Causality links between consumer and producer prices: Some empirical evidence.

Guglielmo Maria Caporale (*)

Margarita Katsimi (+)

Nikitas Pittis (++)

This paper reexamines the relationship between consumer and producer prices in the G7 countries (United States, Canada, Germany, France, Italy, United Kingdom, and Japan), and it improves on the existing literature in two ways. First, it takes into account causality links arising from the transmission mechanism of monetary policy, which are generally overlooked. Second, it employs the causality testing method for unstable systems recently introduced by Toda and Yamamato (1995), which results in standard asymptotics, thereby obtaining valid statistical inference. The empirical results are consistent with the conventional wisdom according to which there is unidirectional causality running from producer to consumer prices, bidirectional causality (or even no significant links) only being found when the causality links reflecting the monetary transmission mechanism are ignored.

1. Introduction

The relationship between consumer and producer prices has often been characterized in the literature as a one-sided lag structure, with producer prices leading. This is reported, for instance, by Silver and Wallace (1980), who carried out Sims causality tests and also used the Hatanaka and Wallace (1979) procedure to estimate the parameters of the lag distribution (see also Engle 1978; Guthrie 1981). Colclough and Lange (1982), though, took issue with these authors, noticing that there are theoretical reasons to expect causality to run also from consumer prices to producer prices. Furthermore, in the earlier study, the Sims test had not been applied adequately, that is, the significance of the leads as a group had not been tested. Instead, Colclough and Lange (1982) performed both Granger and Sims tests and concluded that in fact causality runs in the opposite direction or might be bidirectional. In both cases, only U.S. data were used.

Additional evidence was provided by Cushing and McGarvey (1990, hereafter C&M), who concluded that "the magnitude of feedback from producer to consumer prices is greater than that from consumer to producer prices," to the extent that a one-sided Granger causal pattern can be assumed, as consumer prices have very little incremental power. They also argued that the addition of the money supply does not produce significant changes, the feedback from producer to consumer prices still dominating, and that such a causal ordering is perfectly consistent with a flexible price model with strong demand effects.

Robust evidence on the causality links between producer and consumer prices is of crucial importance, as, unless there are only unidirectional links from producer to consumer prices, the producer price index, which is often used as a leading indicator for inflation, might not in fact be very informative about future inflation. (1) Therefore, this paper reexamines the relationship between consumer and producer prices in the G7 countries and differs from earlier contributions, in particular, the study by C&M, in three important respects. First, our analysis avoids an important possible source of bias affecting other studies on this topic, that is, the omission of monetary variables (this is in contrast to the theoretical setup of C&M, which implies unidirectional causality from wholesale to consumer prices). As shown in Caporale and Pittis (1997), leaving out "relevant" variables can invalidate causality inference. We show that, contrary to what C&M argue, including variables that capture the monetary transmiss ion mechanism affects inference dramatically, unidirectional causality being found where previously causality appeared to run often in both directions--causality from producer to consumer prices is found in all cases. Second, we adopt an appropriate methodology for carrying Out causality tests within systems that might be unstable. This is the causality testing strategy recently introduced by Toda and Yamamoto (1995), which results in standard asymptotics and valid inference. Compared to other approaches, such as the one advocated by Toda and Phillips (1993), it also has the advantage that it does not require any pretesting in order to determine the dimension of the cointegration space, and it is relatively easy to implement in practice. Third, we provide evidence for the G7 countries as opposed to the United States only.

The layout of this paper is as follows. Section 2 provides a brief overview of the theoretical arguments on the relationship between consumer and producer prices. Section 3 discusses the consequences of adopting an "incomplete" model for causality inference and suggests an appropriate testing strategy for the case of unstable systems. Section 4 presents the empirical results. Section 5 offers some concluding remarks.

