International Macroeconomics and Finance: Theory and Empirical Methods Phần 9 pdf

9.2. PRICING TO MARKET 297

From the money demand functions it follows that the steady state

change in the nominal exchange rate is

Sà = Mà − Mà ∗ − 1

²

h

Cà − Cà∗

i

. (9.171)

Adjustment to Monetary Shocks under Sticky Prices

Consider an unanticipated and permanent monetary shock at time t,

where Màt = Mà , and Mà ∗

t = Mà ∗. As in Redux, the new steady state is

attained at t + 1, so that Sàt+1 = Sà, Pàt+1 = P , à and Pà∗

t+1 = Pà∗.

Date t nominal goods prices are set and fixed one-period in advance.

By (9.10) and (9.11), it follows that the general price levels are also

predetermined, Pàt = Pà∗

t = 0. The short-run versions of (9.141) and

(9.142) are

Mà = 1

²

Càt + β

²(1 − β)

àδt, (9.172)

Mà ∗ = 1

²

Cà∗

t + β

²(1 − β)

[àδt + Sà − Sàt]. (9.173)

Subtracting (9.173) from (9.172) gives

Màt − Mà ∗

t = 1

²

(Càt − Cà∗

t ) − β

²(1 − β)

(Sà − Sàt). (9.174)

From (9.153) and (9.154) you get

Càt = àδt + Cà + P , à (9.175)

Cà∗

t = àδt + Cà∗ + Pà∗ + Sà − Sàt. (9.176)

At t + 1 PPP is restored, Pà = Pà∗ + Sà. Subtract (9.176) from (9.175)

to get

Cà − Cà∗ = Càt − Cà∗

t − Sàt. (9.177)

The monetary shock generates a short-run violation of purchasing power

parity and therefore a short-run international divergence of real interest

rates. The incompleteness in the international asset market results in

imperfect international risk sharing. Domestic and foreign consumption

movements are therefore not perfectly correlated.

298CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICS

To solve for the exchange rate take Sà from (9.171) and plug into

(9.174) to get

"

1 + β

²(1 − β)

# ³

Màt − Mà ∗

t

¥

= 1

²

³

Càt − Cà∗

t

¥

+ β

²2(1 − β)

³

Cà − Cà∗

¥

+ β

²(1 − β)

Sàt.

Using (9.177) to eliminate Cà − Cà∗, you get

Sàt = β + ²(1 − β)

β(² − 1)

h

²(Màt − Mà ∗

t ) − (Càt − Cà∗

t )

i

. (9.178)

This is not the solution because Càt − Cà∗

t is endogenous. To get the

solution, you have from the consolidated budget constraints (9.143)

and (9.144)

Càt = nxàt(z) + (1 − n)[Sàt + àvt(z)] − βàbt, (9.179)

Cà∗

t = (1 − n)àx∗

t (z∗

) + n[àv∗

t (z∗

) − Sàt] + β n

1 − n

àbt, (9.180)

(201-202)⇒ and you have from (9.147)ó(9.150)

xàt(z) = Càt; àx∗

t (z∗

) = Cà∗

t ; àvt(z) = Cà∗

t ; àv∗

t (z∗

) = Càt. (9.181)

Subtract (9.180) from (9.179) and using the relations in (9.181), you

have

Sàt = (Càt − Cà∗

t ) + β

2(1 − n)2

àbt. (9.182)

Substitute the steady state change in relative consumption (9.170) into

(9.177) to get

àb = −2θ(1 − n)

β(1 + θ) [Càt − Cà∗

t − Sàt], (9.183)

and plug (9.183) into (9.182) to get

Càt − Cà∗

t − Sàt = 2θ

(1 + θ)

[Càt − Cà∗

t − Sàt].

It follows that Càt−Cà∗

t −Sàt = 0. Looking back at (9.183), it must be the

case that àb = 0 so there are no current account effects from monetary

shocks. By (9.164) and (9.165), you see that Cà = Cà∗ = 0, and by

9.2. PRICING TO MARKET 299

(9.155) and (9.156) it follows that Pà = Mà , and Pà∗ = Mà ∗. Money is

therefore neutral in the long run.

Now substitute Sàt = Càt − Cà∗

t back into (9.178) to get the solution

for the exchange rate

Sàt = [²(1 − β) + β](Màt − Mà ∗

t ). (9.184)

The exchange rate overshoots its long-run value and exhibits more

volatility than the monetary fundamentals if the consumption elastic￾ity of money demand 1/² < 1.14 Relative prices are unaffected by the

change in the exchange rate, àpt(z) − qàt(z∗) = 0. A domestic monetary

shock raises domestic spending, part of which is spent on foreign goods.

The home currency depreciates Sàt > 0 in response to foreign firms repa￾triating their increased export earnings. Because goods prices are fixed

there is no expenditure switching effect. However, the exchange rate

adjustment does have an effect on relative income. The depreciation

raises current period dollar (and real) earnings of US firms and reduces

current period euro (and real) earnings of European firms. This redis￾tribution of income causes home consumption to increase relative to

foreign consumption.

Real and nominal exchange rates. The short-run change in the real

exchange rate is ⇐(205)

Pàt − Pà∗

t − Sàt = −Sàt,

which is perfectly correlated with the short-run adjustment in the nom￾inal exchange rate.

Liquidity effect. If rt is the real interest rate at home, then (1 + rt) =

(Pt)/(Pt+1δt). Since Pàt = 0, it follows that àrt = −(Pà + àδt) = −(àδt +Mà )

and (9.175)ó(9.172) can be solved to get

àδt = (1 − β)(² − 1)M, à (9.185)

which is positive under the presumption that ² > 0. It follows that ⇐(206)

14Obstfeld and Rogoff show that a sectoral version of the Redux model with

traded and non-traded goods produces many of the same predictions as the pricing￾to-market model.