Testing Steady-State Implications for the NAIRU

Bardsen, Gunnar; Nymoen, Ragnar Working Paper Testing Steady-State Implications for the NAIRU Arbeidsnotat, No. 2000/3 Provided in Cooperation with: Norges Bank, Oslo Suggested Citation: Bardsen, Gunnar; Nymoen, Ragnar (2000) : Testing Steady-State Implications for the NAIRU, Arbeidsnotat, No. 2000/3, ISBN 82-7553-159-4, Norges Bank, Oslo, https://hdl.handle.net/11250/2500411 This Version is available at: https://hdl.handle.net/10419/209777 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/deed.no 2000/3 Oslo May 25, 2000 Arbeidsnotat Research Department Testing steady-state implications for the NAIRU. by Gunnar Bårdsen and Ragnar Nymoen Arbeidsnotater fra Norges Bank kan bestilles over Internett: www.norges-bank.no/publikasjoner eller ved henvendelse til Norges Bank, Abonnementsservice, PB 1179 Sentrum, 0107 Oslo Telefon 22 31 63 83, Telefaks 22 41 31 05 Norges Banks arbeidsnotater inneholder forskningsarbeider og utredninger som vanligvis ikke har fått sin endelige form. Hensikten er blant annet at forfatteren kan motta kommentarer fra kolleger og andre interesserte. Synspunkter og konklusjoner står for forfatterens regning. Arbeidsnotater/working papers from Norges Bank can be ordered via Internet: www.norges-bank.no/english/publications or from Norges Bank, Subscription service, P.O.Box. 1179 Sentrum, 0107 Oslo, Norway. Tel. +47 22 31 63 83, Fax. +47 22 41 31 05 Norges Bank's Working papers present research projects and reports (not usually in their final form), and are intended inter alia to enable the author to benefit from the comments of colleagues and other interested parties. Views and conclusions expressed are the responsibility of the author alone. ISSN 0801-2504 ISBN 82-7553-159-4 Testing steady-state implications for the NAIRU∗ Gunnar Bårdsen Norwegian University of Science and Technology Ragnar Nymoen University of Oslo First version, 25 April, 2000. This version, 30 April, 2002. Abstract Estimates of the NAIRU are usually derived either from a Phillips curve or from a wage curve. This paper investigates the correspondence between the operational NAIRU-concepts and the steady state of a dynamic wage-price model. We derive the parameter restrictions that secure that correspondence. The full set of restrictions can be tested by econometric analysis of the wageprice system, and this method is demonstrated for Norwegian data. A set of necessary conditions can be tested from estimated wage curves alone. Existing international evidence from empirical wage equations are re-interpreted in light of these conditions. Keywords: Phillips curve, wage curve, steady state, natural rate, NAIRU, dynamic modelling. JEL classification: C51, C52, E24, E31, J30. 1 Introduction Governments and international organizations customarily refer to NAIRU calculations in their discussions of employment and inflation prospects1,andtheexistence of a NAIRU consistent with a vertical long-run Phillips curve is crucial to the framework of monetary policy.2An alternative to a Phillips-curve NAIRU is based on ∗We would like to thank James H. Stock and two referees for helpful comments on an earlier version. Versions of this paper have been presented at the conference “European Unemployment and Wage Determination” at the European University Institute, Florenze in 1998 and in seminars at the University of Science and Technology, Trondheim, at Sveriges Riksbank, at Statistics Norway and at the University of Oxford. Comments from participants on these occasions are gratefully acknowledged. Discussion with and comments from Øyvind Eitrheim, Steinar Holden, Per Jansson, Kåre Johansen, Dag Kolsrud, Bjørn Naug, Bjarne Strøm and Anders Vredin have been very helpful. All numerical results were produced by PcGive 9.3 and PcFiml 9.3, see Doornik and Hendry (1997, 1999), Please address correspondence to: Ragnar Nymoen, University of Oslo,Department of Economics, P.O. Box 1095 Blindern, N-0317 Oslo, Norway. Phone: + 47 22 85 51 48. Fax + 47 22 50 35 35. Internet: [email protected] 1See Elmeskov and MacFarlan (1993), Scarpetta (1996) and OECD (1997, Chapter 1) for examples. 2See the discussion in King (1998) for a central banker’s views. 