Anticipated shocks and the acceleration hypothesis: the implication of wage indexation.

Lai, Ching-Chong

I. Introduction

In his well cited contribution, Sachs [14] sets up a macromodel embodying the wage setting process, perfect foresight, and the portfolio balance feature. It examines the exchange-rate and current-account responses to unanticipated fiscal expansion under alternative wage indexation rules. He finds that, in the nominal wage rigidity (no wage indexation) model, the exchange-rate depreciation coincides with a current account deficit; in the real-wage rigidity (full wage indexation) case, the exchange rate again depreciates with a current-account deficit and appreciates with a surplus [14, 744-45].(1) Sachs's result is consistent with Kouri's [12] acceleration hypothesis: a current-account deficit is accompanied by currency depreciation, and conversely.

After the publication of the Dornbusch and Fischer [8] paper, the literature on acceleration hypothesis has shifted from unanticipated shocks to anticipated shocks. Dornbusch and Fischer [8] find that a negative correlation between the exchange rate and the current account prevails prior to the implementation of anticipated shocks. Consequently, their conclusion indicates the acceleration hypothesis is not held when the economy experiences anticipated shocks. Bhandari [4] and Papell [13] claim that the status of current account and the response of exchange rate can have either a positive or a negative correlation in response to anticipated shocks. Based on the fact that Sachs [14] does not deal with the anticipated disturbances, the first purpose of this paper thus tries to shed light on whether the alternative wage indexation schemes will affect the validity of the acceleration hypothesis in response to an anticipated fiscal expansion.

In an interesting paper, Aoki [1] bases on the modified Dornbusch [7] model and 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 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 opposite direction; (ii) the response of exchange rate during some beginning periods moves further away from its eventual new equilibrium value.(2) Aoki [1] further claims that two requirements should be satisfied to establish 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 [1, 415-6].(3) Based on Sachs' [14] framework, the second purpose of this paper is to show that even if the model exhibits a saddlepoint stability rather than the global instability proposed by Aoki [1], the misadjustment pattern of exchange rate can be observed in response to an anticipated fiscal expansion.

The rest of the paper is organized as follows. The structure of the Sachs [14] model is outlined in section II. Section III will present a complete dynamic adjustment under alternative wage indexation rules. Finally, section IV will give the concluding remarks.

II. The Sachs Model

The Sachs [14] model can be summarized as follows. Consider an open economy that is "small" enough to regard the foreign price and interest rate as exogenously determined. Domestic production is limited to a single final commodity, which is partly consumed domestically and partly exported. Domestic consumers have access to both domestic good and imported good. These goods are regarded by domestic residents as imperfect substitutes. Three assets are available to domestic residents: domestic money, domestic bonds, and foreign bonds. The latter two are regarded as perfect substitutes. Market participants form their expectations with perfect foresight. Accordingly, the economy can be characterized by the following macroeconomic relationships:

q = -[Alpha](w - [p.sub.c]) + (1 - [Lambda])[Alpha] [Pi]; [Alpha] [is greater than] 0, 0 [is less than] [Lambda] [is less than] 1 (1)

w = [w.sub.0] + [Theta] [p.sub.c]; (2)

q = [[Gamma].sub.1]D* + [[Gamma].sub.2]g + [[Gamma].sub.3]T; [[Gamma].sub.1], [[Gamma].sub.2], [[Gamma].sub.3] [is greater than] 0 (3)

T = -[[Theta].sub.1]q + [[Theta].sub.2]q* - [[Theta].sub.3]7[Pi]; [[Theta].sub.1], [[Theta].sub.2], [[Theta].sub.3] [is greater than] 0 (4)

m - p = [Phi]q - bR + [Delta]D*; [Phi], b, [Delta] [is greater than] 0 (5)

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

[Pi] = p - p* - e (8)

[p.sub.c] = [Lambda]p - (1 - [Lambda])(p* + e) (9)

where q = output, w = nominal wage, [p.sub.c] = general price level, [Pi] = terms of trade, [w.sub.0] = minimum wage (or contract wage), [Theta] = the degree of wage indexation, D* = nominal stock of foreign bonds (denominated in foreign currency), g = government spending, T = trade balance, q* = foreign output, m = nominal money supply, p = domestic price level, R = domestic interest rate, R* = foreign interest rate, p* = foreign prices of imported goods, e = exchange rate (defined as the domestic currency price of foreign currency), lower-case letters denote logarithms of upper-case variables, and an overdot denotes the rate of change with respect to time.

