Monetary announcement and commodity price dynamics: a portfolio balance model.

Hu, Shih-wen ; Lai, Ching-chong ; Wang, Vey 等

I. Introduction

Over the last two decades, there have appeared a number of studies concerning the dynamic adjustment of commodity prices from both theoretical and empirical viewpoints.' Among the literature, Van Duyne (1979) presents a portfolio balance model, and analyzes how commodity prices will react as the economy experiences a bad harvest and a commodity speculation. Frankel (1986) sets up a macroeconomic model, which can be treated as an application of the Dornbusch (1976) model, and finds that agricultural product prices will display an overshooting following an unanticipated expansion in money supply. There are however at least two points ignored in the Frankel (1986) analysis. First, some empirical studies including Frankel and Hardouvelis (1985) and Barnhart (1989), indicate that the commodity prices will react following the policy announcement but prior to the policy implementation. Second, the interaction linking the disequilibrium in the agricultural product market to the stock of agricultural products, which Van Duyne (1979) emphasizes, is not modelled.

This paper attempts to construct a portfolio balance model to capture the linkage between the flow and stock of agricultural products? We will portray an economy with the following features: market participants form their expectations with perfect foresight; the economy produces two kinds of goods: agricultural products and manufactured products; and the public hold three financial assets: money, bonds, and agricultural products? based on such a framework, we try to shed light on how the pre-announcement monetary policy will govern the transitional adjustment of commodity prices.

The rest of the paper is arranged as follows. The structure of the model is outlined in section II. The adjustment of commodity prices in response to announced monetary expansion is examined in section III. Finally, section IV summarizes the main findings of the paper.

II. The Theoretical Framework

Basically, the framework we shall develop can be treated as a modified Van Duyne (1979) model, which is a portfolio balance model of the financial sector. The model is now popular in the macroeconomic setting, and its origin should be attributed to Tobin (1969). Specifically, we consider a closed economy in which: (i) two types of goods, namely agricultural products (or "auction products") and manufactured products (or "customer products"), are produced in the economy; (ii) there are three assets held by domestic residents: money, bonds, and agricultural goods, and these assets are regarded as gross substitutes; (iii) market agents form their expectations with perfect foresight.

In accordance with the above description of the economy, the model can be specified by the following macroeconomic relationships:

[Mathematical Expression Omitted] (1)

[Mathematical Expression Omitted] (2)

[Mathematical Expression Omitted] (3)

[Mathematical Expression Omitted] (4)

[Mathematical Expression Omitted] (5)

W = M + B + [P.sub.c],C (6)

where [D.sup.n] = demand for manufactured products; [P.sub.n] = price of manufactured products; [P.sub.c] = price of agricultural goods; [X.sup.n] = supply of manufactured products; m = the desired portfolio share of the residents' financial wealth on money balance; r = interest rate, k = the difference between the convenience yield and the storage costs; W = nominal wealth; M = nominal money supply; b = the desired portfolio share of the residents' financial wealth on bonds; B = supply of domestic bonds; c = the desired portfolio share of the residents' financial wealth on agricultural products; C = stock of agricultural products; [X.sup.c] = supply of agricultural products; [D.suP.x] = demand for agricultural products. An overdot indicates the rate of change with respect to time.

Equation (1) is the equilibrium condition for the manufactured good market. The equilibrium condition for money, bonds, and agricultural products, which are imperfect substitutes for each other, is given respectively by equations (2)-(4). As specified in all portfolio balance models, they require that available stocks of money, bonds, and agricultural products equal stock demands for three assets. The demands for these three assets are proportional to the wealth where the shares add up to unity. Furthermore, the allocation of portfolios among three assets depends upon the return on holding bonds r and the return on holding agricultural (auction) goods [Mathematical Expression Omitted] Equation (5) specifies that the stock of agricultural products will change over time as there is a flow excess supply of agricultural products. This specification is similar to those in Van Duyne (1979) and Baland (1993).

Equation (6) defines that the nominal wealth of the domestic residents is the sum of the nominal value of three assets they hold. It is clear from equations (2)-(4) and (6) that the relations [M.sub.1] + [b.sub.1] + [c.sub.1] = 0, [m.sub.2] + [b.sub.2] + [c.sub.2] = 0, and m + b + c = 1 should be held at all time.

