DRAFT FOR STAFF USE ONLY PRIMARY COMMODITY PRICES, THE BUSINESS CYCLE AND THE REAL EXCHANGE RATE OF THE DOLLAR Heywood Fleisig (Consultant) Sweder van Wijnbergen CPD Discussion Paper No. 1985-19 May 23, 1985 (Revised July 1985) CPD Discussion Papers report on work in progress and are circulated for Bank staff use to stimulate discussion and comment. The views and interpretations are those of the authors. "Primary Commodity Prices,the Business Cycle and the Real Exchange Rate of the Dollar". Abstract An empirical stylized fact is that primary exporters' terms of trade worsen when the dollar appreciates and improve when the dollar depreciates.In our theoretical analysis,we demonstrate that a depreciation of the dollar will worsen a primary exporters'terms of trade, the smaller the US share in the w!orld market for the primary commodity,the lower the US demand elasticity for that good,and the larger the US share in the exporter's imports.We present empirical findings that support the theoretical analysis.Also,we find strong cyclical sensitivity of real commodity prices and evidence of their secular decline. May 23, 1985 Revised July, 1985 Primary Commodity Prices, the Business Cycle, and the Real Exchange Rate of the Dollar Heywood Fleisig Global Analysis and Projections Division Economic Analysis Projections Department World Bank and Sweder van Wijnbergen Trade and Adjustment Policy Division Country Policy Department World Bank and Centre for Economic Folicy Research London The World Bank does not accept responsibility for the views expressed herein which are those of the authors and should not be attributed to the World Bank or to its affiliated organizations. The findings, interpretations, and conclusions are the results of research supported by the Bank; they do not necessarily represent official policy of the Bank. The designations employed, the presentation of material, and any maps used in this document are solely for the convenience of the reader and do not imply the expression of any opinion whatsoever on the part of the World Bank or its affiliates concerniftg the legal status of any country, territory, city, area, or of its authorities, or concerning the delimitation of its boundaries, or national affiliation. EGL. 01-SVW -2- 1. Introduction Under floating exchange rates, a persistent stylized fact has emerged: for exporters of primary products, the'terms of trade appear to worsen when the dollar appreciates and to improve when the dollar depreciates (Dornbusch (1985)). As debt grows, this matter becomes more important - dollar exchange rate changes interact with dollar- denominated debt through the terms of trade and substantially change the burden of debt repayment. That, in turn, alters the size of serviceable debt and developing county growth prospects. This paper proposes an explanation of that phenomenon that follows from the normal play of competitive price-adjusting markets. It finds that a real depreciation of the dollar will worsen the terms of trade of a primary-product exporter the smaller the share of the United States in the world market for that good, the lower the U.S. elasticity of demand for those goods, and the higher the elasticity of demand of other industrial country importers and, finally, the largey the share of U.S. goods in the imports of the primary-product exporter. The second part of the paper presents some empirical findings that confirm this model at the aggregats. level. The theoretical results strongly constrain the elasticity of the terms of trade with respect to the real exchange rate to lie between zero and one. Our more disaggregated results are more mixed in support. More likely, however, better results await taking account of disparate supply conditions and of relative shifts in industrial country GDP to empirically isolate the effects of the exchange rate change. EGL. 01-SVW - 3 - 2. A Si2ple Model Consider a 3-region world; two regions (US and GE) produce a final good each. The U.S. and GE good are imperfect substitutes and consumed in all three regions. The third region, BR, produces an intermediate product used in the other two regions. Take the GE good as numeraire; p is the relative price of U.S. goods and q the relative price of the intermediate. We use revenue functions R and R to describe production behavior in the U.S. and GE, and expenditure functions -7, E and E to describe consumer behavior in the U.S, GE and BR. The budget constraint each region faces is: US: R(p, q) = E(p, 1; u) GE: R (1, q) = E*(p, 1; u ) (1) BR: Zq = E(p, 1; u) where Z is the aggregate supply of primary commodities by BR. P is the relative price of U.S. goods in terms of GE goods. Q is the price of the primary commodity, also in terms of GE goods. U, U and U are welfare inthe U.S., GE and BR. In the analytical section we. only consider the case of fixed commodity supply Z ; introducing price responsive commodity supply is straightforward and left to the interested reader. Our approach is strictly partial equilibrium in that we investigate the implication of a parametrically determined change in the EGL. 01-SVW real exchange rate between final goods, p, on commodity prices. We therefore can discard final-goods market clearing conditions and concentrate on the market for primary commodities for given real exchange rate p between U.S. an GE goods. By standard properties of the revenue function, demand for commodities equals minus the derivative of the revenue function with respect to the relevant price, so the primary commodity market clears when: R + R + Z = 0. (2) q q Differentiating and collecting terms yields: R d qp .