2. An Economic Interpretation of the Relationship between Consumer and Producer Prices

The producer price index (PPI) is widely used as a leading indicator for the consumer price index (CPI). This causality is related to supply-side developments and stems mainly from the production timing: The retail sector adds value with a lag to existing production. In the framework of a fairly standard open economy macro model, (2) the retail sector uses existing domestic production as an input. Consumer prices will depend on the producer price of the home good, the price of the imported good, the exchange rate, the level of indirect taxes, the marginal cost of retail production, and a possible markup. A fully fledged model that offers a theoretical basis for Granger causality from wholesale to consumer prices is the one developed by Gushing and McGarvey (1990). In their model, the production of final goods in each period uses primary goods produced in the previous period as input, so that supply-side disturbances in the primary goods market affect wholesale prices and consumer prices in the next period. Th ey find that, as long as primary goods are used with a lag as input in the production of consumption, wholesale prices will Granger cause consumer prices independently from the parameters governing the exogenous stochastic processes.

In a subsequent paper, Colclough and Lange (1982) argued that the causality from consumer prices to producer prices had not received much attention in the literature. Their theoretical argument stems from derived demand analysis. (3) The demand for final goods and services determines the demand for inputs between competing uses. In this framework, the cost of production reflects the opportunity cost of resources and intermediate materials, which in turn reflects the demand for final goods and services. The obvious implication is that consumer prices should affect producer prices. The theoretical model of Gushing and McGarvey (1990) investigates this link by allowing for demand-side effects: Demand for primary goods depends on the expected future price of consumer goods. Under this assumption, the consumer price will depend on current demand and past expectations of current demand, whereas the wholesale price depends on expected future demand. A Granger causal relationship running from consumer to wholesale pr ices would exist only for certain values of the disturbances' parameters.

Consumer prices may also affect producer prices through labor supply if wage earners in the wholesale sector aim at preserving the purchasing power of their income. Whether this effect occurs with a lag or instantaneously will probably depend on the nature of the wage-setting process and the expectations formation mechanism. (45) In addition, whether an increase in consumer prices can feed through to producer prices will depend critically on the behavior of monetary authorities. If the monetary authority announces an inflation target, which is considered to be credible by wage setters, then an increase in consumer price inflation above the central banks' target rate is perceived as temporary and has no effect on wages and, hence, producer prices. (6)

3. Econometric Issues

Two econometric issues that arise when testing for links between consumer and producer prices are selecting the "correct" model in the context of which causality relationships are to be analyzed and carrying out tests that result in valid statistical inference.

The first issue is addressed by Caporale and Pittis (1997), who analyze how causality inference in the context of a bivariate vector autoregression (VAR) is affected by the omission of a third relevant variable and show that in general this results in invalid inference about the causality structure of the bivariate system (see also Lutkepohl 1982). More specifically, they examine how causality inference within a system consisting of [y.sub.t] and [x.sub.t] is affected by the omission of another variable, [w.sub.t], which causes (i) none, (ii) one, and (iii) both the variables in the VAR. They also derive conditions under which causality inference is invariant to the selection of a bivariate or a trivariate model. The most general condition for invariance to model selection requires the omitted variable not to cause any of the variables in the bivariate system, although it allows the omitted variable to be caused by the other two. (7)

As for causality testing in unstable, possibly cointegrated VARs, (8) this issue was initially analyzed by Sims, Stock, and Watson (1990) in the context of a trivariate VAR and then examined in a more general setting by Toda and Phillips (1993). These studies show that, in general, Wald test statistics for noncausality restrictions in the context of the unrestricted VAR will have nonstandard limit distributions in which nuisance parameters are also present, although they will have a [chi square] asymptotic distribution, free of nuisance parameters, if there is "sufficient" cointegration with respect to the variables whose causal effects are being tested (see Toda and Phillips 1993, 1994). This depends on the presence and location of unit roots in the VAR. Unfortunately, this information is difficult to obtain from the estimation of a VAR in levels. In particular, sequential testing strategies, such as the one developed by Toda and Phillips (1993), where the cointegration rank has to be determined before carry ing out causality tests, are potentially subject to severe pretesting biases, as the tests for cointegration ranks in Johansen-type error correction models (ECMs) are very sensitive to the values of the nuisance parameters (see Toda 1995). Therefore, it would be useful to be able to rely on an alternative testing procedure that does not require pretesting for the cointegration properties of the system. Such a procedure has recently been developed by Toda and Yamamoto (1995) and is summarized in the following.

