Dundee Discussion Papers in Economics The Relationship between the Markup and Inflation in the G7 Economies and Australia Anindya Banerjee and Bill Russell Department of Economic Studies, University of Dundee, Dundee. DD1 4HN Working Paper No. 119 December 2000 ISSN:1473-236X The Relationship between the Markup and Inflation in the G7 Economies and Australia* Anindya Banerjee† Bill Russell# Abstract An I(2) analysis of inflation and the markup is undertaken for the G7 economies and Australia. We find that the levels of prices and costs are best described as I(2) processes and that except for Japan a linear combination of the log levels of prices and costs cointegrate to the markup that is integrated of order 1. It is also shown that the markup in each case cointegrates with inflation and that higher inflation is associated with a lower markup in the long-run. Keywords: Inflation, Wages, Prices, Markup, I(2), Polynomial Cointegration. JEL Classification: C32, C52, E24, E31 * † Wadham College and Department of Economics, University of Oxford and Department of Economics, European University Institute, #Department of Economic Studies, University of Dundee. We would like to thank Giuseppe Bertola, Roger Farmer, David Hendry, Katarina Juselius, Bent Nielsen and participants at Nuffield College and EUI seminars and Luca Nunziata and Catia Montagna for help with the Italian data. The paper was also presented at the conference of the Royal Economic Society in St Andrews and the World Congress of the Econometric Society 2000 in Seattle. The systems estimation reported in this paper was undertaken using the CATS in RATS modelling programme. The gracious hospitality of Nuffield College, at which the latter-named author was a Visiting Economics Fellow while the paper was written, is gratefully acknowledged. The paper was funded in part by ESRC grants no: L116251015 and R000234954. CONTENTS 1 INTRODUCTION................................................................................................1 2 AN IMPERFECT COMPETITION MARKUP MODEL OF PRICES....................3 2.1 The I(2) System.................................................................................................................................... 4 2.2 The Data ............................................................................................................................................... 5 2.3 The I(2) System Results....................................................................................................................... 8 3 ESTIMATING THE I(1) SYSTEM .....................................................................12 4 CONCLUSION .................................................................................................15 REFERENCES .........................................................................................................19 APPENDIX: DATA SOURCES AND TRANSFORMATIONS ..................................22 1 INTRODUCTION The proposition examined in this paper is that there exists a long-run relationship in the sense proposed by Engle and Granger (1987) where the markup decreases as inflation increases and vice versa.1 This paper estimates this relationship using data from the G7 economies and Australia. A central feature of our analysis is that the level of prices and costs may be taken to be integrated of order 2, denoted I(2), for the purposes of modelling. In other words, both the differences of prices and costs and their levels that comprise the markup display persistent behaviour over the samples investigated. This requires us to make use of recently developed techniques for the estimation of I(2) processes developed by Johansen (1995a, b) inter alia.2 Bénabou (1992) argues within a price-taking model that higher inflation leads to greater competition and therefore a lower markup. In contrast, Russell, Evans and Preston (1997), Chen and Russell (1998), Russell (1998), Athey, Bagwell and Sanichiro (1998) and Simon (1999) focus on the difficulties that price-setting firms face when adjusting prices in an inflationary environment where there is missing information. In this case the lower markup k 1 The logarithm of the markup, mu , is defined as mu ≡ p − ψ i ci where p and the ci ’s are the i =1 k logarithms of prices and the costs of production respectively, and ψ i = 1 . If the latter condition is not i =1 satisfied then the relationship between prices and costs cannot be termed the markup. 2 An alternative way to proceed with the empirical investigation would be to consider the mean of inflation shifting from high early in the sample to low later in the sample with the markup shifting correspondingly in the opposite direction. This so-called co-breaking approach would consider inflation and the markup series to be I(0) with breaks – to give the appearance of I(1) series - but with the breaks in both series happening at roughly the same time in order to generate a relationship. See Campos, Ericsson and Hendry (1996) and Hendry and Mizon (1998) for a general discussion of breaking and co-breaking. 