(3) dp -(R +R ) .-qq qq Homogeneity of degree one of the revenue function implies: R q + R p =0. qq q qp We can rewrite (3), therefore, as q dp R + R qq qq or EGL. 01-SVW -5- E:q _ (5) P u + (1E- ) q q 9 is the value share of total primary commodity imports going to the U.S. and e is the price elasticity of primary commodity demand in q country i. Accordingly, the elasticity of the real price of primary commodities, in terms of GE goods, with respect to the real exchange rate between U.S. an GE is positive and below one. In the empirical analysis we will look at commodity prices in terms of U.S. goods, q = q/p. Clearly simple rearranging yields e q =I a.- ---.(6) cu + (1- ) q q What (5) and (6) tell us is straightforward: when the dollar appreciates in real terms against the currencies of other industrial countries, the real commodity price will fall in terms of U.S. goods and rise in terms of "other" industrial countries' goods (GE). The fall in real dollar terms will be the larger, the smaller is the U.S. share in the world imports of that primary commodity, and the lower are U.S. demand elasticities compared with the demand elasticities in other industrial countries. This makes perfect common sense: a large U.S. share or relatively high U.S. demand elasticity will tie commodity prices to those of U.S. goods and so prevent a relative price fall. A large fall in terms of U.S. goods would obviously be bad news for countries like Brazil that export primary commodities and import a lot from the U.S. EGL. 01-SVW -6- For equal demand elasticities (su = eg), simple rearranging q q gives the elasticity for commodity prices expressed in terms of an * * arbitrary price index 7r =r (p, 1), for example, the CPI of the commodity exporters; define q = q/T* and we get P (7) for eu = . So, for example, if the share of U.S. goods in the q q Brazilian CPI exceeds the share of the United States in world primary commodity imports, real primary commodity prices in terms of the Brazilian CPI will fall (assuming equal demand elasticities in all industrial countries). Alternatively, we could look at the commodity exporter's import bundle, assuming again equal demand elasticities (Su = eg). If the share of U.S. goods in the primary exporter's q q imports exceeds the U.S. share in world primary commodity markets, the terms of trade of the primary goods exporter will deteriorate if the dollar appreciates. 3. Data and empirical results: primary commodities in aggregate. As a measure of commodity prices we use the world Bank (1980 dollar) index of all commodities excluding fuel (World Bank ( )). For the price of U.S. goods, we use the U.S. GNP deflator (PNUS); For the price of "other industrial countries" goods (PNGE), we use the corresponding dollar denominated GNP deflator with (1980) GNP weights (OECD NA). We derive the real exchange rate (or, more appropriately, EGL. 01-SVW -7- terms of trade) between the U.S. and other industrial countries from these two indices: RPUO = PNUS/PNGE. Similarly, the real price of commoditi6s in terms of U.S. goods is RPCUS = PNCOM/PNUS. Finally, we use as the standardized OECD-wide unemployment rate a cyclical indicator from the OECD Economic Outlook. A printout of the variables and detailed information on sources is given in the appendix. A variable using a prefix "L" stands for "natural log of." Using aggregate data, with current and one-period lagged values of the right hand-side variables, we get: LRCUS = 2.50 - 0.61 LRPUO - 0.16 LRPUS(-1) (7.40) (1.00) (0.28) -0.07 UNR - 0.10 UNR(-1) -0.06t (8) (0.50) (0.79) (3.25) 2 R = 0.97 1970-1984 OLS F=64.4 DW = 2.25 COND = 118 High collinearity between current and lagged variables prevents estimation of the lag structure with any precision, although the overall significance of the variables is high, judging from the F-statistic. Dropping the two variables with lower t-statistic on their coefficient (RPUO(-1) and UNR) yields a substantial improvement in individual significance; the condition number of the datamatrix is much reduced, and, not surprisingly, the total effect of relative prices or for that matter unemployment does not change significantly: EGL. 01-SVW -8- LRCPUS = 2.32 - 0.59 LRPUO - 0.15 UNR(-1) - 0.07t (9) (13.6) (3.24) (2.95) (3.98) R2 = 0.97 1970-1984 OLS F= 125.1 DW = 2.22 COND = 34 These results show a strong real exchange rate effect: a ten percent real appreciation of the dollar versus other industrial countries leads to a 6 percent decline in commodity prices in terms of U.S. goods, clearly bad news for a country like '3razil that exports primary commodities and imports a great deal from the U.S. The results also suggest a significant downward trend in primary commodity prices for given final goods price structure (7 percent a year), supporting the Prebisch (1950) hypothesi- of a secular- decline in real primary commodity prices and a strong pro-cyclical effect: a one percentage point decrease in unemployment throughout the OECD would raise real commodity prices (in terms of either final good) with 15 percent, or, using an Okun's law type rule of thumb, one percentage point extra output growth in the 0CD will lead to a 5 percent improvement in real commodity prices. 