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The Specification of Money Demand, Fiscal Policy, and Exchange Rate Dynamics
WEN-YA CHANG Fu-Jen Catholic University Taipei, Taiwan
CHING-CHONG LAI ISSP, Academia Sinica Taipei, Taiwan
The Specification of Money Demand, Fiscal Policy, and Exchange Rate Dynamics * This paper incorporates the Holmes and Smyth (1972) specification, that is, the transactions demand for money should depend on consumer expenditure rather than national income, into the Dornbusch (1976) model. Based on such an amended model, we focus on how exchange rates adjust over time following an anticipated permanent increase in government spending. It is found that whether the domestic currency will depreciate or appreciate following a balancedbudget fiscal expansion is sensitive to plausible specification in the money demand function. In addition, it is also found that the misadjustment pattern of exchange rate can be observed in response to a balanced fiscal expansion, even if the system displays the saddlepoint stability rather than the global instability proposed by Aoki (1985).
1. Introduction There is a wide body of work dealing with the effect of fiscal policy on exchange rate variability. Sachs (1980) explicitly introduces the wage-setting process and the long-run wealth effects of current-account balances into the Mundell (1963) model. He finds that if a wealth effect is ignored in the short run, a rise in government spending with a balanced budget leads to a currency appreciation. If the wealth flows due to current-account imbalances are taken into account in the long run, a balanced-budget fiscal expansion will result in a currency devaluation. The latter contrasts with the Mundell result.1 Daniel (1989) considers the uncertainty about the implementation *The authors would like to thank two anonymous referees for their valuable comments and suggestions, which have led to significant improvements in the quality of the paper. Financial support from the National Science Council of Taiwan, under grant NSC 83-0301-H-030-006, is gratefully acknowledged. 1 Marion (1982) uses a discrete-time stochastic macromodel with rational expectations to examine the exchange-rate effects of fiscal policy. Her results are parallel to those of Sachs (1980).
Journal of Macroeconomics, Winter 1997, Vol. 19, No. 1, pp. 79–102 Copyright 䉷 1997 by Louisiana State University Press 0164-0704/97/$1.50
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Wen-Ya Chang and Ching-Chong Lai date of a future policy change, and shows that an increase in the fiscal deficit can be responsible for sustained home currency appreciation. Based on a static Mundell (1963) model, Ahtiala (1989) proposes that, if the demand for real balances is defined in terms of a basket of consumer prices, a fiscal expansion unambiguously causes a currency appreciation. Putting the aggregate supply function of the Purvis (1979) specification into Dornbusch’s (1976) model, Devereux and Purvis (1990) conclude that the domestic currency will definitely appreciate following an unanticipated fiscal expansion. Based on the modified Dornbusch (1976) model, Aoki (1985) examines the exchange-rate responses to anticipated supply shocks. He finds that an entirely different type of exchange-rate adjustment pattern—misadjustment path—can arise when economic variables respond to anticipated shocks in rational expectations models or perfect foresight models. According to Aoki’s definition, a misadjustment path of exchange rate possesses two features: (i) impact adjustment and long-run adjustment of exchange rate are in the opposite direction; (ii) the response of the exchange rate during some beginning periods moves further away from its eventual new equilibrium value.2 Aoki (1985, 415–6) further claims that two requirements should be satisfied to establish the misadjustment path: (i) the dynamic system must have at least two unstable eigenvalues; (ii) the first arrival of the news of a future shock must lead the realization of the shock by more than a minimum of time.3 In their influential article, Holmes and Smyth (1972) propose that the transactions demand for money should depend on tax revenues either through disposable income or through consumption based on theoretical and empirical viewpoints. With such originality, they find that the tax multiplier may be positive. After the publication of the Holmes and Smyth article, an outpouring of literature (for example, Mankiw and Summers 1986; Marselli and Vannini 1988; Smith and Smyth 1990, 1991; Sumner 1990, 1991) has provided empirical support for the Holmes-Smyth specification, and has established a consumption-based transactions model of money demand as the preferred framework.4 These studies give us an inspiration regarding how 2
Aoki (1986a, 1986b) uses somewhat complicated models to derive the misadjusting pattern of exchange rate and of terms of trade. 3 Aoki (1985, 419) claims in his footnote 2 that “the existing literature does not deal adequately with one basic difference between the adjustment paths due to anticipated and unanticipated shocks, because each of the models reported in the literature usually contains only one unstable eigenvalue and adjustment paths generated by dynamics with two unstable roots are not considered. In the former situations, no misadjustment phenomenon can be observed” (italics added). In his other article, Aoki (1986b, 287) also makes a similar assertion in footnote 4. In effect, however, we will show below that the misadjustment can arise in a model containing only one unstable eigenvalue. 4 Marselli and Vannini (1988) and Sumner (1990, 1991) name Holmes and Smyth’s (1972) proposal on the money demand function “the Holmes-Smyth effect.”
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The Specification of Money Demand the conclusions of the existing literature on exchange-rate dynamics are robust enough to sustain changes in the specification of the money demand function. This paper thus makes a new attempt to incorporate alternative specifications of money demand function into Dornbusch’s (1976) model, and reevaluates the exchange-rate responses to anticipated fiscal expansion constrained by a balanced government budget. Within such an amended framework, it can be shown that whether the domestic currency will depreciate or appreciate following a balanced fiscal expansion is sensitive to the specification of the money demand function. Moreover, this paper also finds that even if the model exhibits a saddlepoint stability, the misadjustment pattern of exchange rate can be observed in response to an anticipated fiscal expansion with a balanced budget. The rest of the paper is organized as follows. The structure of the model is outlined in Section 2. The dynamic adjustment paths of the exchange rate, which is sensitive to the specification of the money demand function, will be identified in Section 3. Section 4 examines the adjustment patterns of the exchange rate when exchange-rate expectations are formed with adaptive manner. Finally, Section 5 summarizes the main findings of our analysis.
2. The Model The theoretical model we shall develop can be regarded as a variant of Dornbusch’s (1976) model. Following Dornbusch, we assume that: (i) the open economy is specified to be small in the sense that it cannot influence foreign interest rates and the foreign prices of its imports; (ii) domestic output is fixed at its full-employment level, given freely flexible wages in the labor market; (iii) the domestic price adjusts with a lag, not instantaneously;5 (iv) market participants form their expectations with perfect foresight. Accordingly, the analytical framework can be described by the following functions: P˙ ⳱ p[C(Y ⳮ s) Ⳮ I(R) Ⳮ G Ⳮ B(Y, EP*/P) ⳮ Y] ,
(1)
L[(1 ⳮ h)Y Ⳮ hC, R] ⳱ M/P ,
(2)
˙ , R ⳱ R* Ⳮ E/E
(3)
G⳱s,
(4)
5 Recent papers by Rotemberg (1982), Meese (1984), and Carlton (1986) present evidence that support the existence of price stickiness.
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Wen-Ya Chang and Ching-Chong Lai where P ⳱ domestic price level, p ⳱ speed of adjustment, Y ⳱ fullemployment output, C ⳱ consumption expenditure, s ⳱ tax revenue, I ⳱ investment expenditure, R ⳱ domestic nominal interest rate, G ⳱ government expenditure, B ⳱ balance of trade, E ⳱ exchange rate (defined as the domestic currency price of foreign currency), P* ⳱ foreign prices of imported goods, L ⳱ real demand for money, h ⳱ index parameter, M ⳱ nominal money supply, R* ⳱ foreign nominal interest rate, q ⳱ EP*/P ⳱ terms of trade, and an overdot denotes the rate of change with respect to time (t). As customary, we impose the following restrictions on the behavior functions: 1 C1 dC/d(Y ⳮ s) 0, I1 dI/dR 0, B1 B/Y 0, B2 B/q 0,6 L1 L/[(1 ⳮ h)Y Ⳮ hC] 0, L2 L/R 0. Equation (1) describes that the domestic price adjusts sluggishly in response to excess demand in the goods market. Equation (2) is the equilibrium condition for the money market. It is worth mentioning that h ⳱ 0 represents the standard money demand function, in which the transactions demand for money is a function of national income; while h ⳱ 1 is consistent with the Holmes-Smyth (1972) proposal, in which the transactions demand for money is specified to be a function of consumer expenditure. Equation (3) describes the interest rate parity as domestic bonds and foreign bonds are perfect substitutes. Equation (4) states that government spending is entirely financed by tax revenue along the lines of Rodriguez (1979), Sachs (1980), and Chang and Lai (1992).7 3. The Long-Run Equilibrium and Dynamic Adjustment In this section, we start by discussing the stationary property of the system, and then examine the evolutionary behavior of the economy. Substituting Equation (4) into Equations (1) and (2), the resulting system can be solved for three endogenous variables: P, R, and E. At long-run equilibrium, P˙ ⳱ E˙ ⳱ 0 and P, R, and E are at their stationary levels, Pˆ, Rˆ, and Eˆ. Without loss of generality, it is assumed that initially P ⳱ P* ⳱ E ⳱ 1 throughout the paper. It is a straightforward task to obtain the following long-run relationships:
6
ˆ R/G ⳱0,
(5)
ˆ P/G ⳱ hL1C1/M ,
(6)
ˆ E/G ⳱ [hL1C1B2 ⳮ M(1 ⳮ C1)]/MB2 .
(7)
This assumption implies that the Marshall-Lerner condition is satisfied. As domestic output is kept at the full-employment level, our conclusions are robust even if the income tax rate is endogenous. 7
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The Specification of Money Demand Obviously, in response to a balanced fiscal expansion, the domestic interest rate remains intact and whether the domestic price and the exchange rate will change depends crucially on the specification of the money demand function. As conventional wisdom suggests, if money demand is a function of national income (h ⳱ 0), the domestic price stays put, and the domestic currency appreciates unambiguously in response to an increase in the balanced government budget. However, if money demand is a function of consumption expenditure (h ⳱ 1), the domestic price definitely rises, and the home currency may depreciate or appreciate depending on the relative strength between the impact effect of a balanced government spending in the goods market and the induced expenditure-switching effect of changes in domestic price resulting from the money market.8 The economic explanation for the above two extreme results is as follows. In the long run, the domestic interest rate is fixed from outside at the level of the foreign interest rate. Given that the interest rate is fixed, upon the shock of a balanced government purchase, the domestic price must remain intact to maintain the money market in equilibrium if the money demand is a function of full-employment national income. Due to the fact that both domestic interest rate and domestic price keep constant, the exchange rate thus will decrease to eliminate the excess demand in the goods market which comes from an expansion of the balanced government budget. On the other hand, if money demand is a function of consumption expenditure, following the balanced fiscal expansion, the domestic price must increase to instantaneously clear the money market. Thereafter, a rise in domestic price will result in a deterioration in the balance of trade via the expenditureswitching effect and create an excess supply pressure in the goods market. Meanwhile, a balanced fiscal expansion will directly create an excess demand pressure in the goods market. As a consequence, if the expenditureswitching effect dominates the impact effect of government spending, the balanced government purchases will lead to a currency devaluation. Other8 In long-run equilibrium, P˙ ⳱ E˙ ⳱ 0, it is clear from Equation (3) that Rˆ ⳱ R* is true. Substituting Rˆ ⳱ R* and Equation (4) into Equation (2) with h ⳱ 1, we have
ˆ P/G ⳱ L1C1/M 0 . Similarly, substituting Rˆ ⳱ R* and Equation (4) into Equation (1) with h ⳱ 1, in response to a balanced fiscal expansion it follows that ˆ ˆ B2 • E/G ⳱ ⳮ(1 ⳮ C1) Ⳮ B2 • P/G 0. Obviously, the first term of the RHS in the above equation is the impact effect of a balanced fiscal expansion in the goods market, and the second term is exactly the induced expenditureswitching effect of changes in domestic price coming from the money market.