Equation (1) is the aggregate supply function. Equation (2) describes alternative forms of wage indexation scheme. If there is no wage indexation ([Theta] = 0), nominal wages are rigid at [w.sub.0]. If nominal wages are fully indexed to the general price ([Theta] = 1), real wages are fixed at [w.sub.0].(4) Equations (3) and (4) describe the aggregate demand function and the trade balance, respectively. Equation (5) is the equilibrium condition for the money market. Equation (6) describes the interest rate parity as domestic bonds and foreign bonds are perfect substitutes. Equation (7) states that domestic holdings of foreign bonds will change over time in response to the current-account balance, which is the sum of the trade balance and the service balance. Equation (8) is the definition of terms of trade. Finally, equation (9) defines the general price to be a multiplicatively weighted average of the price of domestic and imported goods.

III. Dynamic Adjustment

This section deals with the interaction between the dynamics of anticipated fiscal expansion and the current account balance with alternative wage indexation schemes.

We now proceed to analyze the dynamic behavior of the economy. Following Sachs [14], linearize equation (7) around T = D* = 0, [Mathematical Expression Omitted] and E = P = 1 initially and manipulate the resulting equation and equations (1)-(6), (8) and (9), it obtains(5)

[Mathematical Expression Omitted]

where

[a.sub.11] = {[Alpha][Theta](1 - [Lambda])(1 + [[Gamma].sub.3][[Theta].sub.1]) + [[Gamma].sub.3][[Theta].sub.3][1 + [Alpha][Phi](1 - [Theta])]}/b[Delta] [is greater than] 0,

[a.sub.12] = ([[Gamma].sub.1] + [Delta][Delta] + [Omega][Phi][[Gamma].sub.1])/b[Delta] [is greater than] 0,

[a.sub.21] = [Alpha](1 - [Theta])[[Theta].sub.3]/[Delta] [is greater than or equal to] 0,

[a.sub.22] = R* - ([Omega][[Theta].sub.1] + [[Theta].sub.3])[[Gamma].sub.1]/[Delta] [is greater than or less than to] 0,

[c.sub.1] = [[Gamma].sub.2](1 + [Phi][Omega])/b[Delta] [is greater than] 0, and

[c.sub.2] = -([Omega][[Phi].sub.1] + [[Theta].sub.3])[[Gamma].sub.2]/[Delta] [is less than] 0,

[Omega] = [Alpha][(1 - [Theta])[Lambda] + (1 - [Lambda])] [is greater than] 0, and

[Delta] = [[Gamma].sub.3][[Theta].sub.3] + (1 + [[Gamma].sub.3][[Theta].sub.1])[Omega] [is greater than] 0.

In what follows, we will show that the sign of [a.sub.21] is currently related to the degree of wage indexation [Theta], and in turn generates a distinctive match between the current-account balance and the exchange-rate adjustment, which is not presented in the literature.(6)

Let S be the characteristic root of the dynamic system, we then have the following characteristic equation:

[S.sup.2] - ([a.sub.11] + [a.sub.22])S + ([a.sub.11][a.sub.22] - [a.sub.12][a.sub.21]) = 0. (11)

Since the exchange rate is a forward-looking variable, and the stock of foreign bonds is a stock variable and will accumulate or decumulate over time through the current-account surplus or deficit, it is necessary to assume [S.sub.1][S.sub.2] = [a.sub.11][a.sub.22] - [a.sub.12][a.sub.21] [is less than] 0 for the system to be convergent.(7) This implies that the system displays the saddle-point stability which is common to perfect foresight models. Due to the fact that the wage indexation scheme will contribute different adjustment patterns of exchange rate and current account behavior, in what follows we will in turn examine the adjustment process to a current announcement of a future increase in government spending under alternative wage indexation rules.

Full Wage Indexation

Under full wage indexation ([Theta] = 1), it is clear from equation (10) that [S.sub.1] = 1/b [is greater than] 0, [S.sub.2] = R* - [[Alpha][[Theta].sub.1](1 - [Lambda]) + [[Theta].sub.3]][[Gamma].sub.1]/[[[Gamma].sub.3][[Theta].sub.3] + [Alpha](1 - [Lambda])(1 + [[Gamma].sub.3][[Theta].sub.1])] [is less than] 0 which is required for the stability. The evolution of the system can be illustrated by means of a phase diagram like Figure 1. It is obvious from equation (10) that the slopes of loci [Mathematical Expression Omitted] and [Mathematical Expression Omitted] with [Theta] = 1 are

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

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 and must be flatter than the [Mathematical Expression Omitted] locus, while the divergent branch UU coincides with the [Mathematical Expression Omitted] schedule.

