The popular theory of overshooting was firstly introduced by Dornbush (1976) as an explanation of movements in exchange rate. He showed that the overshooting of foreign currency happens when the spot price reacts more than proportionally to an unexpected movement in the money supply, thus it overshoots its long-run equilibrium. After the initial overshoot, the exchange rate should return back to its long-run equilibrium. Since his pioneering work, the overshooting model has been introduced in different variations explaining various assets movements. As an example, Frankel and Rodriguez (1982) introduced the overshooting model for restrictions on capital mobility, and Driskill (1981) investigated the overshooting response in the case of foreign bonds and their substitutability. Papell (1984) introduced the undershooting model for the condition of accommodative monetary policy, which could lead to the underestimation of the spot exchange rate. However, it was Frankel (1986) who introduced the theory of overshooting in the context of commodity prices and monetary policy. Frankel’s (1986) original idea was that monetary policy must have an important effect on agricultural commodity prices since even the prices are flexible, while prices of other goods are sticky.
His contribution to the overshooting theory can be found in refusing the original idea of Dornbush (1976), and followers of his theory, that overshooting is predominantly an outcome of the exchange rate. Frankel (1986) built his argument on the assumption that monetary policy has an impact on the real prices of commodities. The rise in inflation led to a shift out of money into commodities. Thus, the increased demand for commodities, in combination
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with expected increases in inflation, drove the commodity prices. As he further explains, an increase in the nominal interest rate, due to raising inflation, leads to shifts out of commodities. Thus, Frankel (1986) directly applies the overshooting model developed by Dornbush (1976) by the simple substitution of prices of foreign currencies to prices of basic commodities. The assumption of Frankel’s (1986) model of overshooting is that a restrictive monetary policy that can be presented as a cut in money supply in the long-run, leads to a drop in commodity prices, while in the short-run there will not be any reaction since commodity prices are assumed to be fixed in the short-run.
The reduction in the money supply understandably leads to an increase in interest rates. The arbitrage condition, which is an unconditional assumption of Frankel’s model, holds that commodities are storable, so the rate of return on interest rates cannot be higher than the expected rate of increase in commodity prices and the storage costs discussed in previous section. The commodity prices are expected to overshoot in order to achieve future capital gain that is sufficient to compensate a higher interest rate. A similar approach was developed by Boughton and Branson (1988) as an extension to the original model of Frankel (1986) to capture the relationship between commodity prices and industrial prices. The model therefore presents the theoretical relationship between commodity prices and industrial prices with the role of expectations in commodity price movements due to monetary policy changes. An important condition to the model is the role of financial markets, since commodity prices are determined in spot markets, thus prices are able to react immediately to new information about expected future inflation.
Boughton and Branson (1988) assumed that in the case of unexpected monetary decisions, the commodity prices overshoot and lead industrial prices. Indeed world food prices and crude oil prices often result from adverse supply shocks or large increases in input costs so a supply shock is highly possible. In the model (Figure 3.1), the commodities enter consumer price inflation as final goods, showing the role of commodity prices as a leading indicator of inflationary effects.
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Source: Adopted from Boughton and Branson (1988)
Where Pm stands for the price of manufacturing goods and Pc for the price of commodities
goods, S represents the equilibrium in the money market which Frankel (1986) expressed as:
(3.1)
Where m is the logarithm of nominal money, represents the share of manufactures in the consumer price inflation, y is real output and i is the official nominal interest rate and includes the relationship between the expected commodity price inflation and interest rate, thus:
(3.2)
Where b represents the net storage costs and the real return to holding commodities for final use. From Figure 3.1 the relationship between commodity prices and manufacturing prices is inversed. In the equilibrium at E0, commodity prices are expected to stay at the current level and the interest rate is equal to the real return for holding commodities for final use. A question that arises is: what would be the reaction of commodity and manufacturing prices in the case of a shock? It is necessary to note that the commodity and manufacturing price movements depend on the nature of the shock. According to Boutghton and Branson (1988), in terms of monetary shock in the short-term, it is important to consider the different speed of price adjustment. While industrial prices adjust gradually, so in the short-term the industrial price can be held as a constant, commodity prices are able to react immediately to new information about expected future inflation.
Therefore, in the short-term, due to the faster adjustment of commodity prices, commodity prices (Pc’) rise until they overshoot. The point where commodity prices are considered to have overshot is presented in Figure 3.2 as new equilibrium E0’. Rises in commodity prices
until they are considered as overvalued can be explained by the assumption of the model, s Pm Pc Pc Pm E0
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which assumes a change in the money supply, and therefore a change in the short-term official interest rate.
Keynes (1930) named this condition of the market as the "Gibson paradox" since classical economic theory assumed that the natural or full stock equilibrium rate of interest is fairly stable over time. If this was true, then upward movements of the market rate would have generally produced a gap between the market and natural rates, and this would have generated a deflationary gap between the desired saving and investment rates. Similarly, downward movements in market interest rates produce inflationary pressure (Sargent, 1973). The fact that the theory does not correspond to the pattern implied by these considerations is the Gibson paradox. Keynes (1930) explained it as the relationship between prices and interest rates, and argued that prices tend to rise when the market rate at that time is below the natural rate. In this case the natural interest rate is represented as net storage costs and the real return of holding commodities for final use.
Indeed, the initial increase in commodity prices was driven by a cut in the interest rate as the interest rate is now lower than b. Consequently, due to the expectations that commodity prices will fall in the future (so the market is in equilibrium again), the initial price has to rise in order to decline later in the adjusting period. In the long-run, the general price level adjusts to the change in the money supply and commodity prices decline, moving up along the S line until the money supply, interest rate, and commodity price create a new long-run equilibrium at E1 (Figure 3.2).
Source: Adopted from Boughton and Branson (1988)
S’ E0 S E1 E0’ Pc’ Pc Pm Figure 3.2: Overshooting
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As is shown, the monetary shock causes overshooting. Although, as described by Boughton and Branson (1988), in the case of a supply side shock the commodity prices undershoot. Figure 3.3 shows the reaction of commodity prices to a supply side shock assuming that the monetary policy does not react to increases in prices. The black lines represent the original equilibrium in the market, the same as in Figure 3.2. A supply shock raises the equilibrium, thus the original Pm line shifts down along the Pc line and creates a new long-run equilibrium
in E1.
Source: Adopted from Boughton and Branson (1988)
Since monetary action is excluded from the model, the commodity price jumps into a new equilibrium at E0’ and continues to rise while industrial prices fall toward the new equilibrium
at E1. Although traditional theories might explain the motivation for holding inventories, they
cannot fully explain the situation of the commodity markets during 2000s. Due to the lack in explanation of commodity movements in the 2000s, new approaches for traditional theories and explanations of factors behind the recent increases in commodity prices have been developed.