Econometric Inflation Targeting

Bardsen, Gunnar; Jansen, Eilev S.; Nymoen, Ragnar Working Paper Econometric Inflation Targeting Arbeidsnotat, No. 1999/5 Provided in Cooperation with: Norges Bank, Oslo Suggested Citation: Bardsen, Gunnar; Jansen, Eilev S.; Nymoen, Ragnar (1999) : Econometric Inflation Targeting, Arbeidsnotat, No. 1999/5, ISBN 82-7553-143-8, Norges Bank, Oslo, https://hdl.handle.net/11250/2500538 This Version is available at: https://hdl.handle.net/10419/209769 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 Econometric inflation targeting∗ Gunnar Bårdsen Norwegian University of Science and Technology and Norges Bank Eilev S. Jansen Norges Bank and Norwegian University of Science and Technology Ragnar Nymoen University of Oslo and Norges Bank First version: 13 April 1999. This version: 22 June 1999. Abstract Inflation targeting makes the Central Bank’s conditional inflation forecast the operational target for monetary policy. Successful inflation targeting requires knowing the transmission mechanisms to inflationfromshocksaswell as instruments. The econometric implications are that the exogeneity assumptions of a conditonal forecasting model of inflation are crucial to the quality of the forecasts. We advise that econometric inflation forecasting should be basedonacorewage-pricemodel,graftedintoawidersetofequationsthat capture the important transmission mechanisms between inflation and policy instruments (interest rate, exchange rate) as well as between inflation and shockstotheeconomy. Wedevelopamodeloftheinflation process in Norway by estimating a dynamic model of wages and prices, supplemented with marginal models of the transmission mechanisms of shocks and instruments. The exogeneity assumptions are tested and accepted. Finally, we demonstrate the model responses to shocks and corresponding changes in monetary instruments and examine the suitability of the full system for inflation forecasting. Keywords: inflation targeting, monetary policy, wages and prices, cointegration, dynamic modelling. JEL classification: C3,C5,E3,E5,J3. ∗Versions of this paper have been presented at the Conference “Macroeconomic Transmission Mechanisms” at the Norwegian University of Science and Technology, Trondheim, April 1999, and in seminars at the Norwegian University of Science and Technology, Trondheim, at Norges Bank, at the University of Oslo, and at Queensland University of Technology, Brisbane. Comments from participants on these occasions are gratefully acknowledged. Discussions with and comments from Øyvind Eitrheim, Paul Fisher, David Hendry, Steinar Holden, Søren Johansen, Adrian Pagan and Fredrik Wulfsberg have been very helpful. The views expressed are those of the authors and should not be interpreted as reflecting those of Norges Bank. This working paper was finished while Gunnar Bårdsen was visiting School of Economics and Finance, Queensland University of Technology. The hospitality and excellent working conditions offered are gratefully acknowledged. 1 Introduction Central Banks that wish to stabilize inflation have to take account of the lags in the effects of monetary policy on inflation. Indeed, the recent formalization of inflation targeting as a monetary policy regime makes it clear that the central bank’s conditional inflation forecast becomes the operational target for monetary policy. Shocks to the forecasted inflation rate must be assessed numerically and counteracted with the use of monetary policy instruments, sometimes modelled as “policy rules”. Successful inflation targeting therefore requires knowing the transmission mechanisms of shocks as well as instruments. Econometric models are therefore found to be in demand not only as an aid in the preparation of inflation forecasts, but also as a way of elucidating the transmission mechanisms–both to policy makers and to the general public. In this way, inflation targeting moves the quality of econometric methodology and practice into the limelight of economic policy debate. For example, the econometric model’s coherency with all available information, and the invariance of model parameters with respect to changes in policy, become imperative for the quality of the policy recommendations, see Ericsson et al. (1998) for a general exposition. This paper offers an empirical investigation of the relationships between shocks, instruments for monetary policy, and inflation in Norway–one candidate economy to opt for formal inflation targeting rather than a managed nominal exchange rate. One possible gain from this exercise is to avoid unintended consequences on the activity level, arising from making policy decisions based on an erroneous model of the relationship between interest rates and inflation, as seem to have been the case in Canada, see Fortin (1996). For an opposing view, see Freedman and Macklem (1998). The chains of causation between shocks, interest rates, and inflation can be long and tangled. The need for economic theory in developing models of the transmission mechanisms are evident, but the credibility of these theoretical models must also be substantiated by econometric testing. So far the literature on inflation targeting has been dominated by theoretical contributions, see e.g. Svensson (1999), and of the documentation of practical policy conduct found in the inflation reports issued by the central banks in the countries that have adopted inflation targeting, e.g. Canada, Sweden, New Zealand, UK, Israel, Mexico and Australia. Few attempts exist to address the issues raised by inflation targeting from an econometric point of view. Two exceptions are the work by Jacobson et al. (1999) and Haldane and Salmon (1995). Jacobson et al. (1999) investigate the empirical basis for inflation targeting in