2 with higher inflation is interpreted as the higher cost of overcoming the missing information with higher inflation. Importantly, Russell et al., Chen and Russell and Russell argue that information remains missing in the steady state and that the relationship between rates of steady state inflation and the markup will also remain in the steady state.3 Banerjee, Cockerell and Russell (1998) using Australian inflation data find strong empirical support of the proposition. An important question is whether the findings in Banerjee et al. are in some way peculiar to the Australian data. The ‘peculiarity’ of the data may be due to the nature of the shocks encountered over the sample examined, the behaviour of the Australian monetary authorities or the structure of the economy. Alternatively, the findings may be applicable to developed western economies in general when inflation is nonstationary. To this end we proceed to examine the proposition for the G7 economies and Australia. The empirical investigation proceeds in two stages. First we estimate an I(2) system for each economy of the core variables of interest, namely prices and costs. Except for Japan, we find that a polynomially cointegrating relationship is present between the level of the markup and the changes in the core variables.4 Having obtained an estimate from the I(2) analysis of the long-run relationship between the markup and general inflation of the core variables, we proceed to estimate an I(1) system in order to obtain the direct relationship between price 3 The steady state is defined as all nominal variables growing at the same constant rate. 4 Polynomial cointegration occurs when the cointegrated levels of the data cointegrate with the differences in the levels. In our case the I(2) levels of prices and costs cointegrate to the markup which is I(1) and the markup then cointegrates with inflation which is also I(1). For a detailed discussion concerning polynomial cointegration see Johansen (1995b). 3 inflation alone and the markup. The estimated I(1) system is a particular and full reduction of the I(2) system and corroborates the findings in the I(2) system. While differences emerge between the economies, the finding of polynomial cointegration for the G7 economies and Australia is remarkably robust. The only exception is Japan where the levels of prices and costs cointegrate to an I(1) variable but it cannot be interpreted as the markup. Therefore, it appears that except for Japan the proposition that there exists a negative long-run relationship between inflation and the markup is consistent with the data in the G7 economies as well as in Australia. 2 AN IMPERFECT COMPETITION MARKUP MODEL OF PRICES We propose estimating an imperfect competition markup equation in the Layard / Nickell tradition for the eight economies.5 It is assumed that in the long-run firms desire a constant markup, q , of prices, p , on unit costs net of the cost of inflation. Short-run deviations in the markup are due to the business cycle and non-modelled shocks. For an open economy the main inputs are labour and imports and we can write the inflation cost long-run markup equation as:6 mu = p − δ ulc − (1 − δ ) pm = q − λ ∆p 5 (1) For the standard Layard / Nickell model see Layard, Nickell and Jackman (1991) or Carlin and Soskice (1990). For a detailed discussion of empirical models relating the markup with inflation see Cockerell and Russell (1995) and Banerjee et al. (1998). 6 Banerjee et al. (1998) derives equation (1) and considers in some detail issues concerning the integration properties of the data. The form of the long-run price equation is a generalisation of that estimated in de Brouwer and Ericsson (1998) in the sense that we allow for dynamic error correction. Two other papers estimating markup models of inflation are Richards and Stevens (1987) and Franz and Gordon (1993). 4 where ulc and pm are unit labour costs and unit import prices respectively and δ and λ are positive parameters. Lower case variables are in logarithms and ∆ represents the change in the variable. When the inflation cost coefficient, λ , is zero, inflation imposes no costs on the firm in the long-run and the long-run markup equation collapses to the standard Layard / Nickell model. In the more general case when λ > 0 inflation imposes costs on the firm in terms of a lower markup net of the cost of inflation.7 This is given by q − λ ∆p . The coefficients δ and 1 − δ in (1) are the long-run price elasticities with respect to unit labour costs and import prices respectively. Linear homogeneity is imposed as the coefficients sum to one so that q represents the markup of prices on costs. Linear homogeneity suggests that all else equal an increase in costs is fully reflected in higher prices in the long-run leaving the markup unchanged. 