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Wen-Ya Chang and Ching-Chong Lai wise, the balanced government expansion will result in an appreciation of home currency. We now proceed to analyze the dynamic behavior of the economy. Substituting Equation (4) into Equations (1) and (2) and manipulating the resulting equations, we have the following two differential equations: E˙ ⳱ H(E, P, G) ,
(8)
P˙ ⳱ J(E, P, G) ,
(9)
where H1 ⳱ E˙/E ⳱ 0, H2 ⳱ E˙/P ⳱ ⳮM/L2 0, H3 ⳱ E˙/G ⳱ hL1C1/L2 ⱕ 0, J1 ⳱ P˙/E ⳱ pB2 0, J2 ⳱ P˙/P ⳱ ⳮp(MI1/L2 Ⳮ B2) 0, J3 ⳱ P˙/G ⳱ p(1 ⳮ C1 Ⳮ hI1L1C1/L2) 0. Let k be the characteristic root of the dynamic system and linearize the system around the steady-state equilibrium. It gives the following characteristic equation: k2 ⳮ (H1 Ⳮ J2) • k Ⳮ (H1 J2 ⳮ J1H2) ⳱ 0 .
(10)
Since H1 J2 ⳮ J1H2 ⳱ pB2M/L2 0, the two characteristic roots of the dynamic system will be of opposite signs, implying that the system exhibits the saddlepoint stability which is common to rational expectations and perfect foresight models. For expository convenience, we assume that k1 0 k2. It follows from Equations (8) and (9) that the general solution for E and P is9 ˆ E ⳱ E(G) Ⳮ A1 exp(k1t) Ⳮ A2 exp(k2t) ,
(11)
ˆ P ⳱ P(G) Ⳮ (k1/H2)A1 exp(k1t) Ⳮ (k2/H2)A2 exp(k2t) ,
(12)
where A1 and A2 are unknown parameters. The evolution of the exchange rate and the domestic price can be illustrated by a diagram similar to those used by Dornbusch (1976) and Frenkel and Rodriguez (1982). From Equations (8) and (9) it is clear that the slopes of loci E˙ ⳱ 0 and P˙ ⳱ 0 are P/E|E⳱0 ⳱0, ˙ 1 P/E|P⳱0 ⳱ ⳮJ1/J2 0 . ˙ 9
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See, for example, Gandolfo (1980, 263–65).
(13) (14)
The Specification of Money Demand
Figure 1.
As indicated by the direction of the arrows in Figure 1, the lines SS and UU represent the stable and unstable branches, respectively. Evidently, the convergent saddle path SS is always downward sloping, while the divergent branch UU is always upward sloping and must be flatter than the P˙ ⳱ 0 locus. We now analyze the dynamic behavior of the economy, in which at time t ⳱ 0 the fiscal authorities announce the government spending constrained by a balanced budget will increase from G0 to G1 at a specific date t ⳱ T in the future. First, we discuss the case that the money demand is a function of national income rather than consumption expenditure (h ⳱ 0). In Figure 2, the initial equilibrium, where E˙ ⳱ 0 intersects P˙ ⳱ 0(G0), is at Q0; the initial exchange rate and domestic price are E0 and P0, respectively. 85
Wen-Ya Chang and Ching-Chong Lai
Figure 2.
Upon the shock of an anticipated permanent increase in a balanced government spending, E˙ ⳱ 0 remains intact, while P˙ ⳱ 0(G0) shifts upward to P˙ ⳱ 0(G1),10 and intersects at point Q , with E and P being Eˆ and P0, * respectively. Before we proceed with the analysis, three points should be noted. First, for expository convenience, in what follows 0Ⳮ denotes the instant Given that h ⳱ 0, it is clear from Equations (8) and (9) that
10
P/G|E⳱0 ⳱0, ˙ P/G|P⳱0 ⳱ (1 ⳮ C1)/(I1M/L2 Ⳮ B2) 0 . ˙
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The Specification of Money Demand after the announcement made by the authorities, and Tⳮ and TⳭ denote the instant before and after policy implementation, respectively. Second, during the dates between 0Ⳮ and Tⳮ, the government spending with a balanced budget remains intact and the point Q0 should be treated as the reference point to govern the dynamic adjustment. Third, since the public becomes aware that a balanced fiscal policy will increase from G0 to G1 at the moment of TⳭ, the economy should move to a point exactly on the stable arm SS at that instant of time in order to ensure the system to be convergent. Based on this information, at the instant of anticipated fiscal announcement, the domestic currency will at once appreciate from E0 to E0Ⳮ, while the domestic price remains intact at the level of P0 because it adjusts with a lag. In consequence, the economy will jump from the point Q0 to Q0Ⳮ on impact. Since the point Q0Ⳮ lies horizontally to the west of the point Q0, from 0Ⳮ to Tⳮ, as arrows indicate, both E and P will continue to decrease, and the economy will move from Q0Ⳮ to QT. At time TⳭ, the balanced fiscal expansion has been enacted and the economy exactly reaches the point QT on the convergent stable path SS. Thereafter, from TⳭ onwards, the exchange rate will continue to fall and the domestic price will turn to rise as the economy moves along the SS curve towards its new long-run equilibrium Q . This * result is exactly the dynamic Mundell result and is parallel to that of Daniel (1989) with certainty. We now turn to examine the case in which the money demand is a function of consumption expenditure (h ⳱ 1). Again, the economy is at Q0 initially in Figures 3 and 4. In response to an anticipated balanced fiscal expansion, both E˙ ⳱ 0(G0) and P˙ ⳱ 0(G0) shift upward to E˙ ⳱ 0(G1) and P˙ ⳱ 0(G1), but the relative extent of movements is uncertain.11 Figure 3 corresponds to the situation where the E˙ ⳱ 0 schedule shifts upward by more than P˙ ⳱ 0 does, and Figure 4 illustrates the opposite situation where the vertical movement of E˙ ⳱ 0 curve is smaller than that of P˙ ⳱ 0. In Figure 3, E˙ ⳱ 0(G1) and P˙ ⳱ 0(G1) intersect at point Q and the * new stationary value of exchange rate, Eˆ, is greater than the initial level, E0. Following the same consideration and illustration as those in Figure 2, at Given that h ⳱ 1, it is obvious from Equations (8) and (9) that
11
P/G|E⳱0 ⳱ L1C1/M 0 , ˙ P/G|P⳱0 ⳱ (1 ⳮ C1 Ⳮ I1L1C1/L2)/(I1M/L2 Ⳮ B2) 0 . ˙ Then, a comparison of the above relationships gives P/G|P⳱0 ⳮ P/G|E⳱0 ⳱ [M(1 ⳮ C1) ⳮ L1C1B2]/M(I1M/L2 Ⳮ B2) 0 ˙ ˙ as (1 ⳮ C1) L1C1B2/M .
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Wen-Ya Chang and Ching-Chong Lai
Figure 3.
the instant of anticipated fiscal announcement, the domestic currency immediately depreciates from E0 to E0Ⳮ, while the domestic price stays put because it adjusts with a lag. Consequently, the economy will jump from Q0 to Q0Ⳮ on impact. Since the point Q0Ⳮ lies horizontally to the east of the point Q0, from 0Ⳮ to Tⳮ, as arrows indicated in Figure 3, both E and P continue to increase, and the economy will move from Q0Ⳮ to QT. At time TⳭ, as the balanced fiscal expansion has been implemented, the economy arrives at the point QT on the stable arm SS. Thereafter, from TⳭ onwards, E decreases and P continues to increase, and the economy then moves along SS to reach the new stationary state Q*. Obviously, this adjustment pattern 88
The Specification of Money Demand of exchange rate in response to a fiscal expansion is equivalent to that of Gray and Turnovsky (1979) and Wilson (1979) for a monetary expansion, and runs in sharp contrast with the existing literature on exchange-rate dynamics associated with anticipated fiscal expansion. On the other hand, the situation where the vertical shift of E˙ ⳱ 0 is less than that of P˙ ⳱ 0 is depicted in Figure 4. As indicated in the figure, the new steady-state value of exchange rate, Eˆ, is smaller than the initial value, E0. Moreover, according to the long-run properties of Equations (6) and (7) with h ⳱ 1, the slope of the line connecting the old stationary state (Q0) and the new steady state (Q ) is * ˆ ˆ P/E|Q0Q* ⳱ (P/G)/(E/G) ⳱ L1C1B2/[L1C1B2 ⳮ M(1 ⳮ C1)] 0 .
(15)
In addition, it follows from Equations (11) and (12) that the slope of stable arm SS which corresponds to A2 ⳱ 0 is P/E|SS ⳱ k1/H2 0 .
(16)
Equipped with the information of Equations (15) and (16), two cases may happen: |P/E|SS| |P/E|Q0Q*| .
(17)
Figure 4(a) corresponds to the situation where the line connecting the longrun equilibrium states is steeper than the stable arm; while Figure 4(b) portrays the situation where the line connecting the long-run equilibrium states is flatter than the convergent stable path. In Figure 4(a), the initial equilibrium is at point Q0 and the initial exchange rate and domestic price are E0 and P0, respectively. Upon the shock of anticipated permanent increase in the balanced government spending, the domestic currency instantaneously depreciates from E0 to E0Ⳮ, while the domestic price is unchanged. As a consequence, the economy jumps from Q0 to Q0Ⳮ on impact. Since the point Q0Ⳮ lies horizontally to the east of the point Q0, from 0Ⳮ to Tⳮ, as arrows indicated in Figure 4(a), both E and P continue to increase and the economy moves from Q0Ⳮ to QT. At time TⳭ, as the balanced fiscal expansion has been carried out, the economy arrives at the point QT on the convergent stable path SS. Thereafter, from TⳭ onwards, E decreases and P continues to increase, and the economy then moves along SS to reach the new long-run equilibrium Q*. Evidently, this adjustment pattern of exchange rate is entirely consistent with Aoki’s (1985) definition of misadjustment: the direction of impact response is opposite to 89
Wen-Ya Chang and Ching-Chong Lai
Figure 4(a).
that of the long-run response; the adjustment of exchange rate during dates between 0Ⳮ and Tⳮ moves further away from its new equilibrium value. On the other hand, Figure 4(b) corresponds to the case that the line linking the long-run equilibrium states is flatter than the convergent stable path. Following a similar description in Figure 4(a), at the instant 0Ⳮ, the domestic currency appreciates at once from E0 to E0Ⳮ, while the domestic price remains intact. Consequently, the economy will jump from Q0 to Q0Ⳮ on impact. Since Q0Ⳮ lies horizontally to the west of the point Q0, from 90
The Specification of Money Demand
Figure 4(b).