The basic idea is to artificially augment the correct order, say, k, of the VAR by the maximal order of integration, say, [d.sub.max], exhibited by the process of interest. One can then estimate a (k + [d.sub.max]) th-order VAR and ignore the coefficients of the last [d.sub.max] lagged vectors and test linear or nonlinear restrictions on the first k coefficient matrices by means of a Wald test, using the standard asymptotic theory.

To be more specific, consider the following VAR, which allows for a linear trend:

[Z.sub.t] = [PHI] + [PHI]t + [[PI].sub.1][Z.sub.t-1] + ... + [[PI].sub.k][Z.sub.t-k] + [E.sub.t], t = 1, ..., T (1)

where [E.sub.t] ~ N(0, [OMEGA]).

Suppose that we are interested not in the integration/cointegration properties of Equation 1 but rather in testing economic hypotheses that can be expressed as restrictions on the coefficients of the model as follows:

[H.sub.0]:f([pi]) = 0, (2)

where [pi] = vec(P) is a vector of parameters from the model (Eqn. 1), P = [[PI].sub.1], ..., [[PI].sub.k]], and f(.) is a twice continuously differentiable m-vector valued function with F([phi]) = [phi]f([phi])/[phi][phi]' and rank (F(.)) = m.

Assume that the maximum order of integration that is expected to characterize the process of interest is at most two, that is, [d.sub.max] = 2. Then, in order to test the hypothesis (Eqn. 2), one estimates the following VAR by ordinary least squares (OLS):

[Z.sub.t] = [[PHI].sub.0] + [[PHI].sub.1]t + [[PI].sub.1][Z.sub.t-1] + ... + [[PI].sub.k][Z.sub.t-k] + [[PI].sub.k+1][Z.sub.t-k-1] ... + [[PI].sub.p][Z.sub.t-p] + [E.sub.t] (3)

where p [greater than or equal to] k + d = k + 2, that is, at least two more lags than the true lag length k are included. The parameter restriction (Eqn. 2) does not involve the additional matrices [[PI].sub.k+1],..., [[PI].sub.p], since these consist of zeroes under the assumption that the true lag length is k.

Equation 3 can be written in more compact notation as follows:

[Z.sub.t] = [PHI][[tau].sub.t] + P[x.sub.t] + [psi][y.sub.t] + [E.sub.t], (4)

where

[PHI] = [[[PHI].sub.0], [[PHI].sub.1]], [[tau].sub.t] = [1, t], [x.sub.t] = [[Z'.sub.t-1],..., [Z'.sub.t-k]]', [y.sub.t] = [[Z'.sub.t-k-1],..., [Z'.sub.t-p]]',

P = [[[PI].sub.k+1],..., [[PI].sub.k]], [psi] = [[[PI].sub.k+1],..., [[PI].sub.p]],

or, in the usual matrix notation,

Z' = [PHI]T' + PX' + [psi]Y' + E', (4a)

where X = [x.sub.1],..., [x.sup.T]' and so on.

One can then construct the following Wald statistic [W.sub.2], to test the hypothesis (Eqn. 2):

[W.sub.2] = f([PHI])'[[F([PHI]){[[SIGMA].sub.E] [cross product] [(X'QX).sup.-1]}F([PHI])'].sup.-1]f([PHI]) (5)

where [[SIGMA].sub.E] = [T.sup.-1]E'E, Q = [Q.sub.[tau]] - [Q.sub.[tau]][(Y'[Q.sub.[tau]]Y).sup-1] Y&prime[Q.sub.[tau]], and [Q.sub.[tau]] = [I.sub.T] - T[(T'T).sup.-1]T'.