We now study the adjustment process of the economy, in which at time t = 0 the authorities announce the government spending will increase from [g.sub.0] to [g.sub.[Tau]] at a specific date t = [Tau] in the future. In Figures 2(a) and 2(b), the initial equilibrium, where [Mathematical Expression Omitted] intersects [Mathematical Expression Omitted], is at [K.sub.0]; the initial exchange rate and foreign bonds stock are [e.sub.0] and [D*.sub.0], respectively. Upon the shock of anticipated fiscal expansion, both [Mathematical Expression Omitted] and [Mathematical Expression Omitted] shift leftwards to [Mathematical Expression Omitted] and [Mathematical Expression Omitted], but the [Mathematical Expression Omitted] schedule shifts by more than [Mathematical Expression Omitted] shifts.(8) The new long-run equilibrium is at point K*, and the new stationary value of exchange rate, [Mathematical Expression Omitted], is greater than [e.sub.0], while the new stationary value of foreign bonds stock, [Mathematical Expression Omitted], is smaller than [D*.sub.0].(9) As a consequence, the line connecting the old steady state ([K.sub.0]) and the new steady state ([K.sub.*]), namely the LL schedule, is always downward sloping. In addition, the stable arm SS is also downward sloping from Figure 1. Accordingly, two cases may happen.(10) Figure 2(a) corresponds to the situation where the LL line is flatter than the stable arm; while Figure 2(b) portrays the situation where the LL line is steeper than the convergent stable path.

Before we proceed with the analysis, three points should be noted. First, for expository convenience, in what follows 0+ denotes the instant after the announcement made by the authorities, and [Tau]- and [Tau]+ denote the instant before and after policy implementation, respectively. Second, during the dates between 0+ and [Tau]-, the government spending remains intact and the point [K.sub.0] should be treated as the reference point to govern the dynamic adjustment. Third, since the public become aware that the government spending will increase from [g.sub.0] to [g.sub.[Tau]] at the moment of [Tau]+, 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, in Figure 2(a), at the instant of anticipated fiscal announcement, the domestic currency will at once appreciate from [e.sub.0] to [e.sub.0]+, while the stock of foreign bonds is fixed because it is a predetermined variable. In consequence, the economy will jump from the point [K.sub.0] to [K.sub.0+] on impact. Since the point [K.sub.0+] lies vertically below the point [K.sub.0], from 0+ to [Tau]-, as arrows indicate, e will continue to decrease and D* stays put at [D*.sub.0], and the economy will move from [K.sub.0+] to [K.sub.[Tau]]. At time [Tau]+, a fiscal expansion has been enacted, the economy exactly reaches the point [K.sub.[Tau]] on the convergent stable path SS. Thereafter, from [Tau]+ onwards, the domestic currency turns to depreciate and the stock of foreign bonds decumulates as the economy moves along the SS curve towards its new long-run equilibrium K*. Evidently, this adjustment pattern of exchange rate is entirely consistent with Aoki's [1] definition on misadjustment: the direction of impact response is opposite to that of the long-run response; the adjustment of exchange rate during dates between 0+ and [Tau]- moves further away from its new long-run equilibrium value [Mathematical Expression Omitted].

On the other hand, Figure 2(b) corresponds to the case that the LL line is steeper than the convergent stable path. Following the similar description as that in Figure 2(a), at the instant 0+, the domestic currency will immediately depreciate from [e.sub.0] to [e.sub.0+], while the stock of foreign bonds keeps unchanged. Consequently, the economy will jump from the point [K.sub.0] to [K.sub.0+] on impact. Since the point [K.sub.0+] lies vertically above the point [K.sub.0], from 0+ to [Tau]-, as arrows indicate, e continues to increase and D* remains intact at [D*.sub.0], and the economy moves from [K.sub.0+] to [K.sub.[Tau]]. At the moment of fiscal expansion, the economy arrives at the point [K.sub.[Tau]] on the stable arm SS. Thereafter, from [Tau]+ onwards, e will continue to rise and the stock of foreign bonds decumulates, the economy thus moves along SS towards the new steady state. Therefore, in response to anticipated fiscal shock, the exchange rate undershoots on impact and then continues to increase until its long-run equilibrium value, [Mathematical Expression Omitted], is reached.