0Ⳮ to Tⳮ, as arrows indicate, both E and P continue to decrease, and the economy will move from Q0Ⳮ to QT. At the moment of fiscal expansion, the economy reaches the point QT on the stable arm SS. Thereafter, from TⳭ onwards, as E continues to fall and P turns to rise, the economy moves along SS toward the new steady state Q*. Therefore, following an anticipated fiscal shock, the exchange rate undershoots on impact and then continues to decrease until its long-run equilibrium value, Eˆ, is reached. The above graphical analyses [Figures 4(a) and 4(b)] tell us that, even though the dynamic system is characterized by the saddlepoint stability, the misadjustment phenomenon will arise if the line connecting the long-run equilibrium states is steeper than the stable arm. This conclusion runs in 91
Wen-Ya Chang and Ching-Chong Lai contrast with Aoki’s (1985) result, which claims that the misadjustment can occur only when the economy is characterized by the global instability.
4. Dynamics with Adaptive Expectations In order to highlight the role played by exchange-rate expectations, this section turns to examine how the economy will respond when exchangerate expectations are formed adaptively instead of rationally.12 Let Ee be the expected exchange rate. The interest rate parity stated in Equation (3) can be expressed as R ⳱ R* Ⳮ (Ee ⳮ E)/E .
(3a)
If perfect foresight is assumed for exchange-rate expectations, (Ee ⳮ E)/E equals E˙/E. Now in the case of adaptive expectations, the expectations mechanism displays the following manner: E˙ e ⳱ b(E ⳮ Ee) .
(18)
Equation (18) states that, if the current exchange rate exceeds the expected exchange rate, market participants will revise upward their expectations about the future exchange rate (Levin 1994). As a consequence, Equations (1), (2), (3a), (4) and (18) constitute the whole picture of the economy under adaptive expectations. Since the interest rate, R, and the exchange rate, E, adjust freely to maintain the asset markets in equilibrium, Equations (2) and (3a) must hold at any point of time. Solving Equations (2) and (3a) with (4) for R and E, given E ⳱ 1 and Ee ⳱ E initially, we obtain the reduced forms: R ⳱ f(P, G) ,
(19)
E ⳱ h(Ee, P, G) ,
(20)
where f1 ⳱ ⳮM/L2 0, f2 ⳱ hL1C1/L2 ⱕ 0, h1 ⳱ 1, h2 ⳱ M/L2 0, h3 ⳱ ⳮ hL1C1/L2 ⱖ 0. It is obvious from Equation (20) that in response to a balanced fiscal expansion, the specification of the money demand function is also the key factor to determine whether the exchange rate will respond on impact. More specifically, if money demand is a function of national income (h ⳱ 0), the exchange rate remains intact in response to a balanced fiscal expansion. This result is consistent with Levin’s (1994, 53) finding. 12
This section was suggested by an anonymous referee, to whom we are grateful.
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The Specification of Money Demand However, if money demand is a function of consumption expenditure (h ⳱ 1), the home currency will definitely depreciate in response to an increase in the balanced government budget. This finding contrasts with the Levin (1994) conclusion. Before we proceed to deal with dynamics of the economy, three points should be noted. First, the long-run equilibrium requires P˙ ⳱ E˙e ⳱ 0 (hence Eˆe ⳱ Eˆ), and the long-run equilibrium under adaptive expectations is the same as that under perfect foresight. Accordingly, the comparative-static results of Equations (5)–(7) can be applied to the case of adaptive expectations. Second, as the main focus of the analysis is on dynamics of spot exchange rate E rather than expected exchange rate Ee, we have to convert E˙e into E˙. Third, with adaptive expectations the expected exchange rate is backward looking in nature; we thus cannot deal with the problem of anticipated fiscal expansion. As a result, we turn to discuss an unanticipated permanent increase in government spending instead of an anticipated one in this section. Now we start to examine the dynamic feature of the economy under adaptive expectations. Substituting Equation (18) into Equation (3a), we have R ⳱ R* ⳮ E˙ e/bE .
(21)
Since the interest rate parity will hold at all times, differentiating Equation (3a) with respect to time, we yield R˙ ⳱ E˙ e ⳮ E˙ .
(22)
Combining Equation (21) with Equation (22) gives ˙ R ⳱ R* ⳮ (R˙ Ⳮ E)/bE .
(23)
Due to the fact that the money market also holds at any instant of time, differentiating Equation (2) with respect to time, we obtain ˙ 2. R˙ ⳱ ⳮMP/L
(24)
Substituting Equation (24) into Equation (23) and rearranging the resulting equation, we have ˙ ⳱ bR* ⳮ bR Ⳮ MP/L ˙ 2E . E/E
(25)
Finally, substituting Equation (19) into Equations (25) and (1) and manip93
Wen-Ya Chang and Ching-Chong Lai ulating the resulting equations, we have the following two differential equations: E˙ ⳱ H*(E, P, G) , P˙ ⳱ J(E, P, G) ,
(26) (9)
˙ where H*1 ⳱ E˙/E ⳱ pMB2/L2 0, H* 2 ⳱ E/P ⳱ M[b ⳮ p(MI1/L2 ˙ Ⳮ B2)]/L2 0, H* 3 ⳱ E/G ⳱ [Mp(1 ⳮ C1 Ⳮ hI1L1C1/L2) ⳮ hbL1C1]/ L2 0, and J1, J2, and J3 are identical to those in the previous section. Let be the characteristic root of the dynamic system and linearize the system around the long-run equilibrium. We then have the following characteristic equation: 2 ⳮ (H*1 Ⳮ J2) Ⳮ (H*J 1 2 ⳮ J1H*) 2 ⳱ 0 .
(27)
It is clear from Equation (27) that H* 1 Ⳮ J2 0 and H*J 1 2 ⳮ J1H* 2 ⳱ ⳮbMJ1/ L2 0, which imply that both characteristic roots of the dynamic system are negative. The system exhibits a totally stable equilibrium. In addition, it is straightforward from Equation (27) that the evolution of the system will be non-cyclical if 2 X ⳱ (H*1 Ⳮ J2)2 ⳮ 4(H*J 1 2 ⳮ J1H*) 2 ⳱ (MJ1/L2 Ⳮ J2) Ⳮ 4bMJ1/L2 0 .
Conversely, if X 0, the adjustment path will be cyclical. Similarly, we also present a graphical analysis to illustrate the evolution of E and P in response to an unanticipated fiscal shock. As indicated in Equations (26) and (9), the slope of the curve P˙ ⳱ 0 is identical to that in the case of perfect foresight (Equation (14)); while the slope of the E˙ ⳱ 0 locus is P/E|E⳱0 ⳱ ⳮH*/H* ˙ 1 2 ⳱ ⳮJ1/( J2 Ⳮ b) 0 as b ⳮ J2 .
(28)
Moreover, it can be easily inferred that, if b ⳮJ2, X (MJ1/L2 ⳮ J2)2 0 is true. It implies that the adjustment exhibits a non-cyclical convergence to the steady-state equilibrium when the E˙ ⳱ 0 schedule has a positive slope. However, if b ⳮJ2, X has an ambiguous sign, which implies that the adjustment shows either non-cyclical or cyclical convergence to the stationary equilibrium. To save space, we only discuss the case of a positively sloped E˙ ⳱ 0 locus. In addition, we call the combinations of E and P that will keep the asset markets in equilibrium the AA curve. Given Ee and G, from Equation (20) the slope of the AA curve is 94
The Specification of Money Demand
Figure 5.
P/E|AA ⳱ 1/h2 0 .
(29)
Since the asset markets are cleared at all times, the economy is not allowed to deviate from the AA locus. First, we study the dynamic behavior of the economy in which the money demand is a function of national income (h ⳱ 0). In Figure 5, the initial equilibrium is at Q0, where the schedule of E˙ ⳱ 0(G0) intersects the P˙ ⳱ 0(G0) curve, and the AA(Ee0) curve passes through it; the initial exchange rate and domestic price are E0 and P0, respectively. In response to a fiscal expansion, curve AA(Ee0 ) remains intact, but both E˙ ⳱ 0(G0) and P˙ ⳱ 0(G0) will shift leftward with an equal magnitude to E˙ ⳱ 0(G1) and P˙ ⳱ 0(G1).13 E˙ ⳱ 0(G1) intersects P˙ ⳱ 0(G1) at point Q ,14 with E and P * It is evident from Equations (20), (26) and (9) with h ⳱ 0 that
13
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Wen-Ya Chang and Ching-Chong Lai being Eˆ and P0, respectively. At the instant of a balanced fiscal expansion, the exchange rate and interest rate will stay put since the asset markets are not disturbed in Equations (19) and (20). In the meantime, an excess demand in the goods market will arise as a result of a balanced fiscal expansion. However, even there exists an excess demand on domestic goods, the price of domestic goods remains intact at the level of P0 because it adjusts with a lag. In consequence, the economy remains at the point Q0 on impact. At the next instant, the resultant excess demand in the goods market bids up the domestic price, which in turn causes the interest rate to rise and the exchange rate to fall. As arrows indicated in Figure 5, the economy moves northwestward from Q0 at the outset. Thereafter, the increased interest rate reduces investment and both the increased domestic price and decreased exchange rate lead to a shrinking trade balance. These induced effects hence combine to eliminate the excess demand in the goods market. Accordingly, whether the domestic price continues to rise depends on the direct effect of a fiscal expansion and the latter induced effects. At the beginning periods, as the fiscal expansion exerts larger effects than the latter, the domestic price continues to rise. When time goes by and the economy passes through the P˙ ⳱ 0(G1) curve, the direct effect of fiscal shock is outweighed by the induced effects, and the domestic price turns to decrease as a result of an excess supply of goods. Therefore, the economy turns to move southwestward to reach Q*. Next, we turn to discuss the case that the money demand is a function of consumption expenditure (h ⳱ 1). Again, the economy is at Q0 initially in Figures 6 and 7. Upon the shock of a balanced fiscal expansion, E˙ ⳱ 0(G0) will shift either rightward or leftward to E˙ ⳱ 0(G1). P˙ ⳱ 0(G0) unambiguously shifts left to P˙ ⳱ 0(G1).15 The AA(Ee0, G0) curve will definitely shift rightward to the AA(Ee0, G1) locus, but its movement may be either larger E/G|AA ⳱ h3 ⳱ 0 , E/G|E⳱0 ⳱ ⳮ(1 ⳮ C1)/B2 0 , ˙ E/G|P⳱0 ⳱ ⳮ(1 ⳮ C1)/B2 0 . ˙ In the long-run equilibrium, E˙e ⳱ 0 will be true and Eˆ ⳱ Eˆe will follow. As a consequence, the AA(Eˆe) schedule will pass through the point Q*. To simplify the figure, the AA(Eˆe) curve will not be drawn in Figure 5. Similarly, the final position of curve AA(Eˆe, G1) will not be shown in Figures 6 and 7 for the same reason. 15 Given that h ⳱ 1, from Equations (26) and (9) we have 14
E/G|E⳱0 ⳱ ⳮ[Mp(1 ⳮ C1 Ⳮ I1L1C1/L2) ⳮ bL1C1]/MpB2 0 ˙ if Mp(1 ⳮ C1 Ⳮ I1L1C1/L2) bL1C1 , E/G|P⳱0 ⳱ ⳮ(1 ⳮ C1 Ⳮ I1L1C1/L2)/B2 0 . ˙
96
The Specification of Money Demand
Figure 6.
or smaller than that of E˙ ⳱ 0 if the E˙ ⳱ 0 schedule shifts rightward.16 It is clear from Equation (20) with h ⳱ 1 that
16
E/G|AA ⳱ ⳮL1C1/L2 0 . When Mp(1 ⳮ C1 Ⳮ I1L1C1/L2) bL1C1, from footnote 15 we have E/G|E⳱0 0. ˙
97
Wen-Ya Chang and Ching-Chong Lai
Figure 7.