Toda and Yamamoto's theorem 1 (1995, pp. 234-5) proves that the Wald statistic (Eqn. 5) converges in distribution to a [chi square] random variable with m degrees of freedom, regardless of whether the process [Z.sub.t], is stationary, I(1), I(2), possibly around a linear trend, or whether it is cointegrated.

Since the true lag length of the process is rarely known in practice, this method also requires some pretesting to determine it. Sims, Stock, and Watson (1990) were the first to show that lag selection procedures, commonly employed for stationary VARs, which are based on testing the significance of lagged vectors by means of Wald (or LM or LR) tests, are also valid for VARs with I(1) processes, which might exhibit cointegration. Toda and Yamamoto (1995) proved that the validity of this argument can be extended to processes with an order of integration higher than one, as long as the true lag length is greater than or equal to the order of integration. In other words, the asymptotic distribution of a Wald or likelihood ratio test for the hypothesis that the lagged vector of order p is equal to zero is [chi square], unless the process is Markovian and I(2).

4. Empirical Results

The empirical analysis was carried out for the G7 countries. We estimated first a bivariate VAR consisting of the logarithms of consumer price and producer price indices in addition to a constant and a linear time trend. The series are quarterly and were obtained from Datastream. The corresponding national data sources are the following: Bank of Canada, Banque de France, Deutsche Bundesbank, Istituto Nazionale di Statistica, Bank of Japan, Bank of England, and Federal Reserve. The selected sample goes from 1976:1 to 1999:4. A VAR including earlier observations was found to exhibit parameter instability, which would result in invalid statistical inference. The observed instability was not purely of the type that could be handled by the inclusion of impulse dummies but appeared to reflect regime changes. This is not surprising, as in the period before the first quarter of 1976, two major structural breaks occurred, namely, the first oil shock and the transition from fixed to flexible exchange rates, the latter of which generated more persistent inflation (see Alogoskoufis and Smith 1991).

As suggested by Toda and Yamamoto (1995), the first step consists of determining the order of the VAR, so as to artificially augment it at a later stage by the maximum order of integration of the series involved. We started by estimating a VAR(5) and then dropped one lag at a time. Their significance was tested by means of F-statistics, which, as already mentioned, have standard limit distributions and therefore result in valid inference on the order of the VAR. The SIC for the optimal order selection was also used as a further check on the optimal lag length. Moreover, misspecification tests were carried out for serial correlation and/or dynamic heteroskedasticity in the residuals of the VAR, since the Toda and Yamamoto procedure assumes i.i.d. errors. The results (not reported) suggest that the optimal lag length for the bivariate VAR is 2 for the United States, Italy, Germany, France, and Canada and 3 for Japan and the United Kingdom.

The next step is to estimate VARs artificially augmented by the maximum order of integration in the series. It is quite natural to assume that the logs of CPI and PPI are at maximum I(2), since there is some evidence that inflation series might be I(1). Therefore, we augmented the bivariate VARs estimated previously by two lags and tested for noncausality zero restrictions on the parameters of the original VARs. The results are presented in Table 1. In the case of Canada, there is no causality at all; in the case of France and Germany, there is causality in one direction, running from PPI to CPI; and in the rest of the cases, namely, Italy, Japan, the United Kingdom, and the United States, the evidence points toward bidirectional causality. This evidence is not consistent with the conventional wisdom according to which producer prices lead consumer prices.

As argued previously, the omission of an important causing variable from the bivariate system may significantly affect inference on causality between the variables in the bivariate system. We therefore considered a five-variate VAR, including the money supply (M1), real gross domestic product (GDP), and the three-month interest (the data sources being the same as before). (9) The inclusion of these variables aims at capturing the transmission mechanism of monetary policy. (10) As in the bivariate case, we first tested for the order of the VARs. The results from the selection procedure, together with the misspecification tests, suggest that the order of the VARs in the five-variate case are as follows: US = 3, UK 2, JP 3, IT = 2, GE = 3, FR = 2, and CA = 4. As previously, we augmented the five-variate VARs by two additional lags, since the maximum order of integration of the additional variables is not expected to be greater than two.

