Real Exchange Rates and Commodity Prices
  • 1 https://isni.org/isni/0000000404811396, International Monetary Fund

This paper examines the relations between fluctuations in real exchange rates among the major currencies and fluctuations in real commodity prices. Increased exchange rate volatility calls for a better understanding of these relations. To the best of our knowledge, no systematic study of those effects has been performed on a wide range of commodities, although Sjaastad and Scacciavillani (1993) have done so for gold. We build on their approach and construct a supply and demand multi-country model, with world market clearing, which incorporates speculative and non-speculative demands for inventories and “static” and “rational” expectations. We estimate the model using several econometric methods on monthly data from January 1972 to January 1992 for 65 commodity prices. The paper finds that, for a small group of commodities, the dollar-denominated price is significantly influenced by the deutsche mark and the yen. The empirical results show that geographical proximity matters, and that supply and demand elasticities are important in determining the commodity price in world markets above and beyond the size of the share of those commodities in world trade.

Abstract

This paper examines the relations between fluctuations in real exchange rates among the major currencies and fluctuations in real commodity prices. Increased exchange rate volatility calls for a better understanding of these relations. To the best of our knowledge, no systematic study of those effects has been performed on a wide range of commodities, although Sjaastad and Scacciavillani (1993) have done so for gold. We build on their approach and construct a supply and demand multi-country model, with world market clearing, which incorporates speculative and non-speculative demands for inventories and “static” and “rational” expectations. We estimate the model using several econometric methods on monthly data from January 1972 to January 1992 for 65 commodity prices. The paper finds that, for a small group of commodities, the dollar-denominated price is significantly influenced by the deutsche mark and the yen. The empirical results show that geographical proximity matters, and that supply and demand elasticities are important in determining the commodity price in world markets above and beyond the size of the share of those commodities in world trade.

I. Introduction

Since the breakdown of the Bretton-Wood system, nominal and real exchange rates between major currencies as well as nominal and real prices of internationally traded commodities have displayed increasing volatility. Policy makers and economists have claimed that “excessive” variability in real commodity prices might have disruptive effects in developing as well as in industrialized countries. In developing countries, often “price variability results in large swings in export earnings that can be disruptive of investment and growth” [Winters and Sapsford (1988)].

In the last two decades, a number of theoretical and empirical contributions have dwelt on the phenomenon of increasing instability in commodity prices. On the theoretical side, those studies provided the link between exchange rates fluctuations and commodity prices fluctuations, using a standard supply-demand framework and world market clearing conditions; however, little attention has been placed thus far on the role of both inventory and expectations on commodity prices determination. On the empirical side, some studies concentrated on analyzing the actual time series properties of commodity prices, while others tested the fit and prediction power of reduced form equations resulting from theoretical models.

Along the lines developed by Sjaastad (1985), we formalize a model, which allows for a role for expectations, flows and stocks in commodity prices determination. The model features flows demand and supply on the part of consumers and producers, as well inventory demand on the part of speculators and producers. Speculators hold inventories to exploit expected profits and producers hold inventories when production is “high” as a precaution for periods when it is “low”. This “precautionary” inventory allows producers to keep the level of ex ante committed deliveries when production falls because of adverse shocks. We assume that commodities are traded at world markets, that their prices obey the law of one price and that world market clears.

The model’s reduced form equation allows us to estimate the “market power” that each of the main blocs--The United States, European Union and Japan--possesses in determining commodity prices, the degree of market integration, and the role of inventory and real interest rate in the determination of the real prices of commodities. The gain in building a new, complete structural model is that the derived reduced form equation should reflect more the underlying economic factors. The reader should keep in mind that the quality of the estimates of each bloc’s market power is conditional on the quality of the reduced form equation as a whole. 1/

In the empirical section of the paper, we confront the theory with the evidence. The main theoretical and empirical conclusions include: (i) the blocs’ relative market power are not uniform across commodities. The country or bloc that has the most influence in determining the world price of a commodity is not always the country or bloc in whose currency the commodity price is denominated, or the country or bloc with the largest market share in world trade, or the country or bloc producing the commodity in question; (ii) relative elasticities can play an important role in determining the price of commodities in world markets; (iii) the degree of market integration is perceived in the reaction of a commodity price to changes in the exchange rates. Market integration can arise because of geographic proximity or because of state intervention; (iv) the magnitude of the response of a commodity price to fluctuations in exchange rates is affected by the presence of precautionary and speculative demand for inventories. This elasticity is lower the lower is the degree of the speculators’ risk aversion, the higher is the quality of the speculators’ information and the higher is the response of producers’ demand for precautionary inventories to favorable supply shock; and (v) the effect of real interest rate on the equilibrium real price of commodities is stronger, presumably, on those more “storable” commodities

The paper is organized as follows. After a brief review of the literature, Section II develops the model and obtains both the static and rational expectation solution for the path of commodity prices. Section III sets up the econometric specifications in consonance with the theoretical finding of the previous section. Section IV discusses the empirical results and Section V contains concluding remarks. The Appendix contains the derivation of key results as well as the description and sources of the variables used in the empirical section.