III. Dynamic Adjustment

This section examines the evolution of agricultural prices and the stock of agricultural products when the economy experiences an announced monetary expansion. One point should be noted at this stage. Due to the Walras law in the asset markets, one of the market equilibrium conditions of three assets is redundant; we thus do not explicitly deal with the equilibrium condition for the stock market of agricultural goods.

Without loss of generality, we assume that P = [P.sub.n] = 1 and [Mathematical Expression Omitted] initially. In addition, for saving space, in what follows we only deal with monetary shock. Given dB = 0, the model can then be manipulated into the following two differential equations:

[Mathematical Expression Omitted] (7)

[Mathematical Expression Omitted] (8)

where

[Mathematical Expression Omitted] (7a)

[Mathematical Expression Omitted] (7b)

[Mathematical Expression Omitted] (7c)

[Mathematical Expression Omitted] (8a)

[Mathematical Expression Omitted] (8b)

We first examine the long-run property of the model. At the long-run equilibrium, [Mathematical Expression Omitted] and [P.sub.c] and C are at their stationary levels, namely [Mathematical Expression Omitted] and [Mathematical Expression Omitted]. By Cramer's rule, it is a straightforward task from equations (7) and (8) to derive the following steady-state relationship:

[Mathematical Expression Omitted] (9)

[Mathematical Expression Omitted] (10)

Equations (9) and (10) tell us that an expansion in money supply will generate a positive effect on both agricultural commodity prices and agricultural commodity stock. This result is familiar from old-fashioned IS-LM analysis, even though long-run money neutrality is standard in recent literature. The present result is consistent with the empirical evidence found by Devadoss and Meyers (1987) and Lapp and Smith (1992), but runs contrast with the theoretical conclusion proposed by Frankel (1986).(5)

We now begin to trace out the dynamic behavior of the economy. Letting [Lambda]be the characteristic root of the dynamic system and linearing the system around the stationary equilibrium, we then have the following characteristic equation:

[[Lambda].sup.2] ([[Omega].sub.1] + [[Omega].sub.2]) [Lambda] + ([[Omega].sub.1][[Psi].sub.2] - [[Omega].sub.2][[Psi].sub.1]) = 0 (11)

Since [[Omega].sub.1][[Psi].sub.2] = [[Omega].sub.2][[Psi].sub.1] [less than] 0, the two characteristic roots of the dynamic system are of opposite sign, implying the system displays the saddlepoint stability which is common to perfect foresight models.

The dynamic behavior of the system can be described by means of a phase diagram like Figure 1. It is clear from equations (7) and (8) that the slopes of loci [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are:

[Mathematical Expression Omitted] (12)

[Mathematical Expression Omitted] (13)

As indicated by the direction of the arrows in Figure 1, the lines SS and UU represent the stable and unstable branches, respectively.(6) As is evident, the convergent saddle path SS is always downward sloping and must be flatter than the [Mathematical Expression Omitted] locus, while the divergent branch UU is always upward sloping and must be steeper than the [Mathematical Expression Omitted] schedule.

We now analyze the dynamic behavior of the economy, in which at time t = 0 the monetary authorities announce the money supply will experience a permanent rise from [M.sub.0] to [M.sub.1] at a specific date t = T in the future. In both Figure 2a and Figure 2b, the initial equilibrium, where [Mathematical Expression Omitted] intersects [Mathematical Expression Omitted], is at [Q.sub.0]; the initial agricultural product prices and initial level of agricultural commodity stock are [P.sub.c0] and [C.sub.0], respectively. Upon the permanent monetary shock, both [Mathematical Expression Omitted] and [Mathematical Expression Omitted] shift upwards to [Mathematical Expression Omitted] and [Mathematical Expression Omitted], respectively; but [Mathematical Expression Omitted] shifts by a greater distance than [Mathematical Expression Omitted] does.(7) The new long-run equilibrium is established at [Q.sub.*], and the results are both [P.sub.c0] and [C.sub.0] increase to [P.sub.c*] and [C.sub.*]. In both Figure 2a and Figure 2b, we can draw a line connecting the old steady state [Q.sub.o] and new steady state [Q.sub.*]. This line is named the LL schedule, and it is always upward sloping. As is evident, the relative steepness between the LL schedule and the divergent branch UU is ambiguous. Figure 2a depicts the situation where the LL line is steeper than the UU line, while Figure 2b portrays the situation where the LL line is flatter than the UU line.(8)

