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

11.2 A Second Generation ModelIn Þrst-generation models, exogenous domestic credit expansion causesinternational reserves to decline in order to maintain a constant moneysupply that is c

11.2 A Second Generation Model

In Þrst-generation models, exogenous domestic credit expansion causesinternational reserves to decline in order to maintain a constant moneysupply that is consistent with the Þxed exchange rate A key feature

of second generation models is that they explicitly account for the 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 deÞcit and/or impose exchangecontrols Exchange rate defense is therefore costly The government’swillingness 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

pol-in turn depends on the public’s expectations The government engages

in a cost-beneÞt calculation to decide whether to defend the exchangerate or to realign

We will study the canonical second generation model due to feld [112] In this model, the government’s decision rule is nonlinear andleads to multiple (two) equilibria One equilibrium has low probability

Obst-of devaluation whereas the other has a high probability The costs tothe authorities of maintaining the Þxed exchange rate depend on thepublic’s expectations of future policy An exogenous event that changesthe public’s expectations can therefore raise the government’s assess-ment of the cost of exchange rate maintenance leading to a switch fromthe 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 ployment, and various public announcements by authorities that sug-gested a weakening resolve to defend the exchange rate In regard tothe Asian crisis, expectations may have shifted as information aboutover-expansion in Thai real-estate investment and poor investment al-location of Korean Chaebol came to light

unem-Obstfeld’s 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 foreignprice level to zero and assume PPP, pt = st Output is given by aquasi-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 today’s wage was negotiatedand set one-period in advance so as to keep the ex ante real wageconstant

wt= Et−1(st) (11.24)Optimal Exchange Rate Management

We Þrst study the model where the government actively manages, butdoes not actually Þx 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 Þrst 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 assumethat there exists an entrenched but unspeciÞed labor market distortionthat prevents the natural level of output from reaching the sociallyefficient 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 ¯y > 0 When it misses the output target, itbears a cost of (¯y− yt)2/2 > 0

The second cost is incurred when there is inßation Under PPPwith the foreign price level Þxed, the domestic inßation rate is thedepreciation rate of the home currency, δt≡ st− st−1 Together, policyerrors generate current costs for the policy maker `t, according to thequadratic loss function

by electing officials to fulÞll its wishes

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)

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 government’s

current choice set The problem that is within the government’s 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 yesterday’s exchange rate and E0(s) be the public’s

expec-tation of today’s exchange rate formed yesterday The government Þrst

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

today’s 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 government’s reaction function

s = s0+α

θ [α(w− s) + ¯y + u] (11.26)Notice that the government’s choice of s depends on yesterday’s 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

Now, you can get the rational expectations equilibrium depreciation

δ = α¯y

θ +

λu

The equilibrium depreciation rate exhibits a systematic bias as a result

of the output distortion ¯y.3 The government has an incentive to set

y = ¯y Seeing that today’s nominal wage is predetermined, it attempts

to exploit this temporary rigidity to move output closer to its target

value The problem is that the public knows that the government will

do this and they take this behavior into account in setting the wage

The result is that the government’s behavior causes the public to set a

wage that is higher than it would set otherwise

Fixed Exchange Rates

The foregoing is an analysis of a managed ßoat Now, we introduce

a reason for the government to Þx the exchange rate Assume that in

addition to the costs associated with policy errors given in (11.25), the

government pays a penalty for adjusting the exchange rate Where does

this cost come from? Perhaps there are distributional effects associated

with exchange rate changes where the losers seek retribution on the

policy maker The groups harmed in a revaluation may differ from

those harmed in a devaluation so we want to allow for differential costs

associated with devaluation and revaluation.4 So let cd be the cost

associated with a devaluation and cr be the cost associated with a

revaluation The modiÞed current-period loss function is

otherwise We also assume that the central bank either has sufficient

3 This is the inßationary bias that arises in Barro and Gordon’s [7] model of

monetary policy

4 Devaluation is an increase in s which results in a lower foreign exchange value

of the domestic currency Revaluation is a decrease in s, which raises the foreign

exchange value of the domestic currency.

reserves to mount a successful defense or has access to sufficient lines

of credit for that purpose

The government now faces a binary choice problem After observingthe output shock u and the wage w it can either maintain the Þx orrealign To decide the appropriate course of action, compute the costsassociated with each choice and take the low-cost route

Maintenance costs Suppose the exchange rate is Þxed at s0 Theexpected rate of depreciation is δe = E0(s)− s0 If the governmentmaintains the Þx, adjustment costs are cd = cr = 0, and the depreci-ation rate is δ = 0 Substituting real wage w− s0 = δe and output

δe= w− s0 and collecting terms gives

δ = λ

α[αδ

e+ ¯y + u] (11.32)Equating (11.31) and (11.32) you get the real wage

Realignment rule A realignment will be triggered if `R < `M Thecentral bank devalues if u > 0 and 2cd > λ[αδe+ ¯y + u]2 It will andrevalue if u < 0 and 2cr > λ[αδe+ ¯y + u]2 The rule can be writtenmore compactly as