1. Literature review

The increasing volatility in commodity prices after the breakdown of the Bretton-Wood system and the importance of those prices as transmitter of shocks, particularly for developing countries, have spawned a number of empirical and theoretical papers on commodity price determination. Those studies sought to spell out the time-series property of the actual behavior of commodity prices and to build theoretical models capable of mimicking the empirical evidence.

Time-series studies were carried out with model-free techniques for individual and aggregated commodity prices. Chu and Morrison (1984) studied the behavior of nominal and real primary commodity prices for the period of 1957-83 and for the subperiods of 1957-71 and 1972-83. 1/ The most salient features the authors reported were the marked increase in nominal and real commodity price instability after 1972, 1/ the rise in nominal prices by about 130 percent, on average, during the second subperiod, and the lack of a definite trend that real price series exhibited throughout 1957-83. Cuddington (1992) uses time series techniques to re-examine the Prebisch-Singer hypothesis of secular deterioration in primary commodity prices relative to manufacture good prices. He considers 26 individual commodities over the period 1900-1983 and concludes that the Prebisch-Singer hypothesis should certainly not be considered a universal phenomenon or “stylized fact.”

Reinhart and Wickham (1994) discussed thoroughly the time series property of real commodity prices for the period 1957-1993. 2/ They report some descriptive statistics for the four groups of real prices they studied during the sampling periods of: 1957:I-1969:II, 1970:I-1979:IV and 1980:11993:11. The stylized facts include a lower mean and mode value for the most recent sample period, a sustained and sharp increase, since early 1970s, in real price volatility, 3/ positive skewness although closer to normality in the recent sample period, and kurtosis although large shocks became relatively infrequent during the recent sample period. As the appropriate policy response to external shocks channeled through real commodity prices depends on whether the shocks are perceived to be temporary or permanent, the authors were concerned whether the series exhibited stationarity or not during the whole sample period. They used most of the recently developed tests to assess stationarity with and without structural breaks. Here, as in previous studies, the results are ambiguous. When no structural breaks were assumed, they could not reject the unit root hypothesis (at standard confidence level) for any of the four price indices. However, with a one-time structural break, 4/ the tests indicated that the metal index was stationary around the broken trend, while the food and beverages indices were not. For all commodities the results were inconclusive as some tests rejected the unit root hypothesis and others did not.

Reinhart and Wickham also posed the question whether the observed decreasing trend in real commodity prices, since the early 1980s, is cyclical or secular. They concluded it is mostly of a secular nature and singled out a few determining factors: (i) “the marked and secular slowdown in the growth of output in the industrial countries in the early 1970s, with 1973 constituting the end of the strong postwar expansion phase for most countries;” (ii) a surge in the commodities supply triggered by two distinct elements, namely, the expansion in export volume on the part of developing countries, after the mid-1980s, to service the debt; and permanent technological changes, information diffusion and factor productivity; and (iii) the failure during the 1980s and the 1990s of a number of international commodity price agreements. Furthermore, the authors noted that the secular price weakening was reinforced by some adverse recent cyclical factors such as the industrial countries’ weak performance and the low demand for and rising supply of commodities in the former Soviet Union.

To the best of our knowledge, Ridler and Yandle (1972) were the first to analyze the effect of exchange rate changes on commodity prices. For a given commodity, the authors started from an equilibrium situation between the world demand for imports (which depends only on the world price of the commodity in importers’ currency) and the world supply of exports (which depends only on the world price of the commodity in exporters’ country), They then performed comparative static to obtain the percentage change in the dollar (numeraire) price of the commodity as a weighted average of the percentage change in exporters’ and importers’ nominal exchange rates in terms of the numeraire currency. 1/ The authors did not explicitly consider real exchange rates or other supply and demand variables.