1 a negative relationship between the level of the real wage and the rate of unemployment, dubbed the wage curve by Blanchflower and Oswald (1994), coupled with firms’ price setting schedule. As noted by Blanchard and Katz (1999), the wage curve has become the new consensus framework of the NAIRU in Europe, while a Phillips-curve version, dubbed “the triangle model of inflation” by Gordon (1983), applies to the US, see Gordon (1998) and Staiger et al. (2002) for recent contributions.3 In this paper we investigate the steady-state connotations of NAIRUs. Are the Phillips-curve or wage-curve NAIRUs good predictors of the true steady-state values of the rate of unemployment ground out by a dynamic model of the macro economy? To answer this question, we derive in Section 2 the testable conditions for correspondence between a Phillipsor wage-curve NAIRU and the steady-state unemployment rate in a more general system. Section 3 contains an application of the implied testing procedure to Norwegian data. Finally, the framework is used to re-interpret existing evidence from wage equations of a larger number of countries. Section 4 concludes. 2 An encompassing framework The model is an extension of Kolsrud and Nymoen (1998). The variables are, in logarithms, the nominal wage wt, the producer price of domestic products qt,the consumer price pt, the rate of unemployment utand productivity prt.4Nominal wages and prices are integrated of order 1,denotedI(1). The rate of unemployment may also be non-stationary, e.g., its mean can change, but after removal of deterministic shifts, we assume that ut∼I(0). 2.1 Long-run properties A cointegrated long-run wage equation, consistent with the bargaining approach and the assumed temporal properties of the data, is thus (1) wt−qt−¯prprt−¯p−q(p−q)t=−¯uut+mwt ∼I(0), The term (p−q)tis the wedge between the consumer real wage and the producer real wage. The role of the wedge as a source of wage pressure is contested in the literature and the theoretical predictions depend on the specification of the utility functions of unions and employers, see Rødseth (2000, Chapter 8.5) for an exposition. The term mwt is a catch-all for exogenous institutional and economic factors. In the empirical version of the model we include the replacement ratio in the unemployment insurance system. 3Recenty, the Phillips curve has enjoyed a revival in the theory of monetary policy, see Clarida et al. (1999), and it dominates in the theoretical literature on inflation targeting in particular, see e.g. Svensson (2000), which of course lifts its importance in Europe. 4We abtract from the payroll tax rate. The rate of unemployment enters linearly in some US studies, see e.g Fuhrer (1995). However, for most other datasets, a concave transform improves the fit and the stablity of the relationship, see e.g. Nickell (1987) and Johansen (1995). 2 A second cointegration relationship stems from firms’ normal-cost pricing5 (2) qt−wt+prt=mqt ∼I(0). Identification is achieved through additional restrictions. Section 3.1 gives an example. Other approaches have been used for aggregate data, cf. Bårdsen et al. (1998). 2.2 Wage-price dynamics We specify the following dynamic equations for wage and price growth: (3) ∆wt=°wq∆qt+°wp∆pt−°uut−1 −®w£w−q−¯prpr −¯p−q(p−q)+¯uu−mw¤t−1+cw; 0≤°wp +°wq ≤1; and (4) ∆qt=°qw∆wt+°qb∆bt−®q[q−w+pr −mq]t−1+cq; 0≤°qw +°qb ≤1; where ∆is the difference operator (∆xt=xt−xt−1)andbtdenotes import prices.6 Note that, in 3, either °uor ®wis zero. The consumer price index ptis defined by (5) pt=Áqt+(1−Á)bt;0<Á<1: The model implies a first order system for real wages (w−q)tand the real exchange rate (b−q)t. Appendix A shows that under mild parameter restrictions, there is a stable solution for an exogenously determined steady-state rate of unemployment, uss (e.g., by an independent ARMA process). The model encompasses both the wage curve and the Phillips curve specifications. A Phillips curve requires ®w=®q=0, while a wage curve specification implies °u=¯p−q=0.Consequently, it should be possible to identify the model specificNAIRUsasspecialcasesofthe general steady-state unemployment uss. 2.3 The wage curve NAIRU The static wage-curve NAIRU ¯uwis obtained by imposing ¯pr =1and ¯p−q=0on (1)-(2): ¯uw=mw+mq ¯u ; as shown in Figure 1. It shows the downward sloping wage curve, represented by the restricted (1), while price setting is represented by (2) as the horizontal line. ThestaticwagecurveNAIRUisdefined by the intersection between the two lines, 5For simplicity we abstract from movements the mark-up over the cycle. 6The dynamics is kept deliberately simple for ease of exposition. See Bårdsen and Fisher (1999) for an example with more complex dynamics. 