058 0.143 0.373 The vecor 2 normalized in relaion o P wihou resricions wih X' = [ P W U csum Q Trend] is given by: ' 1 2 0.962 0.396 0.158 0.058 6 PSS(2000) models. 7 Elabored on CATS in RATS by he resricion B'*alpha=0 wih B'=[0 1 0] selecing r=2 in he model W U P ; csum Q & Q, lag 3.
The Phillips Curve in Ialy 79 so, we have he ecm1 and he ecm2: ECM1 = ECM2 = W - 0.707 P + 1.058 U 0.143 csumq + 0.373 Trend P - 0.962 W + 0.396 U 0.158 csumq + 0.058 Trend and herefore, he long-erm relaionships are: W = 0.707 P - 1.058 U + 0.143 csumq - 0.373 Trend P = 0.962 W - 0.396 U + 0.158 csumq - 0.058 Trend ha is, firsly, he wage inflaion rae relaes posiively o he inflaion rae, negaively o he unemploymen rae and posiively o he average labour produciviy growh index The Trend means here are ohers facores he have some influence on wage inflaion. Secondly, he inflaion rae relaes posiively o he wage inflaion rae, negaively o he unemploymen rae and posiively o he average labour produciviy growh index. The Trend means here are ohers facores he have some influence on inflaion rae. According Kousas and Serleis (2003) he evidence is consisen wih a verical long-run Phillips curve for mos counries in he sample, wih he excepion of Ialy, so is in accordance of our long-run relaionship for Ialy. Schreiber and Wolers (2007) finds also a coinegraion relaionship beween inflaion and unemploymen in Germany. 4.2 Esimaion of he Shor-Term Model The esimaion of he mulivariae model wih only variables inroduced iniially in VAR(3) allows us o ge he resuls in Table 3. Table 3 Mulivariae model esimaion Equaion/ Regressor W P No. Observaions T=49 [64-12] T=49 [64-12] Inercep -2.5461[.558] -14.0490[.001] W (-1) -.36032[.233] -.54006[.061] P (-1).46902[.060].48843[.038] U(-1) 1.3617[.087].78117[.289] Q (-1).20231[.342].56179[.007] W (-2) -.22868[.290] -.26921[.186] P (-2).32515[.127].24820[.212] U(-2).98682[.160] -.0059655[.993] Q (-2).09977[.679] -.12000[.596] ECM1(-1) 8.4370[.000].52461[.791] ECM2(-1) -6.2350[.005] -8.2123[.000]
80 Agosinho Silvesre Rosa U -1.4917[.012] -.73138[.177] Q.21961[.365].26881[.239] 2 R.48428.35138 SEE 2.0913 1.9625 DW 2.1302 2.0467 LM(1, 35) 1.3634[.251] 1.2138[.278] RESET(1, 35) 1.8292[.185] 3.3723[.075] BJ(2).21542[.898] 6.1678[.046] HET(1, 47).3021E-3[.986] 3.4911[.068] ARCH(3, 33) 1.3933[.262] 1.0991[.363] Noe: see annex abou diagnosic ess descripion and oher noes. Source: Calculaions were performed by he auhor. The variaion of he wage inflaion rae relaes posiively and significanly a 1% level o he error correcion mechanism (ECM1) wih an adjusmen coefficien of abou (8.0) and relaes negaively and significanly a 1% level o he error correcion mechanism (ECM2) wih an adjusmen coefficien of abou (-6.0); herefore, here is a significan response o he long-erm disequilibria. Besides his adjusmen, he wage inflaion rae responds posiively and significanly o a lagged inflaion rae and negaively and significanly o he unemploymen rae. The variaion of he inflaion rae relaes posiively and significanly a 1% o he error correcion mechanism (ECM2), wih an adjusmen coefficien of abou (-8.0). I relaes posiively and significanly a 5% o lagged variaion of inflaion rae and o he lagged average labour produciviy growh. I presens a negaive and bu no significan relaion o he variaion of he unemploymen rae. The diagnosic ess indicae ha, in boh equaions, he residuals are no auocorrelaed, are homoescedasics, and he auoregressive condiional heeroescedasiciy is also absen unil he hird order. We canno rejec correc specificaion of he model. In boh equaions, CUSUM and CUSUMSQ ess do no cross any of he significan bars a 5% level. Wih he aim of obaining a parsimonious Phillips curve model, we ried o remove from he equaion of W all he variables no significan a 5% level, using he Wald es on he join nulliy of is coefficiens. We rejec he exclusion of hese variables from he model wih he 2 (9) = 26.8059[.002], so we leave he average labour produciviy and we canno rejec he exclusion of eigh variables from he model wih he 2 (8)= 12.8718[.116], so he parsimonious model is W = f(inp,, P 1,, ECM1-1, ECM2-1, U, Q ). The esimaion of he W equaion wih hese regressors (W1 equaion Table I Annex) presens all he coefficiens significan a 5%, excep he inercep and he ECM2(-1), and he diagnosic ess are very good. W is a funcion of he lagged variaion of he inflaion rae and of he ECM1 (long-erm relaionship beween W and he oher variables), and is also funcion of he variaion in unemploymen rae and of he average labour produciviy growh. We canno rejec eiher he predicive capaciy afer 2005 or he srucural sabiliy before and afer 2005 (W2 equaion).