Sweden within a vector autoregressive framework. Our paper departs from Jacobson et al. (1999) in three main respects: we try to make judgements about the exogeneity status of the variables; in our empirical work we test an explicit theoretical model of the inflation process; finally, we model the transmission mechanisms of “shocks” as well as instruments. There is some common ground between our approach and the paper by Haldane and Salmon (1995), in that both investigations start form a core model of the supply-side. Nevertheless, in terms of methodology and the eventual model properties, the differences are easy to see. First, we attempt test to theoretical predictions, for example the existence or not of a vertical long-run supply schedule, that Haldane and Salmon (1995) impose without testing. Second, the estimated inflation uncertainty is much smaller in our 1 dynamic forecasts than in Haldane and Salmon’s study. 2 Main issues Many of the issues and problems encountered by an attempt to chart the unknown waters between shocks, instruments and inflation can be identified in Figure 1, where we have identified the following steps: 1. Construct a model of the core inflation process, corresponding to Wage-price model in the figure, and how that system is influenced by three categories of “exogenous” variables: Monetary Policy instruments,Economy endogenous explanatory variables (unemployment, import prices etc.) and Non-modelled variables (tax-rates, world-prices). 2. Estimate relationships between Policy instruments and Economy endogenous variables. 3. Investigate invariance of the inflation model to changes in policy regimes (indicatedbytheshadedboxedinthefigure), in particular fixed versus floating exchange rate regimes. All items involve substantive use of econometric methods and economic data. Issue 1 involves dynamic modelling of wages and price based on a theoretical model of the supply-side. In the theoretical model in Section 3, goods and labour markets are assumed to be imperfectly competitive. Another premise of the model is that both firms and workers (through their unions) try to control the real wage. The model predicts that there are two long-run real wage equations, corresponding to each side of the bargain. In equilibrium, the two real wage claims are reconciled, and the rate of inflation equals imported inflation: the sum of the rate of nominal currency depreciation and the rate of change in import prices.1 Out of equilibrium, the two claims on real wages are inconsistent and domestic inflation moves away from imported inflation. The inflation mechanism is a wage-price spiral: Firms adjust nominal prices to attain their real wage target and workers strive to adjust nominal wages in a pursuit of their own real wage target. Accordingly, the engine room in the domestic inflationprocessistheconflicting real wage claims arising in imperfectly competitive product and labour markets. Econometrically, the claims equations are cointegration relationships and they appear in the form of equilibrium-correction mechanisms (EqCMs) in the dynamic model, see Section 4. Often homogeneity of the static wage and price system is seen a the fundamental requirement for the model to possess a long-run aggregate supply schedule that is vertical, i.e. a non-accelerating-inflation rate of unemployment (NAIRU). However, the NAIRU is a characteristic of the static equilibrium, while the meaningful equilibrium concept for a dynamic wage-price model is the long-run steady state. In general, the steady-state equilibrium has different properties than 1Reconciliation of conflicting claims is a property of the steady state solution of the dynamic wage-price model. In the steady state all three real wage variables–workers’ and firms’ real wage claims and the actual real wage–are all constant. However, they are not equal, as implied by the static equilibirum, see Kolsrud and Nymoen (1998) for a discussion. 2 the static equilibrium. For example, the dynamic steady state does not imply a NAIRU, even though the cointegrating relationships obey static homogeneity. Figure 1: Model based inflation forecasts. Static homogeneity of wage price systems is in fact rarely rejected empirically, it is a weak restriction on the system. Dynamic homogeneity is different, it is usually thought of a strong restriction that is often rejected. Interestingly, Kolsrud and Nymoen (1998) shows that the dynamic wage-price model has a non-NAIRU steadystate equilibrium also in the case of dynamic homogeneity. Only for the unlikely case that wage growth is homogenous in producer price growth–so there are no effects of changes in the consumer price index on the growth rate of wages–does dynamic homogeneity imply a NAIRU property in our model. These restrictions aretestableintheempiricalversionofourcoremodeloftheinflation process, and we do so in Section 5. Why is the non-NAIRU implications of the model so robust to restrictions on the system? The answer is that the NAIRU property is derived for a wageprice system that is essentially static: If real wage claims for some reason become inconsistent, inflation is non-constant until the system is back at equilibrium. Hence, in the static model, inflation is a disequilibrium phenomenon. Once we formulate the wage-price model as a dynamic equilibrium-correction system, a different aspect of inflation is brought to the forefront–that of equilibrating conflicting real-wage claims. In brief, the generic arbiter of conflicting claims is inflation itself. There is no unique supply side determined level of unemployement (NAIRU) that achieve the reconciliation of claims, see section 3.2. Issue 2 involves the formulation of marginal models for the variables that were assumed exogenous in the formulation of