Figure 6 corresponds to the situation where the E˙ ⳱ 0 curve shifts rightward. However, to save space the movement of AA is smaller than that of E˙ ⳱ 0. Figure 7 describes the other situation where the E˙ ⳱ 0 locus shifts leftward and its horizontal movement is smaller than that of P˙ ⳱ 0.17 Then, a comparison of the above relationships gives E/G|E⳱0 ⳮ E/G|AA 0 ˙
if Mp[L1C1(B2 ⳮ I1)/L2 ⳮ (1 ⳮ C1)] Ⳮ bL1C1 0 .
17 If Mp(1 ⳮ C1 Ⳮ I1L1C1/L2) bL1C1 is true, from footnote 15 we can derive the following result:
|E/G|P⳱0 | |E/G|E⳱0 |. ˙ ˙
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The Specification of Money Demand In Figure 6, E˙ ⳱ 0(G1) and P˙ ⳱ 0(G1) intersect at point Q and the * new long-run value of exchange rate, Eˆ, is greater than the initial level, E0. At the moment of a balanced fiscal expansion, the exchange rate at once increases and interest rate immediately decreases on impact so as to maintain the asset markets in equilibrium. Meanwhile, an increase in government spending, a rise in exchange rate, and a fall in interest rate lead to an excess demand in the goods market, but the domestic price is still at P0 since it adjusts with a lag. Consequently, the economy will jump from Q0 to a point on the AA(Ee0, G1) locus, Q0Ⳮ, on impact, as a result of a fiscal expansion. At the next instant, there are two conflicting channels to influence adjustment of the exchange rate: (i) since the current exchange rate exceeds the expected rate, the expected exchange rate will be revised to move upward, which causes the exchange rate to rise; and (ii) the resultant excess demand bids up the domestic price which leads to a fall in the exchange rate. Whether the exchange rate will increase depends on the relative strength of these channels.18 Apparently, the former will surmount the latter since the point Q0Ⳮ lies horizontally to the west on the E˙ ⳱ 0(G1) curve, and hence the exchange rate increases. As arrows indicated in Figure 6, the economy will continue to move northeastward from Q0Ⳮ towards the new steady state Q*. Therefore, in response to a balanced fiscal expansion, the exchange rate undershoots on impact and then continues to increase until its long-run equilibrium value, Eˆ, is reached, even if the public form their expectations with the adaptive manner.19 On the other hand, the situation where both loci E˙ ⳱ 0 and P˙ ⳱ 0 shift leftward and the horizontal shift of the former is smaller than the latter, is depicted in Figure 7. As indicated in the figure, the new steady-state value of exchange rate, Eˆ, is less than the initial value, E0. In addition, in response to an increase in the balanced government budget, the AA(Ee0, G0) curve shifts rightward to AA(Ee0, G1). Under such a situation, following a similar description as that in Figure 6, at the instant of a fiscal expansion, the exchange rate will at once rise from E0 to E0Ⳮ on impact, while the domestic price remains intact because it adjusts with a lag.20 In consequence, the economy will jump from the point Q0 to a point on the AA(Ee0, G1) locus, Q0Ⳮ, on impact. Since the point Q0Ⳮ lies horizontally to the east on the E˙ 18
It is clear from Equation (20) that E/Ee ⳱ h1 0 ,
E/P ⳱ h2 0. If the movement of AA is greater than that of E˙ ⳱ 0, the exchange rate may overshoot on impact in response to a balanced fiscal expansion; thereafter E first continues to decrease, and then turns to increase when the economy passes through the E˙ ⳱ 0(G1) curve. 20 The economic reasoning can imitate that of Figure 6; we do not repeat to save space. 19
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Wen-Ya Chang and Ching-Chong Lai ⳱ 0(G1) schedule, as arrows indicate, E turns to decrease and P continues to increase, and the economy will move from Q0Ⳮ to Q .21 Therefore, in * response to a fiscal expansion, the exchange rate misjumps on impact and then continues to decrease until its long-run equilibrium value, Eˆ, is reached.
5. Concluding Remarks This paper first introduces the proposal of Holmes and Smyth (1972), namely, that the money demand function should be determined by consumer expenditure rather than national income, into the well-known Dornbusch (1976) model. Based on this framework, we first analyze how exchange rates adjust over time with perfect foresight, following an anticipated permanent increase in government spending with a balanced budget. It is found that, whether the domestic currency will depreciate or appreciate in response to a balanced-budget, fiscal expansion is sensitive to plausible specification in the money demand function. If the money demand is specified to be a function of national income, a balanced-budget fiscal expansion will definitely contribute an appreciation of the home currency. However, if the money demand is a function of consumption expenditure, a balanced fiscal expansion may lead to a currency depreciation or appreciation depending on the relative strength between the impact effect of a balanced fiscal expansion in the goods market and the induced expenditure-switching effect of changes in domestic price resulting from the money market. In addition, it is also found that the adjustment pattern of exchange rate in response to a balanced fiscal expansion may be misadjusting, even if the system exhibits the saddlepoint stability rather than the global instability as proposed by Aoki (1985, 1986b). Finally, if the public form their expectations with the adaptive manner, whether the home currency depreciates on impact in response to an increase in the balanced government budget also depends on a plausible specification in the money demand function. If the money demand is specified to be a function of national income, the home currency will remain intact on impact as a result of a balanced-budget fiscal expansion. However, if the money demand is a function of consumption expenditure, a balanced fiscal expansion definitely leads to a currency depreciation on impact. Received: April 1994 Final version: February 1996 21 The other possibility of dynamic adjustment is that E continues to decrease, while P first continues to rise, and then turns to decrease when the economy passes through the P˙ ⳱ 0(G1) schedule.
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The Specification of Money Demand References Ahtiala, Pekka. “A Note on Fiscal Policy under Flexible Exchange Rates.” European Economic Review 33 (September 1989): 1481–86. Aoki, Masanao. “Misadjustment to Anticipated Shocks: An Example of Exchange-Rate Response.” Journal of International Money and Finance 4 (September 1985): 415–20. ———. “Dynamic Adjustment Behaviour to Anticipated Supply Shocks in a Two-Country Model.” Economic Journal 96 (March 1986a): 80–100. ———. “Effects of Anticipated Central Bank Actions on Tobin’s Q, Share Prices and Exchange Rate in a Small Open Economy.” European Economic Review 30 (April 1986b): 285–304. Carlton, Dennis W. “The Rigidity of Prices.” American Economic Review 76 (September 1986): 637–58. Chang, Wen-ya, and Ching-chong Lai. “The Role of Supply-Side Effect of Taxes on the Balanced Budget Multiplier.” Public Finance/Finances Publiques 47 (1992): 185–92. Daniel, Betty C. “One-Sided Uncertainty about Future Fiscal Policy.” Journal of Money, Credit, and Banking 21 (May 1989): 176–89. Devereux, Michael B., and Douglas D. Purvis. “Fiscal Policy and the Real Exchange Rate.” European Economic Review 34 (September 1990): 1201–11. Dornbusch, Rudiger. “Expectations and Exchange Rate Dynamics.” Journal of Political Economy 84 (December 1976): 1161–76. Frenkel, Jacob A., and Carlos A. Rodriguez. “Exchange Rate Dynamics and the Overshooting Hypothesis.” IMF Staff Papers 29 (March 1982): 1–30. Gandolfo, Giancarlo. Economic Dynamics: Methods and Models. Amsterdam: North-Holland, 1980. Gray, Malcolm R., and Stephen J. Turnovsky. “The Stability of Exchange Rate Dynamics under Perfect Myopic Foresight.” International Economic Review 20 (October 1979): 643–60. Holmes, James M., and David J. Smyth. “The Specification of the Demand for Money and the Tax Multiplier.” Journal of Political Economy 80 (January/February 1972): 179–85. Levin, Jay H. “Fiscal Policy, Expectations, and Exchange-Rate Dynamics.” Review of International Economics 2 (February 1994): 50–61. Mankiw, N. Gregory, and Lawrence H. Summers. “Money Demand and the Effects of Fiscal Policies.” Journal of Money, Credit, and Banking 18 (November 1986): 415–29. Marion, Nancy P. “The Exchange-Rate Effects of Real Disturbances with Rational Expectations and Variable Terms of Trade.” Canadian Journal of Economics 15 (February 1982): 104–18. Marselli, Riccardo, and Marco Vannini. “The Holmes-Smyth Effect: Some 101
Wen-Ya Chang and Ching-Chong Lai Preliminary Exercises with the UK Demand for Narrow Money.” Applied Economics 20 (June 1988): 711–20. Meese, Richard A. “Is the Sticky Price Assumption Reasonable for Exchange Rate Models?” Journal of International Money and Finance 3 (August 1984): 131–39. Mundell, Robert A. “Capital Mobility and Stabilization Policy under Fixed and Flexible Exchange Rates.” Canadian Journal of Economics and Political Science 29 (November 1963): 475–85. Purvis, Douglas D. “Wage Responsiveness and the Insulation Properties of a Flexible Exchange Rate.” In Inflation and Employment in Open Economies, edited by Assar Lindbeck, 225–45. New York: North-Holland, 1979. Rodriguez, Carlos A. “Short- and Long-Run Effects of Monetary and Fiscal Policies under Flexible Exchange Rates and Perfect Capital Mobility.” American Economic Review 69 (March 1979): 176–82. Rotemberg, Julio J. “Sticky Prices in the United States.” Journal of Political Economy 90 (December 1982): 1187–1211. Sachs, Jeffrey. “Wages, Flexible Exchange Rates, and Macroeconomic Policy.” Quarterly Journal of Economics 94 (June 1980): 731–47. Smith, Marlene A., and David J. Smyth. “Choosing among Multiple Nonlinear Non-nested Regression Models with Different Dependent Variables.” Economics Letters 34 (October 1990): 147–50. ———. “Multiple and Pairwise Non-nested Tests of the Influence of Taxes on Money Demand.” Journal of Applied Econometrics 6 (January/March 1991): 17–30. Sumner, Michael. “The Policy Implications of Deflationary Tax Cuts.” Applied Economics 22 (June 1990): 719–22. ———. “Leakages from the Money Demand Function.” Applied Economics 23 (March 1991): 531–34. Wilson, Charles A. “Anticipated Shocks and Exchange Rate Dynamics.” Journal of Political Economy 87 (June 1979): 639–47.