The above graphical analyses tell us that the anticipated fiscal expansion, which will ultimately depreciate the domestic currency, can initially lead to the combination of a balanced current account and a home currency appreciation (or depreciation). This neutral correlation between the exchange rate and the current account stands in contrast to the Kouri's acceleration hypothesis and the observation from Dornbusch and Fischer [8], Bhandari [4] and Papell [13]. Moreover, 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 flatter than the stable arm. This conclusion runs in sharp contrast with Aoki's [1] result, which claims that the misadjustment can occur only when the economy is characterized by the global instability.

No Wage Indexation

If there is no wage indexation ([Theta] = 0), it is evident from equation (10) that [a.sub.22] = R* - {[[Gamma].sub.1]([Alpha][[Theta].sub.1] + [Theta]3)/[[Gamma].sub.3][[Theta].sub.3] + [Alpha](1 + [[Gamma].sub.3][[Theta].sub.1])]} [is greater than or less than] 0 while [a.sub.11][a.sub.22] - [a.sub.12][a.sub.21] [is less than] 0 must be satisfied for the stability.(11) Due to the fact that whether [a.sub.22] is positive or negative, the anticipated fiscal expansion will generate similar adjustment patterns of relevant variables, following Sachs [14] we only discuss the situation where [a.sub.22] [is less than] 0.

The dynamic behavior of the system can be shown by a phase diagram like Figure 3. From equation (10), the slopes of loci [Mathematical Expression Omitted] and [Mathematical Expression Omitted] with [Theta] = 0 are

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

As indicated by the direction of the arrows in Figure 3, the lines SS and UU represent the stable and unstable paths, respectively. Apparently, the stable arm SS is always downward sloping and must be flatter than the [Mathematical Expression Omitted] schedule, while the unstable arm UU is always upward sloping and must be steeper than the [Mathematical Expression Omitted] locus.

We now investigate the dynamic adjustment of the economy in which the government spending is anticipated to expand in the future. In Figures 4(a) and 4(b), the initial equilibrium is at [K.sub.0], where [Mathematical Expression Omitted] intersects [Mathematical Expression Omitted]; the initial exchange rate and foreign bonds stock are [e.sub.0] and [D*.sub.0], respectively. In response to the fiscal shock, both [Mathematical Expression Omitted] and [Mathematical Expression Omitted] shift leftwards to [Mathematical Expression Omitted] and [Mathematical Expression Omitted], but the movement of [Mathematical Expression Omitted] loci is greater than that of [Mathematical Expression Omitted].(12) The new stationary equilibrium is at point [K.sub.*], and the new long-run value of exchange rate, [Mathematical Expression Omitted], is greater than [e.sub.0], while the new long-run value of foreign bonds stock, [Mathematical Expression Omitted], is smaller than [D*.sub.0].(13) Following the same analysis of full wage indexation, two cases may happen. Figure 4(a) depicts the situation where the LL line is flatter than the stable arm; while Figure 4(b) describes the opposite situation where the LL line is steeper than the convergent stable path.

In Figure 4(a), following the same illustration as that of Figure 2, at the instant of anticipated fiscal announcement, the domestic currency will instantaneously appreciate from [e.sub.0] to [e.sub.0+], while the stock of foreign bonds remains intact because it is a predetermined variable. As a consequence, the economy will jump from the point [K.sub.0] to [K.sub.0+] on impact. Since the point [K.sub.0+] lies vertically below the point [K.sub.0], from 0+ to [Tau]-, as arrows indicate, e will continue to fall and D* will continue to decrease, the economy will move from [K.sub.0+] to [K.sub.[Tau]]. At time [Tau]+, a fiscal expansion has been implemented, the economy arrives at the point [K.sub.[Tau]] on the convergent stable path SS. Thereafter, from [Tau]+ onwards, the domestic currency turns to depreciate and the stock of foreign bonds continues to decumulate as the economy moves along the SS curve towards its new long-run equilibrium [K.sub.*]. Obviously, an important feature of this adjustment pattern in response to an anticipated fiscal expansion is that an appreciation of domestic currency is coupled with a current-account deficit. This runs in sharp contrast with the acceleration hypothesis proposed by Kouri [12]. In addition, the evolutional pattern of exchange rate is exactly in conformity with Aoki's [1] definition on misadjustment.