the wage-price model. That assumption is tested with the aid of the marginal models. The relevant exogeneity concept is weak exogeneity with respect to the parameters of the real wage claims equations. Rejecting weak exogeneity implies that the cointegrating relationships are inefficiently estimated. All three categories (non-modelled, policy and economy endogenous variables) must be weakly exogeneous for the modelling of core inflation as a separate 3 block. Strong exogeneity is only required for Non-modelled variables and Policy instruments. Hence, causation need not to go one way between economy endogenous variables and wages and prices. In the figure we can therefore envisage an arrow going from Wage-price model back to Economy endogenous. Finally, issue 3 entails the invariance of the parameters of the Wage-price model to changes in the marginal models. The possibility that non-constancies in the parameters of the Wage-price model may be a result of parameter changes (“regime shifts”) in the marginal models are indicated by the shaded “bars” in the figure. Invariance can be tested within the sample: If parameter changes in the marginal models can be identified over the sample period, we can test whether the parameters of the core inflation model have remained constant despite the regime shifts. Invariance with respect to structural changes outside thesampleperiodcannotbe tested directly. However, it is possible to gain some insight about the impact of inflation targeting through more indirect methods. First, we note that while the theoretical model in Holden (1999) predicts that introduction of a inflation target will lower wages in the traded sector and increase wages in the non-traded sector of the economy, there is no clear cut implication for the average wage. Second, there now exists a body of evidence from other countries. Sweden, who share many of the wage setting institutions of Norway, changed her monetary regime in 1993: Rødseth and Nymoen (1999) do not find any impact on the parameters of their estimated equation for Swedish manufacturing wages. Also, United Kingdom wage-price formation has recently been investigated in Bårdsen and Fisher (1999) and Bårdsen et al. (1998) with data spanning several changes in regime, including moving from exchange rate targeting to inflation targeting.2The parameters of the model remained constant across these changes in regime. We also note that, unless inflation targeting is in every respect a truly new regime, there may be periods in the sample where monetary instruments were used inawaythatresembleswhatonemightexpectifaformalinflation target regime was in place. In particular, one can argue that this has been the case after December 1992, when the Norwegian Krone (NOK) went floating. Moreover, the exchange rate that we use as a predictor of inflation, i.e. the trade-weighted exchange rate variable, shows variation even in periods where the official target exchange rate is relatively constant. Thus, even a successful exchange rate targeting regime may entail considerable variation in the trade-weighted exchange rate. Hence, while not claiming to prove invariance of the Wage-price model with respect to a shift to formal inflation targeting, we believe that invariance (or lack thereof) to changes in the way the managed float regime have been implemented over the sample is a relevant property of the model. How does the interest rate affect inflation? Four channels can be located with the aid of Figure 1. First, a direct effect can be represented by the arrow from Policy instruments to Wage-price model. If this channel is important empirically, we 2The data covered the period 1976(2)—1993(1). The United Kingdom joined the ERM on 8 October 1990. Membership was suspended on 6 September 1992. The new framework was announced in October first by a short letter from the Chancellor and then his ’Mansion House speech’ later that month. The first Inflation Report was published in February 1993. Prior to 1990 sterling had been ’freely’ floating since the early seventies. 4 should be able to detect significant effects of the interest rates in the equations of the empirical Wage-price model.Apriorithereisalottobesaidforthisdirect effect: The consumer price index includes the cost of housing, and that component of the CPI index is likely to respond to changes in interest rates. Wage claims are often reported to be linked to interest rates, but existing empirical wage equations containnosucheffect, see Nymoen (1989a). Hence, there is no evidence that wage earners are compensated for raising housing costs in excess of that which is already incorporated in the CPI index. A second effect is indirect and works through the product market: Higher interest rates reduce aggregate demand and therefore put downward pressure on inflation if product market disequilibrium (the “output gap”) has a significant effect in the CPI equation. Since it is likely that unemployment also increases, the effect is reinforced by reduced wage claims and wage growth. However, those effects are counteracted if productivity falls in response to the contraction in demand. A third effect is that higher short-term interest rates are likely to strengthen the nominal exchange rate and in turn affect the CPI index. Fourth, and finally, a nominal exchange rate appreciation also means a stronger real exchange rate initially which also puts downward pressure on CPI inflation via a product market disequilibrium term. From the above it is easy to pinpoint aprioridivergent effects from monetary policy (interest rate changes) to CPI-inflation. For example: The direct effects of an increased interest rate rise CPI inflation, so a negative net effect on inflation rests on the three other channels. At