Dornbusch (1985) studied the effects of real exchange rate and income effects in a supply and demand framework. He assumed that a given commodity is traded in an integrated world market with two consuming blocs, the United States and the rest of the world, and that the world demand for the commodity depends on the real price of the commodity in terms of GDP deflators in each of the two blocs and on real activity. Moreover, he assumed an entirely demand driven model, that the law of one price for the commodity holds between the two blocs and that the commodity real price in terms of the U.S. deflator moves to clear the market. In this framework, a real appreciation (depreciation) of the dollar with respect to the rest of the world decreases (increases) the commodity world demand inducing the commodity real price in terms of U.S. deflator to fall (rise). 1/

Borensztein and Reinhart (1994) extended the Dornbusch (1985) model by incorporating in the exogenous commodity supply the volume of primary commodities imported by the industrial countries as a proxy for the supply shocks of the 1980s, and by taking a broader view of world demand. The world demand comprises two blocs, the United States and an aggregate of the rest of the industrial countries; the latter includes output developments in Eastern Europe and the former Soviet Union. Unlike Dornbusch (1985), their empirical estimations yielded the expected magnitude (between 0 and -1) for the elasticity of the real commodity price with respect to the real bilateral exchange rate between the two blocs considered. The authors reported that with their extensions to supply and demand, their econometric projections can better explain the decline in the real commodity prices since early 1980s and remedy much of the systematic overprediction of the demand driven model.

Sjaastad (1985) analyzed the effects of the bilateral real exchange rates among the major currencies on the real (dollar based) price of the commodity. He advanced the hypothesis that changes in the exchange rates among major currencies will cause commodity prices to fluctuate independently of the movements in the general price levels of the major countries. He points out “that fluctuations of the U.S. dollar strongly influence the (dollar) prices of internationally traded goods was particularly evident during the intense real appreciation of the dollar from early 1980 until early 1985. During that period the dollar appreciated by more than 90 percent against the Deutsche Mark (and by 45 percent in real terms), while the IMF dollar-based commodity price index fell by 30 percent.”

Sjaastad considered an internationally-traded homogeneous commodity, the price of which obeys the law of one price. He assumed that worldwide there are N trading blocs, that the numeraire currency, the dollar, is the currency of bloc 1, and that each bloc’s commodity excess demand depends on the commodity price deflated by the general price level and on other supply and demand variables. World market clearing condition closed the model, which yields the following reduced form equation: 1/

pt=Σj=2Nθjetj+Kt(1)

where pt is the logarithm of the real (dollar based) commodity price, eJt is the logarithm of the bilateral real exchange rate between blocs 1 and j, Kt groups together other supply and demand variables and θj is the elasticity of the real commodity price with respect to the bilateral real exchange rate between blocs 1 and j. Note that the θJs are between zero and one.

Interestingly, θj reveals the “market power” of bloc j on commodity i. 2/ Its magnitude measures the relative market power possessed by a participant (bloc) in the world market for the commodity in question. 3/ Each θj depends on the share of country j in the world market of the commodity and on the domestic demand and supply elasticities. If bloc j is a price taker, because of either its relatively small market share or its extremely inelastic excess demand, θj will be zero. If bloc j is a price maker, because of either its relatively large market share or its extremely elastic excess demand, θj will be one. The empirical evidence indicates that the magnitude of θj lies between zero and one and that the blocs’ relative market power are not uniform across commodities. 4/

A key feature of Sjaastad’s model is that the country that has the most influence in determining the world price of a commodity is not always the country in whose currency the commodity price is denominated. One can gain insight into this with an example from the financial markets. The dollar-denominated price of a U.S. company heavily exporting to Japan would be affected by changes in the dollar-Yen exchange rate, whereas the dollar-denominated price of a U.S. company which does not trade with Japan would be quite independent from movements in the dollar-Yen exchange rate.

Sjaastad and Scacciavillani (1993) applied the model developed by Sjaastad (1985) to analyze the gold market for the period 1982-90. They use a dynamic econometric specification to study the effect of fluctuations in the real exchange rate among the major currencies on fluctuations in the price of gold. The authors reported the following empirical findings:

(i) “The volatility of the exchange rates among the major currencies since the dissolution of the Bretton Woods international monetary system has been a major source of price instability in the gold market. Indeed, the instability of real exchange rates between major currencies is responsible for nearly half of the observed volatility in the spot price of gold during the 1982-90 period.”

(ii) “With respect to the international gold market the evidence strongly supports the ‘efficient market* hypothesis in that systematic unexploited profit opportunities have been absent.”