2.1 The I(2) System The I(2) system analysis is an extension of the now standard I(1) system analysis. For a detailed theoretical outline of the I(2) analysis see Haldrup (1998), Johansen (1995a, b) and Paruolo (1996). Alternatively, for a brief ‘penetrable’ survey of the I(2) theory in relation to 7 The long-run price equation (1) cannot be strictly true as it implies that the markup approaches zero as inflation tends to an infinite rate. Russell (1998) overcomes this problem by specifying the cost of inflation in the form; λ1 [∆p (∆p + φ )] where φ is trend productivity. Consequently, as inflation tends to an infinite rate the cost of inflation approaches λ1 . It is assumed that the proposed log-linear model of inflation costs is a fair approximation of the ‘true’ relationship over the small range of inflation experienced by the economies examined. 5 the model estimated here see Banerjee et al. (1998). Other empirical applications of the I(2) theory can be found in Engsted and Haldrup (1999) and Juselius (1998). For illustration, suppose the long-run price equation can be written as a second order vector autoregression of the core variables, xt , of dimension n × 1 : xt = Π 1 xt −1 + Π 2 x t − 2 + Φ Dt + µ + ε t (2) where µ is a vector of unrestricted constant terms and Dt is a vector of predetermined variables that are assumed not to enter the cointegration space and on which the empirical analysis is conditioned. The lower case variables are in logs and in our case n = 3 and the core variables, xt , are the price level, unit labour costs and import prices. It is assumed that the variable ε t is a n − dimensional Gaussian vector of errors. The I(2) analysis provides us with the orthogonal decomposition into the I(0), I(1) and I(2) relationships of the data with dimensions, r , s and n − r − s respectively. Furthermore, the number of polynomially cointegrating vectors is equal to the number of I(2) trends, n − r − s . 2.2 The Data The data are quarterly, seasonally adjusted and taken from the June 1997 OECD Data Compendium.8 The length of the data sample for each economy is the maximum possible from that source given the series involved. West German data is used for Germany to avoid data problems associated with the reunification with East Germany. 8 See the data appendix for further details. 6 Except for the United States the price index is the private consumption implicit price deflator at ‘factor cost’. 9 Unit labour costs are calculated as total labour compensation divided by constant price GDP. Import prices is the implicit price deflator for the imports of goods and services. The consumption deflator at factor cost was initially used for the United States but gave conflicting results. While the I(2) analysis indicated that the level of prices and costs were best described as I(2) statistical processes, there were a number of indicators to suggest that these series did not cointegrate to the markup. As the ‘no markup’ result is not useful in investigating the proposition, the GDP implicit price deflator at factor cost was used.10 The predetermined variables are the log change in the unemployment rate and a number of spike intervention dummies to capture the sometimes erratic short-run wage and price behaviour of firms and labour.11 This is especially the case during the OPEC oil price shocks and large shifts in exchange rates and tax regimes. A step dummy is introduced for the period leading up to March 1968 for the United States, March 1975 for France, and March 1970 for 9 The private consumption implicit price deflator at ‘factor cost’ is calculated as: P = PMP (1 + tax ) where PMP is the consumption implicit price deflator at market prices and tax is the proportion of indirect tax less subsidies in nominal GDP. While the ‘factor cost’ adjustment is theoretically necessary in practice it has little impact on the results. 10 The failure to estimate the markup using the consumption deflator may be because the unit labour cost variable is for the whole economy and a poor proxy for unit labour costs associated with consumption expenditures for the United States. 11 Three lags of the unemployment variable are initially incorporated with insignificant terms subsequently excluded. 