the end of the day the only practical way of discussing these issues is with the aid of impulse responses of an empirical model with propagation mechanisms that are transparent and open to inspection. The development of such a model is the main goal of the rest of the paper. We start in Section 3 by setting out what we see as the essential wage-price process. In line with that theory, Section 4 reports the empirical long-run properties of a wage-price subsystem conditional on output, productivity, unemployment, and the exchange rate being weakly exogenous to the long-run parameters of interest. We derive a congruent and parsimonious dynamic model for wage and price growth in Section 5.1. We supplement this model with marginal models for output, productivity, unemployment, and exchange rates in Section 5.2. The exogeneity assumptions underlying such a modelling strategy are examined in Section 5.3. These building blocks are brought together in a simultaneous model in Sections 6 and 7, whereweevaluatethepropertiesofthemodelforinflation forecasting and policy analysis. Section 8 concludes. 3 Conflicting claims: The core model of inflation Conflicting real wage claims are arguably the primary domestic source of inflation in economies where market forces are impeded by bargaining between organizations and intervention by the government. We use a model of the wage and price interactions that accommodate these basic features. This core model is based on theories of imperfect competition in goods and labour markets, adapted from Kolsrud and Nymoen (1998). The model is dynamic and enables us to determine nominal wage and price adjustments, inflation and the implied real wage in a consistent manner. In general, 5 the model has the interesting property that inflation and real wages stabilize after a shock for any given rate of unemployment–instead of a NAIRU property. However, subject to testable parameter restrictions, the model’s equilibrium property can be changed, so the conflict between real wage ambitions cannot be resolved at any constant rate of inflation–instead one might expect that unemployment equilibrates the claims and a NAIRU property emerging. 3.1 Conflicting real wage claims We have in mind a small open economy (SOE) where unions influence wages through bargaining. The wage-bargaining approach is a prevalent theory of wage-determination in a unionized economy; see Carlin and Soskice (1990) and Lindbeck (1993). A simple log-linear wage equation derived from the bargainers’ respective utility functions and budget constraints can be written as: w∗ t=δ12ppt+δ13prt−δ15ut−δ16τ1t−δ17τ2t+(1−δ12)pt,(1) where w∗ tdenotes the target nominal wage from the wage bargaining side of the economy and the {δij}are the coefficients. The real wage faced by firmsisaffected by producer prices ppt, productivity prt, and a payroll tax-rate τ1t. The real wage faced by employees is affected by consumer prices pt,andincometax-rateτ2t.The unemployment rate, ut, represents the degree of tightness in the labour market which influences the outcome of the wage bargain. In an economy with imperfect competition firms set their prices (producer prices) to reflect a mark-up m2over marginal costs. Assuming a constant returns to scale production function, the target nominal price pp∗is set as a constant mark-up over normal unit labour costs: pp∗ t=m2+wt−prt+τ1t.(2) Note that theory would usually start with the representative firm, perhaps with an additional term for bought-in material costs. Strictly speaking, we assume that all such costs originate in the firm sector and that (2) is a valid aggregation. At first sight, this seems to exclude on important channel for import prices on inflation. However, in the following we are focusing on nominal wages and the consumer price index, p,defined as pt≡(1 −ζ)ppt+ζpit+ητ3t,0<ζ<1,0<η≤1,(3) where the import price index pitnaturally enters. The parameter ζmeasures of the openness of the economy. Also, the size of the parameter ηwill depend on how much of the retail price basket is covered by the indirect tax-rate index τ3t. We assume that (3) also holds for planned variables. Hence, substituting out pp∗ tfrom p∗ t≡(1 −ζ)pp∗ t+ζpit+ητ3t, we obtain the target equations 6 w∗ t=(1+ζd12)pt+δ13prt−ζd12pit−δ15ut−δ16τ1t−δ17τ2t−ηd12τ3t,(4) p∗ t=(1−ζ)(wt−prt+τ1t)+ζpit+ητ3t,(5) or, in terms of real wages for workers and firms: rw∗ w=ζd12pt+δ13prt−ζd12pit−δ15ut−δ16τ1−δ17τ2t−ηd12τ3t,(6) rw∗ f=ζwt+(1−ζ)(prt−τ1t)−ζpit−ητ3t(7) where rw∗ w=w∗ t−ptand rw∗ f=wt−p∗ t,andd12 =δ12/(1 −ζ). The static equilibrium considered in a number of earlier studies is defined by rw∗ w=rw∗ f=rwe,whererweis the static equilibrium real wage. The two equation are seen to imply a NAIRU, see e.g. Layard et al. (1994). The NAIRU is independent of the price level, if (4) and (5) are both homogenous of degree one. However, and rather obviously, the static model has no implications for the dynamics of prices and wages.3Hence, to be able to derive formal implications for the changes in wtand pt (i.e. for inflation) we must decide on a dynamic version of the model, as discussed by Kolsrud and Nymoen (1998). For the dynamic model the relevant equilibrium concept is the steady state of the system, which in general (in the case of a stable dynamic system) is different from the static equilibrium corresponding to (6) and (7). We now turn to these issues. 