4. Empirical Results: disaggregated commodity groups. The same qualitative results showld be replicable with individual commodities. Since relative prices between different primary commodities have changed over the period under consideration, aggregation bias may exist in the aggregate results reported above. We EGL. 01-SVW -9- have, therefore, repeated the analysis for four more disaggregated commodity groups: food, non-food agriculture, copper, and minerals and metals (for a precise description of the classification see World Bank ( )). In each case we estimated the general form of our basic equation, with two lags on the real exchange rate and OECD unemployment included, in addition to a time trend and the lagged endogenous variable. We then subsequently removed the variables with lowest significance, to arrive at the results reported belowl Consider first the relative price of non-food agricultures in terms of US goods, RPAUS ALRPAUS 0.01 - 1.60 ALRPUO - 0.16 AUNR - 0.21 RAUS(-1) (10) (0.14) (2.70) (1.76) (2.46) 2 ^ R - 0.42 p = -.47 1970-1984 The low is a consequence of first differencing: estimating the nnmerically equivalent equation in levels of endogenous variable yields an R2 of .96. The results indicated cyclical effects similar to the overall equation , althaugh less precisly estimated; a strong autoregressive price trend (the negative lagged endogenous variable); and finally a very strong negative real exchange rate effect. In fact 1/ The results of the unrestricted equations plus the data are available on request. EGL. 01-SVW -10 - the strongly negative term is inconsistent with the model dreived above, since it is larger in absolute value than the upper limit derived from our theory, one. The same result obtains for the other agricultural price index, food RPFUS: LPFUS = 3.01 - 1.55 LRPUO - 0.27 UNR-0.04 t (11) (13.4) (6.04) (4.76) (2.35) 2 ^ R = 0.98 p = -0.35 1970-1984 We find, once again, a stong negative real exchange rate effect and strong cyclical dependence. As with non-food agriculture, the exchange rate effect exceeds its theoretical limit of one (in absolute value). The two metal price indices we tried fitted our theoretical priori betteer. In examing the the price equation for copper (RPCOUS:) for example, we found that ARPCOUS - 1.91 - 9.90 ALRPUO - 0.16 AUNR (2.05) (0,85) (0.86) (12) - 0.82 LRPCOUS(-1) - 0.11 t (2.60) (2.09) R2= 0.47 1970-1984 (12) Although. estimated with much less precision on the individual parameters, the point estimates do satisfy the theoretical constraints derived in section 2. Finally the price index for all mineral and metals, LRPMUS: EGL. 01-SVW LRPMUS = 2.15 - 0.06 UNF(-1) - 0.10 * t (13) (16.9) (1.47) (6.40) 2 R = 0.98 1970-1984 The results indicate a complete absence of real exchange rate effects; metal and mineral prices are apparently tied almost completely to the U.S. market with no significant impact coming from changes in the U.S. - other industrial countries real exchange rate. There is moreover, a weak cyclical effect and a strong negative time trend. 5. Conclusion In this paper we set out to explain an empirical regularity that has emerged at least since the break-down of the Bretton Woods system of fixed exchange rate parities: for exporters of primary products, the terms of trade appear to worsen when the dollar appreciates in real terms, and to improve when the dollar depreciates. In the theoretical analysis we present a simple explanation that follows from the normal play of competitive price-adjusting markets. It finds that a real depreciation of the dollar will worsen the terms of trade of a primary-product exporter the smaller the share of the United States in the world market for that good, the lower the U.S. elasticity of demand for those goods, and the jghei' the elasticity of demand of other industrial country importers and, finally, the larger the share of U.S. goods in the imports of the primary-product exporter. EGL. 01-SVW - 12 - The empirical results presented in the next section confirm this model at the aggregate level. We furthermore find a strong cyclical sensitivity of real commodity prices: a one percentage point increase in the unemployment rate in the OECD is shown to lead to a fall in real commodity prices of 15 percent. We finally find strong support for the Prebisch (1950) hypothesis of secular decline in real commodity prices. EGL. 01-SVW - 13 - References Dornbusch, R. (1985), "The Effects of OECD Macroeconomic Policies on Non-Oil Developing Countries: a Review", World Bank, WDR-1985 Background Paper, forthcoming in Colaco F. and S. van Wijnbergen eds. (1986), International Capital Flows and the Developing Countries, in preparation. Organisation for Economic Cooperation and Development (1984a) National Accounts, Paris. . (1984b), Economic Outlook, Paris. Prebisch, R. (1950), "The Economic Development of Latin America and its Principal Problems", Economic Bulletin for Latin America, vol. 7, pp. 1-22, Radetzki, M. (1985), "What Happens to Dollar Prices in International Commodity Markets When the Dollar Appreciates?", Mimeo Institute for International Economic Studies, Stockholm. World Bank, Commodity Studies and Projections, Computer Data Bank.