The Phillips Curve in Ialy 81 In all he esimaed equaions, we can verify he coefficien sabiliy as he Chow(1960) ess sugges. The coefficien of ECM1-1 is more sable, abou 7.0. The coefficien of P 1 varies beween 0.3 and 0.37, he coefficien of U varies beween -1.3 and -2.7 and he coefficien of Q varies beween 0.56 and 0,71. In all equaions of he parsimonious model, CUSUM and CUSUMSQ ess do no cross any of he significan bars a 5% level. However, no all he residuals are inside he line bands of double-sandard deviaion. In he period 1964-2012, as we verify ha he plo of residuals crosses wo sandard error bands in 1979. 5. Conclusion In he long erm, here are wo long-erm relaionships: he wage inflaion rae relaes posiively o he inflaion rae, negaively o he unemploymen rae and posiively o he average labour produciviy growh index, as was expeced; he inflaion rae relaes posiively o he wage inflaion rae, negaively o he unemploymen rae and posiively o he average labour produciviy growh index, as was expeced. In he shor erm, he variaion of he wage inflaion rae relaes posiively and significanly o he error correcion mechanism wih wage inflaion as dependen variable and negaively o he error correcion mechanism wih inflaion rae as dependen variable, herefore, here is a significan response o he long-erm disequilibria. Besides his adjusmen, he wage inflaion rae responds posiively and significanly o a lagged inflaion rae and negaively and significanly o he unemploymen rae. I relaes posiively o he average labour produciviy and is significan in he parsimonious model. We can have a parsimonious model as a relaionship beween he wage inflaion rae, he lagged inflaion rae, he wo errors correcion mechanisms, he unemploymen rae and he average labour produciviy growh. References BALL, L.; MANKIW, N. G. ; ROMER, D. The New Keynesian Economics and he Oupu- Inflaion Trade-off. Brookings Papers on economic Aciviy, 1, pp. 1-82, 1998. CAMPBELL, J. Y.; PERRON, P. Pifalls and Opporuniies: Wha Macroeconomics Should Know abou Uni Roos. NBER Macroeconomics Annual, pp. 141-201, 1991 CHOW, Gregory C. Tess of Equaliy Beween Ses Coefficiens in Two Linear Regressions. Economerica, v. 28, n.3, pp.591-605, 1960. DICKEY, D. A.; PANTULA, S. G. Deermining he Order Differencing in Auoregressive Processes. Journal of Business and Economic Saisics, v. 5, n.4, pp. 455-461, 1987
82 Agosinho Silvesre Rosa FRIEDMAN, M. The Role of Moneary Policy. American Economic Review, v. 58, n.1, pp.1-17, 1968. FRIEDMAN, M. Nobel Lecure: Inflaion and Unemploymen. Journal of Poliical Economy, v. 85, n. 3, pp. 451-472, 1997. GALÍ, J.; GERTLER, M. Inflaion Dynamics: A Sruural Economeric Analysis. Journal of Moneary Economics, v. 44, pp. 195-222, 1999. HANSEN, H.; JUSELIUS, K. CATS in RATS: Coinegraion Analysis of Time Series, Esima, Evanson, Illinois, 1995. HORNSTEIN, A. Inroducion o he New Keynesian Phillips Curve. Economic Quarerly, v. 94, n. 4, pp. 301 309, 2008. JOHANSEN, S. Likelihood-Based Inference in Coinegraion Vecor Auoregressive Models. Oxford: Oxford Universiy Press, 1996. KOUSTAS, Z.; SERLETIS, A. Long-run Phillips-ype Trade-offs in European Union Counries. Economic Modelling, v. 20, pp. 679-701, 2003. LIPSEY, R. G. The Relaion beween Unemploymen and he Rae of Change of Money Wage Raes in he Unied Kingdom, 1862-1957: A Furher Analysis. Economica, v. 27 n.105, pp. 1-31, 1960. LUCAS, R. E., Jr. Some Inernaional Evidence on Oupu-Inflaion Tradeoffs. American Economic Review, v. 63, n. 3, pp. 326-34, 1973. LUCAS, R. E., Jr. Economeric Policy Evaluaion: A Criique. Carnegie-Rocheser Conference Series on Public Policy, v.1, pp.19 46, 1976. MAZUMDER, S. The Volcker Greenspan Bernanke Phillips Curve. Applied Economics Leers, v. 19, pp. 387 391, 2012. NASON, J. M.; and SMITH, G. W. The New Keynesian Phillips Curve: Lessons From Single-Equaion Economeric Esimaion. Economic Quarerly, v. 94, n. 4, pp. 361 395, 2008. PERRON, P.; VOGELSANG, T. J. Nonsaionariy and Level Shifs wih an Applicaion o Purchasing Power Pariy. Journal fo Business and Economic Saisics, v. 10, n. 3, pp. 301-320, 1992. PERRON, P. Furher Evidence on Breaking Trend Funcions in Macroeconomic Variables. Journal of Economerics, v. 80, n. 2, pp. 355-385, 1997. PESARAN, M. H.; SHIN, Y.; SMITH, R. J. Srucural Analysis of Vecor Error Correcion Models wih Exogenous I(1) Variables. Journal of Economerics, v. 97, n. 2, pp. 293-343, 2000. PHELPS, E. S. Phillips Curves, Expecaions of Inflaion and Opimal Unemploymen Over Time. Economica, v. 34, pp. 254-81, 1967.