3 e.g., that there exists a certain level of unemployment ¯uwat which the conflicting real wage claims are equalized and the rate of inflation is constant. w-q u wage setting Price setting uw uss - Figure 1: Real wage and unemployment determination in the static wage curve model. Within our more complete dynamic framework, the wage curve NAIRU uw is derived by imposing a set of restrictions on the wage-price system (3)—(4). The following set of restrictions are required: 1. Identification of the unemployment effect on wages: °u=0. 2. Stationarity of the wage share: ¯pr =1; elimination of the wedge in the longrun wage equation: ¯p−q=0, but maintaining ®w>0,and 3. imposing short-run homogeneity of the particular form °qw =°wq =1;and hence °wp =°qb =0. The model can now be expressed in term of two conflicting equations for ∆(w−q)t. The only solution of the battle of mark-ups is that ut→uw: (6) uw=¯uw+µcw+cq ®w¯u¶: 4 Proponents of the wage curve argue that ut→uwin steady state.7Without the restrictions 1.—3., any rate of unemployment, say uss, can be fully consistent with a steady-state growth rate of the real wage, a stationary wage share and a constant rate of inflation. 2.4 The Phillips curve NAIRU To derive a NAIRU from a Phillips curve, the following set of restrictions are sufficient: 1. No equilibrium correction ®w=®q=0 2. No effectofwage-growthoninflation °qw =0 Equation (3) then simplifies to the wage Phillips-curve (7) ∆wt=cw+°wp∆pt+°wq∆qt−°uut−1; and we define (8) uphil =1 °u£¡°wp +°wq −1¢¼−gpr +cw¤ as the Phillips curve NAIRU–where ¼is steady-state inflation, and gpr denotes the productivity growth rate.8 There is logically no reason why the steady-state real wage should involve uss =uphil.9In this case neither the real wage nor the real exchange rate are dynamically stable for a given level of unemployment. However, uphil is a fixed point, from (7), and one can certainly think of a stabilizing mechanism that links utto the lagged real wage share, meaning that ut→uphil if all shocks are removed from the system. 3 Testing the NAIRU implications The analysis of the previous section argued that there is no reason why dynamic stability of real wages and inflation should imply or require a supply side determined steady state rate of unemployment. Moreover, the common practice of estimating such a quantity from a single Phillips curve or wage curve equation implies restrictions on a more general model of wage and price setting. These restrictions can be tested and the outcome can either strengthen or weaken the belief in the NAIRU qua model of the stationary rate of the rate of unemployment. We first perform a full system analysis of wages, prices and productivity using Norwegian manufacturing data for the period 1962-1994. Next, we use our framework to re-interpret the evidence in existing studies. 7Thus, “Only if the real wage (W=P)desired by wage-setters is the same as that desired by price-setters will inflation be stable. And the variable that bring about this concistency is the level of unemployment”, Layard et al. (1991, p. 18). 8i.e., we take the expectation of (8) and use that E[∆wt−∆qt−∆prt]=0,E[∆qt]=E[∆pt]=¼ and E[∆prt]=gpr. With a ∆prtterm in the Phillips curve, gpr in the expression for uphil will have a coefficient less than unity. Note that in (6), cq=gpr from the property of cointegration. 9Therealexchangerateisunstableduetotheunitrootimpliedby®w=0, however the real exchange rate does not enter into the dynamic equation of the real wage. 5 3.1 Econometric evidence from Norway We first consider cointegration in a semi-closed system. The modelled variables are all in log scale and are denoted as follows:10 wt=hourly wage cost in manufacturing; qt=index of producer prices; (p−q)t=the wedge between the consumer and producer real wage; prt=value added labour productivity; ut=rate of unemployment; rprt=the replacement ratio. The wedge variable (p−q)tincludes a payroll tax-rate and an income tax-rate. The conditioning variables are ∆lmptis the change in the labour market programmes variable lmp,defined as ln(1−the labour market program rate); The lagged inflation rate, ∆pt−1; The change in normal working hours, ∆ht: In addition we include a constant term (unrestricted) and two institutional dummies.11 We estimate a system with one lag of each endogenous variable. We use annual data for the period 1964-1994, i.e., the number of observations (T) is 32, and the number of coefficients is 12. The main series are shown in Figure 2. 