7 Canada. These capture a level shift in the markup that is observable in the data and can be interpreted as reflecting a shift in the competitive environment in these economies.12 The log change in the unemployment rate represents the business cycle in the model. An alternative specification of the empirical model would be to include the level of unemployment in the cointegrating space as an endogenous or exogenous variable. However, it is not clear what the economic relationship between the markup, inflation and the level of unemployment would be in the long-run. There is some indication that the relationship may be highly non-linear and may differ substantially among economies. Furthermore, such an inclusion would alter the interpretation of this variable from that of an indicator of the business cycle. It was therefore decided to allow for the effects of the business cycle by conditioning on a stationary pre-determined variable given by the log change in the unemployment rate and its lags. The integration properties of the data were investigated using PT and DF-GLS univariate unit root tests from Elliott, Rothenberg and Stock (1996).13 Prices are clearly I(2) except for Japan and West Germany which are marginally I(2). Similarly, unit labour costs are mostly I(2) or marginally I(2). One exception is Australia where it appears that unit labour costs may be I(1). The tests also indicate that import prices may be I(1) for many of the economies. However, univariate tests of the logarithm of the ratios of prices to unit labour costs and prices to import prices show clear acceptance of the hypothesis that they are I(1) which can occur only if all the core variables are I(2), given that prices are I(2). Consequently we proceed under the assumption that the core variables are I(2). This assumption is supported by the I(2) and I(1) systems analysis below where the results are consistent only with the 12 Further details of the pre-determined variables are available in Appendix B of Banerjee and Russell (2000). 13 These results are available on request from the authors. 8 assumption that the core variables are I(2). Finally, the log of the unemployment rate is found to be best described as an I(1) variable. 2.3 The I(2) System Results Table 1 shows the results of the joint trace tests for determining r and s for the eight economies. In the case of the United States, Japan, Germany, France and the United Kingdom the hypothesis of r = 1 , n − r − s = 1 is accepted and our findings are corroborated by looking at the roots of the companion matrix (see Appendix B of Banerjee and Russell (2000)).14 The results therefore show that the levels of prices and costs in each of these economies contain an I(2) trend. Moreover, since r = 1 there is only one cointegrating vector and hence it is of the polynomially cointegrating type. 14 The 90 % and 95 % critical values for the case of no pre-determined variables are taken from Paruolo (1996) and are reported in the table below. The 95 % critical values are in italics. Other critical values are available in tables compiled by Rahbek, JØrgensen and Kongsted (1999) and Johansen (1995b). Critical Values for the Joint Trace Test Q(s, r) n-r 3 r 0 2 1 1 2 n-r-s 66.96 70.87 47.96 51.35 33.15 36.12 3 2 35.64 38.82 20.19 22.60 11.11 12.93 1 26.70 29.38 13.31 15.34 2.71 3.84 0 9 Table 1: The ‘Joint Procedure’ for Estimating r and s Estimated Values of Q(s, r) = Q(s|r) + Q(r) United States n-r r 3 0 2 1 1 2 156.87 n-r-s 3 Japan n-r r 91.41 40.15 36.95 3 0 78.70 13.32 8.37 2 1 23.98 1.33 1 2 1 0 n-r-s 2 112.50 r 3 0 2 1 1 2 102.83 n-r-s 3 r 3 0 n-r r 62.40 33.80 31.82 3 0 56.40 21.65 15.79 2 1 24.29 3.95 1 2 1 0 n-r-s 2 2 1 1 2 118.53 3 r 3 0 88.08 64.70 60.13 2 1 1 2 n-r-s 3 12.11 5.24 2.54 1 0 2 92.47 61.31 60.33 64.03 21.36 20.81 2.80 1.79 1 0 97.53 56.72 54.77 78.87 9.04 6.34 9.89 0.75 1 0 111.78 70.76 55.43 86.23 26.93 15.02 20.89 4.53 1 0 3 n-r r 3 0 24.07 21.73 2 1 21.35 3.47 1 2 1 0 n-r-s 2 121.73 13.40 140.76 2 172.64 3 Canada n-r 41.75 United Kingdom 46.25 n-r-s 46.10 France Italy n-r 52.24 3 Germany n-r 79.90 2 Australia n-r r 72.90 51.85 49.36 3 0 44.33 23.08 22.33 2 1 4.83 2.43 1 2 1 0 n-r-s 2 171.41 3 2 Prices and Unit Labour Costs Only Japan n-r r 2 0 1 1 n-r-s 65.54 Germany n-r r 34.84 30.34 2 0 4.30 3.61 1 1 1 0 n-r-s 2 r 2 0 1 1 n-r-s 62.54 2 20.05 18.48 6.91 1.83 1 0 29.67 26.96 5.58 4.96 1 0 2 France n-r 43.96 Canada n-r r 33.69 32.61 2 0 5.54 4.47 1 1 1 0 n-r-s 71.67 2 Notes: Statistics are computed with 4 lags of the core variables. See Appendix B of Banerjee and Russell (2000) for details of the predetermined variables on which the analysis is conditioned. Q(s|r) is the likelihood ratio statistic for determining s conditional on r. Q(r) is the likelihood ratio statistic for determining r in the I(1) analysis. Critical values are given in Paruolo (1996) as shown in footnote 14. 