Before we proceed to study how the economy will respond in the presence of an anticipated monetary expansion, three points should be addressed. First, for expository convenience, in what follows [0.sup.+] denotes the instant after the announcement made by the monetary authorities; [T.sup.-] and [T.sup.+] denote the instant before and after policy implementation, respectively. Second, during the dates between [0.sup.+] and [T.sup.-], the money supply remains at its initial level [M.sub.0], and the point [Q.sub.0] should be treated as the reference point to govern the dynamic adjustment of P and C. Third, since the public become aware that the money stock will increase from [M.sub.0] to [M.sub.1] at the moment of [T.sup.+], the economy should move to a point exactly on the stable arm SS([M.sub.1]) at that instant of time for ensuring the system to be convergent.

We first discuss the situation where the LL schedule is steeper than the unstable arm UU. Under such a situation, two patterns of adjustment possibly occur depending on the length of lead time between policy announcement and implementation T. In Figure 2a, if T is relatively large, at the instant of [0.sup.+], agricultural product prices will at once increase from [P.sub.c0] to [[P.sub.c0].sup.+], while the stock of agricultural products remains at its initial level [C.sub.0] because it is a stock variable. In consequence, the economy will jump from the point [Q.sub.0] to [Q.sub.0+] on impact. Since the point [Q.sub.0+] lies vertically above the point [Q.sub.0], from [0.sup.+] to [T.sup.-], as arrows indicate, both P and C continue to rise, and the economy will move from [Q.sub.0+] to [Q.sub.T]. At time [T.sup.+], as a monetary expansion is enacted, the economy exactly reaches the point [Q.sub.T] on the convergent saddle path SS([M.sub.1]). Subsequently, from [T.sup.+] onwards, [P.sub.c] continues to rise and C becomes less as the domestic economy moves along the SS([M.sub.1]) locus towards its new long-run equilibrium represented by point [Q.sub.*]. Given that the time lag between policy announcement and implementation is relatively long, two interesting conclusions can be drawn in Figure 2a. First, in response to a pre-announced rise in money supply, the agricultural prices will display an undershooting phenomenon. Second, rising agricultural prices accompany an accumulation of agricultural products during the dates prior to the monetary expansion, while rising agricultural prices are matched by a decrease in agricultural products after policy implementation.

However, if T is relatively short, at the instant of [0.sup.+], agricultural product prices will immediately rise from [P.sub.c0] to [P[prime].sub.c[0.sup.+]], while the stock of agricultural products is fixed at [C.sub.0] because it is a stock variable. Consequently, the economy will jump discretely from [Q.sub.0] to [Q[prime].sub.[0.sup.+]] on impact. Since the point [Q[prime].sub.[0.sup.+]] lies vertically above the point [Q.sub.0], from [0.sub.+]+ to [T.sup.-], as arrows indicate, both [P.sub.c] and C continue to rise, and the economy will move from [Q[prime].sub.[0.sup.+]] to [Q[prime].sub.T]. At time [T.sup.+], as a monetary expansion is implemented, the economy exactly reaches the point [Q[prime].sub.T]. on the convergent saddle path SS([M.sub.1]). Subsequently, from [T.sub.+] onwards, P begins to fall and C continues to accumulate as the domestic economy moves from [Q[prime].sub.T] towards its new long-run equilibrium [Q.sub.*] along the SS([M.sub.1]) locus. As a result, we obtain two interesting findings under the situation where the time lag between policy announcement and implementation is relatively short. First, in response to a preannounced rise in money supply, the agricultural prices will overshoot their long-run value.(9) Second, rising agricultural prices accompany an accumulation of agricultural products during the period of time between the announcement and realization of the monetary expansion, while falling agricultural prices are matched by an accumulation of agricultural products after policy implementation.