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CHING-CHONG LAI ISSP, Academia Sinica Taipei, Taiwan
The Specification of Money Demand, Fiscal Policy, and Exchange Rate Dynamics * This paper incorporates the Holmes and Smyth (1972) specification, that is, the transactions demand for money should depend on consumer expenditure rather than national income, into the Dornbusch (1976) model. Based on such an amended model, we focus on how exchange rates adjust over time following an anticipated permanent increase in government spending. It is found that whether the domestic currency will depreciate or appreciate following a balancedbudget fiscal expansion is sensitive to plausible specification in the money demand function. In addition, it is also found that the misadjustment pattern of exchange rate can be observed in response to a balanced fiscal expansion, even if the system displays the saddlepoint stability rather than the global instability proposed by Aoki (1985).
1. Introduction There is a wide body of work dealing with the effect of fiscal policy on exchange rate variability. Sachs (1980) explicitly introduces the wage-setting process and the long-run wealth effects of current-account balances into the Mundell (1963) model. He finds that if a wealth effect is ignored in the short run, a rise in government spending with a balanced budget leads to a currency appreciation. If the wealth flows due to current-account imbalances are taken into account in the long run, a balanced-budget fiscal expansion will result in a currency devaluation. The latter contrasts with the Mundell result.1 Daniel (1989) considers the uncertainty about the implementation *The authors would like to thank two anonymous referees for their valuable comments and suggestions, which have led to significant improvements in the quality of the paper. Financial support from the National Science Council of Taiwan, under grant NSC 83-0301-H-030-006, is gratefully acknowledged. 1 Marion (1982) uses a discrete-time stochastic macromodel with rational expectations to examine the exchange-rate effects of fiscal policy. Her results are parallel to those of Sachs (1980).
Journal of Macroeconomics, Winter 1997, Vol. 19, No. 1, pp. 79–102 Copyright 䉷 1997 by Louisiana State University Press 0164-0704/97/$1.50
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Wen-Ya Chang and Ching-Chong Lai date of a future policy change, and shows that an increase in the fiscal deficit can be responsible for sustained home currency appreciation. Based on a static Mundell (1963) model, Ahtiala (1989) proposes that, if the demand for real balances is defined in terms of a basket of consumer prices, a fiscal expansion unambiguously causes a currency appreciation. Putting the aggregate supply function of the Purvis (1979) specification into Dornbusch’s (1976) model, Devereux and Purvis (1990) conclude that the domestic currency will definitely appreciate following an unanticipated fiscal expansion. Based on the modified Dornbusch (1976) model, Aoki (1985) examines the exchange-rate responses to anticipated supply shocks. He finds that an entirely different type of exchange-rate adjustment pattern—misadjustment path—can arise when economic variables respond to anticipated shocks in rational expectations models or perfect foresight models. According to Aoki’s definition, a misadjustment path of exchange rate possesses two features: (i) impact adjustment and long-run adjustment of exchange rate are in the opposite direction; (ii) the response of the exchange rate during some beginning periods moves further away from its eventual new equilibrium value.2 Aoki (1985, 415–6) further claims that two requirements should be satisfied to establish the misadjustment path: (i) the dynamic system must have at least two unstable eigenvalues; (ii) the first arrival of the news of a future shock must lead the realization of the shock by more than a minimum of time.3 In their influential article, Holmes and Smyth (1972) propose that the transactions demand for money should depend on tax revenues either through disposable income or through consumption based on theoretical and empirical viewpoints. With such originality, they find that the tax multiplier may be positive. After the publication of the Holmes and Smyth article, an outpouring of literature (for example, Mankiw and Summers 1986; Marselli and Vannini 1988; Smith and Smyth 1990, 1991; Sumner 1990, 1991) has provided empirical support for the Holmes-Smyth specification, and has established a consumption-based transactions model of money demand as the preferred framework.4 These studies give us an inspiration regarding how 2
Aoki (1986a, 1986b) uses somewhat complicated models to derive the misadjusting pattern of exchange rate and of terms of trade. 3 Aoki (1985, 419) claims in his footnote 2 that “the existing literature does not deal adequately with one basic difference between the adjustment paths due to anticipated and unanticipated shocks, because each of the models reported in the literature usually contains only one unstable eigenvalue and adjustment paths generated by dynamics with two unstable roots are not considered. In the former situations, no misadjustment phenomenon can be observed” (italics added). In his other article, Aoki (1986b, 287) also makes a similar assertion in footnote 4. In effect, however, we will show below that the misadjustment can arise in a model containing only one unstable eigenvalue. 4 Marselli and Vannini (1988) and Sumner (1990, 1991) name Holmes and Smyth’s (1972) proposal on the money demand function “the Holmes-Smyth effect.”
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The Specification of Money Demand the conclusions of the existing literature on exchange-rate dynamics are robust enough to sustain changes in the specification of the money demand function. This paper thus makes a new attempt to incorporate alternative specifications of money demand function into Dornbusch’s (1976) model, and reevaluates the exchange-rate responses to anticipated fiscal expansion constrained by a balanced government budget. Within such an amended framework, it can be shown that whether the domestic currency will depreciate or appreciate following a balanced fiscal expansion is sensitive to the specification of the money demand function. Moreover, this paper also finds that even if the model exhibits a saddlepoint stability, the misadjustment pattern of exchange rate can be observed in response to an anticipated fiscal expansion with a balanced budget. The rest of the paper is organized as follows. The structure of the model is outlined in Section 2. The dynamic adjustment paths of the exchange rate, which is sensitive to the specification of the money demand function, will be identified in Section 3. Section 4 examines the adjustment patterns of the exchange rate when exchange-rate expectations are formed with adaptive manner. Finally, Section 5 summarizes the main findings of our analysis.
2. The Model The theoretical model we shall develop can be regarded as a variant of Dornbusch’s (1976) model. Following Dornbusch, we assume that: (i) the open economy is specified to be small in the sense that it cannot influence foreign interest rates and the foreign prices of its imports; (ii) domestic output is fixed at its full-employment level, given freely flexible wages in the labor market; (iii) the domestic price adjusts with a lag, not instantaneously;5 (iv) market participants form their expectations with perfect foresight. Accordingly, the analytical framework can be described by the following functions: P˙ ⳱ p[C(Y ⳮ s) Ⳮ I(R) Ⳮ G Ⳮ B(Y, EP*/P) ⳮ Y] ,
(1)
L[(1 ⳮ h)Y Ⳮ hC, R] ⳱ M/P ,
(2)
˙ , R ⳱ R* Ⳮ E/E
(3)
G⳱s,
(4)
5 Recent papers by Rotemberg (1982), Meese (1984), and Carlton (1986) present evidence that support the existence of price stickiness.
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Wen-Ya Chang and Ching-Chong Lai where P ⳱ domestic price level, p ⳱ speed of adjustment, Y ⳱ fullemployment output, C ⳱ consumption expenditure, s ⳱ tax revenue, I ⳱ investment expenditure, R ⳱ domestic nominal interest rate, G ⳱ government expenditure, B ⳱ balance of trade, E ⳱ exchange rate (defined as the domestic currency price of foreign currency), P* ⳱ foreign prices of imported goods, L ⳱ real demand for money, h ⳱ index parameter, M ⳱ nominal money supply, R* ⳱ foreign nominal interest rate, q ⳱ EP*/P ⳱ terms of trade, and an overdot denotes the rate of change with respect to time (t). As customary, we impose the following restrictions on the behavior functions: 1 C1 dC/d(Y ⳮ s) 0, I1 dI/dR 0, B1 B/Y 0, B2 B/q 0,6 L1 L/[(1 ⳮ h)Y Ⳮ hC] 0, L2 L/R 0. Equation (1) describes that the domestic price adjusts sluggishly in response to excess demand in the goods market. Equation (2) is the equilibrium condition for the money market. It is worth mentioning that h ⳱ 0 represents the standard money demand function, in which the transactions demand for money is a function of national income; while h ⳱ 1 is consistent with the Holmes-Smyth (1972) proposal, in which the transactions demand for money is specified to be a function of consumer expenditure. Equation (3) describes the interest rate parity as domestic bonds and foreign bonds are perfect substitutes. Equation (4) states that government spending is entirely financed by tax revenue along the lines of Rodriguez (1979), Sachs (1980), and Chang and Lai (1992).7 3. The Long-Run Equilibrium and Dynamic Adjustment In this section, we start by discussing the stationary property of the system, and then examine the evolutionary behavior of the economy. Substituting Equation (4) into Equations (1) and (2), the resulting system can be solved for three endogenous variables: P, R, and E. At long-run equilibrium, P˙ ⳱ E˙ ⳱ 0 and P, R, and E are at their stationary levels, Pˆ, Rˆ, and Eˆ. Without loss of generality, it is assumed that initially P ⳱ P* ⳱ E ⳱ 1 throughout the paper. It is a straightforward task to obtain the following long-run relationships:
6
ˆ R/G ⳱0,
(5)
ˆ P/G ⳱ hL1C1/M ,
(6)
ˆ E/G ⳱ [hL1C1B2 ⳮ M(1 ⳮ C1)]/MB2 .
(7)
This assumption implies that the Marshall-Lerner condition is satisfied. As domestic output is kept at the full-employment level, our conclusions are robust even if the income tax rate is endogenous. 7
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The Specification of Money Demand Obviously, in response to a balanced fiscal expansion, the domestic interest rate remains intact and whether the domestic price and the exchange rate will change depends crucially on the specification of the money demand function. As conventional wisdom suggests, if money demand is a function of national income (h ⳱ 0), the domestic price stays put, and the domestic currency appreciates unambiguously in response to an increase in the balanced government budget. However, if money demand is a function of consumption expenditure (h ⳱ 1), the domestic price definitely rises, and the home currency may depreciate or appreciate depending on the relative strength between the impact effect of a balanced government spending in the goods market and the induced expenditure-switching effect of changes in domestic price resulting from the money market.8 The economic explanation for the above two extreme results is as follows. In the long run, the domestic interest rate is fixed from outside at the level of the foreign interest rate. Given that the interest rate is fixed, upon the shock of a balanced government purchase, the domestic price must remain intact to maintain the money market in equilibrium if the money demand is a function of full-employment national income. Due to the fact that both domestic interest rate and domestic price keep constant, the exchange rate thus will decrease to eliminate the excess demand in the goods market which comes from an expansion of the balanced government budget. On the other hand, if money demand is a function of consumption expenditure, following the balanced fiscal expansion, the domestic price must increase to instantaneously clear the money market. Thereafter, a rise in domestic price will result in a deterioration in the balance of trade via the expenditureswitching effect and create an excess supply pressure in the goods market. Meanwhile, a balanced fiscal expansion will directly create an excess demand pressure in the goods market. As a consequence, if the expenditureswitching effect dominates the impact effect of government spending, the balanced government purchases will lead to a currency devaluation. Other8 In long-run equilibrium, P˙ ⳱ E˙ ⳱ 0, it is clear from Equation (3) that Rˆ ⳱ R* is true. Substituting Rˆ ⳱ R* and Equation (4) into Equation (2) with h ⳱ 1, we have
ˆ P/G ⳱ L1C1/M 0 . Similarly, substituting Rˆ ⳱ R* and Equation (4) into Equation (1) with h ⳱ 1, in response to a balanced fiscal expansion it follows that ˆ ˆ B2 • E/G ⳱ ⳮ(1 ⳮ C1) Ⳮ B2 • P/G 0. Obviously, the first term of the RHS in the above equation is the impact effect of a balanced fiscal expansion in the goods market, and the second term is exactly the induced expenditureswitching effect of changes in domestic price coming from the money market.