3.2 Inflation So far the model is made up of the competing claims equations for the real wage and a definitional equation for the consumer price index. Formally, the model is not determined since we have more unknowns than equations. In terms of economic content the model is incomplete since nothing has been said about the development of targeted and actual real wages. Although firms and unions have separate views about what real wage level should be, they can only influence real wages through nominal adjustment of wages and prices. In this way conflicting views about the appropriate real wage level become an important source of inflation. In the following, we embed the conflict view of inflationinamodelthatcaptures all the other relevant causes of inflation. In particular we allow wage growth, ∆wt,to interact with current and past price inflation, changes in unemployment, changes in tax-rates, and previous deviations from the desired wage level ∆wt−α12,0∆ppt=c1+α11 (L)∆wt+α12 (L)∆ppt+β12 (L)∆prt −β14 (L)∆ut−β15 (L)∆τ1t−β16 (L)∆τ2t(8) −γ11 (w−w∗)t−m+β18 (L)∆pt+²1t, where ∆is the difference operator, the αij (L)and βij (L)are polynomials in the lag operator L: α1j(L)=α1j,1L+···+α1j,(m−1)Lm−1,j=1,2, β1j(L)=β1j,0+β1j,1L+···+β1j,(m−1)Lm−1,j=2,4,5,6. 3Clearly, the common statement that inflation increases if rw∗ w>rw ∗ fand falls if rw∗ w<rw ∗ f is ad hoc. 7 1980 1985 1990 1995 -.1 0 .1 .2 Elasticity of unemployment in wage equation β +2se -2se 1980 1985 1990 1995 -.4 -.3 Elasticity of import price index in price equation β +2se -2se 1980 1985 1990 1995 10 15 Test of overidentifying restrictions on the cointegrating vetors 5% significance level critical value Sequence of tests Figure 3: Identified cointegration vectors. Recursively estimated parameters and the χ2(8) test of parameter constancy of Table 2, Panel 4. On the basis of Table 2 we therefore conclude that the steady-state solution of our system can be represented as w=p+pr −0.1u p=0.6(w+τ1−pr)+0.4pi +τ3. 5 Modelling the I(0) system 5.1 The wage-price model We have established the steady-state properties of the wage-price model, as predicted by (4) and (5). We now want to estimate (10) in order to test the predictions of the model set out in Section 3. We impose the estimated steady state from Panel 4, Table 2, on a subsystem for {∆wt,∆pt} conditional on {∆prt,∆yt,∆ut−1,∆τ1t, ∆τ3t} with all variables entering with two additional lags. In addition to gapt−1, we also augment the system with {∆ht,i80q2,i70q1,Wdum,Pdum}tocapture short-run effects, as described above. Following Hendry and Mizon (1993), Hendry (1995), and Doornik and Hendry (1996), we start out by simplifying the system by deleting insignificant terms, establishing a parsimonious statistical representation of the data in I(0)-space. The 14 1975 1980 1985 1990 1995 -.02 0 .02 Wage growth residuals +2σ −2σ 1-step residuals 1975 1980 1985 1990 1995 -.01 0 .01 Inflation residuals +2σ −2σ 1-step residuals 1975 1980 1985 1990 1995 .5 1Forecast Chow-test Sequence of Chow-test statistics 5% significance level critical value Figure 4: Recursive residuals for the conditional I(0) sub-system, together with recursive Chow-tests. diagnostics of the system are reported in the upper part of Table 3, while recursive tests of parameter constancy are reported in Figure 4. First, the two 1-step residuals with their ±2 estimated residual standard errors, ±2σin the graphs. The third panel shows the a sequence of recursive forecast Chow-tests together with their one-off5 per cent critical level. Next, we test whether the dynamic restrictions implied by (10) are dataacceptable–see Appendix A, arriving at 15 "1−1 −0.13 (0.05) 1#"d ∆w c ∆p#t =   00−0.4×0.36 0 −L2−0.36 (0.08)L2 0.06L (0.02) 00.4×0.07 0 0.13L20.07 (0.03)L2          gap ∆pr ∆pi ∆u ∆τ1 ∆τ3        t (18) −  0.08 (0.01) 0 00.08 (0.01)  ·L−L−100.1L00 −0.6L20.6−0.40−0.6−L2¸           w p pr pi u τ1 τ3          t−1 Table 3: Diagnostics for the system and the model. Diagnostic tests for the conditional subsystem ˆσ∆w=1.02% ˆσ∆p=0.42% AR 1−5F(20,190) = 1.43[0.11] Normality χ2(4) = 5.10[0.28] Heteroscedasticity F(66,242) = 0.76[0.90] Diagnostic tests for the model in (18) ˆσ∆w=1.01% ˆσ∆p=0.41% Correlation of residuals =−0.5 Overidentification χ2(9) = 9.92[0.60] AR 1−5F(20,200) = 1.20[0.26] Normality χ2(4) = 4.14[0.39] Heteroscedasticity F(66,257) = 0.81[0.84] The lower part of Table 3 contains diagnostics for the model (18). We note that the insignicance of Overidentification χ2(9) shows that the theory restrictions in (10) are not refuted by the data. The first equation in (18) shows that a one percent in the rate of inflation rises wage growth by one percent. However, closer inspection of the equation shows that this is not the case in general: The wage equation includes an indirect tax-rate, lagged, with a negative coefficient. The effects of the discretionary policy variables are not shown, but they include a negative coefficient of the VAT dummy (i70q1t) and (ceteris paribus) positive effects of price controls (Pdumt). Hence discretionary policies have clearly succeeded in affecting consumer real wage growth over the sample period. However, in periods where such policies are off, aggregate wages 16 react quickly to “normal” or expected consumer price increases as captured by the unit coefficient of ∆pt. Import price growth is likely to be the most important “unexpected” part of price inflation, so given the unit coefficient on ∆pt,itisnot surprising that ∆pitis attributed a negative estimated coefficient. The equilibriumcorrection term is highly significant, as expected. Finally, the change in normal working-time ∆htenters the wage equation with a negative coefficient, as expected. In addition to equilibrium-correction and the dummies representing incomes policy, price inflation is significantly influenced by wage growth and the output gap, together with effects from import prices and indirect taxes–as predicted by the theoretical model. As discussed by Kolsrud and Nymoen (1998), the question whether systems like ours have a NAIRU property hinges on the detailed restrictions on the short run dynamics. We note that the