10 For the remaining economies, Italy, Canada and Australia, there is a marginal rejection of r = 1 , n − r − s = 1 . However we choose to accept this null hypothesis since the critical values on which inference is based are asymptotic and have been computed under the assumption that there are no pre-determined variables, including dummies, in the system. Not only would taking account of pre-determined variables raise the critical values (thereby leading to acceptance of the maintained hypothesis), the evidence from the roots of the companion matrix for these economies are unambiguously in favour of our hypothesis.15 The subsequent I(1) system analysis in the next section confirms these results. Imposing r = 1 and n − r − s = 1 on each system imposes a polynomial cointegrating vector on the analysis in each case. Table 2 reports the normalised cointegrating vectors with linear homogeneity imposed for each economy. Except for Japan the hypothesis of linear homogeneity is accepted and, therefore, the levels of prices and costs cointegrate to the markup in the polynomially cointegrating vector. For Japan, Germany, France and Canada import prices enter the markup with an insignificant coefficient. The analysis is therefore re-estimated excluding import prices and the results of the joint trace tests for the two variable systems are reported in Table 1 and again support the hypothesis that r = 1 and n − r − s = 1 . Reported in Table 2 are the normalised cointegrating vectors. The results now hold as before for Germany, France and Canada but the estimated coefficients for Japan are not interpretable as the markup since the test for linear homogeneity continues to be rejected strongly. 15 The moduli of the first four roots are 1.0, 1.0, 1.0, 0.7144 for Italy, 1.0, 1.0, 0.9881, 0.8161 for Canada and 1.0, 1.0, 0.9417, 0.6533 for Australia under the assumption of r = 1 . A finding of n − r − s = 0 would therefore not be consistent with the third root of close to unity for these economies if r = 1 is maintained. 11 Table 2: Cointegrating Vectors of the I(2) System Analysis Sample Periods Levels Prices US 61:4-97:2 Japan 66:1-96:1 1 - 0.767 - 0.063 - 0.233 0.279 0.030 ‘Standard Errors’ for ulc & pm Differences 0.012 0.073 0.096 0.030 ∆ Prices ∆ Unit Labour Costs ∆ Import Prices - 0.357 0.718 - 0.243 - 0.607 - 1.839 - 0.687 - 1.378 - 0.334 1.027 - 0.243 - 0.809 - 1.839 - 0.695 - 1.378 - 0.699 - 0.301 - 1.390 1.444 - 0.486 - 2.95 - 3.678 - 2.333 - 2.756 0.35 [0.55] 9.76 [0.00] 15.41 [0.08] 6.93 [0.64] 5.60 [0.47] Italy 72:1-97:1 23.58 [0.00] 0.40 [0.53] 10.87 [0.28] 3.96 [0.91] 27.10 [0.00] 23.11 [0.00] 0.01 [0.93] 2.26 [0.13] 14.05 [0.12] 31.81 [0.00] 4.19 [0.65] 2.52 [0.11] 0.23 [0.63] 0.43 [0.51] 13.48 [0.14] 8.48 [0.49] 7.49 [0.28] 0.47 [0.49] Sum of the Coefficients Differences of p, ulc, & pm Test and Diagnostics Linear Homogeneity Weight on Imports: 1 − δ = 0 LM(1) LM(4) D-H(N) Sample Periods Levels Prices 1 - 1.279 France 71:4-97:1 1 - 0.937 δ Import Prices: 1 − δ Unit Labour Costs: 1 -1 Germany 71:1-94:4 1 -1 1 - 1.030 - 1.534 3.08 [0.55] 3.80 [0.43] 10.63 [0.03] UK 61:4-97:1 1 1 - 0.953 0.76 [0.94] 10.65 [0.03] 5.85 [0.21] Canada 62:1-97:1 1 - 0.717 1 - 0.877 1 - 0.922 - 0.283 - 0.123 - 0.078 - 0.215 ‘Standard Errors’ for ulc & pm Differences 0.064 0.024 0.038 0.051 ∆ Prices ∆ Unit Labour Costs ∆ Import Prices - 2.735 - 0.690 - 1.591 - 2.219 -1.600 - 2.840 - 0.658 - 1.572 - 2.219 - 1.364 - 2.468 - 0.915 - 1.817 - 8.043 - 2.263 - 4.980 δ Import Prices: 1 − δ Unit Labour Costs: Sum of the Coefficients Differences of P, ULC, & PM Test and Diagnostics Linear Homogeneity 1 -1 2.34 [0.67] 6.22 [0.18] 2.55 [0.64] Australia 67:1-97:1 1 - 0.785 - 2.463 - 4.538 - 5.427 7.27 6.49 1.11 1.23 4.22 [0.01] [0.01] [0.29] [0.27] [0.04] 10.48 6.13 2.43 14.75 Weight on Imports: 1 − δ = 0 [0.00] [0.01] [0.12] [0.00] LM(1) 6.19 16.94 16.98 4.40 20.51 [0.72] [0.05] [0.05] [0.40] [0.02] LM(4) 16.15 10.33 13.33 4.34 11.73 [0.06] [0.32] [0.15] [0.36] [0.23] D-H(N) 3.87 7.32 3.98 7.41 4.77 [0.69] [0.29] [0.68] [0.12] [0.57] Notes: Figures reported in [ ] are probability values. LM(1) and LM(4) are Lagrange multiplier tests of autocorrelation of order 1 and 4 respectively. D-H(N) are Doornik-Hansen test for normal errors. Reported as tests of linear homogeneity and zero weight on coefficient are likelihood ratio tests distributed as χ12 . 12 Since the steady state is defined by the condition ∆p = ∆ulc = ∆pm we see in Table 2 that for the economies where the markup is defined, the sum of the coefficients on the difference terms is negative. This implies that there is a negative relationship between general inflation and the markup in the long-run. 3 ESTIMATING THE I(1) SYSTEM The I(2) analysis provides estimates of polynomial cointegration between a linear combination of the markup and the differences in the core variables. In an economic sense it is necessary for ∆p = ∆ulc = ∆pm in the very long-run. However, the method of summing the coefficients on the difference terms provides only an approximate estimate of the relationship between inflation and the markup, given that the variables may grow at different rates over the finite samples. Furthermore, the theoretical models of Russell et al. (1997), Chen and Russell (1998) and Russell (1998) posit a long-run relationship between the markup and steady state price inflation alone. Having established polynomial cointegration in the I(2) analysis, a particular reduction to I(1) space helps us establish the relationship of primary concern to us, namely; between price inflation and the markup. In order to implement this reduction we make use of the result