We now turn to illustrate another situation where the LL schedule is flatter than the unstable arm UU. In Figure 2b two distinct patterns of adjustment should be recognized corresponding to the length of the transition period T. One possibility is that T is substantially large. If this is the case, upon receiving the new information (t = [0.sup.+]), agricultural product prices will immediately rise from [P.sub.c0] to [P.sub.c0+], and the economy will jump upward from [Q.sub.0] to [Q.sub.[0.sup.+] on impact. During the dates between [0.sup.+] and [T.sup.-], the economy will move along the unstable branch [Q.sub.0+][Q.sub.T]. At the instant [T.sup.+], when the monetary expansion comes into force, the economy reaches the point [Q.sub.T] on the saddle path SS([M.sub.1]). Thereafter, P keeps falling and C keeps rising as the economy moves along the SS([M.sub.1]) locus from QT towards its new stationary equilibrium [Q.sub.*]. The other possibility is that T is substantially small. In this case, at the instant [0.sup.+], agricultural product prices will at once rise from [P.sub.c0] to [P[prime].sub.c]0.sup.+], while the stock of agricultural products remains at its initial level [C.sub.0] because it is a stock variable. In association with the discrete adjustment in [P.sub.c], the economy will jump from the point [Q.sub.0] to [Q[prime].sub.[0.sup.+]. During the time interval [0.sup.+] and [T.sup.-], as the arrows indicate, both [P.sub.c] and C continue to increase, and the economy moves from [Q[prime].sub.[0.sup.+] to [Q[prime].sub.T]. At the instant [T.sup.+], as the monetary expansion is implemented, the economy should move to the point [Q[prime].sub.T] which is exactly on the convergent saddle path SS([M.sub.1]). From [T.sup.+] onwards, P continues to fall and C continues to rise as the economy moves along the SS([M.sub.1]) schedule from [Q[prime].sub.T] towards its new steady state [Q.sub.*]. The results in Figure 2b reveal a fact running counter to those in Figure 2a. That is, the length of the transition date T plays a critical role in determining whether agricultural prices will overshoot or undershoot their long-run value, but plays no role in determining the dynamic pattern of both P and C during the post-implementation period.(10)

IV. Concluding Remarks

This paper first sets up a simple portfolio balance model, and then investigates how commodity prices will behave as the monetary authorities conduct a pre-announced monetary policy. Two major conclusions emerge from the analysis. First, agricultural product prices will rise discretely on impact but may either overshoot or undershoot its long-run level at the instant of policy announcement. The crucial factor for determining whether the initial jump in agricultural prices overshoots or undershoots its long-run magnitude is the time lag between policy announcement and implementation. Second, during the period following the announcement but prior to the monetary expansion, rising agricultural prices are matched by an accumulation in the stock of agricultural products. When the monetary expansion actually takes place, two possible patterns of adjustment may happen: rising agricultural prices are matched by a decrease in the stock of agricultural products and falling agricultural prices are coupled with an accumulation in the stock of agricultural products.

Appendix

This appendix will provide a detailed mathematical derivation regarding the adjustment of commodity prices when the economy experiences an anticipated shock. Given that [P.sub.c] = [P.sub.n] = 1 and [Mathematical Expression Omitted] initially and that B does not change over time (i.e., dB = 0), substituting equation (6) into (1), (2), (3), and (5) and totally differentiating the resulting equations yield:

[Mathematical Expression Omitted] (A1)

[Mathematical Expression Omitted] (A2)

[Mathematical Expression Omitted] (A3)

[Mathematical Expression Omitted] (A5)

Putting (A2) and (A3) together to delete dr and reminding that m + b + c = 1 and [m.sub.1] + [b.sub.1] + [c.sub.1] = 0, we have:

[Mathematical Expression Omitted] (A6)

On the other hand. from equation (A1) we obtain:

[Mathematical Expression Omitted] (A7)

Substituting equation (A7) into (A5) and rearranging the terms, we have:

[Mathematical Expression Omitted] (A8)

Equations (A6) and (A8) can be expressed by the following reduced forms:

[Mathematical Expression Omitted] (A9)

[Mathematical Expression Omitted] (A10)

where

[Mathematical Expression Omitted]

Equations (A9) and (A10) are identical to equations (7) and (8) in the text.