In Figure 4(b), following the similar description as that in Figure 4(a), at the instant 0+, the domestic currency will immediately depreciate from [e.sub.0] to [e.sub.0+], while the stock of foreign bonds remains fixed. Consequently, the economy will jump from the point [K.sub.0] to [K.sub.0+] on impact. Since the point [K.sub.0+] lies vertically above the point [K.sub.0], from 0+ to [Tau]-, as arrows indicate, e continues to increase and D* continues to accumulate with the current-account surplus, and the economy moves from [K.sub.0+] to [K.sub.[Tau]]. At time [Tau]+, a fiscal expansion is carried out, the economy exactly reaches the point [K.sub.[Tau]] on the stable arm SS. Thereafter, from [Tau]+ onwards, the exchange rate keeps rising and the stock of foreign bonds turns to decumulate as the economy moves along the SS curve towards its new long-run equilibrium K*. Apparently, the adjustment pattern of a current-account surplus accompanying a currency devaluation prior to the policy implementation is again opposite to the acceleration hypothesis.

Why do alternative wage indexation rules lead to the sharp difference in the status of the current account and the behavior of the exchange rate prior to the implementation of fiscal expansion? This question can be illuminated by examining the current-account balance (equation (7) with (4)). Given that the economy is initially in equilibrium, the fiscal expansion is not as yet carried out and D* is a predetermined variable, full wage indexation will completely insulate the domestic output (q) and the terms of trade ([Pi]) from disturbances via exchange-rate adjustment. As a result, the trade balance (and hence the current account) is balanced regardless of the response of exchange rate to an expected fiscal expansion.(14) By contrast, no wage indexation will lead to a contraction (expansion) of domestic output and an increase (decrease) in [Pi] as the domestic currency appreciates (depreciates). As a consequence, the trade account (and hence the current account) ultimately runs into deficit (surplus) and results in a decumulation (accumulation) in the stock of foreign bonds.(15)

IV. Concluding Remarks

Based on the Sachs model, this paper has analyzed the evolutional behavior of exchange rate and current account in response to an anticipated fiscal expansion under alternative wage indexation schemes. Two central conclusions emerge from the analysis. First, Kouri's acceleration hypothesis which defines a current-account surplus (deficit) in association with a currency appreciation (depreciation) will not hold as the economy faces an anticipated fiscal disturbance. With full wage indexation, the balanced current account can associate with either currency appreciation or currency depreciation prior to the fiscal expansion. However, with no wage indexation, a current-account deficit (surplus) will couple with an appreciation (depreciation) of home currency. Second, the adjustment pattern of exchange rate in response to an anticipated fiscal expansion may be misadjusting, even if the system exhibits the saddlepoint stability rather than the global instability proposed by Aoki.

1. From the following graphical analyses in this paper, we can understand that an unanticipated fiscal expansion cannot possibly lead to the situation where the exchange-rate appreciation coincides with a current-account surplus in the real-wage rigidity case.

2. Aoki [2; 3] uses somewhat complicated models to derive the misadjusting pattern of exchange rate and of terms of trade.

3. Aoki [1,419] claimed in his footnote 2, "..., 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." In his other article, Aoki [3, 287] also made similar argument in footnote 4. In effect, however, we will show below that the misadjustment can arise in a model containing only one unstable eigenvalue.

4. Equations (1) and (2) can be justified by the behavior of firms, labor, and contract-setting developed by Gray [11] and Fischer [9]. The detailed derivations of similar equations are provided by Flood and Marion [10] for an open economy.

5. The procedure to derive equation (10) is as follows. First, substituting equations (2), (4), (8) and (9) into equations (1), (3) and (5), we have the following results:

q = [[Alpha][[Gamma].sub.3][[Theta].sub.3](1 - [Theta])e + [Omega][[Gamma].sub.1]D* + [Omega][[Gamma].sub.2]g]/[Delta],

p = {[[[Gamma].sub.3][[Theta].sub.3] + [Alpha][Theta](1 - [Lambda])(1 + [[Gamma].sub.3][[Theta].sub.1])]e + [[Gamma].sub.1]D* [[Gamma].sub.2]g}/[Delta],

R = {{[Alpha][Theta](1 - [Lambda])(1 + [[Gamma].sub.3][[[Theta].sub.1]) + [[Gamma].sub.3][[Theta].sub.3][1 + [Alpha][Phi](1 - [Theta])]}e

+ ([[Gamma].sub.1] + [Delta][Delta] + [Omega][Phi][[Gamma].sub.1])D* + [[Gamma].sub.2](1 + [Phi][Omega])g}/b[Delta].