that the decomposition into the I(0), I(1) and I(2) directions is an orthogonal one. In particular, the vectors β 1′ and β 2′ lie in the space orthogonal to β 3′ . Thus if β 3′ ≡ (1, a, b ) , æ 1 1 ö ç 0 . then a basis for the space orthogonal to β 3′ is given by the matrix H = ç − 1 a ç ç 0 −1 b è æ H ′ xt ö Therefore çç , where f is any 3 × 1 vector that satisfies the restriction that f ′ β 3 ≠ 0 , è f ′ ∆x t 13 provides the transformation to I(1) which keeps all the cointegrating and polynomially ′ cointegrating information. Hence if we take f to be (1, 0, 0 ) , then the trivariate system ö ∆p t æ ∆p t ö æç ÷ ç ç given by ç mulc t ÷ = p t − 1 ulct is a valid full reduction and under linear homogeneity a ç rer ÷ çç 1 p pmt − t è b è t a = b = 1 .16 Furthermore we can retrieve the implicit markup of prices on unit costs from this I(1) system by rearranging the estimated long-run or cointegrating relationship.17 ′ Tests of the number of cointegrating vectors in the I(1) system (∆p t , mulct , rert ) show that except for the United States the hypothesis of one cointegrating vector is accepted.18 For the United States there is a marginal rejection of the hypothesis although the eigenvalues of the companion matrix strongly support the finding of 1 cointegrating vector. Given also the argument in Section 2.3 that the critical values are likely to be affected by the presence of dummy variables we proceed on the basis of one cointegrating vector for all the economies. Table 3 reports the adjustment coefficients and the error correction terms for each economy. We see that the ECM appears strongly in each of the ‘markup’ equations and, except for Italy, is insignificant in the ‘real exchange rate’ equations. We see also that the adjustment coefficient in the ‘Markup Equation’ is on average three times that in the ‘Inflation Equation’. This suggests that when these economies are shocked away from the long-run relationship, adjustment back to equilibrium is more through changes in the markup, via the goods and 16 Hans Christian Kongsted suggested this transformation in Banerjee et al. (1998). 17 The markup of prices on import prices might be loosely referred to as the ‘real exchange rate’ due to its similarity with the relative price of traded and non-traded goods as used by Swan (1963) as a measure of the real exchange rate in his classic article. 18 Appendix C of Banerjee and Russell (2000) reports the results of the I(1) analysis in more detail. 14 labour markets, than by changes in the rate of inflation through actions of the monetary authorities. Table 3: I(1) System Adjustment Coefficients and Error Correction Terms Dependent Variable ‘Markup’ Equation ∆mulc ‘Real Exchange Rate’ Equation ∆rer Inflation Equation Error Correction Term ∆2 p - 0.061 (- 2.0) mulc t + 0.059 rert + 1.960 ∆p t - 0.116 (- 4.7) - 0.017 (- 1.4) mulc t + 4.748 ∆p t France - 0.194 (- 4.9) - 0.092 (- 3.7) mulc t + 2.672 ∆p t Italy - 0.039 (- 2.7) - 0.079 (- 2.3) - 0.030 (- 5.1) mulc t + 0.459 rert + 11.926 ∆p t United Kingdom - 0.278 (- 6.4) 0.009 (0.1) - 0.080 (- 3.2) mulct + 0.139 rert + 2.874 ∆p t Canada - 0.085 (- 3.0) - 0.068 (- 4.6) mulc t + 4.318 ∆p t Australia - 0.189 (- 4.0) - 0.041 (- 2.0) mulct + 0.166 rert + 6.276 ∆p t United States - 0.298 (- 5.7) Germany - 0.182 (- 1.2) 0.125 (1.5) Note: Reported in brackets are t-statistics. Table 4 reports the implicit long-run price elasticities with respect to costs from the I(1) analysis and the equivalent estimates from the I(2) analysis. Also shown are the estimated inflation cost coefficients, λ , from the I(1) and I(2) analyses.19 The long-run impact of a one percentage point increase in annual steady state inflation on the markup is shown in the final column and range between 0.3 percent for the United States and 2 percent for Italy. It appears likely, therefore, that the long-run relationship between inflation and the markup is important in an economic sense. 19 The latter are an approximation calculated by assuming ∆p = ∆ulc = ∆pm for each economy in Table 1. 15 Table 4: I(1) and I(2) Estimates of the Markup and the Inflation Cost Coefficient, λ United States Germany France Italy United Kingdom Canada Australia Analysis Prices Unit Labour Costs Import Prices Inflation Cost Long-run Effect on Coefficient λ the Markup of a 1 Percentage Point Change in ∆p I(1) 1 - 0.944 - 0.056 - 1.851 0.5 I(2) 1 - 0.937 - 0.063 - 1.390 0.3 I(1) 1 -1 - 4.748 1.2 I(2) 1 -1 - 3.678 0.9 I(1) 1 -1 - 2.672 0.7 I(2) 1 -1 - 2.756 0.7 I(1) 1 - 0.685 - 0.315 - 8.174 2.0 I(2) 1 - 0.717 - 0.283 - 8.043 2.0 I(1) 1 - 0.878 - 0.122 - 2.523 0.6 I(2) 1 - 0.877 - 0.123 - 2.263 0.6 I(1) 1 -1 - 4.318 1.1 I(2) 1 -1 - 4.538 1.1 I(1) 1 - 0.858 - 0.142 - 5.383 1.3 I(2) 1 - 0.785 - 0.215 - 5.427 1.4 Note: A percentage point increase in annual inflation is equivalent to an increase in ∆p of 0.25 per quarter. 