(iii) “While gold is usually denominated in U.S. dollars, the dollar bloc has but a small influence on the international price of gold.”

(iv) “The major gold producers of the world (South Africa, the former U.S.S.R., and Australia) appear to have no significant influence on the world price of gold.”

(v) “The world gold market is dominated by the European currency bloc which possesses approximately two-thirds of the ‘market power’ enjoyed by all participants in the market. Accordingly, real appreciations or depreciations of the European currencies have profound effects on the price of gold in all other currencies.”

(vi) “Gold appears to be a store of value as it was found that ‘world’ inflation increases the desire to hold gold; it is estimated that the real price of gold rises just over 1 percent in response to a one point increase in the rate of world inflation.”

The authors made clear that they do not claim their empirical findings for the gold case can be generalized to other commodities.

Deaton and Laroque (1992) used a standard rational expectations competitive storage model to mirror the actual time series properties of thirteen commodity prices. While their model does explicitly introduce the role of inventory and expectations in commodity prices determination, it does not incorporate the role of exchange rates. They assumed a deterministic consumption demand as an implicit function of the commodity price deflated by a general price level, a stochastically inelastic supply, and risk neutral inventory holders who can borrow or lend from a perfect capital market. A central feature of their model “is the explicit recognition of the fact that it is impossible for the markets as a whole to carry negative inventories, and this introduces an essential nonlinearity which carries through into nonlinearity of the predicted commodity price series.”

Our paper contributes to the above literature by examining real commodity prices determination in a setting explicitly allowing for speculative as well as precautionary inventories on the part of speculators and producers, respectively. The dynamic econometric specification is based on the real commodity dynamic path solution derived from the theoretical model. Unlike Deaton and Laroque (1992), our model does not take into account the fact that aggregate inventories can not be negative.

II. The Model

We model the relation between movements in real exchange rates among the major currencies and in real commodity prices within a framework of producers, consumers and speculators. By explicitly considering a demand for inventories on the part of speculators and producers, the analysis stresses the role of expectations, flows and stocks in determining the real prices of commodities. However, first we use a standard supply-demand graphical analysis to gain insight on how changes in the nominal and real exchange rate and in other variables change the nominal and real prices of a commodity.

1. A graphical analysis

Consider two major commercial blocs (e.g., the United States and Europe) trading a given commodity, whose price is quoted in dollars. Europe has an excess demand for the commodity in question, DEU, and the United States has an excess supply, SUS (shown in figure 1). The quantity supplied and demanded respond to their relevant real (relative) prices, namely, the dollar price of the commodity deflated by the general price level in the U.S. and the Deutsche mark price of the commodity deflated by the general price level in Europe. Since the vertical axis of each figure represents the nominal price of the commodity in terms of both U.S. dollars, PD, and Deutsche marks, PDM, the supply shift parameters include the general price level in the United States, P¯US, a weather proxy variable (if we were dealing with an agricultural commodity), and technology. By the same token, the demand shift parameters include the general price level in Europe, P¯US, and the price of the dollar in terms of Deutsche marks, E. The commodity under consideration is homogeneous and its price obey the law of one price, i.e., PD E - PDM. At the initial equilibrium (point A in figure 1), E and PD are normalized to unity, which, since the law of one price holds, implies that PDM also equal unity.

Figure 1.
Figure 1.

US Dollar Depreciation (Deutsche Mark Appreciation) and its Effect on the US Dollar and Deutsche Mark Prices of a Given Commodity

Citation: IMF Working Papers 1996, 027; 10.5089/9781451844474.001.A001

Starting from an initial equilibrium, point A in Figure 1, consider a 10 percent nominal--and real, as both general price levels do not change--depreciation of the dollar vis-a-vis the Deutsche mark. For a given PD, the dollar depreciation must produce a proportional reduction in PDM for the law of one price to hold. This reduces the real price, PDM/P¯US thus increasing the demand for the commodity, which is shown as a shift from point A to point B. 1/ Although the law of one price holds at point B, it is not an equilibrium point since quantity demanded, QB, exceeds quantity supplied, QA; therefore, prices have to change to clear the market. The excess demand increases PD (and the quantity supplied along SUS), which, in turn, implies that PDM decreases but less than in proportion to the depreciation of the dollar for the law of one price to hold. The market clears, at point C at a higher nominal (and real) U.S. dollar price, P’D, and at a lower nominal (and real) Deutsche mark price, P’DM. 2/

The market power possessed by each bloc can be measured as the relative change in real prices in response to a relative change in the real exchange rate. Thus, market power depends on the structure of the market, that is, on supply and demand price elasticities. Figure 1 portrays a case in which Europe has more market power (as price setter) than the United States. This follows since, as we can see in the graph, the percentage change in the dollar real price, P’D - 1, divided by the percentage change in the real exchange rate, P’D - P’DM, is closer to unity. An opposite polar example would be a case in which the United States is a total price setter--ensuing from a totally elastic supply. In this case, the dollar real price would remain constant while the Deutsche mark real price would change in proportion to the change in the real exchange rate.