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Wen-Ya Chang and Ching-Chong Lai wise, the balanced government expansion will result in an appreciation of home currency. We now proceed to analyze the dynamic behavior of the economy. Substituting Equation (4) into Equations (1) and (2) and manipulating the resulting equations, we have the following two differential equations: E˙ ⳱ H(E, P, G) ,
(8)
P˙ ⳱ J(E, P, G) ,
(9)
where H1 ⳱ E˙/E ⳱ 0, H2 ⳱ E˙/P ⳱ ⳮM/L2 0, H3 ⳱ E˙/G ⳱ hL1C1/L2 ⱕ 0, J1 ⳱ P˙/E ⳱ pB2 0, J2 ⳱ P˙/P ⳱ ⳮp(MI1/L2 Ⳮ B2) 0, J3 ⳱ P˙/G ⳱ p(1 ⳮ C1 Ⳮ hI1L1C1/L2) 0. Let k be the characteristic root of the dynamic system and linearize the system around the steady-state equilibrium. It gives the following characteristic equation: k2 ⳮ (H1 Ⳮ J2) • k Ⳮ (H1 J2 ⳮ J1H2) ⳱ 0 .
(10)
Since H1 J2 ⳮ J1H2 ⳱ pB2M/L2 0, the two characteristic roots of the dynamic system will be of opposite signs, implying that the system exhibits the saddlepoint stability which is common to rational expectations and perfect foresight models. For expository convenience, we assume that k1 0 k2. It follows from Equations (8) and (9) that the general solution for E and P is9 ˆ E ⳱ E(G) Ⳮ A1 exp(k1t) Ⳮ A2 exp(k2t) ,
(11)
ˆ P ⳱ P(G) Ⳮ (k1/H2)A1 exp(k1t) Ⳮ (k2/H2)A2 exp(k2t) ,
(12)
where A1 and A2 are unknown parameters. The evolution of the exchange rate and the domestic price can be illustrated by a diagram similar to those used by Dornbusch (1976) and Frenkel and Rodriguez (1982). From Equations (8) and (9) it is clear that the slopes of loci E˙ ⳱ 0 and P˙ ⳱ 0 are P/E|E⳱0 ⳱0, ˙ 1 P/E|P⳱0 ⳱ ⳮJ1/J2 0 . ˙ 9
84
See, for example, Gandolfo (1980, 263–65).
(13) (14)
The Specification of Money Demand
Figure 1.
As indicated by the direction of the arrows in Figure 1, the lines SS and UU represent the stable and unstable branches, respectively. Evidently, the convergent saddle path SS is always downward sloping, while the divergent branch UU is always upward sloping and must be flatter than the P˙ ⳱ 0 locus. We now analyze the dynamic behavior of the economy, in which at time t ⳱ 0 the fiscal authorities announce the government spending constrained by a balanced budget will increase from G0 to G1 at a specific date t ⳱ T in the future. First, we discuss the case that the money demand is a function of national income rather than consumption expenditure (h ⳱ 0). In Figure 2, the initial equilibrium, where E˙ ⳱ 0 intersects P˙ ⳱ 0(G0), is at Q0; the initial exchange rate and domestic price are E0 and P0, respectively. 85
Wen-Ya Chang and Ching-Chong Lai
Figure 2.
Upon the shock of an anticipated permanent increase in a balanced government spending, E˙ ⳱ 0 remains intact, while P˙ ⳱ 0(G0) shifts upward to P˙ ⳱ 0(G1),10 and intersects at point Q , with E and P being Eˆ and P0, * respectively. Before we proceed with the analysis, three points should be noted. First, for expository convenience, in what follows 0Ⳮ denotes the instant Given that h ⳱ 0, it is clear from Equations (8) and (9) that
10
P/G|E⳱0 ⳱0, ˙ P/G|P⳱0 ⳱ (1 ⳮ C1)/(I1M/L2 Ⳮ B2) 0 . ˙
86
The Specification of Money Demand after the announcement made by the authorities, and Tⳮ and TⳭ denote the instant before and after policy implementation, respectively. Second, during the dates between 0Ⳮ and Tⳮ, the government spending with a balanced budget remains intact and the point Q0 should be treated as the reference point to govern the dynamic adjustment. Third, since the public becomes aware that a balanced fiscal policy will increase from G0 to G1 at the moment of TⳭ, the economy should move to a point exactly on the stable arm SS at that instant of time in order to ensure the system to be convergent. Based on this information, at the instant of anticipated fiscal announcement, the domestic currency will at once appreciate from E0 to E0Ⳮ, while the domestic price remains intact at the level of P0 because it adjusts with a lag. In consequence, the economy will jump from the point Q0 to Q0Ⳮ on impact. Since the point Q0Ⳮ lies horizontally to the west of the point Q0, from 0Ⳮ to Tⳮ, as arrows indicate, both E and P will continue to decrease, and the economy will move from Q0Ⳮ to QT. At time TⳭ, the balanced fiscal expansion has been enacted and the economy exactly reaches the point QT on the convergent stable path SS. Thereafter, from TⳭ onwards, the exchange rate will continue to fall and the domestic price will turn to rise as the economy moves along the SS curve towards its new long-run equilibrium Q . This * result is exactly the dynamic Mundell result and is parallel to that of Daniel (1989) with certainty. We now turn to examine the case in which the money demand is a function of consumption expenditure (h ⳱ 1). Again, the economy is at Q0 initially in Figures 3 and 4. In response to an anticipated balanced fiscal expansion, both E˙ ⳱ 0(G0) and P˙ ⳱ 0(G0) shift upward to E˙ ⳱ 0(G1) and P˙ ⳱ 0(G1), but the relative extent of movements is uncertain.11 Figure 3 corresponds to the situation where the E˙ ⳱ 0 schedule shifts upward by more than P˙ ⳱ 0 does, and Figure 4 illustrates the opposite situation where the vertical movement of E˙ ⳱ 0 curve is smaller than that of P˙ ⳱ 0. In Figure 3, E˙ ⳱ 0(G1) and P˙ ⳱ 0(G1) intersect at point Q and the * new stationary value of exchange rate, Eˆ, is greater than the initial level, E0. Following the same consideration and illustration as those in Figure 2, at Given that h ⳱ 1, it is obvious from Equations (8) and (9) that
11
P/G|E⳱0 ⳱ L1C1/M 0 , ˙ P/G|P⳱0 ⳱ (1 ⳮ C1 Ⳮ I1L1C1/L2)/(I1M/L2 Ⳮ B2) 0 . ˙ Then, a comparison of the above relationships gives P/G|P⳱0 ⳮ P/G|E⳱0 ⳱ [M(1 ⳮ C1) ⳮ L1C1B2]/M(I1M/L2 Ⳮ B2) 0 ˙ ˙ as (1 ⳮ C1) L1C1B2/M .
87
Wen-Ya Chang and Ching-Chong Lai
Figure 3.
the instant of anticipated fiscal announcement, the domestic currency immediately depreciates from E0 to E0Ⳮ, while the domestic price stays put because it adjusts with a lag. Consequently, the economy will jump from Q0 to Q0Ⳮ on impact. Since the point Q0Ⳮ lies horizontally to the east of the point Q0, from 0Ⳮ to Tⳮ, as arrows indicated in Figure 3, both E and P continue to increase, and the economy will move from Q0Ⳮ to QT. At time TⳭ, as the balanced fiscal expansion has been implemented, the economy arrives at the point QT on the stable arm SS. Thereafter, from TⳭ onwards, E decreases and P continues to increase, and the economy then moves along SS to reach the new stationary state Q*. Obviously, this adjustment pattern 88
The Specification of Money Demand of exchange rate in response to a fiscal expansion is equivalent to that of Gray and Turnovsky (1979) and Wilson (1979) for a monetary expansion, and runs in sharp contrast with the existing literature on exchange-rate dynamics associated with anticipated fiscal expansion. On the other hand, the situation where the vertical shift of E˙ ⳱ 0 is less than that of P˙ ⳱ 0 is depicted in Figure 4. As indicated in the figure, the new steady-state value of exchange rate, Eˆ, is smaller than the initial value, E0. Moreover, according to the long-run properties of Equations (6) and (7) with h ⳱ 1, the slope of the line connecting the old stationary state (Q0) and the new steady state (Q ) is * ˆ ˆ P/E|Q0Q* ⳱ (P/G)/(E/G) ⳱ L1C1B2/[L1C1B2 ⳮ M(1 ⳮ C1)] 0 .
(15)
In addition, it follows from Equations (11) and (12) that the slope of stable arm SS which corresponds to A2 ⳱ 0 is P/E|SS ⳱ k1/H2 0 .
(16)
Equipped with the information of Equations (15) and (16), two cases may happen: |P/E|SS| |P/E|Q0Q*| .
(17)
Figure 4(a) corresponds to the situation where the line connecting the longrun equilibrium states is steeper than the stable arm; while Figure 4(b) portrays the situation where the line connecting the long-run equilibrium states is flatter than the convergent stable path. In Figure 4(a), the initial equilibrium is at point Q0 and the initial exchange rate and domestic price are E0 and P0, respectively. Upon the shock of anticipated permanent increase in the balanced government spending, the domestic currency instantaneously depreciates from E0 to E0Ⳮ, while the domestic price is unchanged. As a consequence, the economy jumps from Q0 to Q0Ⳮ on impact. Since the point Q0Ⳮ lies horizontally to the east of the point Q0, from 0Ⳮ to Tⳮ, as arrows indicated in Figure 4(a), both E and P continue to increase and the economy moves from Q0Ⳮ to QT. At time TⳭ, as the balanced fiscal expansion has been carried out, the economy arrives at the point QT on the convergent stable path SS. Thereafter, from TⳭ onwards, E decreases and P continues to increase, and the economy then moves along SS to reach the new long-run equilibrium Q*. Evidently, this adjustment pattern of exchange rate is entirely consistent with Aoki’s (1985) definition of misadjustment: the direction of impact response is opposite to 89
Wen-Ya Chang and Ching-Chong Lai
Figure 4(a).
that of the long-run response; the adjustment of exchange rate during dates between 0Ⳮ and Tⳮ moves further away from its new equilibrium value. On the other hand, Figure 4(b) corresponds to the case that the line linking the long-run equilibrium states is flatter than the convergent stable path. Following a similar description in Figure 4(a), at the instant 0Ⳮ, the domestic currency appreciates at once from E0 to E0Ⳮ, while the domestic price remains intact. Consequently, the economy will jump from Q0 to Q0Ⳮ on impact. Since Q0Ⳮ lies horizontally to the west of the point Q0, from 90
The Specification of Money Demand
Figure 4(b).