λ[αδe+ ¯y + u]2 > 2ck, (11.36)where k = d if u > 0 and k = r if u < 0 The realignment rule is some-times called an escape-clause arrangement There are certain extremeconditions under which everyone agrees that the authorities should es-cape the Þxed exchange-rate arrangement The realignment costs cd, cr

are imposed to ensure that during normal times the authorities havethe proper incentive to maintain the exchange rate and therefore pricestability

Central bank decision making given δe Let’s characterize the ment rule for a given value of the public’s devaluation expectations

realign-δe By (11.36), large positive realizations of u are big negative hits tooutput and trigger a devaluation Large negative values of u are bigpositive output shocks and trigger a revaluation

(11.36) is a piece-wise quadratic equation For positive realizations

of u, you want to Þnd the critical value ¯u such that u > ¯u triggers adevaluation Write (11.36) as an equality, set ck = cd, and solve forthe roots of the equation You are looking for the positive devaluationtrigger point so ignore the negative root because it is irrelevant Thepositive root is

The points [u, ¯u] are those that trigger the escape option Realizations

of u in the band [u, ¯u] result in maintenance of the Þxed exchange rate.Figure 11.2 shows the attack points for δe = 0.03 with ¯y = 0.01, α = 1,

θ = 0.15, cr = cd= 0.0004

-0.002 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

-0.15 -0.13 -0.11 -0.09 -0.07 -0.05 -0.03 -0.01 0.01 0.03

u

u

Figure 11.2: Realignment thresholds for given δe

Multiple trigger points for devaluation

u and ¯u depend on δe But the public also forms its expectationsconditional on the devaluation trigger points This means that u, ¯uand δe must be solved simultaneously

To simplify matters, we restrict attention to the case where the ernment may either defend the Þx or devalue the currency Revaluation

gov-is not an option We therefore focus on the devaluation threshold ¯u

We will set cr to be a very large number to rule out the possibility of arevaluation The central bank’s devaluation rule is

δ =

(

δ0 = 0 if u < ¯u

δ1 = αλ[αδe+ ¯y + u] if u > ¯u . (11.39)Let P[X = x] be the probability of the event X = x The expecteddepreciation is

δe = E0(δ)

= P[δ = δ0]δ0+ P[δ = δ1]E[(λ/α)(αδe+ ¯y + E(u|u > ¯u))]

= P[u > ¯u](λ/α)[αδe+ ¯y + E(u|u > ¯u)]

Solving for δe as a function of ¯u yields

f (u) = 1/(2a) for −a < u < a and the conditional density given u > ¯u

is, g(u|u > ¯u) = 1/(a − ¯u) It follows that

where fδ(¯u) is deÞned in (11.43) (11.44) has two solutions for ¯u, each

of which trigger a devaluation For parameter values a = 0.03, θ = 0.15,

c = 0.0004, α = 1, ¯y = 0.01 solving (11.44) yields the two solutions

¯

u1 =−0.0209 and ¯u2 = 0.0030 (11.44) is displayed in Figure 11.3 forthese parameter values

(229)⇒

Using (11.43), the public’s expected depreciation associated with ¯u1

is 2.7 percent whereas δe associated with ¯u2 is 45 percent The high

-0.005 0 0.005 0.01 0.015 0.02

Figure 11.3: Multiple equilibria devaluation thresholds

expected inßation (high δe) gets set into wages and the resulting wageinßation increases the pain from unemployment and makes devaluationmore likely Devaluation is therefore more likely under the equilibriumthreshold ¯u2 than ¯u1 When perceptions switch the economy to ¯u2, theauthorities require a very favorable output shock in order to maintainthe exchange rate

There is not enough information in the model for us to say which

of the equilibrium thresholds the economy settles on The model onlysuggests that random events can shift us from one equilibrium to an-other, moving from one where devaluation is viewed as unlikely to one

in which it is more certain Then, a relatively small output shock cansuddenly trigger a speculative attack and subsequent devaluation

Balance of Payments Crises Summary

1 A Þxed exchange rate regime will eventually collapse The result

is typically a balance of payments or currency crisis ized by substantial Þnancial market volatility and large losses offoreign exchange reserves by the central bank

character-2 Prior to the 1990s, crises were seen mainly to be the result ofbad macroeconomic management–policies choices that were in-consistent with the long-run maintenance of the exchange rate.First-generation models focused on predicting when a crisismight occur These models suggest that macroeconomic fun-damentals such as the budget deÞcit, the current account deÞcitand external debt relative to the stock of international reservesshould have predictive content for future crises

3 Second-generation models are models of self-fulÞlling criseswhich endogenize government policy making and emphasize theinteraction between the authorities’s decisions and the public’sexpectations Sudden shifts in market sentiment can weaken thegovernment’s willingness to maintain the exchange rate whichthereby triggers a crisis

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