10The data set is available on the internet: http://folk.uio.no/rnymoen 11The dummy variable IPtis designed to capture the effects of the wage-freeze in 1979 and the wage-laws of 1988 and 1989. It is 1in 1979 and 0:5in 1980 (low wage drift through 1979), 1in 1988 (“firstwage-law”)and0:5in 1989 (“second wage-law”). Similar dummies for incomes policy appear with significant coefficients in earlier studies on both annual and quarterly data (see e.g., Johansen (1995)).The dummy variable i67tis a separate dummy which is 1in 1967 and is zero otherwise. 1967 was a year with large changes in taxes and benefits,inconnectionwitha comprehensive reform of the National Insurance System. 6 Blanchflower, D. G. and A. J. Oswald (1994). The Wage Curve.TheMITPress, Cambridge, Massachusetts. Carruth, A. A. and A. J. Oswald (1989). Pay Determination and Industrial Prosperity . Oxford University Press, Oxford. Clarida, R., J. Gali and M. Gertler (1999). The Science of Monetary Policy: A New Keynesian Perspective. Journal of Economic Literature,37 (4), 1661—1707. Cromb, R. (1993). A Survey of Recent Econometric Work on the NAIRU. Journal of Economic Studies,20 (1/2), 27—51. Davies, E. P. and L. Schøtt-Jensen (1994). Wage and Price Dynamics in EUCountries: Preliminary Empirical Estimates. European Monetary Institute. Doornik, J. A. and D. F. Hendry (1997). Modelling Dynamic Systems using PcFiml 9 for Windows. International Thomson Business Press, London. Doornik, J. A. and D. F. Hendry (1999). Empirical Econometric Modelling Using PcGive. Volume 1 . Timberlake Consultants, West Wickham. Drèze, J. and C. R. Bean (eds.) (1990a). Europe’s Unemployment Problem; Introduction and Synthesis. MIT Press, Cambridge. Drèze, J. and C. R. Bean (1990b). Europe’s Unemployment Problem; Introduction and Synthesis. In Drèze, J. and C. R. Bean (eds.), Europe’s Unemployment Problem, chap. 1. MIT Press, Cambridge. Elmeskov, J. and M. MacFarlan (1993). Unemployment Persistence. OECD Economic Studies, (21), 59—88. Fuhrer, J. C. (1995). The Phillips Curve is Alive and Well. New England Economic Review, 41—56. Gordon, R. J. (1983). ’Credibility’ Vs. ’Mainstream’: Two Views of the Inflation Process. In Nordhaus, W. D. (ed.), Inflation: Prospects and Remedies, Alternatives Fort the 1980s. Center for National Policy, Washington. Gordon, R. J. (1998). Foundations of the Goldilocks Economy: Supply Shocks and the Time-Varying NAIRU. Brookings Papers on Economic Activity, (2), 297—346. Grubb, D. (1986). Topics in the OECD Phillips Curve. Economic Journal,96 , 55—79. Holden, S. and R. Nymoen (2002). Measuring Structural Unemployment: NAWRU Estimates in the Nordic Countries. Scandinavian Journal of Economics,104 , 87—104. Johansen, K. (1995). Norwegian Wage Curves. Oxford Bulletin of Economics and Statistics,57, 229—247. King, M. (1998). Mr King Explores Lessons from the UK Labour Market. BIS Review, (103). 13 Kolsrud, D. and R. Nymoen (1998). Unemployment and the Open Economy WagePrice Spiral. Journal of Economic Studies,25 , 450—467. Layard, R. and S. Nickell (1986). Unemployment in Britain. Economica,53 ,121— 166. Special issue. Layard, R., S. Nickell and R. Jackman (1991). Unemployment: Macroeconomic Performance and the Labour Market. Oxford University Press, Oxford. Nickell, S. (1987). Why is Wage Inflation in Britain so High? Oxford Bulletin of Economics and Statistics,49 , 103—128. Nymoen, R. (1989). Modelling Wages in the Small Open Economy: An ErrorCorrection Model of Norwegian Manufacturing Wages. Oxford Bulletin of Economics and Statistics,51 , 239—258. OECD (1997). Employment Outlook. OECD, Paris. July 1997. Rødseth, A. (2000). Open Economy Macroeconomics. Cambridge University Press, Cambridge. Rødseth, A. and R. Nymoen (1999). Nordic Wage Formation and Unemployment Seven Years Later. Memorandum 10/99, Department of Economics, University of Oslo. Rowlatt, P. A. (1992). Inflation. Chapman and Hall, London. Scarpetta, S. (1996). Assessing the Role of Labour Markets Policies and Institutional Settings on Unemployment: A Cross-Country Study. OECD Economic Studies, (26), 43—98. Staiger, D., J. H. Stock and M. W. Watson (2002). Prices, Wages and the U.S. NAIRU in the 1990s. In Kruger, A. and R. Solow (eds.), The Roaring Nineties. Russell Sage Foundation. Svensson, L. (2000). Open Economy Inflation Targeting. Journal of International Economics,50 , 155—183. 14 Gunnar Bårdsen and Ragnar Nymoen: Testing steady-state implications for the NAIRU. Arbeidsnotat 2000/3 KEYWORDS: Phillips curve Steady state Natural rate NAIRU Dynamic modelling Corresponding principle 20832