The Phillips Curve in Ialy 83 PHILLIPS, A. W. The Relaion Beween Unemploymen and he Rae of Change of Money Wage Raes in he Unied Kingdom, 1861 1957. Economica, v. 25, n. 100, pp. 283-299, 1958. RAHBEK, A.; MOSCONI, R. Coinegraion Rank Inference wih Saionary Regressors in VAR Models. Economerics Journal, v. 2, pp. 76-91, 1999. ROBERTS, J. M. New-Keynesian Economics and he Phillips Curve. Journal of Money, credi and Banking v. 27, n. 4, pp. 975-984, 1995 RUSSEL, B.; CHOWDHURY, R. A. Esimaing Unied Saes Phillips curves wih expecaions consisen wih he saisical process of inflaion. Journal of Macroeconomics, v. 35, pp. 24 38, 2013. SAMUELSON, P.; SOLOW, R. Problem of Achieving and Mainaining a Sable Price Level: Analyical Aspecs of Ani-Inflaion Policy. American Economic Review, v. 50, n. 2, pp. 177-194, 1960. SCHREIBER, S.; WOLTERS, J. The long-run Phillips curve revisied: Is he NAIRU framework daa consisen?. Journal of Macroeconomics, v. 29, pp. 355 367, 2007.
84 Agosinho Silvesre Rosa ANNEX Table I: Parsimonious Equaions of W W1 W2 Equaion/ Regressor T=49 [64-12] T 1 =43,T 2 =7 [64-05] Inercep 3.6034[.157] 3.0251[.218] P (-1).36895[014].30929[032] ECM1(-1) 6.8753[.000] 7.3182[.000] ECM2(-1) -2.1568[.172] -2.6352[.099] ΔU -1.2757[.024] -2.7176[.000] Q.55588[.004].70769[.001] 2 R.39361.53150 SEE 2.3609 2.2164 DW 1.9813 1.9468 LM(1, T-k-1) 1.0019[.322].014913[.903] RESET (1, T-k-1).41720[.522].10152[.752] BJ(2) 1.0458[.593].38770[.824] He(1, T-2) 3.3943[.072].16355[.688] ARCH(3, T-k-3).892701[.453] 2.4166[.083] Chow(T 2,T 1-k) - 1.8464[.107] Cov(k, T 1+T 2-2k) - 2.1293[.072] Noes: Dependen Variable: W ; Esimaion Mehod: OLS; ECM1 = W - 0.707 P + 1.058 U 0.143 csum Q + 0.373 Trend e ECM2 = P - 0.962 W + 0.396 U 0.158 csum Q + 0.058 Trend esimaed on he model: W P ; U csum Q & U Q. Beween square brackes: p-value or sample period (on he op). On he esimaed coefficiens, he null hypohesis is H0: =0, and he Suden es is used. T=number of observaions used in regression; k=number of esimaed coefficiens; T 1 =sub-sample used in esimaion; T 2 =Period pos-sample (forecasing es) or second sub-sample (sabiliy es, only possible when T 1 >k and T 2 >k). Source: Calculaions were performed by he auhor. Diagnosic ess descripion: LM saisic of Lagrange Muliplier es for serially correlaed residuals ; RESET saisic of Ramsey) s RESET es of funcional form misspecificaion; BJ saisic of Jarque-Bera s es of normaliy of regression residuals; HET saisic of Heeroscedasiciy es ; ARCH saisic of Auoregressive Condiional Heeroscedasiciy es; Chow-saisic of Predicive failure es (2 nd es of Chow(1960)); Cov saisic of Chow s es of sabiliy of regression coefficiens (1 s es of Chow(1960)).