4 CONCLUSION One explanation of the negative long-run relationship in the data is that the 1970s were a period when supply shocks from the energy and labour markets were very prevalent. The low markup, therefore, simply reflects the lags in price adjustment following the shocks. The adjustment appears to be very slow for economies with little or no price controls. In most cases the relatively low markups persist for around 10 years following the shocks and the markup does not fully recover until the economy again experiences low inflation. Graph 1 presents the long-run relationship, LR , for the United States and the United Kingdom from the I(1) analysis along with the realisations of the markup and inflation for 16 five distinct inflationary periods indicated by different symbols.20 If the ‘supply shocks’ argument is correct then different mean levels of inflation would not affect the behaviour of the markup. Consequently, realisations of the markup and inflation from different periods of inflation would be distributed evenly along the entire curve in Graph 1. This however is not the case. It may be seen clearly from Graph 1 that if the data were subdivided into periods of inflation with different means, the associated mean levels of the markup are different. For example, for both the United States and the United Kingdom the early 1960s are shown as crosses on Graph 1 and we see that the markup is high during a period of low inflation. The late 1960s and early 1970s are shown as squares and was a period of slightly higher inflation and a slightly lower markup. We can follow the relationship through each inflationary period until the observations return to hover around low inflation and a high markup for the period following the early 1990s recession. If the actual observations are followed individually (and not by periods as in the graph) a loose negative short-run relationship between inflation and the markup may sometimes be observed in the data. However, any short-run relationship is confined to different sections of the long-run curve depending on the general rate of inflation. Thus while short-run mechanisms are almost certainly reflected in some of the data the relationship is strongly driven by the general rate of inflation. 20 Similar graphs can be constructed for the other economies but for brevity only the United States and the United Kingdom is shown here. Appendix D of Banerjee and Russell (2000) reports scatter graphs of inflation and the estimated markup for each economy along with the long-run relationship, LR , for each economy. 17 The ability to separate actual observations of inflation and the markup into distinct periods with higher inflation associated with a lower markup and vice versa, is further confirmation that inflation is a non-stationary process. 18 Graph 1: Periods of Inflation and the Markup UNITED STATES September 1961 to June 1997 Log Change S1961-J1964 (cross) S1964-S1972 (square) D1972-J1982 (circle) S1982-J1991 (dash) S1991-J1997 (triangle) LR Annualized Qtly Inflation 0.12 0.10 0.08 0.06 0.04 0.02 0.00 94 96 98 100 102 104 Markup (100=period average) UNITED KINGDOM December 1961 to March 1997 Log Change Annualized Qtly Inflation 0.25 D1961-J1967 (cross) S1967-S1973 (square) D1973-J1982 (circle) S1982-S1993 (dash) D1993-M1997 (triangle) LR 0.20 0.15 0.10 0.05 0.00 -0.05 85 90 95 100 105 Markup (100=period average) 110 19 REFERENCES Athey, S., K. Bagwell, and C. Sanichiro, “Collusion and Price Rigidity,” MIT Department of Economics Working Paper 98-23 (1998). Banerjee, A, L. Cockerell and B. Russell, “An I(2) Analysis of Inflation and the Markup,” European University Institute Working Paper ECO 98/26 and Applied Economics Discussion Paper Series, University of Oxford 203 (1998). Forthcoming Journal of Applied Econometrics. Banerjee, A, and B. Russell, “The Relationship between the Markup and Inflation in the G7 plus one Economies,” European University Institute Working Paper ECO 2000/7 (2000). Banerjee, A., J. Dolado, J. W. Galbraith and D. Hendry, Cointegration, Error Correction, and the Econometric Analysis of Non-Stationary Data (Oxford: Oxford University Press, 1993). Bénabou, R., “Inflation and Markups: Theories and Evidence from the Retail Trade Sector,” European Economic Review 36, no. 2-3, (April, 1992), 566-574. Campos, J., N. R. Ericsson and D. F. Hendry, “Cointegration tests in the Presence of Structural Breaks,” Journal of Econometrics 70 , no. 1, (January, 1996), 187-220. Carlin, W. and D. Soskice, Macroeconomics and the Wage Bargain: A Modern Approach to Employment, Inflation and the Exchange Rate (Oxford: Oxford University Press, 1990),. Chen, Y. and B. Russell, “A Profit Maximising Model of Disequilibrium Price Adjustment with Missing Information,” University of Dundee Department of Economic Studies Discussion Papers 92 (1998). 