The graphical analysis can readily incorporate the role of expectations by treating E, P¯US and P¯EU as forward-looking variables, i.e., whose current values are determined by the expected current and future values of the relevant fundamentals. For example, starting from an initial equilibrium, point A in figure 1, expectations of a future real depreciation of the dollar induces a real depreciation today (equal to a fraction of the expected real depreciation), which, in turn, affects equilibrium real prices (point C in Figure 1).

Summing up, the graphical analysis reveals the following: (i) a current or expected real depreciation (appreciation) of the dollar increases (decreases) the equilibrium dollar real price of the commodity regardless of which bloc has excess supply or demand; (ii) the market power (as price setter) possessed by each bloc can be measured by the elasticity of the dollar real price with respect to the real exchange rate, which lies between zero and one depending upon the market structure. The closer to one, the lesser is the market power of the United States relative to other blocs, and the closer to zero, the larger is the market power of the United States relative to other blocs; (iii) assuming, as in figure 1, that the United States has an excess supply and Europe an excess demand for a given commodity, a real depreciation (appreciation) of the dollar leads to an increase (decrease) of the equilibrium quantity of the commodity; and (iv) assuming that the United States has excess demand and Europe has excess supply for a given commodity, a real depreciation (appreciation) of the dollar leads to a decrease (increase) of the equilibrium quantity of the commodity.

The graphical analysis does not lend itself to analyze movements in a commodity real prices caused by movements in the real exchange rate in a model with more than two trading blocs, stochastic shocks, inventory demand and intertemporal speculation. To include those features in the analysis, we setup a formal model with closed-form solution. As we will see, the theoretical model yields explicit formulation, which is useful for specifying the econometric model and for interpreting the expected sign of key estimated coefficients. In particular, the model makes explicit the possibility that a real dollar depreciation (appreciation) either increases or decreases the dollar real price of a commodity depending upon the value taken by parameters related to the inventory demands.

2. Setup of the formal model

The market for commodity i = 1,…,M in country j = 1,…,N is populated by producers, consumers and speculators, whose decisions to produce, consume and hold inventories of each commodity are guided by the following behavioral equations. 1/

Dtj=d0j+d1jPtj+d2jqtj+d3jrtj+εtd,j(2)
Stj=s0j+s1jptj+s2jztj+εts,j(3)
It1,j=k1j(p˜t+1jptjr˜tj)(4)
It2,j=h0j+h1jS1j(5)
Itj=It1,j+It2,j(6)

where superscript j denotes the country and subscript t the time. DtJ is the quantity demanded for the commodity and StJ the quantity produced of the commodity, It1,j represents the amount of inventory that speculators want to carry forward to the next period and It2,j the amount of inventory that producers want to carry forward to the next period. ptJ is the logarithm of the real commodity price, i.e., the commodity price in terms of country j’s currency deflated by the country j’s general price index, qtJ stands for the logarithm of the real income and r˜tj is the expected real interest rate. ztJ, denotes a stochastic supply shock idiosyncratic to country j. ztJ, which might be persistent, can take negative values for adverse shocks (droughts, strikes, wars, red tape, corruption), positive values for favorable shocks (weather bonanzas, trade liberalization, deregulation, government subsidy) and zero for no shocks. єtd,J and єts,J are demand and supply innovations, that is, i.i.d. shocks with zero means, and p˜tj is the one step ahead forecast conditional on the available information at the beginning of the forecast period, i.e., P˜t+kj=E[pt+kj|Gt+k1j]

In (2), the quantity demanded varies directly with real income (d2j>0), and inversely with the current relative price (d1j<0) and the expected real rate of interest (d3j<0), d1J reflects intratemporal substitution possibilities between the commodity in question and other goods and commodities, while d3j reflects intertemporal substitution possibilities between consuming the commodity this period or next. In (3), the quantity supplied varies directly with the current relative price (s1J>0) and with the stochastic supply shock (s2J>0). The parameters and the motivation for equations (4) and (5) (inventory demands) are analyzed below.

a. Inventory demands

We distinguish two types of inventory holders: speculators and producers. The amount of inventory hold by each depends on different variables as we assume they have distinct motives for carrying forward the commodity.

