Relative Prices and Money: Some Canadian Evidence

Peter S. Sephton Associate professor, Department of Economics,

University of New Brunswick, Fredericton, E3B 5A3. Received 9 June 1988, accepted 12 June 1989

INTRODUCTION Many authors have investigated whether relative prices respond to changes in money. Neoclassical models suggest that, while there may be short-run effects of changes in money on relative prices, money is neutral in the long run. Specific reference is usually made to the price of agricultural commodities relative to the price of manufactured goods, with the view that commodity prices are relatively flexible and can respond to news. The prices of manufactured goods are assumed to be set as a markup over unit costs in an administered fashion and to be less likely to react to short-run phenomena. Indeed, recent work by Frankel (1986) and Sephton (1988a) has shown that monetary policy can force commodity prices to depart from their historical record. Frankel illustrated that commodity prices can overshoot their new steady-state level in response to a positive monetary shock. Elsewhere I have shown that an optimal monetary policy aimed at minimizing commodity price inflation and interest rate variability can lead to non-trend-sta- tionary commodity prices; that is, commodity prices that depart from historical growth patterns. Whether money alters relative prices is an important topical mac- roeconomic issue for both the industrialized and the developing nations.

The aim of this paper is to examine data on the food and nonfood components of Statistics Canada’s Consumer Price Index (CPI) to determine whether monetary policy can alter the price of food relative to non-food items in the CPE. To this end, a vector autoregressive description of the data is presented. A preliminary analysis of the series indicates that the natural logarithms of a wide definition of money and the relative price of food are subject to a unit root. Hence the series to be modeled are the first differences of the logs of money and prices. Previous work by Bessler (1982) and Devadoss and Meyers (1987) worked in levels rather than stationary first differences, using data on Brazil and the United States, respectively. Their empirical findings might be sensitive to the presence of unit roots in their data. The present analysis does not suffer from this shortcoming.

Recent work by Engle and Granger (1987) has shown that vector autoregres- sive models using difference-stationary data are appropriate only as long as the series are not cointegrated. If they are cointegrated, standard VAR models in first differences will suffer from omitted-variables bias in that they omit important error correction terms. Here, test results indicate the absence of cointegration, so a

Canadian Journal of Agricultural Economics 37 (1989) 269-278 269

270 CANADIAN JOURNAL OF AGRICULTURAL ECONOMICS

Table I . Unit root and cointegration tests'

Unit root test 0, test

Cointenation tests CRDW DF ADF

M 3.746 P 3.536 AM 6.478 AP 8.91

0.044 - 1.295 -2.169 0.078 -2.031 - 2.364

"Unit root test includes seasonal dummy variables, with the maintained hypothesis of a sixth-order process, as was the case in the ADF cointegration test. Critical 5% values are approximately 6.3 for the unit root test and 0.386, 3.37 and 3.17 for the CRDW, DF and ADF tests, respectively.

traditional approach to the description of the VAR system can be undertaken. The empirical results suggest that money alters relative prices in the short run but that neutrality prevails in the long run. A simulation experiment illustrates that a tem- porary shock to money causes a temporary cycle in the relative price of food. Monetary policy is capable of altering relative prices only in the short run.

The next section discusses the unit root and cointegration tests as well as the method used to select the dynamic structure of the model. Empirical results, the simulation experiment, and suggestions for further work follow.

RELATIVE PRICES AND MONEY Data on the M2 definition of money2 and the food and nonfood components of the CPI were obtained on a seasonally unadjusted basis from January 1972 to October 1987? To ensure that the data could be described by a vector autoregressive sys- tem, the series were first examined to determine whether they were stationary. The 0, test of Dickey and Fuller (1981) was performed, where the null hypothesis is that each series is subject to a unit root with possible drift. Table 1 presents the test results using the logarithms of money, M , and relative prices, P, defined to be the price of food relative to non-food items in the CPI. At the 5% level of signif- icance, each series is found to be first-difference stationary. To ensure that a higher order of differencing was unnecessary, the first differences of M and P were tested for the presence of a unit root. Table 1 confirms that money and relative prices are indeed first- and not second-difference stationary.

Engle and Granger (1 987) have argued that if two series are first-difference stationary, then a vector autoregressive description of the data is admissible only when the series are not cointegrated. They offer several tests for the null hypothesis of non-cointegration. The test that seems the most powerful is the one they call the Augmented Dickey-Fuller test (ADF). This test and two others, the Cointe- grating Regression Durbin-Watson test (CRDW) and the Dickey-Fuller test (DF), were undertaken. Table 1 illustrates that at the 5% level of significance, all tests

RELATIVE PRICES AND MONEY 27 1

do not reject the null hypothesis of non-cointegration. This implies that error cor- rection terms need not be included in the search for the dynamic relationship between changes in M and changes in P.