We then examine the long-ran property of the model. At the long-run equilibrium, [Mathematical Expression Omitted] and [P.sub.c] and C are at their stationary levels, namely [Mathematical Expression Omitted] and [Mathematical Expression Omitted]. It follows from equations (A9) and (A10) with m+b+c = 1 and [m.sub.1] + [b.sub.1] + [c.sub.1] = 0 that:

[Mathematical Expression Omitted] (A11)

Cramer's rule generates

[Mathematical Expression Omitted] (A12)

[Mathematical Expression Omitted] (A13)

Equations (A12) and (A13) repeat the results in equations (9) and (10) in the text. For expository convenience, the above relationships can be expressed by the following reduced forms:

[Mathematical Expression Omitted] (A14)

[Mathematical Expression Omitted] (A15)

For notational simplicity, define

[Mathematical Expression Omitted] (A16)

[Mathematical Expression Omitted] (A17)

We now turn to discuss the dynamic nature of the system. Letting [Lambda] be the characteristic root of the dynamic system, from equations (A9) and (A10) we have the following characteristic equation:

[Mathematical Expression Omitted] (A18)

Since [[Omega].sub.1][[Psi].sub.2] - [[Omega].sub.2][[Psi].sub.1] [less than] 0, the two characteristic roots of the dynamic system, namely [[Lambda].sub.1] and [[Lambda].sub.2], are of opposite sign, implying the system displays the saddlepoint stability which is common to perfect foresight models. For ease of exposition, in what follows let [[Lambda].sub.1] be the negative root and [[Lambda].sub.2] be the positive root (i.e., [[Lambda].sub.1] [less than] 0 less than] [[Lambda].sub.2]).

It follows from equations (A9) and (A10) that the general solution for [P.sub.c] and C can be written as: [see Gandolfo (1980, pp. 263-65) and Turnovsky (1995, pp. 138-39)]

[Mathematical Expression Omitted] (A19)

[Mathematical Expression Omitted] (A20)

where [A.sub.1] and [A.sub.2] are unknown parameters.

In Figure 1, the stable branch SS is associated with the value [A.sub.2] = 0 in equations (A19) and (A20), i.e., the positive (unstable) root is excluded in the trajectory. Hence, the stable branch satisfies the following relation:

[Mathematical Expression Omitted] (A21)

It is clear from equation (A21) that the slope of the saddle path SS is:

[Mathematical Expression Omitted] (A22)

On the other hand, the unstable branch UU is associated with the value A1 = 0 in equations (A19) and (A20), i.e., the negative (stable) root is excluded in the trajectory. Accordingly, the unstable branch satisfies

[Mathematical Expression Omitted] (A23)

The slope of the unstable branch UU thus is:

[Mathematical Expression Omitted] (A24)

It follows from equation (A18) that the two characteristic roots have the following relationship:

[Mathematical Expression Omitted] (A25)

[Mathematical Expression Omitted] (A26)

Then from equations (A25) and (A26) we have:

[Mathematical Expression Omitted]

The above equation can be alternatively expressed as:

[Mathematical Expression Omitted] (A27)

Given that (1 - [[Psi].sub.2]/[[Lambda].sub.2]) [greater than] 0 and [[intersection].sub.2][[Psi].sub.1]/[[Lambda].sub.2] [greater than] 0, the requirement to satisfy equation (A27) is:

[[Lambda].sub.2] - [[Omega].sub.1] [greater than] 0 (A28)

Equations (A24) and (A28) lead us to infer:

[Mathematical Expression Omitted] (A29)

Based on equations (A19) and (A20), we now can deal with the evolutionary behavior of relevant variables in the presence of an anticipated monetary expansion. The experiment we conduct is that, at time t = 0, the monetary authorities announce that money supply will permanently rise from MO to [M.sub.1] at a future specific date t = T. Equipped with equations (A19) and (A20), we can use the following equations to describe the process of such a monetary policy switch:

[Mathematical Expression Omitted] (A30)