The results are reported in Table 2 and can be summarized as follows. In the case of Canada, for which there was no evidence of any causality links between CPI and PPI in the bivariate model, unidirectional causality running from PPI to CPI is now found. This is consistent with the theoretical results discussed previously, according to which the omission of a relevant causing variable is likely to affect inference on causality between the original two. In the present context, causality appears to be running from M1 to CPI. Some evidence for causality running from M1 to PPI is also detected. As a consequence, the bivariate findings on causality links between CPI and PPI are reversed. In the case of Italy, M1 was found to cause PPI, and the interest rate was found to cause PPI. The causality structure between CPI and PPI has changed in the sense that now only unidirectional causality running from PPI to CPI is detected. As for the United States, the interest rate was found to cause CPI, which again resulted in detecting causality running only from PPI to CPI. In the cases of France, Germany, and Japan, the evidence also suggests that causality is unidirectional, running from PPI to CPI. For the first two countries, the evidence is consistent with that obtained from the bivariate analysis, although in the case of France the "omitted" M1 seems to cause CPI and PPI. This is an interesting case in which the omission of a variable does not alter causality inference in the incomplete model, although it does affect the estimates of the transition matrices corresponding to CPI and PPI, which are different in the five-variate and bivariate case. Finally, in the case of the United Kingdom, where the interest rate affects both CPI and PPI, the causality inference drawn from the bivariate and the five-variate models is different. In the five-variate model, we detect unidirectional causality running from PPI to CPI as opposed to the bidirectional causality found in the bivariate model.

Table 2 provides strong support for unidirectional causality from PPI to CPI for all countries. This unambiguous result is obtained by taking into account two possibilities: the possibility that the VAR contains unit roots of unknown number and location and that the VAR may be incomplete. When these two factors are taken into account, the results are clear and consistent with the predominant view that PPI is a leading indicator for CPI. Although there are theoretical reasons to expect causality to run also from CPI to PPI, this causality pattern is not supported by the five-variate model. The causality from CPI to PPI could be rationalized in a derived demand analysis framework where demand for final goods affects the production cost through the price of inputs. Moreover, causality from CPI to PPI may reflect the fact that wage setters in the wholesale sector increase wages when they observe an increase in consumer prices. The absence of this causality link when one allows for the transmission of monetary pol icy may imply that monetary authorities react to inflationary pressures so that the CPI impact on PPI is eliminated through the inclusion of monetary variables.

5. Conclusions

This paper has provided some new evidence on the empirical relationship between consumer and producer prices. In addition to having a much wider country coverage, it has employed a causality testing method that is appropriate even for systems that exhibit unit roots, namely, the Toda and Yamamoto (1995) procedure, and it has addressed the issue of the possible omission of relevant variables, such as the money supply, interest rates, and output from the analysis. Valid statistical inference has therefore been obtained. By contrast, existing empirical studies are vitiated by their use of unreliable statistical tests and by the adoption of "incomplete" models, where ignoring causality links with other variables biases the results (see Caporale and Pittis 1997).

The empirical evidence is consistent with the conventional wisdom according to which producer prices lead consumer prices. In all countries, the causality structure confirms with the widely held prior of a one-sided lag structure from producer to consumer prices. Furthermore, it appears that the omission of variables capturing the monetary transmission often results in misleading inference. Such results significantly improve the findings of earlier papers, such as the one by C&M, where a one-sided Granger causal structure was preferred both on theoretical grounds (its consistency with flexible price models with strong demand effects) and on empirical grounds (the inclusion of money not being found to affect the inference), but where causality testing was not based on valid asymptotics.

(*.) Centre for Monetary and Financial Economics, South Bank University London, 103 Borough Road, London SEl OAA, UK; E-mail [e-mail]; corresponding author.

(+.) Department of International and European Economic Studies, Athens University of Economics and Business, 76 Patision Avenue, 10434 Athens, Greece.