In (4), It1,J is the amount of inventory that speculators carry forward into t+1 to exploit expected profits. 1/ Thus, the speculators relevant relative price is the expected discounted future real commodity price relative to the current real commodity price. Rational speculators with Constant Absolute Risk Aversion (CARA) utility function and facing normally distributed returns would demand an amount of inventory given by the following expression:

It1=E[rt+10|Gt]rtρvar(rt+10|Gt)

where ρ is the risk aversion coefficient and rt0 is the return on the commodity, thus E[rt+10|Gt]rtp¯t+1ptrt.. Furthermore, we assume that the speculators’ information set, Gt, is the same across countries.

If P˜t+1=E[Pt+1|Gt]+vt, then var(rt+10|Gt)=σv2 which is the forecast error variance. 1/ Hence the speculative inventory response to a change in the relevant relative price is given by k1 = 1/(ρ σv2), which is an increasing function of the quality of the speculator’s information and a decreasing function of the speculator’s degree of risk aversion, ρj. Therefore, the inventory demand schedule on the part of the speculators is:

It1=k1(P¯t+1Ptrt)

In (5), It2 is the amount of inventory that producers carry forward into t+1 as a precaution to keep the level of contractually agreed deliveries when production is hit by adverse shocks. Thus, producers hold inventory in direct relation to the level of production (0<h1<1); that is, they accumulate larger inventories when production is “larger” than expected as a safeguard for temporary or persistent unexpected adverse shocks (negative realizations of zt) affecting production. 2/ Therefore, the possibility of adverse shocks to production, which might even be persistent, is what motivate producers to hold “precautionary” inventories. 3/

3. World market clearing

World-market clearing condition for a given commodity requires the world excess demand be zero. Defining the excess demand at time t for a given commodity in country j as Ztj, world-market clearing for that commodity require

Σj=1Nztj=Σj=1N(Dtj+ItjIt1jstj)=0(7)

Assuming that the law of one price and the uncovered interest rate parity hold, and choosing the dollar as the reference currency, we derive in the Appendix the equilibrium process for the real (dollar) price of the commodity in question, which is represented by equation (8).

γ0+γ1Pt1+γ2Pt+γ5(P¯t+1P¯t)+γ4rt+γ5rt1+Σj=1NXtj=0(8)

where

Xtj=γ3jqtj+γ6jγtj+γ7jzt1j+(γ5jγ1j)et1j+(γ4jγ2j)etj(γ4j+γ5j)e¯tjγ1=Σj=1Nγ1j,i=0,,5

Equation (8) shows the equilibrium law of motion for the real commodity price (p) as a function of current and one-period lagged values of aggregate supply shocks (z), aggregate demand and supply innovations (ε), real rate of interest (r), and real exchange rate (e), as well as of current aggregate income (q) and of expected one-period forward values of both the real commodity price and the real exchange rate. Therefore, we have to specify the formation of expectations to completely characterize the solution to (8).

4. Static expectations solution

To solve for pt in the reduced form equation (8), we impose the static expectations hypothesis, i.e., forcing the expectations on future prices to be equal to the current prices. 1/ This coincides with the rational expectation solution when pt and ejt follow random walk processes. In this case, P¯t+1=Pt and e¯t+1j=etj yield (9)

pt=γ0γ2γ1γ2pt1γ4γ2rtγ5γ2rt1+1γ2Σj=1N(γ2j+γ5j)etj+1γ2Σj=1N(γ1jγ5j)et1j1γ2Σj=1Nγ3jqtj1γ2Σj=1N(γ6jztj+γ7jzt1j+εtj)(9)

where

γi=Σj=1Nγij,i=0,,5

In the Appendix (derivation of equation (8)), we establish the expected signs for the gammas as follows: γ3j>0, γ4j<0, γ5j>0, γ7j<0, γ6j<0(if 0< h1 < 1) and γ2j < 0 (if 0 < h1 < ħ), while the signs for γ0j and γ1j are a priori unknown. We can now establish the sign, and in some cases the value, of the elasticity of the real commodity price with respect to the right-hand side variables in (9), η(Pt,i), where i index those right-hand side variables.