[Mathematical Expression Omitted] (A31)

where [0.sup.-] and [0.sup.+] denote the instant before and after the announcement made by the monetary authorities, [T.sup.-] and [T.sup.+] denote the instant before and after money expansion, and [A.sub.1], [A.sub.2], [A.sup.*], and [A.sup.*].sub.2] are undetermined coefficients. There are some supplementary explanation for the specification of equations (530) and (531). First, the initial money stock is Mo and the system is assumed to be in its stationary equilibrium initially, so that, at the instant t = [0.sup.-], [P.sub.c] and C are equal to [Mathematical Expression Omitted] and [Mathematical Expression Omitted]. Second, from [0.sup.+] to [T.sup.-], the money stock is not yet increased, the stationary values of [P.sub.c] and C during this time interval are associated with [M.sub.0]. Third, from [T.sup.+] onwards, money stock has increased, the stationary values of P and C during this period correspond to [M.sub.1].

To understand the exact time paths of [P.sub.c] and C from [0.sup.+] to [T.sup.-] and [T.sup.+] onwards, we must determine appropriate values for the arbitrary parameters [A.sub.1], [A.sub.2], [[A.sup.*].sub.1], and [[A.sup.*].sup.2]. These unknown parameters can be determined by the following conditions:

[C.sub.0] = [[C.sub.0[.sup.+] (A32)

[[C.sub.T].sup.-] = [[C.sub.T].sup.+] (A33)

[P.sub.c], [T.sup.-] = [P.sub.c], [T.sup.+] (A34)

[[A.sup.*].sub.2] = 0 (A35)

Equations (A32) and (A33) restrict the stock of agricultural products to move continuously because C is a stock variable. Equation (A34) is the continuity condition of the forward-looking variable P. Equation (A35) is the transversality (stabilIty) condition; it states that the economy should move along the saddle path after a monetary expansion is enacted.

Substituting equations (A30), (A31), and (A35) into (A32), (A33), and (A34) yields:

[Mathematical Expression Omitted] (A36)

[Mathematical Expression Omitted] (A37)

[Mathematical Expression Omitted] (A38)

From equations (A12),(A13),(A16), and (A17) we know that:

[Mathematical Expression Omitted] (A39)

[Mathematical Expression Omitted] (A40)

Substituting equation (A39) into (A38) and (A40) into (A37), equations (A36), (A37), (A38) can be rewritten as:

[Mathematical Expression Omitted] (A41)

[Mathematical Expression Omitted] (A42)

[Mathematical Expression Omitted] (A43)

Applying Cramer's rule, the solutions to [A.sub.1], [A.sub.2], and [[A.sup.*].sub.2] are:

[Mathematical Expression Omitted] (A44)

[Mathematical Expression Omitted] (A45)

[Mathematical Expression Omitted] (A46)

where

[Mathematical Expression Omitted]

Finally, substituting the values of [A.sub.1], [A.sub.2], [[A.sup.*].sub.1] and [[A.sup.*].sub.2] (= 0) into equations (A30) and (A31), we can obtain the complete solutions for [P.sub.c] and C.

It is obvious from equation (A30) that, at the instant of news arrival, [P.sub.c] will instantaneously respond by:

[Mathematical Expression Omitted] (A47)

Substituting (A44) and (A45) into (A47) yields:

[Mathematical Expression Omitted] (A48)

It is obvious from equation (A48) that the initial jump of agricultural product prices depends on the length of lead time between policy announcement and implementation T. With the limiting case T = 0, from equations (A39) and (A48) we have:

[Mathematical Expression Omitted] (A49)

It implies that an unanticipated rise in money supply will lead to an overshooting in agricultural product prices.

It also can be derived from equation (A48) that:

[Mathematical Expression Omitted] (A50)

where [T.sup.*] is the critical value of lead time. Equation (A50) indicates that whether the initial jump of agricultural product prices overshoots or undershoots its long-run magnitude depends on whether the length of the transition date T is less or greater than [T.sup.*]. This result confirms what we state in Section III.