0Ⳮ to Tⳮ, as arrows indicate, both E and P continue to decrease, and the economy will move from Q0Ⳮ to QT. At the moment of fiscal expansion, the economy reaches the point QT on the stable arm SS. Thereafter, from TⳭ onwards, as E continues to fall and P turns to rise, the economy moves along SS toward the new steady state Q*. Therefore, following an anticipated fiscal shock, the exchange rate undershoots on impact and then continues to decrease until its long-run equilibrium value, Eˆ, is reached. The above graphical analyses [Figures 4(a) and 4(b)] tell us that, even though the dynamic system is characterized by the saddlepoint stability, the misadjustment phenomenon will arise if the line connecting the long-run equilibrium states is steeper than the stable arm. This conclusion runs in 91
Wen-Ya Chang and Ching-Chong Lai contrast with Aoki’s (1985) result, which claims that the misadjustment can occur only when the economy is characterized by the global instability.
4. Dynamics with Adaptive Expectations In order to highlight the role played by exchange-rate expectations, this section turns to examine how the economy will respond when exchangerate expectations are formed adaptively instead of rationally.12 Let Ee be the expected exchange rate. The interest rate parity stated in Equation (3) can be expressed as R ⳱ R* Ⳮ (Ee ⳮ E)/E .
(3a)
If perfect foresight is assumed for exchange-rate expectations, (Ee ⳮ E)/E equals E˙/E. Now in the case of adaptive expectations, the expectations mechanism displays the following manner: E˙ e ⳱ b(E ⳮ Ee) .
(18)
Equation (18) states that, if the current exchange rate exceeds the expected exchange rate, market participants will revise upward their expectations about the future exchange rate (Levin 1994). As a consequence, Equations (1), (2), (3a), (4) and (18) constitute the whole picture of the economy under adaptive expectations. Since the interest rate, R, and the exchange rate, E, adjust freely to maintain the asset markets in equilibrium, Equations (2) and (3a) must hold at any point of time. Solving Equations (2) and (3a) with (4) for R and E, given E ⳱ 1 and Ee ⳱ E initially, we obtain the reduced forms: R ⳱ f(P, G) ,
(19)
E ⳱ h(Ee, P, G) ,
(20)
where f1 ⳱ ⳮM/L2 0, f2 ⳱ hL1C1/L2 ⱕ 0, h1 ⳱ 1, h2 ⳱ M/L2 0, h3 ⳱ ⳮ hL1C1/L2 ⱖ 0. It is obvious from Equation (20) that in response to a balanced fiscal expansion, the specification of the money demand function is also the key factor to determine whether the exchange rate will respond on impact. More specifically, if money demand is a function of national income (h ⳱ 0), the exchange rate remains intact in response to a balanced fiscal expansion. This result is consistent with Levin’s (1994, 53) finding. 12
This section was suggested by an anonymous referee, to whom we are grateful.
92
The Specification of Money Demand However, if money demand is a function of consumption expenditure (h ⳱ 1), the home currency will definitely depreciate in response to an increase in the balanced government budget. This finding contrasts with the Levin (1994) conclusion. Before we proceed to deal with dynamics of the economy, three points should be noted. First, the long-run equilibrium requires P˙ ⳱ E˙e ⳱ 0 (hence Eˆe ⳱ Eˆ), and the long-run equilibrium under adaptive expectations is the same as that under perfect foresight. Accordingly, the comparative-static results of Equations (5)–(7) can be applied to the case of adaptive expectations. Second, as the main focus of the analysis is on dynamics of spot exchange rate E rather than expected exchange rate Ee, we have to convert E˙e into E˙. Third, with adaptive expectations the expected exchange rate is backward looking in nature; we thus cannot deal with the problem of anticipated fiscal expansion. As a result, we turn to discuss an unanticipated permanent increase in government spending instead of an anticipated one in this section. Now we start to examine the dynamic feature of the economy under adaptive expectations. Substituting Equation (18) into Equation (3a), we have R ⳱ R* ⳮ E˙ e/bE .
(21)
Since the interest rate parity will hold at all times, differentiating Equation (3a) with respect to time, we yield R˙ ⳱ E˙ e ⳮ E˙ .
(22)
Combining Equation (21) with Equation (22) gives ˙ R ⳱ R* ⳮ (R˙ Ⳮ E)/bE .
(23)
Due to the fact that the money market also holds at any instant of time, differentiating Equation (2) with respect to time, we obtain ˙ 2. R˙ ⳱ ⳮMP/L
(24)
Substituting Equation (24) into Equation (23) and rearranging the resulting equation, we have ˙ ⳱ bR* ⳮ bR Ⳮ MP/L ˙ 2E . E/E
(25)
Finally, substituting Equation (19) into Equations (25) and (1) and manip93
Wen-Ya Chang and Ching-Chong Lai ulating the resulting equations, we have the following two differential equations: E˙ ⳱ H*(E, P, G) , P˙ ⳱ J(E, P, G) ,
(26) (9)
˙ where H*1 ⳱ E˙/E ⳱ pMB2/L2 0, H* 2 ⳱ E/P ⳱ M[b ⳮ p(MI1/L2 ˙ Ⳮ B2)]/L2 0, H* 3 ⳱ E/G ⳱ [Mp(1 ⳮ C1 Ⳮ hI1L1C1/L2) ⳮ hbL1C1]/ L2 0, and J1, J2, and J3 are identical to those in the previous section. Let be the characteristic root of the dynamic system and linearize the system around the long-run equilibrium. We then have the following characteristic equation: 2 ⳮ (H*1 Ⳮ J2) Ⳮ (H*J 1 2 ⳮ J1H*) 2 ⳱ 0 .
(27)
It is clear from Equation (27) that H* 1 Ⳮ J2 0 and H*J 1 2 ⳮ J1H* 2 ⳱ ⳮbMJ1/ L2 0, which imply that both characteristic roots of the dynamic system are negative. The system exhibits a totally stable equilibrium. In addition, it is straightforward from Equation (27) that the evolution of the system will be non-cyclical if 2 X ⳱ (H*1 Ⳮ J2)2 ⳮ 4(H*J 1 2 ⳮ J1H*) 2 ⳱ (MJ1/L2 Ⳮ J2) Ⳮ 4bMJ1/L2 0 .
Conversely, if X 0, the adjustment path will be cyclical. Similarly, we also present a graphical analysis to illustrate the evolution of E and P in response to an unanticipated fiscal shock. As indicated in Equations (26) and (9), the slope of the curve P˙ ⳱ 0 is identical to that in the case of perfect foresight (Equation (14)); while the slope of the E˙ ⳱ 0 locus is P/E|E⳱0 ⳱ ⳮH*/H* ˙ 1 2 ⳱ ⳮJ1/( J2 Ⳮ b) 0 as b ⳮ J2 .
(28)
Moreover, it can be easily inferred that, if b ⳮJ2, X (MJ1/L2 ⳮ J2)2 0 is true. It implies that the adjustment exhibits a non-cyclical convergence to the steady-state equilibrium when the E˙ ⳱ 0 schedule has a positive slope. However, if b ⳮJ2, X has an ambiguous sign, which implies that the adjustment shows either non-cyclical or cyclical convergence to the stationary equilibrium. To save space, we only discuss the case of a positively sloped E˙ ⳱ 0 locus. In addition, we call the combinations of E and P that will keep the asset markets in equilibrium the AA curve. Given Ee and G, from Equation (20) the slope of the AA curve is 94
The Specification of Money Demand
Figure 5.
P/E|AA ⳱ 1/h2 0 .
(29)
Since the asset markets are cleared at all times, the economy is not allowed to deviate from the AA locus. First, we study the dynamic behavior of the economy in which the money demand is a function of national income (h ⳱ 0). In Figure 5, the initial equilibrium is at Q0, where the schedule of E˙ ⳱ 0(G0) intersects the P˙ ⳱ 0(G0) curve, and the AA(Ee0) curve passes through it; the initial exchange rate and domestic price are E0 and P0, respectively. In response to a fiscal expansion, curve AA(Ee0 ) remains intact, but both E˙ ⳱ 0(G0) and P˙ ⳱ 0(G0) will shift leftward with an equal magnitude to E˙ ⳱ 0(G1) and P˙ ⳱ 0(G1).13 E˙ ⳱ 0(G1) intersects P˙ ⳱ 0(G1) at point Q ,14 with E and P * It is evident from Equations (20), (26) and (9) with h ⳱ 0 that
13
95
Wen-Ya Chang and Ching-Chong Lai being Eˆ and P0, respectively. At the instant of a balanced fiscal expansion, the exchange rate and interest rate will stay put since the asset markets are not disturbed in Equations (19) and (20). In the meantime, an excess demand in the goods market will arise as a result of a balanced fiscal expansion. However, even there exists an excess demand on domestic goods, the price of domestic goods remains intact at the level of P0 because it adjusts with a lag. In consequence, the economy remains at the point Q0 on impact. At the next instant, the resultant excess demand in the goods market bids up the domestic price, which in turn causes the interest rate to rise and the exchange rate to fall. As arrows indicated in Figure 5, the economy moves northwestward from Q0 at the outset. Thereafter, the increased interest rate reduces investment and both the increased domestic price and decreased exchange rate lead to a shrinking trade balance. These induced effects hence combine to eliminate the excess demand in the goods market. Accordingly, whether the domestic price continues to rise depends on the direct effect of a fiscal expansion and the latter induced effects. At the beginning periods, as the fiscal expansion exerts larger effects than the latter, the domestic price continues to rise. When time goes by and the economy passes through the P˙ ⳱ 0(G1) curve, the direct effect of fiscal shock is outweighed by the induced effects, and the domestic price turns to decrease as a result of an excess supply of goods. Therefore, the economy turns to move southwestward to reach Q*. Next, we turn to discuss the case that the money demand is a function of consumption expenditure (h ⳱ 1). Again, the economy is at Q0 initially in Figures 6 and 7. Upon the shock of a balanced fiscal expansion, E˙ ⳱ 0(G0) will shift either rightward or leftward to E˙ ⳱ 0(G1). P˙ ⳱ 0(G0) unambiguously shifts left to P˙ ⳱ 0(G1).15 The AA(Ee0, G0) curve will definitely shift rightward to the AA(Ee0, G1) locus, but its movement may be either larger E/G|AA ⳱ h3 ⳱ 0 , E/G|E⳱0 ⳱ ⳮ(1 ⳮ C1)/B2 0 , ˙ E/G|P⳱0 ⳱ ⳮ(1 ⳮ C1)/B2 0 . ˙ In the long-run equilibrium, E˙e ⳱ 0 will be true and Eˆ ⳱ Eˆe will follow. As a consequence, the AA(Eˆe) schedule will pass through the point Q*. To simplify the figure, the AA(Eˆe) curve will not be drawn in Figure 5. Similarly, the final position of curve AA(Eˆe, G1) will not be shown in Figures 6 and 7 for the same reason. 15 Given that h ⳱ 1, from Equations (26) and (9) we have 14
E/G|E⳱0 ⳱ ⳮ[Mp(1 ⳮ C1 Ⳮ I1L1C1/L2) ⳮ bL1C1]/MpB2 0 ˙ if Mp(1 ⳮ C1 Ⳮ I1L1C1/L2) bL1C1 , E/G|P⳱0 ⳱ ⳮ(1 ⳮ C1 Ⳮ I1L1C1/L2)/B2 0 . ˙
96
The Specification of Money Demand
Figure 6.
or smaller than that of E˙ ⳱ 0 if the E˙ ⳱ 0 schedule shifts rightward.16 It is clear from Equation (20) with h ⳱ 1 that
16
E/G|AA ⳱ ⳮL1C1/L2 0 . When Mp(1 ⳮ C1 Ⳮ I1L1C1/L2) bL1C1, from footnote 15 we have E/G|E⳱0 0. ˙
97
Wen-Ya Chang and Ching-Chong Lai
Figure 7.