The sign of η(Pt,Pt-1) is a priori unknown. We can, however, single out the elements affecting its sign. A high quality of the speculator’s information, a low degree of risk aversion on the part of speculators and a low elasticity of producer’s inventory demand with respect to the level of production will most likely produce a positive value of the elasticity under consideration, and a negative value otherwise. The sign of η(Pt, rt) is most likely negative as expected. A higher expected real rate of interest at time t reduces both current consumption demand (equation (2)) and current speculative demand for the commodity (equation (4)), which, ceteris paribus, reduces the current real price of the commodity. The sign of η(Pt,rt-l) or, equivalently, the sign of likely positive as expected. As we just examine, a temporary higher expected real interest rate at t reduces the real price of a commodity at t. Since, at t, the expected real interest rate was temporarily higher, at t+1, the expected real rate of interest is lower, which by the same reasoning as before, it leads to a higher real price of the commodity at t+1.

The sign of η(Pt, ejt) is most likely positive and its value lies between 0 and 1. 1/ That is, a real depreciation of the dollar with respect to the j’s country’s currency (an increase in ejt) increases, in some proportion, the real price of the commodity. And the larger (smaller) is the proportional increase in the real price, the larger (smaller) is the market power as a price setter of country j. This result corresponds exactly with the graphical analysis for cases that 0<h1j<1. The sign of η(Pt, ejt-1) is most likely positive as expected. 2/ The sign of η(Pt,qjt) is most likely positive as expected. This is an straightforward income effect. The sign of η(Pt,zjt) is most likely negative as expected. A positive (favorable) realization of the supply stochastic shock at t increases the supply schedule thus reducing the current real price of a commodity, and the sign of η(Pt,zjt-1) is most likely negative as expected.

5. Rational expectations solution

To solve for pt in the reduced form equation (8), we impose the rational expectations hypothesis, i.e., forcing the expectations on future prices to be consistent with the model conditional on available information.

Let p*t+j be the j+1 step ahead price forecast based on the available information at t-1, and let P˜t+j be the one step ahead price expectation based on the available information at t+j-1.

Pt+j*=E[Pt+j|Gt1]P¯t+j=E[Pt+j|Gt1]Pt1=Pt1*,P¯t=Pt*,P¯t+1=Pt+1*+vtwithE[vt|Gt1]=0

Taking expectations on (8) conditional on Gt-1, yields

Pt+1*θ1Pt*θ2Pt1*=Ωt1(10)

where

θ1=1γ2γ5>1,θ2=γ1γ5>1Ωt1=1γ5{γ0+E[γ4rt+γ5rt1+Σj=1NXtj|Gt1]}

Ωt-1 is the forcing process of the second order difference equation (9). The j-step ahead rational forecast is derived from equation (10).

III. Commodity Price Regression Functions

1. Regression function under static expectations

The regression function under condition of static expectations follows from taking first differences to equation (9). By differentiating once, we insure stationarity. 1/ All the variables, except the expected real rate of interest, are in logarithm.

Δpt=β1Δpt1+β2,0Δrt+β2,1Δrt1+Σj=2k3β3,0jΔetj+Σj=2k3β3,1jΔet1j+β4qt+ut(12)

Regression (12) differs from equation (9) in some aspects: (i) all variables in (12), except the real interest rate, are expressed as first difference of logarithm in order to impose stationarity in the series; (ii) the current and lagged real interest rate is ex-post rather than ex ante; (iii) the number of blocs under consideration, k3, is smaller than N; (iv) qt is the logarithm of an index of industrial production in industrial countries to avoid potential multicolinearity problem as industrial production growth might be correlated across countries; and (v) ut is an stochastic error term including the current and lagged stochastic supply shocks, and a positive autocorrelated term at one lag, which includes supply and demand innovations. Therefore, ut would, most likely, be an autoregressive process.

The results of running regression (12) for 65 commodities are presented in Tables 2 to 6 in the Appendix.

2. Regression function under rational expectations

Substituting for P˜tandP˜t+1 in (8), yields

pt=β0+β1pt1+Σi=0β2,irti+Σi=0Σj=2Nβ3,ietijΣi=0Σj=1Nβ4,ijqtij+Σi=0Σj=1Nβ5,ijπt1j+εti(13)

εt is positively autocorrelated at one lag. Moreover, as prices and exchange rates are often considered to be non stationary process, (11) will be estimated using first differences.