wage growth equation comes close to being homogenous in consumer price and import price growth. Using, ∆pt≡(1−ζ)∆ppt+ζ∆pitthis is seen to imply that wage growth is almost homogenous in domestic producer prices (∆ppt) and imported inflation. However, this does not imply that we are close to having a NAIRU property: Kolsrud and Nymoen (1998) show that a necessary condition for the NAIRU property is that wage growth is homogenous with respect to ∆pptalone. That homogeneity restriction does not hold in equation (18): Using the estimated value of ζ=0.38 from (2) the implied wage elasticities with respect to ∆pptand ∆pitare 0.62 and 0.24.7The wage equation therefore implies that we do not have a NAIRU model here. Instead we expect that inflation stabilizes for any given rate of unemployment, hence the model has a NAIRI property with the NAIRI given as the rate of imported inflation, see Section 3.3 above. The model tracks the realized values well, as Figure 5 documents. The stability of the model is shown in Figure 6, which contains the one-step residuals and recursive Chow-tests for the model. Finally, the lower left panel of Figure 6 shows that the model encompasses of the system at every sample size. 7If we introduce ∆pptin the model we find a signicant effect of the fourth lag, ∆ppt−4with coefficient 0.14.Thecoefficient of ∆ptfalls to 0.71but retain a t-value of 4.2.Ifweuseζ=0.38 the implied elasticity with respect to producer price growth is 0.58, practically the same as implied by the maintained model. 17 1970 1975 1980 1985 1990 1995 0 .025 .05 .075 Actual (thick line) and fitted quarterly rate of wage growth 1970 1975 1980 1985 1990 1995 0 .02 .04 .06 Actual (thick line) and fitted quarterly rate of CPI-inflation Figure 5: Actual and fitted values of quarterly wage and price inflation. 1975 1980 1985 1990 1995 -.02 0 .02 1-step residuals of wage equation 1-step residuals +2σ −2σ 1975 1980 1985 1990 1995 -.01 -.005 0 .005 .01 1-step residuals of price equation 1-step residuals +2σ −2σ 1975 1980 1985 1990 1995 5 10 15 Test of overidentifying restrictions Sequence of overidentifying test statistics 5% significance level critical value 1975 1980 1985 1990 1995 .25 .5 .75 1Forecast-Chow test for the model. Sequence of Chow-statistics for the model 5% significance level critical value Figure 6: Recursive stability tests for the model. The upper panels show recursive residuals for the model.The lower panels show recursive encompassing tests (left) and recursive Chow-tests (right). 18 5.2 Marginal models We have established a wage-price model conditional upon the rate of unemployment ut, average labour productivity prt, import prices pit, and GDP mainland output yt. In this section we present marginal models for these four variables. This serves three purposes: First, we make use of the marginal model to test the hypothesis of weak exogeneity that underlies the wage-price model. Second, none of these variables are likely to be strongly exogenous, even if the assumption of weak exogeneity should hold. For example, import prices depend by definition on the nominal exchange rate. Below we report a model that links the exchange rate to the lagged real exchange rate, which in turn depend on the domestic price level. Third, all of these variables are potentially affected by interest rates and are therefore potential channels for monetary instruments to influence inflation. 5.2.1 The nominal exchange rate vt The nominal exchange rate affects wages and prices via import prices pi. Hence, as afirststepinthecompletionofthemodel,wemakeuseoftheidentity pit=vt+pft, and attempt to model the (log) of the trade weighted exchange rate index vt.However, Akram and Eitrheim (1999) model the exchange rate as equilibrium correcting to the real exchange rate vt−pt+pckt, where pcktis log of a trade weighted index of foreign consumer prices. We build upon their work, but also include an interest rate arbitrage effect from (RSt−4∆pt−1)−(RSECUt−4∆pckt), giving the combined equilibrium-correction term EqCMv(t)=(RSt−4∆pt−1−RSECUt−4∆pckt)+(v−p+pck)t−1 where RSECUtis the foreign interest rate, and pcktis the (logarithm of) the foreign consumer price index (in foreign currency). Akram (1999) documents significant non-linear effects of the USD price of North-Sea oil. Our model is built along the same lines and therefore features non-linear effects from oil prices (OILt)in the form of two smooth transition functions, see Teräsvirta (1998), OILSTt=1/{1+exp [4 (OILt−14.47)]} and DOILST =1/[1 + exp (OIL −OILt−1)] . The main implication of these terms is that an oil price below 14 USD depreciates the krone, while a high oil-price (above 20 USD) appreciates the krone. In addition, 19 1980 1985 1990 1995 -.02 0 .02 Exchange rate 1-step residuals +2σ −2σ 1980 1985 1990 1995 -.025 0 .025 Mainland GDP 1-step residuals +2σ −2σ 1980 1985 1990 1995 -.1 0 .1 Unemployment +2σ −2σ 1-step residuals 1980 1985 1990 1995 -.025 0 .025 Productivity +2σ −2σ 1-step residuals Figure 7: Marginal equations: 1 step residuals and ±2recursively estimated residual standard errors (σ) there is a negative (appreciation) effect of the change in the money market interest rate ∆RSt. Finally, there is a composite dummy Vdum t=i78q2+2×i82q3+i86q4+i87q4 to take account of devaluation events. Figure 7 shows the sequence of 1-step residuals for the estimated ∆vtequation, together with similar graphs for the three other marginal models reported below. ∆vt=0.27 (0.07) ∆(v−p+pck)t−1−0.1 (0.04)EqCMv(t)−0.13 (0.02) ∆oilt×OILSTt −0.03 (0.007) ∆oilt−2×OILSTt−0.02 (0.007) ∆oilt−1×DOILSTt −0.24 (0.08) ∆RSt+0.02 (0.004)Vdum t T= 1972 (1) −1996 (4) = 100 ˆσ=0.96% AR 1−5F(5,88) = 1.24[0.30] Normality χ2(2) = 1.35[0.50] Heteroscedasticity F(31,61) = 0.88 [0.64] 20 5.2.2 GDP output yt