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

• Author: Chang, Wen-Ya

1. 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.

2. 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.

3. 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)...