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COPYRIGHT 2001 MIT Press Journals
I. Introduction
THE proposition examined in this paper is that there exists a long-run relationship in the sense proposed by Engle and Granger (1987) wherein 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 modeling. In other words, both the differences of prices and costs and their levels that comprise the markup display persistent behavior 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, 1995b) inter alia.(2)
Benabou (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 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 of 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 behavior 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 co-integrating 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 to obtain the direct relationship between price 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.
Although differences emerge between the economies, the finding of polynomial co-integration for the G7 economies and Australia is remarkably robust. The only exception is Japan where the levels of prices and costs co-integrate 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.
II. 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 nonmodeled shocks. For an open economy, the main inputs are labor and imports, and we can write the inflation cost long-run markup equation as(6)
(1) mu = p - [Delta]ulc - (1 - [Delta])pm = q - [Lambda][Delta]p,
where ulc and pm are unit labor costs and unit import prices, respectively, and [Delta] and [Lambda] are positive parameters. Lowercase variables are in logarithms, and [Delta] represents the change in the variable.
When the inflation cost coefficient, [Lambda], 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 [Lambda] [is greater than] 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 - [Lambda][Delta]p.
The coefficients [Delta] and 1 - [Delta] in equation (1) are the long-run price elasticities with respect to unit labor costs and import prices, respectively. Linear homogeneity is imposed as the coefficients sum to 1 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.
A. 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, 1995b), and Paruolo (1996). Alternatively, for a brief "penetrable" survey of the I(2) theory in relation to 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, [x.sub.t], of dimension n x 1:
[x.sub.t] = [[Pi].sub.1][x.sub.t-1] + [[Pi].sub.2][x.sub.t-2] + [Phi][D.sub.t] + [Mu] + [[Epsilon].sub.t],
where [Mu] is a vector of unrestricted constant terms, and [D.sub.t] is a vector of predetermined variables that are assumed not to enter the cointegration space and on which the empirical analysis is conditioned. The lowercase variables are in...
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