Finally, we intend to address how the relative steepness between both LL and UU schedules governs the dynamic behavior of C after money expansion is realized. According to the long-run properties reported in equations (A12), (A13), (A16), and (A17), the slope of the LL locus in Figure 2a and Figure 2b is:

[Mathematical Expression Omitted] (A51)

Comparing (A51) with (A29) gives

[Mathematical Expression Omitted] (A52)

It follows from equations (A30) and (A31) with [[A.sup.*].sub.2] = 0 that, for the period t [greater than or equal to] [T.sup.+], the adjustment of [P.sub.c] and C is:

[Mathematical Expression Omitted] (A53)

[Mathematical Expression Omitted] (A54)

Due to the facts that [[Lambda].sub.1] [less than] 0, [[Lambda].sub.1] - [[Omega].sub.1] / [[Omega].sub.2] [less than] 0, AND [[E.suP.[Lambda][1.sup.T] [greater than] 0, it is a straightforward task to obtain that:

For t [greater than or equal to] [t.sup.+]

[Mathematical Expression Omitted] (A55)

Equation (A55) indicates that, when the monetary expansion actually takes place, the adjustment patterns of C and P solely depend upon the sign of [[A.sup.*].sub.1]. Then, it is immediately inferred from equations (A46) and (A52) that:

[Mathematical Expression Omitted] (A56)

Given that A [Mathematical Expression Omitted],

and [M.sub.1] - [M.sub.0] [greater than] 0, we can infer from equations (A55) and (A56) that:

For t [greater than or equal to] [T.sup.+]

[Mathematical Expression Omitted] (A57)

[Mathematical Expression Omitted] (A58)

Equation (A57) confirms the results revealed in Figure 2b. That is, under the situation where the LL schedule is flatter than the unstable arm UU, falling agricultural product prices are definitely coupled with an accumulation in the stock of agricultural products during the post-implementation period. On the other hand, equation (A58) establishes the results depicted in Figure 2a. That is, under the situation where the LL schedule is steeper than the unstable arm UU, two possible patterns of adjustment may prevail during the post-implementation period. That is, rising agricultural prices are matched by a decrease in the stock of agricultural products and falling agricultural prices are coupled with an accumulation in the stock of agricultural products.

Notes

1. The related literature on this topic includes Van Duyne (1979), Bordo (1980), Frankel and Hardouvelis (1985), Frankel (1986), Barnhart (1989), and Moutos and Vines (1992), among many others.

2. Chambers (1984) sets out a portfolio balance model portraying the interdependence between agricultural and financial markets. However, Chambers (1984) confines itself to short-run analysis, and does not link the relationship between the flow and stock of agricultural commodities.

3. Frankel (1984, p. 560) argues that "The [agricultural] commodities are relatively homogeneous, storable, and transportable and are traded on competitive markets." Thus, in accordance with Van Duyne (1979), in this paper the domestic residents treat the agricultural stock as a financial asset.

4. For a detailed explanation of the yield for holding agricultural (auction) products, see Frankel (1986) and Moutos and Vines (1992).

5. The long-run money neutrality means that both long-run agricultural and manufactured prices increase equiproportionately with the monetary expansion. Frankel (1984) and Obstfeld (1986) provide a more detailed discussion on the neutrality of money.

6. A detailed derivation of the slopes of both lines SS and UU is provided in the Appendix.

7. It follows from equations (7) and (8) that:

[Mathematical Expression Omitted]

Using the relations [m.sub.1] + [b.sub.1] + [c.sub.1] = 0, m + b + c = 1, mW = M, bW = B, and cW = C (since [P.sub.c] = 1 initially), we then have:

[Mathematical Expression Omitted]

8. See equations (A29), (A51), and (A52) in the Appendix for a more detailed discussion.

9. With the limiting case T = 0, the economy will jump from [Q.sub.0] to [Q[double prime].sub.[0.sup.+]], and an unanticipated expansion in money supply will lead to an overshooting in agricultural product prices.

10. Details of mathematical derivations are provided in the Appendix.

We are grateful to an anonymous referee of this journal for excellent guidance in revising the paper. Needless to say, any remaining deficiencies are the authors' responsibility.

References

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Shih-wen Hu, Associate Professor, Department of Economics, Feng Chia University, Talchung, Taiwan.

Ching-chong Lai, Research Fellow, Sun Yat-Sen Institute for Social Sciences and Philosophy, Academia Sinica, Taipei, and the Dean of the College of Business, Feng Chia University, Taichung, Taiwan.

Vey Wang, Associate Professor, Department of Economics, Feng Shia University, Taichung, Taiwan.