Eq. 1 describes the VAR system, where a&!,) is a lag polynomial in the lag operator L. The elements of the parameter space are constrained to include only lagged values of money growth and price inflation. Contemporaneous correlation in the residuals accounts for the current impact of shocks across equations. The residuals are otherwise assumed to conform to the properties associated with the classic1

A method for determining the lengths of the lag polynomials must be chosen. There are basically three approaches that can be taken. The first is an ad hoc choice of the lag length at, say, six, 12 or 24 months. There is little merit in this approach. If the choice of lag length is too short, standard statistical tests will be invalid because of the omitted variables problem and associated standard error biases. If the parameter space is too large, estimates will be imprecise and multicollinearity will prevail.

The second approach is to use a Bayesian metric that takes into account the fact that the truth is to be gleaned from a sequence of nested tests. Schwarz’s (1978) Bayesian Estimation Criterion can be used to select the dynamics, yet Geweke and Meese (198 1) found it to underfit in samples of fewer than 200 observations. Since our estimation period spans April 1974 to October 1987 inclusive (164 observa- tions), the costs of underfitting make this approach unattractive, notwithstanding the fact that it is the only approach that will asymptotically choose the true model.

The third method of choosing the design matrix is based on using a metric that optimizes an objective function that can be justified on grounds that seem reasonable. Many candidates exist in this category, each with advantages over competitiors. The most popular method in the macroeconomics literature seems to be Akiake’s Final Prediction Error Criterion The FPE balances the risk of including too many lags against the costs associated with the exclusion of rel- evant lags. Hsaio (1981) has shown that the WE can be interpreted as a series of F tests of exclusion restrictions, with varying levels of significance at each stage in the specification of the system. The lag length i minimizes the WE, defined as:

T + M SSR, FPE, = - -

T - M T where

T = the sample size, M = the number of regressors in the equation, and

SSR, = the associated sum of squared residuals.

272 CANADIAN JOURNAL OF AGRICULTURAL ECONOMICS

o-oooosY

0.000052-

0.000051-

0.00005

0.000047 r 0 B ie 16 24 30

LAG LENGTH (HONTHS)

Figure 1 . FPE money, own lag.

Fackler (1985) provided an excellent summary of the steps necessary to apply the FPE in the selection of the design matrix. While the FPE does not choose the true model asymptotically, it does perform well, and will be used to describe the dynamic relationship between money growth and relative price inflation.

Figure 1 illustrates the relationship between the FPE and the lag length for the choice of the own lag, a,,(L), in the money equation. The FPE is minimized at a lag length of six months. Given this own lag, the WE is again used to choose the dynamic impacts of P on M. Figure 2 illustrates that the lag length that mini- mizes the FPE is one. A test of the hypothesis that relative price inflation does not cause money growth-that is, that the lag length should be zero-yields a f test value of 0.46. This suggests that relative price inflation does not cause money growth. Hence

Figure 3 illustrates the choice of the own lag, a22 (L) , for inflation, minimizing the WE at a one month lag. The choice of the money lags, aZ1 (L), conditional on the selection of the own lag leads to the inclusion of 23 lagged values of money growth (Figure 4). Changes in money lead to changes in relative price inflation. Eq. 4 presents the estimated structure, with:

such that:

(L) is set to zero from this point on.

a i ( L ) = a , L + a$* + a 3 3 + ... + aiLk (3)

RELATIVE PRICES AND MONEY

0.93 - 0.92 - 0.91 - 0.90 - 0.89.

0.88-

0.87-

0.86.

: 0.85-

0.84.

0.83 - 0.82 - 0.81 - 0.80.

0.79 - 0.78-

0.77,

273

, . . . . . I '

0.00005

0.000052

0.000051

0.00005 1 0.000047 5 0.000046

0.000045

12 18 24 30 LAG LENGTH (MONTHS)

Figure 2. FPE money, price lag.

274 CANADIAN JOURNAL OF AGRICULTURAL ECONOMICS

0.62.

0.m.

0.60.

0.79. w L

0.7a.

0.77-

0.74 I

0 6 12 18 24 30 LAG LBNCTM (MONTHS)

Figure 4. FPE price, money lag.

Residual diagnostics in Table 2 indicate the absence of twelfth-order auto- regressive or moving average errors, twelfth-order autoregressive conditional het- eroskedasticity (ARCH), and heteroskedasticity based on error variances that grow over time. The estimates are temporally stable, as evidenced by a stability test with the sample of December 198 1 . These results suggest that the model adequately describes the relationship between money growth and relative price inflation over the estimation period.

It is interesting to test the hypothesis that changes in money growth affect relative price inflation only in the short run. This can be done through a comparison of the llkelihood functions across the unrestricted and restricted models, where the restricted model constrains the coefficients of lagged money growth in the price equation to sum to zero; that is, a,, (L) = 0. The calculated likelihood ratio statistic is I .09, well within the critical 5% value of 3.89. This illustrates that money growth has a temporary affect on relative price inflation.

This is what we would expect: in the long run, food and nonfood prices respond to money growth in the same proportion so that there is no relative price inflation. It is consistent with Frankel’s (1986) overshooting model, in that relative prices can respond in the short run to monetary stimuli but must eventually reach their steady state level.