20 Cockerell, L. and B. Russell, “Australian Wage and Price Inflation: 1971-1994,” Reserve Bank of Australia Research Discussion Paper 9509 (1995). de Brouwer, G and N. R. Ericsson, “Modelling Inflation in Australia,” Journal of Business & Economic Statistics 16, no. 4, (October, 1998), 433-449. Elliott, G., T.J. Rothenberg and J.H. Stock, “Efficient Tests for an Autoregressive Unit Root,” Econometrica 64, no. 4, (July, 1996), 813-836. Engle, R.F. and C.W.J. Granger, “Co-integration and Error Correction: Representation, Estimation, and Testing,” Econometrica 55, no. 2, (May, 1987), 251-276. Engsted, T., and N. Haldrup, “Multicointegration in Stock-Flow Models,” Oxford Bulletin of Economics and Statistics 61, no. 2, (May, 1999), 237-254. Franz, W., and R. J. Gordon, “German and American Wage and Price Dynamics,” European Economic Review 37, no. 4, (May, 1993), 719-762. Haldrup, N., “An Econometric Analysis of I(2) Variables,” Journal of Economic Surveys 12, no. 5, (December, 1998), 595-650. Hendry, D. F. and G. E. Mizon, “Exogeneity, Causality, and Co-breaking in Economic Policy Analysis of a Small Econometric Model of Money in the UK,” Empirical Economics 23, no. 3, (1998), 267-294. Johansen, S., “A statistical analysis of cointegration for I(2) variables,” Econometric Theory 11, no. 1, (March, 1995a), 25-59. Johansen, S., Likelihood-Based Inference in Cointegrated Vector Autoregressive Models, (Oxford: Oxford University Press 1995b). 21 Juselius, K., “A Structured VAR in Denmark under Changing Monetary Regimes,” Journal of Business and Economic Statistics 16, no. 4, (October, 1998), 400-411. Layard, R., S. J. Nickell and R. Jackman, Unemployment, Macro-economic Performance and the Labour Market, (Oxford: Oxford University Press 1991). Paruolo, P., “On the determination of integration indices in I(2) systems,” Journal of Econometrics 72, no. 1-2, (May, 1996), 313-356. Rahbek, A., C. JØrgensen and H. C. Kongsted, “Trend-stationarity in the I(2) cointegration model,” Journal of Econometrics 90, no. 2, (June, 1999), 265-289. Richards, T., and G. Stevens, “Estimating the Inflationary Effects of Depreciation,” Reserve Bank of Australia Research Discussion Paper 8713 (1987). Russell, B., “A Rules Based Model of Disequilibrium Price Adjustment with Missing Information,” University of Dundee Department of Economic Studies Discussion Papers 91 (1998). Russell, B., J. Evans and B. Preston, “The Impact of Inflation and Uncertainty on the Optimum Price Set by Firms,” University of Dundee Department of Economic Studies Discussion Papers 84 (1997). Simon, J., “Markups and Inflation,” MIT Department of Economics Mimeo (1999). Swan, T. W., “Longer-Run Problems of the Balance of Payments,” in Arndt H. W. and W. M. Corden (eds.), The Australian Economy (Melbourne: Cheshire 1963), 384-395. 22 APPENDIX: DATA SOURCES AND TRANSFORMATIONS The data are quarterly and drawn from the June 1997 OECD Statistical Compendium. The table below reports the identification codes of the series used in the estimation of the models. Data Codes for the OECD Statistical Compendium Series United States Japan Germany France Current Price GDP 421008SC 461008SC 131008SC 141008SC Constant Price GDP 421108SR 461108SR 131108SR 141108SR Indirect Taxes less Subsidies 421304SC 461304OC* 131304OC* 141304SC Private Consumption Deflator 421201SK 461201SP 131201SP 141201SP Total Labour Compensation 421301SC 461301OC* 131301OC* 141301SC Standardised Unemployment Rate 4242889J 464286A3 134280A2 144286A3(2) 461205SP (1) Imports of Goods and Services Deflator Series 421205SK 141205SP United Kingdom Canada Australia (5) 261008SC 441008SC 541008SC (5) 261108SL 441108SL 541108S1 Indirect Taxes less Subsidies Series 28 (5) 261304SC 441304SC 541304SC Private Consumption Deflator 161201SP 261201SP 141201SP 541201S2 Total Labour Compensation 161301SM 261301SC 141301SC 541301SC Standardised Unemployment Rate 164286A3 UKOCSUN%E(3) 144286A3 544286A3(4) Imports of Goods and Services Deflator 161205SP 261205SP 141205SP 541205S2 Current Price GDP Constant Price GDP Italy Derived Series 29 Series 29 * Not seasonally adjusted. (1) Derived from 131006SC and 131106SR (current price and constant price imports of goods and services respectively). (2) Prior to March 1982 use 144295A3. (3) Prior to March 1975 use UKOCUNE%E plus 0.954839. (4) Prior to March 1978 use 544295A3. (5) Italian data from www.bbs.istat and Conti economici nazionali trimestroli 70.1-97.4 (03/98). Constant price data from C3VAGKD, current price data from C3VAGLD. Notes: The following transformations of the data were performed. (a) Unit labour costs = total labour compensation divided by constant price gross domestic product (GDP). (b) The private consumption implicit price deflator at ‘factor cost’ is calculated as: PMP is the consumption implicit price deflator at market prices and less subsidies in current price GDP. P = PMP (1 + tax ) where tax is the proportion of indirect tax (c) Total labour compensation and indirect taxes less subsidies for Japan and Germany were seasonally adjusted by exponential smoothing using ESMOOTH in RATS.