International Macroeconomics and Finance: Theory and Empirical Methods Phần 10 pptx

11.2. A SECOND GENERATION MODEL 335

11.2 A Second Generation Model

In first-generation models, exogenous domestic credit expansion causes

international reserves to decline in order to maintain a constant money

supply that is consistent with the fixed exchange rate. A key feature

of second generation models is that they explicitly account for the pol￾icy options available to the authorities. To defend the exchange rate,

the government may have to borrow foreign exchange reserves, raise do￾mestic interest rates, reduce the budget deficit and/or impose exchange

controls. Exchange rate defense is therefore costly. The governmentís

willingness to bear these costs depend in part on the state of the econ￾omy. Whether the economy is in the good state or in the bad state

in turn depends on the publicís expectations. The government engages

in a cost-benefit calculation to decide whether to defend the exchange

rate or to realign.

We will study the canonical second generation model due to Obst￾feld [112]. In this model, the governmentís decision rule is nonlinear and

leads to multiple (two) equilibria. One equilibrium has low probability

of devaluation whereas the other has a high probability. The costs to

the authorities of maintaining the fixed exchange rate depend on the

publicís expectations of future policy. An exogenous event that changes

the publicís expectations can therefore raise the governmentís assess￾ment of the cost of exchange rate maintenance leading to a switch from

the low-probability of devaluation equilibrium to the high-probability

of devaluation equilibrium.

What sorts of market-sentiment shifting events are we talking about?

Obstfeld offers several examples that may have altered public expecta￾tions prior to the 1992 EMS crisis: The rejection by the Danish public

of the Maastrict Treaty in June 1992, a sharp rise in Swedish unem￾ployment, and various public announcements by authorities that sug￾gested a weakening resolve to defend the exchange rate. In regard to

the Asian crisis, expectations may have shifted as information about

over-expansion in Thai real-estate investment and poor investment al￾location of Korean Chaebol came to light.

336 CHAPTER 11. BALANCE OF PAYMENTS CRISES

Obstfeldís Multiple Devaluation Threshold Model

All variables are in logarithms. Let pt be the domestic price level and

st be the nominal exchange rate. Set the (log) of the exogenous foreign

price level to zero and assume PPP, pt = st. Output is given by a

quasi-labor demand schedule which varies inversely with the real wage

wt − st, and with a shock ut

iid

∼ N(0, σ2

u)

yt = −α(wt − st) − ut. (11.23)

Firms and workers agree to a rule whereby todayís wage was negotiated

and set one-period in advance so as to keep the ex ante real wage

constant

wt = Et−1(st). (11.24)

Optimal Exchange Rate Management

We first study the model where the government actively manages, but

does not actually fix the exchange rate. The authorities are assumed

to have direct control over the current-period exchange rate.

The policy maker seeks to minimize costs arising from two sources.

The first cost is incurred when an output target is missed. Notice that

(11.23) says that the natural output level is Et−1(yt) = 0. We assume

that there exists an entrenched but unspecified labor market distortion

that prevents the natural level of output from reaching the socially

efficient level. These distortions create an incentive for the government

to try to raise output towards the efficient level. The government sets

a target level of output Øy > 0. When it misses the output target, it

bears a cost of (Øy − yt)2/2 > 0.

The second cost is incurred when there is inflation. Under PPP

with the foreign price level fixed, the domestic inflation rate is the

depreciation rate of the home currency, δt ≡ st −st−1. Together, policy

errors generate current costs for the policy maker `t, according to the

quadratic loss function

`t = θ

2

(δt)

2 +

1

2

[Øy − yt]

2

. (11.25)

Presumably, it is the publicí desire to minimize (11.25) which it achieves

by electing officials to fulfill its wishes.

11.2. A SECOND GENERATION MODEL 337

The static problem is the only feasible problem. In an ideal world,

the government would like to choose current and future values of the

exchange rate to minimize the expected present value of future costs ⇐(225)

Et

X∞

j=0

βj

`t+j ,

where β < 1 is a discount factor. The problem is that this opportunity

is not available to the government because there is no way that the

authorities can credibly commit themselves to pre-announced future

actions. Future values of st are therefore not part of the governmentís

current choice set. The problem that is within the governmentís ability

to solve is to choose st each period to minimize (11.25), subject to

(11.24) and (11.23). This boils down to a sequence of static problems

so we omit the time subscript from this point on.

Let s0 be yesterdayís exchange rate and E0(s) be the publicís expec￾tation of todayís exchange rate formed yesterday. The government first

observes todayís wage w = E0(s), and todayís shock u, then chooses

todayís exchange rate s to minimize ` in (11.25). The optimal exchange￾rate management rule is obtained by substituting y from (11.23) into

(11.25), differentiating with respect to s and setting the result to zero.

Upon rearrangement, you get the governmentís reaction function

s = s0 +

α

θ [α(w − s)+Øy + u] . (11.26)

Notice that the governmentís choice of s depends on yesterdayís pre￾diction of s by the public since w = E0(s). Since the public knows that

the government follows (11.26), they also know that their forecasts of

the future exchange rate partly determine the future exchange rate. To

solve for the equilibrium wage rate, w = E0(s), take expectations of

(11.26) to get

w = s0 +

αyØ

θ . (11.27)

To cut down on the notation, let

λ = α2

θ + α2 .