Δpt=β1Δpt1+Σi=0k2β2,iΔrti+Σi=0k3Σj=2Nβ3,ijΔetijΣi=0k4β4,iΔqti+Σi=1k5β5,iΔπti+δt(14)

where k2, k3, k4 and k5 denote the number of lags used in practice.

The lag structure depends on the form of the linear predictor representing the conditional expectation E[Xt+K | Gt-1] and the roots of the difference equation defining p*t.

IV. Empirical Results

Using the model described above, we estimate the long term effect on individual real commodity prices 1/ of bilateral real exchange rates dollar-Deutsche mark and dollar-yen. as well as changes in international real interest rates and world industrial production. We use different econometric methods, including; (i) regressions on the log first differences of the variables to insure stationarity; (ii) regressions on the log first differences with long lags to study the long term responses; and (iii) error correction representation. Recall that, according to the model (see equation (9)), the elasticity of the commodity price with respect to the exchange rate is between zero and one.

We transformed all variables, except real interest rate, in first difference to induce stationarity. We tested, with the Augmented Dickey Fuller (ADF) test, the stationarity of the series in their levels and their first difference form. The ADF test allows for a constant term, a deterministic time drift, and five lagged differences of the dependent variable. The test shows that the level of the bilateral real exchange rates, the level of industrial production, ex-post real interest rate, and the level of real commodity prices are stationary (see Table 1). 2/

Table 1.

Augmented Dickey-Fuller Test on the Levels and First Differences of Exogenous Variables and Commodity Prices, 1970:1 - 1993:6

The table shows the values of the t-statistics on a in the following regressions: ΔYt = μ + Bt + αYt-1 + Σ5i=5 δi ΔYt-i + εt

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According to the ADF test, some variables are stationary in their levels. The hypotheses of a unit root is rejected, at a 2.5 percent significance, for interest rate, banana, coconut oil, copra, rice (long grain), sugar (U.S. import), and it is rejected, at a 5 percent significance level, for cotton (industrial), diammonium phosphate, fish, groundnut, groundnut meal, shrimp, soybean, and soybean meal (see Table 1). For these variables, the regressions on the first differences would imply over-differentiation and therefore losing information contain in the series and, also, the cointegration tests would have no meaning for these series as they are stationary in the first place. We still report the results of differences-based regressions, however, for lack of methods to estimate regression equations which includes stationary and non-stationary variables.

According to the ADF test, all time series are stationary in their first difference form, except for natural gas, for which, the hypotheses of a unit root is accepted at a 5 percent significance level.

First, on the basis of equation (12), we regress the difference of individual real commodity prices on its own lag, and on the difference of the real bilateral exchange rates, on the ex-post real interest rate and on the difference of world industrial production, together with their lags. We use Cochrane Orcutt procedure to control for the autocorrelation of residuals. The short-term response of the commodity price to a change in the Deutsche mark (resp. the yen) is just the sum of the coefficients of the Deutsche mark (resp. the yen) and its lag. The hypotheses that the sum of coefficients on the Deutsche mark and the Deutsche mark lagged (as well as for the yen and the yen lagged) was tested.

The results, shown in Table 2, includes: the Deutsche mark was significant at the 5 percent level for a few of the commodities studied; beef, butter (price quoted in London), cocoa, copper, gold, groundnut oil, lamb, phosphoric rock, sugar (European import price), tin, wheat, and zinc. The yen was significant at the same level for beef, butter (price quotes in New Zealand), gold, logs, maize, phosphoric acid, wheat. If the level of significance is lowered somewhat, other commodities could be included as aluminum, lead, phosphoric acid, soybean meal for the Deutsche mark, ammoniac, gasoline for the yen. 1/ For some commodities, the elasticities are significant but of the wrong sign (i.e., they are negative). Those commodities are groundnut oil, phosphoric acid, and wheat for the Deutsche mark, and beef, gasoline, maize for the yen. One necessary condition for the elasticity of the commodity price with respect to the contemporaneous exchange rate to be negative is that the supplier’s inventory reacts so much to an increase in supply that the supply net of inventory would be a decreasing function of gross supply, which is hardly believable. The negative short term elasticities puzzle remains to be solved.

Table 2.

Regression of the First Difference of the Logarithm of the Dollar Price of Commodities on the Set of Independent Variables

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Table 3.

Regressions of the Level of the Logarithm of the Dollar Price of Commodities on the Set of Independent Variables

(Long-run equilibrium reduced form equation, or cointegration regressions)

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