The model for ∆ytis adapted from the “AD” equation in Bårdsen and Klovland (1998): ∆yt=−0.71 (0.08) ∆yt−1−0.51 (0.09) ∆yt−2−0.32 (0.05)EqCMy(t)+0.70 (0.12) ∆crt−1+0.06 (0.01) [i85q1+i86q2]t T= 1972 (1) −1996 (4) = 100 ˆσ=1.61% AR 1−5F(5,86) = 1.44[0.22] Normality χ2(2) = 3.04[0.22] Heteroscedasticity F(31,59) = 1.09[0.38] Apart from the autoregressive part, the model is mainly driven by the equilibriumcorrection mechanism for the product market, denoted EqCMy(t): EqCMy(t)=yt−3−0.5cot−3−0.4yft−3−0.1(pi −p)t−2+0.9RRBt−1, where co is real public consumption expenditure, yf is real foreign demand, (pi−p)is accounting for the real exchange rate, and RRB denotes the real bond rate, defined as RRB =RBt−4∆pt where RB is the nominal bond rate (5 year maturity). The equilibrium-correction term EqCMy(t),measuringthedifference between (log) mainland GDP and aggregate demand, has an estimated adjustment coefficient of −0.32, suggesting a fairly quick reaction to shocks to demand–the median lags to shocks in co and RRB are 5 and 3 quarters, respectively. The variable ∆crt−1captures the impact of financial deregulation (real credit expansion) on output. ∆crt−1is important for explaining output growth in the mid 80s, but in addition an impulse dummy for 1985p1 and 1986p2 are required to capture the two highest growth rates in this period. The estimated equation also includes a constant and three seasonal dummies. 5.2.3 Unemployment ut The change in the rate of unemployment is explained by output growth. Another important factor is labour market policy, represented by the variable amunt(log of the ratio of labour market programmes to total unemployment) and of a variable STUt−1that captures non-linearities in labour demand (see Moene et al. (1997)). STU acts as a shift in the intercept of the equation, the shift occurring at a 4% rate of unemployment (our measurement of u). The interaction with ∆co and ∆yf indicates that demand growth factors have relatively bigger effects in periods of high unemployment. There is are two sets of seasonals in this equation that are designed to capture the gradual change in seasonal pattern over the period. The coefficients are omitted, together with the constant. This equation has direct implications for the properties of the full model, see section 6 below. In particular, the level unemployment cannot be permanently influenced by fiscal policy (a change in the level of co) or monetary policy (a change in RRB). This follows since utis a function of GDP growth, not the level of GDP. 21 Hence, although the wage-price part of the system does not imply a NAIRU, the equilibrium rate of unemployment implied by the full model is independent of the level of aggregate demand. Instead, it is determined by the growth rate of the economy and of the governments willingness to accommodate open unemployment by labour market programmes. There is one important caveat which stems from the non-linear variable STU: If for example a cut in the interest rate causes the rate of unemployment to fall below 4% (the threshold value of STU), equilibrium unemployment reduces. The estimated coefficients of ut−1and STUt−1indicate that equilibrium unemployment is shifted down by 1.5 percentage points. More generally, in a situation where the economy runs a rate of unemployment in the neighbourhood of the threshold value, transitory shocks may be transformed into permanent effects on the rate of unemployment. ∆ut=0.30 (0.07) ∆ut−1−0.24 (0.04)ut−1−1.79 (0.37) ∆yt−1.13 (0.22) ∆yt−1−0.14 (0.04)amunt+0.46 (0.08)STUt−1 −0.62 (0.32) ∆co ×STUt−3−7.45 (3.08) ∆yf ×STUt−3−0.76 (0.33) ∆(pi −p)t−1 T= 1967 (1) −1996 (4) = 120 ˆσ=0.081 AR 1−5F(5,99) = 1.42[0.23] Normality χ2(2) = 4.83[0.09] Heteroscedasticity F(27,76) = 1.61[0.06] 5.2.4 Productivity prt The productivity equation is basically an autoregressive process augmented with anegativeeffect of ∆ut−1and dummies that help whiten the residuals (again the estimated constant and three centered seasonals are omitted). ∆prt=−0.37 (0.06) ∆3prt−1−0.03 (0.01) ∆ut−1−0.08 (0.01)i86 (2)t+0.04 (0.01) [i79q2−i91q3]t T= 1967 (1) −1996 (4) = 120 ˆσ=1.35% AR 1−5F(5,107) = 3.14[0.01] Normality χ2(2) = 5.42[0.07] Heteroscedasticity F(17,94) = 1.37[0.17] 5.3 Testing exogeneity Weak and super exogeneity refer to different aspects of “exogeneity”, namely the question of “valid conditioning” in the context of estimation and policy analysis respectively–see Engle et al. (1983). In the light of the results reported above, it is important to assess the possible exogeneity of output, productivity, unemployment, and exchange rates. First, the cointegrating vectors have been estimated conditional on output, productivity, unemployment, and exchange rates, and efficient estimation requires that these variables are weakly exogenous for the cointegration vectors (see 22 e.g. Johansen (1992)). Second, policy analysis involves as a necessary condition that the wage and price equations are invariant to the interventions occurring in the marginal models of output, productivity, unemployment, and exchange rates; together with weak exogeneity (if that holds) invariance implies super exogeneity. As a means to perform tests of weak and super exogeneity, we supplement the two equation models for wages and prices for Norway, with the marginal models for output, productivity, unemployment, and exchange rates. These marginal models (described in the previous section) can be written on the form     ∆yt ∆pr ∆ut ∆vt    =A(L)     ∆yt−1 ∆prt−1 ∆ut−1 ∆vt−1    +B·Xt+C·DUMt +DµEqCMw(t) EqCMp(t)¶+     εy,t εpr,t εu,t εv,t    .