Figure 6 corresponds to the situation where the E˙ ⳱ 0 curve shifts rightward. However, to save space the movement of AA is smaller than that of E˙ ⳱ 0. Figure 7 describes the other situation where the E˙ ⳱ 0 locus shifts leftward and its horizontal movement is smaller than that of P˙ ⳱ 0.17 Then, a comparison of the above relationships gives E/G|E⳱0 ⳮ E/G|AA 0 ˙
if Mp[L1C1(B2 ⳮ I1)/L2 ⳮ (1 ⳮ C1)] Ⳮ bL1C1 0 .
17 If Mp(1 ⳮ C1 Ⳮ I1L1C1/L2) bL1C1 is true, from footnote 15 we can derive the following result:
|E/G|P⳱0 | |E/G|E⳱0 |. ˙ ˙
98
The Specification of Money Demand In Figure 6, E˙ ⳱ 0(G1) and P˙ ⳱ 0(G1) intersect at point Q and the * new long-run value of exchange rate, Eˆ, is greater than the initial level, E0. At the moment of a balanced fiscal expansion, the exchange rate at once increases and interest rate immediately decreases on impact so as to maintain the asset markets in equilibrium. Meanwhile, an increase in government spending, a rise in exchange rate, and a fall in interest rate lead to an excess demand in the goods market, but the domestic price is still at P0 since it adjusts with a lag. Consequently, the economy will jump from Q0 to a point on the AA(Ee0, G1) locus, Q0Ⳮ, on impact, as a result of a fiscal expansion. At the next instant, there are two conflicting channels to influence adjustment of the exchange rate: (i) since the current exchange rate exceeds the expected rate, the expected exchange rate will be revised to move upward, which causes the exchange rate to rise; and (ii) the resultant excess demand bids up the domestic price which leads to a fall in the exchange rate. Whether the exchange rate will increase depends on the relative strength of these channels.18 Apparently, the former will surmount the latter since the point Q0Ⳮ lies horizontally to the west on the E˙ ⳱ 0(G1) curve, and hence the exchange rate increases. As arrows indicated in Figure 6, the economy will continue to move northeastward from Q0Ⳮ towards the new steady state Q*. Therefore, in response to a balanced fiscal expansion, the exchange rate undershoots on impact and then continues to increase until its long-run equilibrium value, Eˆ, is reached, even if the public form their expectations with the adaptive manner.19 On the other hand, the situation where both loci E˙ ⳱ 0 and P˙ ⳱ 0 shift leftward and the horizontal shift of the former is smaller than the latter, is depicted in Figure 7. As indicated in the figure, the new steady-state value of exchange rate, Eˆ, is less than the initial value, E0. In addition, in response to an increase in the balanced government budget, the AA(Ee0, G0) curve shifts rightward to AA(Ee0, G1). Under such a situation, following a similar description as that in Figure 6, at the instant of a fiscal expansion, the exchange rate will at once rise from E0 to E0Ⳮ on impact, while the domestic price remains intact because it adjusts with a lag.20 In consequence, the economy will jump from the point Q0 to a point on the AA(Ee0, G1) locus, Q0Ⳮ, on impact. Since the point Q0Ⳮ lies horizontally to the east on the E˙ 18
It is clear from Equation (20) that E/Ee ⳱ h1 0 ,
E/P ⳱ h2 0. If the movement of AA is greater than that of E˙ ⳱ 0, the exchange rate may overshoot on impact in response to a balanced fiscal expansion; thereafter E first continues to decrease, and then turns to increase when the economy passes through the E˙ ⳱ 0(G1) curve. 20 The economic reasoning can imitate that of Figure 6; we do not repeat to save space. 19
99
Wen-Ya Chang and Ching-Chong Lai ⳱ 0(G1) schedule, as arrows indicate, E turns to decrease and P continues to increase, and the economy will move from Q0Ⳮ to Q .21 Therefore, in * response to a fiscal expansion, the exchange rate misjumps on impact and then continues to decrease until its long-run equilibrium value, Eˆ, is reached.
5. Concluding Remarks This paper first introduces the proposal of Holmes and Smyth (1972), namely, that the money demand function should be determined by consumer expenditure rather than national income, into the well-known Dornbusch (1976) model. Based on this framework, we first analyze how exchange rates adjust over time with perfect foresight, following an anticipated permanent increase in government spending with a balanced budget. It is found that, whether the domestic currency will depreciate or appreciate in response to a balanced-budget, fiscal expansion is sensitive to plausible specification in the money demand function. If the money demand is specified to be a function of national income, a balanced-budget fiscal expansion will definitely contribute an appreciation of the home currency. However, if the money demand is a function of consumption expenditure, a balanced fiscal expansion may lead to a currency depreciation or appreciation depending on the relative strength between the impact effect of a balanced fiscal expansion in the goods market and the induced expenditure-switching effect of changes in domestic price resulting from the money market. In addition, it is also found that the adjustment pattern of exchange rate in response to a balanced fiscal expansion may be misadjusting, even if the system exhibits the saddlepoint stability rather than the global instability as proposed by Aoki (1985, 1986b). Finally, if the public form their expectations with the adaptive manner, whether the home currency depreciates on impact in response to an increase in the balanced government budget also depends on a plausible specification in the money demand function. If the money demand is specified to be a function of national income, the home currency will remain intact on impact as a result of a balanced-budget fiscal expansion. However, if the money demand is a function of consumption expenditure, a balanced fiscal expansion definitely leads to a currency depreciation on impact. Received: April 1994 Final version: February 1996 21 The other possibility of dynamic adjustment is that E continues to decrease, while P first continues to rise, and then turns to decrease when the economy passes through the P˙ ⳱ 0(G1) schedule.
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The Specification of Money Demand References Ahtiala, Pekka. “A Note on Fiscal Policy under Flexible Exchange Rates.” European Economic Review 33 (September 1989): 1481–86. Aoki, Masanao. “Misadjustment to Anticipated Shocks: An Example of Exchange-Rate Response.” Journal of International Money and Finance 4 (September 1985): 415–20. ———. “Dynamic Adjustment Behaviour to Anticipated Supply Shocks in a Two-Country Model.” Economic Journal 96 (March 1986a): 80–100. ———. “Effects of Anticipated Central Bank Actions on Tobin’s Q, Share Prices and Exchange Rate in a Small Open Economy.” European Economic Review 30 (April 1986b): 285–304. Carlton, Dennis W. “The Rigidity of Prices.” American Economic Review 76 (September 1986): 637–58. Chang, Wen-ya, and Ching-chong Lai. “The Role of Supply-Side Effect of Taxes on the Balanced Budget Multiplier.” Public Finance/Finances Publiques 47 (1992): 185–92. Daniel, Betty C. “One-Sided Uncertainty about Future Fiscal Policy.” Journal of Money, Credit, and Banking 21 (May 1989): 176–89. Devereux, Michael B., and Douglas D. Purvis. “Fiscal Policy and the Real Exchange Rate.” European Economic Review 34 (September 1990): 1201–11. Dornbusch, Rudiger. “Expectations and Exchange Rate Dynamics.” Journal of Political Economy 84 (December 1976): 1161–76. Frenkel, Jacob A., and Carlos A. Rodriguez. “Exchange Rate Dynamics and the Overshooting Hypothesis.” IMF Staff Papers 29 (March 1982): 1–30. Gandolfo, Giancarlo. Economic Dynamics: Methods and Models. Amsterdam: North-Holland, 1980. Gray, Malcolm R., and Stephen J. Turnovsky. “The Stability of Exchange Rate Dynamics under Perfect Myopic Foresight.” International Economic Review 20 (October 1979): 643–60. Holmes, James M., and David J. Smyth. “The Specification of the Demand for Money and the Tax Multiplier.” Journal of Political Economy 80 (January/February 1972): 179–85. Levin, Jay H. “Fiscal Policy, Expectations, and Exchange-Rate Dynamics.” Review of International Economics 2 (February 1994): 50–61. Mankiw, N. Gregory, and Lawrence H. Summers. “Money Demand and the Effects of Fiscal Policies.” Journal of Money, Credit, and Banking 18 (November 1986): 415–29. Marion, Nancy P. “The Exchange-Rate Effects of Real Disturbances with Rational Expectations and Variable Terms of Trade.” Canadian Journal of Economics 15 (February 1982): 104–18. Marselli, Riccardo, and Marco Vannini. “The Holmes-Smyth Effect: Some 101
Wen-Ya Chang and Ching-Chong Lai Preliminary Exercises with the UK Demand for Narrow Money.” Applied Economics 20 (June 1988): 711–20. Meese, Richard A. “Is the Sticky Price Assumption Reasonable for Exchange Rate Models?” Journal of International Money and Finance 3 (August 1984): 131–39. Mundell, Robert A. “Capital Mobility and Stabilization Policy under Fixed and Flexible Exchange Rates.” Canadian Journal of Economics and Political Science 29 (November 1963): 475–85. Purvis, Douglas D. “Wage Responsiveness and the Insulation Properties of a Flexible Exchange Rate.” In Inflation and Employment in Open Economies, edited by Assar Lindbeck, 225–45. New York: North-Holland, 1979. Rodriguez, Carlos A. “Short- and Long-Run Effects of Monetary and Fiscal Policies under Flexible Exchange Rates and Perfect Capital Mobility.” American Economic Review 69 (March 1979): 176–82. Rotemberg, Julio J. “Sticky Prices in the United States.” Journal of Political Economy 90 (December 1982): 1187–1211. Sachs, Jeffrey. “Wages, Flexible Exchange Rates, and Macroeconomic Policy.” Quarterly Journal of Economics 94 (June 1980): 731–47. Smith, Marlene A., and David J. Smyth. “Choosing among Multiple Nonlinear Non-nested Regression Models with Different Dependent Variables.” Economics Letters 34 (October 1990): 147–50. ———. “Multiple and Pairwise Non-nested Tests of the Influence of Taxes on Money Demand.” Journal of Applied Econometrics 6 (January/March 1991): 17–30. Sumner, Michael. “The Policy Implications of Deflationary Tax Cuts.” Applied Economics 22 (June 1990): 719–22. ———. “Leakages from the Money Demand Function.” Applied Economics 23 (March 1991): 531–34. Wilson, Charles A. “Anticipated Shocks and Exchange Rate Dynamics.” Journal of Political Economy 87 (June 1979): 639–47.
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