Then, as Sachs [14] does, linearizing equation (7) around T = D* = 0, [Mathematical Expression Omitted] and E = P = 1 initially and substituting the above equations into the resulting equation and equation (6), we will obtain equation (10) in the text.

6. The coefficient [a.sub.21] runs in sharp contrast with that of Sachs [14, 744]. More specifically, under full wage indexation ([Theta] = 1), [a.sub.21] = 0 will result. In addition, under zero wage indexation which associates with [Theta] = 0, although the sign of [a.sub.21] is the same as [b.sub.21] in Sachs' paper, the value of both coefficients is entirely different.

7. If [S.sub.1][S.sub.2] [is greater than] 0 is assumed, the system may be characterized by either two stable roots or two unstable roots. Obviously, the former leads that the number of stable roots is greater than the number of predetermined variables, and the analysis will involve the problem of nonuniqueness. The latter implies that the number of stable roots is less than the number of predetermined variables, and the perfect foresight equilibrium does not exist. See Burmeister [6] and Buiter [5] for a detailed discussion.

8. Given that stability condition requires [S.sub.2] [is less than] 0, it is clear from equation (10) with [Theta] = 1 that

[Mathematical Expression Omitted],

[Mathematical Expression Omitted].

Then, a comparison of the above relationships gives

[Mathematical Expression Omitted].

9. At the long-run equilibrium, [Mathematical Expression Omitted]. From equation (10) with [Theta] = 1 and [S.sub.2] [is less than] 0, we can easily derive the following long-run relationships:

[Mathematical Expression Omitted],

[Mathematical Expression Omitted].

10. The detailed mathematical derivations for dynamic adjustment are upon request from the authors.

11. It is clear from equation (10) with [Theta] = 0 that

[a.sub.11][a.sub.22] - [a.sub.12][a.sub.21] = [[Theta].sub.3][(R*[[Gamma].sub.3] - [[Gamma].sub.1])(1 + [Alpha][Phi]) - [Alpha][Delta]] /b[[Gamma].sub.3][[Theta].sub.3] + [Alpha](1 + [[Gamma].sub.3][[Theta].sub.1])] [is greater than or less than] 0

as

[(R*[[Gamma].sub.3] - [Gamma].sub.1])(1 + [Alpha][Phi]) - [Alpha][Delta]] [is greater than or less than] 0.

For ensuring the system to be convergent, [(R*[[Gamma].sub.3] - [[Gamma].sub.1])(1 + [Alpha][Phi]) - [Alpha][Delta]] [is less than] 0 must hold.

12. From equation (10) with [Theta] = 0, we have

[Mathematical Expression Omitted],

[Mathematical Expression Omitted].

Following similar procedure of footnote 8, we obtain

[Mathematical Expression Omitted]

13. At the long-run equilibrium, [Mathematical Expression Omitted]. Given that stability condition requires [(R*[[Gamma].sub.3] - [[Gamma].sub.1])(1 + [Alpha][Phi]) - [Alpha][Delta]] [is less than] 0, it is obvious from equation (10) with [Theta] = 0 that

[Mathematical Expression Omitted],

[Mathematical Expression Omitted].

14. Substituting equation (4) into equation (7) and recalling q and p from footnote 5, we have

[Mathematical Expression Omitted].

Obviously, under full wage indexation ([Theta] = 1), the above relationship will reduce to

[Mathematical Expression Omitted].

Since initially the combination of D* and g keeps the current account in equilibrium (i.e., [Mathematical Expression Omitted]), and g remains at its initial level prior to the implementation of fiscal expansion, [Mathematical Expression Omitted] must prevail during the dates between 0+ and [Tau]-.

15. If there is no wage indexation ([Theta] = 0), it is easily derived from equations (4) and (7) that

[Mathematical Expression Omitted].

Following the same illumination as the case of full wage indexation, [Mathematical Expression Omitted] is positively related to the adjustment of e.

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