## Abstract

Anticipating fluctuations in commodity prices must be of paramount concern when multilateral financial institutions such as the Fund establish programs and the conditions for them. Although some of these arrangements may provide short-term assistance to members experiencing temporary balance of payments difficulties, those nations whose primary exports are subject to a high degree of price variability require special consideration. To this end, many authors have attempted to explain the temporal behavior of commodity prices (Chu and Morrison (1986) and the references therein). Chu and Morrison have provided a structural model to identify what may be loosely termed the “microeconomic factors” behind fluctuations in commodity prices. In this note I illustrate that nonstationary commodity prices may be the result of an optimal monetary policy; in particular, that commodity prices will be stationary only if the nominal money stock exhibits similar behavior. This result may be of use in the empirical modeling of com-modity prices, as well as in setting conditions for access to some forms of multilateral assistance.

**A**nticipating fluctuations in commodity prices must be of paramount concern when multilateral financial institutions such as the Fund establish programs and the conditions for them. Although some of these arrangements may provide short-term assistance to members experiencing temporary balance of payments difficulties, those nations whose primary exports are subject to a high degree of price variability require special consideration. To this end, many authors have attempted to explain the temporal behavior of commodity prices (Chu and Morrison (1986) and the references therein). Chu and Morrison have provided a structural model to identify what may be loosely termed the “microeconomic factors” behind fluctuations in commodity prices. In this note I illustrate that nonstationary commodity prices may be the result of an *optimal* monetary policy; in particular, that commodity prices will be stationary only if the nominal money stock exhibits similar behavior. This result may be of use in the empirical modeling of com-modity prices, as well as in setting conditions for access to some forms of multilateral assistance.

Figure 1 plots the time-series pattern of copper prices. I use copper as an example because its end use is primarily in cyclically sensitive industries (International Monetary Fund (1986, p. 55)). Until the breakdown of the Smithsonian Agreement in 1973, copper prices seemed fairly stable. Through 1980, however, copper prices varied considerably from their historical record, fell through the first half of 1987 to levels attained in the late 1960s, and in November 1987 were taking off once again (US$1.14 per pound as of November 12, 1987). Although changes in market conditions and exchange rates are obvious candidates for explaining this behavior, so too is a monetary rule that sets money growth on the basis of unexpected changes in copper prices. In the next section I illustrate that, when a central bank smoothes interest rates and prices of both commodities and manufactured goods, it may be optimal to view “bygones as bygones” and allow money growth to depart from its previous path. The implication is that commodity prices will be nonstationary, which may help to account for the price behavior observed in Figure 1.

## I. The Model

The model is log linear in all variables except interest rates, and all parameters are positive by convention. Equation (1) defines the price index *(c _{t})* to be a weighted average of manufactured-goods prices (

*p*) and commodity prices (

_{t}*q*). The second equation sets the expected rate of change of commodity prices (

_{t}*Eq*

_{t+1}–

*q*minus storage costs

_{t})*(sc*equal to the nominal interest rate

_{t})*(i*. This condition recognizes that commodities are homogeneous and storable (Frankel (1986)).

_{t})Equation (3) describes demand, with the relative price of commodities (their price relative to manufactured goods) and the real interest rate (defined in terms of the price index) affecting demand. Equation (4) sets supply as a function of innovations in manufactured-good prices *(p _{t} – E_{t-1}p_{t})*. Money demand appears in equation (5), and the monetary rule is set in equation (6). Money growth is a function of “innovations” (unexpected changes) in interest rates and commodity prices.

^{1}Policy parameters λ

_{1}, λ

_{2}, and λ

_{3}may be chosen independently. The money stock will be trend stationary only if the offset coefficient λ

_{3}has the value of unity. In this case the current monetary response to interest rate (commodity price) changes will be fully offset in the next period. When λ

_{3}=l, the money rule has the trend-stationary solution

*m*, where

_{t}= m + z_{t}*z*is white noise and

_{t}*m*is a constant equal to an initial condition on

*E*. White-noise errors ε

_{t-2}m_{t-1}_{t},

*v*, and

_{t}*u*are assumed to be independent. Given the above, one may write

_{t}Agents observe current local prices, but they do not know the economy-wide price index nor the current level of output. Contemporaneous interest rates are known, as are current commodity prices and the money stock. The method of undetermined coefficients can be used to generate quasi-solutions for *y _{t}, p_{t}, q_{t}, m_{t}, i_{t}*, and

*c*as functions of ε

_{t}_{t},

*v*, u

_{t}_{t},

_{t-1}, m

_{t-1}–

*E*, and

_{t-2}m_{t-1}*sc*. Thus, one has

_{t}Equations (7)–(9), with equations (1), (4), and (6), complete the system, where

Equation (8) illustrates that commodity prices will be trend stationary only if the nominal money stock is trend stationary, a relationship that may help to explain the highly volatile nature of some commodity prices.

## II. Optimal Policy

Central banks like to smooth interest rates and prices to eliminate their adverse effects on employment and on the distribution of wealth in society. To calculate the optimal monetary rule in the “full” model would be a tedious task because the analytical expressions would be difficult to manipulate and interpret. To illustrate that non-trend-stationarity in the money stock may be optimal (hence non-trend-stationary commodity prices), I assume that the variance of supply and money demand stocks is negligible and examine the optimal monetary rule when goods-market shocks prevail.^{2}

The cost function (10) assumes that the central bank views price-level forecasting errors and the variability of expected inflation as costly, with weights w_{1} – w_{3}. The central bank wishes to minimize equation (10) through the choice of λ_{2} and λ_{3}. Because the object is to show that λ_{3} ≠ 1, only the optimal λ_{3} will be reported.^{3} Thus,

where *V(x)* represents the variance of *x*.

The optimal choice of λ_{3} is

with

whence it is clear that

This result indicates that commodity prices may not be trend stationary because the optimal monetary response to a goods-market shock may be to induce non-trend-stationarity in the money supply.

The rationale behind this result lies in the conflict between smoothing interest rates *and* prices. If λ_{3} = 1, agents would expect poilcy to return to its level before the disturbance, thus tying down expectations of future variables. This would require greater variation in prices than would be the case where expectations are not “locked in.” Hence it is optimal, given objectives of both price and interest rate smoothing, to view bygones as bygones and to allow money growth and prices to diverge from their past behavior.

## REFERENCES

Chu, Ke-young, and Thomas K. Morrison, “World Non-Oil Primary Commodity Markets: A Medium-Term Framework of Analysis,”

International Monetary Fund (Washington), Vol. 33 (March 1986), pp. 139–84.*Staff Papers*,Frankel, Jeffrey A., “Expectations and Commodity Price Dynamics: The Over-shooting Model,”

(Lexington, Kentucky), Vol. 68 (May 1986), pp. 344–48.*American Journal of Agricultural Economics*Goodfriend, Marvin, “Interest Rate Smoothing and Price Level Trend-Stationarity,”

(Amsterdam), Vol. 19 (May 1987), pp. 335–48.*Journal of Monetary Economics*

^{}*

Mr. Sephton is Assistant Professor of Economics at the University of New Brunswick, Fredericton, New Brunswick, Canada. He is a graduate of McMaster University, Hamilton, Ontario, and of Queen’s University, Kingston, Ontario.

^{}1

This relation suggests that the model applies to nations that have a strong interest in the evolution of agricultural commodity prices—for example, developing countries whose export earnings represent a substantial fraction of gross domestic product.

^{}2

I assume that λ^{1} = 0 and c_{2} = 1; that is, money growth does not respond to interest rate forecasting errors, and money demand is unit elastic in real income.

^{}3