To generate a more intuitive feel for these results, below I present the results of a simulation experiment in which the money stock is subjected to a temporary

RELATIVE PRICES AND MONEY 275

Table 2. Residual diagnostics"

M P

AR(12)IMA(12)

ARCH( 12)

Heteroskedasticity

Chow stability test

16.524 (0.168) 6.692

(0.877) 0.057

(0.811) 1.565

(0.075)

22.003 (0.037) 20.907 (0.052) 1.777

(0.182) 0.822

(0.744)

"Probability values appear in parentheses. All tests with the exception of the stability test based on the chi-square distribution. Estimation spanned April 1974 to October 1987, inclu- sive, with a constant and 11 seasonal dummy variables included in each equation in the model. Critical 5% chi-square value for the autoregressive-moving average and ARCH tests is 21.026.

disturbance that is fully offset in the period after the perturbation. Abstracting from trend and seasonal factors, Figures 5 and 6 illustrate that while money returns to its original position quickly, relative prices cycle for roughly three years. This result confirms that money has a temporary impact on relative prices that closely resembles overshooting models of exchange rate determination.

FINAL REMARKS

The aim of this paper is to illustrate the relationship between money and relative prices to determine whether monetary policy has consequences for real activity. The empirical results tend to confirm what was expected, in that money is non- neutral in the short run. Money acts only as a veil in the long run.

These results suggest that further work in this area might concentrate on spe- cific commodity prices to determine the channels through which financial events alter relative prices. Care must be taken in any such exercise to apply the tech- nology to nonadministered commodity prices. It would seem on the basis of these results that macroeconomic factors play a role in explaining why commodity prices tend to fluctuate in a way that is not completely explained through an examination of what might be termed microeconomic factors.

NOTES 'See Bessler (1982), Devadoss and Meyers (1987) and references therein for examples. 'M2 includes currency, demand deposits, daily interest chequable savings accounts, non- personal notice deposits, other notice deposits, and personal term deposits.

276

0.5

0.4 - e 0 0 ..

0.3 _1 - z z 1: 0.2 r

3 I Y)

Y 0

* t Y z 0

-

p 0.1

0.0

-0.1

CANADIAN JOURNAL OF AGRICULTURAL ECONOMICS

0 6 12 16 24 30 36 4 2 4 6 I . ' . ' . 5 . . . . . ( .

TIME (MONTHS)

Figure 5 . Simulated money stock.

-1s

0 6 12 19 24 30 36 42 4 6

TIM8 (MONTHS)

I

Figure 6 . Simulated relative price level.

RELATIVE PRICES AND MONEY 277

3Data on M2 and the food and nonfood components of the CPI were obtained from the CANSIM database on a seasonally unadjusted basis. Series identifiers are:

M2 CANSIM B203 1 Food prices CANSIM D484001 Nonfood prices CANSIM D484495

4See Sephton (1988b) and Sephton (1989a, b) for examples of using both the Schwan and the FPE metrics in model specification.

ACKNOWLEDGMENT I thank an anonymous referee for helpful comments. The usual caveat applies.

REFERENCES Bessler, D. A. 1982. Relative prices and money: A vector autoregression on Brazilian data. American Journal of Agriculrural Economics 66(February): 25-30. Devadoss, S. and W. €I. Meyers. 1987. Relative prices and money: Further results for the United States. American Journal of Agricultural Economics 69movember): 83842. Dickey, D. A. and W. A. Fuller. 1981. Likelihood ratio statistics for autoregressive time series with a unit root. Econornetrica 49: 1057-72. Engle, R. and C. W. J. Granger. 1987. Co-integration anderror correction representation, estimation, and testing. Econometrica %(March): 251-76. Fackler, J. 1985. An empirical analysis of the markets for goods, money, and credit. Jour- nal of Money, Credit, and Banking 17(February): 28-42. Frankel, J. 1986. Expectations and commodity price dynamics: The overshooting model. American Journal of Agricultural Economics 68(May): 344-48. Geweke, J. and R. M e . 1981. Estimating regression models of finite but unknown order. International Economic Review 22: 55-70. Hsiao, C. 1981. Autoregressive modelling and money-income causality detection. Journal of Monetary Economics 7: 85-106. Schwarz, G. 1978. Estimating the dimension of a model. The Annals ofstatistics 6: 461- 64. Sephton, P. S. 1988a. World non-oil primary commodity markets: Comment on Chu and Momson. IMF Staff Papers 35(March): 198-203. Sephton, P. S. 1988b. On interest rate innovations and anticipated monetary policy. Eco- nomics Letters 28(December): 177-80. Sephton, P. S. 1989a. Anticipated monetary policy in Canada: Some new evidence. Eco- nomics Letters (forthcoming). Sephton, P. S. 1989b. Does anticipated monetary policy matter? More evidence. Applied Economics (forthcoming .)