(++.) Department of Financial Management and Banking, University of Piraeus, Karaoli--Dimitriou 80, 18534 Piraeus, Greece.

We are grateful to Stephen Hall and two anonymous referees for useful comments and suggestions. The usual disclaimer applies.

Received February 2000; accepted March 2001.

(1.) Clark (1995) argues on theoretical grounds that the pass-through effect from PPI to CPI may be weak. Using standard causality tests, he finds some evidence that producer prices lead consumer prices; by contrast, PPI changes appear not to be able to predict systematically CPI changes. His inference, though, also has the pitfalls discussed here.

(2.) For example, see Alogoskoufis and Martin (1991).

(3.) Derived demand analysis was first developed by Marshall (1961).

(4.) Wages in the wholesale sector may be determined a period in advance so that they will depend on past expectations of current inflation, or they may be determined in each period according to current consumer price inflation. Moreover, wage agreements may include catch-up clauses that relate wages' growth to past inflation.

(5.) Even if consumer prices affect cost and prices in the wholesale sector with a lag, the presence of Granger causality cannot be inferred without examining the properties of the stochastic disturbances.

(6.) This argument has first been demonstrated by Barro and Gordon (1983).

(7.) A complete analysis of causality and forecasting in incomplete systems can be found in Caporale and Pittis (1997).

(8.) For more details, see Caporale and Pittis (1999).

(9.) These variables are also included in VAR models aiming at investigating the real effects of monetary aggregates, such as Clarida and Gali (1994) and Coebrane (1998).

(10.) For an extended discussion on the transmission mechanism, see, among others, Duguay (1994).

References

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Table 1

Bivariate VAR

                                    Wald Tests Based on
                               Artificially Augmented, d = 2
                                        (p-values)
Null
Hypothesis               CA                               FR

PPI does not cause CPI  0.069                            0.001
CPI does not cause PPI  0.136                            0.375

                                       Wald Tests Based on
                                  Artificially Augmented, d = 2
                                            (p-values)
Null
Hypothesis               GE        IT        JP        UK        US

PPI does not cause CPI  0.016     0.046     0.000     0.000     0.934
CPI does not cause PPI  0.352     0.000     0.039     0.007     0.002

The results suggest that the optimal lag length is 2 for the United
States, Italy, Germany, Frances, Canada and 3 for Japan and the United
Kingdom.
Table 2

Five-Variate VAR

                             Wald Tests Based on Artifically
                                 Augmented VAR9k), d = 2
                                       (p-values)
Null
Hypothesis                         CA                  FR

PPI does not cause CPI            0.021               0.002
CPI does not cause PPI            0.344               0.613
M does not cause CPI              0.003               0.006
M does not cause PPI              0.077               0.003
Y does not cause CPI              0.171               0.302
Y does not cause PPI              0.920               0.994
R does not cause CPI              0.467               0.223
R does not cause PPI              0.142               0.640

                                 Wald Tests Based on Artifically
                                     Augmented VAR9k), d = 2
                                            (p-values)
Null
Hypothesis               GE        IT        JP        UK        US

PPI does not cause CPI  0.000     0.040     0.000     0.000     0.055
CPI does not cause PPI  0.341     0.101     0.136     0.119     0.059
M does not cause CPI    0.891     0.336     0.005     0.868     0.563
M does not cause PPI    0.904     0.008     0.530     0.316     0.873
Y does not cause CPI    0.430     0.688     0.712     0.119     0.695
Y does not cause PPI    0.211     0.091     0.309     0.686     0.484
R does not cause CPI    0.158     0.040     0.274     0.005     0.002
R does not cause PPI    0.296     0.118     0.226     0.019     0.572

M, Y, and R stand for money supply (Ml), real GDP, and three-month
interest rate, respectively. The order of the VARs are as follows: US =
3, UK = 2, JP = 3, IT = 2 GE = 2, GE = 3, FR = 2, CA = 4.