(19) A(L)denotes an autoregressive lag-polynomial matrix (all roots outside the unit circle). Bdenotes the matrix of coefficients of the maintained exogenous variables, i.e. the conditional variables Xtin the four marginal models described above. Auxiliary variables affecting the mean of the variables under investigation – i.e. significant dummies and non-linear terms – are collected in the DUMtmatrix, with coefficients C.Bydefinition, the elements in DUMtare included because they pick up linear as well as non-linear features of yt,prt,u tor vtthat are left unexplained by the information set underlying the price wage systems above. In the following, we will refer to the auxiliary variables as structural break dummies, notwithstanding the fact that they depend fundamentally on the initial choice of information set used above to model wages and prices. While the first line of (19) can be seen as necessary step to ensure that the usual assumptions about constant parameters and white-noise residuals are approximately fulfilled for the marginal model, the second line of the equation enables us to test weak exogeneity. Following Johansen (1992) weak exogeneity of yt,prt,u t and vtwith respect to the cointegration parameters requires that the 4×2matrix with equilibrium-correction coefficients D=0, i.e. EqCMw(t)and EqCMp(t)are the equilibrium-correction terms for wages and prices. Note that, in testing weak exogeneity, we are addressing the validity of an assumption underlying the analysis contained in the sections above. 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However, if we allow for a two period lag in the effects of indirect taxes, the substituted out dynamic effects of producer prices on wages become: −ζα12,0 1−ζ∆pit=−ηα12,0 1−ζ∆τ3t−2 so ∆wt=−ηα12,0 1−ζµζ η∆pit+∆τ3t−2¶+··· =−0.36 (0.4∆pit+∆τ3t−2)+··· Here we impose the steady-state estimates ζ=0.4and η=1from Table 1; we impose an immediate effect of producer prices on wages; and we find dα12,0 1−ζ=0.36 from 0.36L2∆τ3t. This hypothesis cannot be rejected with the available data. Following the same kind of argument, the dynamic effects of producer prices on consumer prices are: ∆pt=ηµζ η∆pit+∆τ3t−2¶+··· ∆pt=0.4∆pit+∆τ3t−2+··· , This hypothesis, however, is rejected by the data. However, allowing for a weighted down dynamic effect, say by α22,0<1, of producer prices on consumer prices suggests the following restriction in the inflation equation: ∆pt=α22,0ζ∆pit+α22,0η∆τ3t−2+··· ∆pt=0.07 (0.4∆pit+∆τ3t−2)+··· , whichisacceptedbythedata. BDatadefinitions B.1 Notes 1. Unless another source is given, all data are taken from RIMINI, the quarterly macroeconometric model used in Norges Bank (The Central Bank of Norway). 33 2. For each RIMINI-variable, the corresponding name in the RIMINI-database is given by an entry [RIMINI: variable name] at the end of the description. (The RIMINI identifier is from Rikmodnotat 140, Norges Bank, Research department, 19th April 1999) 3. Several of the variables refer to the mainland economy,defined as total economy minus oil and gass production and international shipping. 4. In the main text, impulse dummies are denoted iyyqx,whereyy gives the year with two digits and xcontains the quarter (1,2,3). Hence i80q2 is 1in the second quarter of 1980, and is 0in all other quarters. B.2 Definitions AMUN Labour market programmes participation rate. Number of persons in active labour market programmes relative to total unemployment (registered plus labour market programmes participation). [RIMINI: AMUN] CO Public consumption expenditure, fixed 1991 prices. Mill. NOK. [RIMINI: CO]. CR Real credit volume fixed 1991 prices. Mill. NOK. Source: Bårdsen and Klovland (1998). gap Output gap defined as log mainland GDP(log of the variable Yas defined below) deviations from trend, where the trend is estimated by the HP-filter using λ=1600. Fixed baseyear (1991) prices. Mill. NOK. HNormal working hours per week. [RIMINI: NH] OIL Per barrel Brent-Blend oil-price. USD. Source: Norges Bank’s database of economic time series. OILST Smooth transition function of North-Sea oil price: OILST =1/(1 + exp(4 ∗(OIL −14.47))) PConsumer price index. 1991=1. [RIMINI: CPI]. PCK Consumer prices abroad in foreign currency. 1991=1. [RIMINI: PCKONK]. PI Deflator of total imports. 1991=1. [RIMINI: PB]. YTotal value added at market prices in the mainland economy. Fixed baseyear (1991) prices. Mill. NOK. [RIMINI: YF]. PR Mainland economy value added per man hour at factor costs, fixed baseyear (1991) prices. Mill. NOK. [RIMINI: ZYF]. RS 3 month Euro-krone interest rate. [RIMINI: RS]. 34 RSECU ECU interest rate.For the epriod 1967(1)-1986(3): Effective interest rate on foreign bonds, NOK-basket weighted. [RIMINI: R.BKUR] For the period 1986(4)-1996(4): ECU weighted effective rate on foreign bonds. [RIMINI: R.BECU]. STU Smooth transition function of the rate of unemployment, Uas defined below, STU =1/(1 + exp((−125) ∗(U−0.04))); τ1Employers tax rate. τ1=WCF/WF −1. τ3Indirect tax rate. [RIMINI: T3]. URate of unemployment. Registered unemployed plus persons on active labour market programmes as a percentage of the labour force, calculated as employed wage earners plus unemployment. [RIMINI: UTOT]. VEffective import weighted value of the NOK. 1991=1. [RIMINI: PBVAL]. WNominal mainland hourly wages. Constructed from Rimini-database series as: W=WIBA∗TWIBA+WOTVJ ∗(TWTV +TWO+TWJ))/TWF WC Nominal mainland hourly wage costs. [RIMINI: WCF]. YF Weighted average of GDP of trading countries, using share of Norwegian exports in 1985 as weights. 1991=1. [RIMINI: UEI]. Wdum Composite dummy for wage freeze: 1 in 1979.1, 1979.2,1988.2 and 1988.3. Pdum Composite dummy for introduction and lift of direct price regulations. 1 in 1971.1, 1971.2,1976.4,1979.1. -1 in 1975.1,1980.1,1981.1,1982.1. Zero otherwise. Vdum Composite dummy for devaluation events. It is used in the marginal model for the exchange rate and it is defined by: Vdum t=i78q2+2×i82q3+i86q4+i87q4 35