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数学代写 - ECON6008: International Money & Finance

时间：2020-11-14

1 The model (equations and variables)

1.1 The model in brief

The model you will analyze is a simplied version of the New-Keynesian small open-

economy (SOE) model in Justiniano and Preston (2010), which in turns, is based on the

model in Monacelli (2005) and Gali and Monacelli (2005). Compared to the model in Jus-

tiniano and Preston, our simplied model assumes that the law of one price (LoP) holds

for all retail imported goods and there is no price indexation for these imported goods.

Aggregate utuations are also only driven by six exogenous shocks: risk premium, mone-

tary policy (money supply), preference ("consumer condence"), foreign in
ation, foreign

output, and foreign interest rate.

The model can be derived from the ground-up (micro-foundations) based on optimizing

households, domestic rms and importers, etc., resulting in a set of non-linear equations.

We will instead work directly with the log-linearized equilibrium equations, listed

below.

1.2 The log-linearized equations

Consumption Euler-equation (the IS equation):

bct = h

1 + h

bct1 + 1

1 + h

Etbct+1 1

1 h

1 + h

hbit Etbt+1i+ g^t (1)

Goods-market clearing condition:

byt = (1 )bct + byt + (2 )bSt (2)

The link between terms of trade and real exchange rate:

bqt = (1 )bSt (3)

Changes (growth rate) of the terms of trade:

bSt bSt1 = bF;t bH;t (4)

1

Domestic-price in
ation (the "Phillips curve"):

(bH;t H ^H;t1) = Et (bH;t+1 H ^H;t) + (1 H)(1 H)

H

cmct (5)

The real marginal cost: cmct = 'byt + bSt + bct (6)

The wedge between CPI- and PPI-in
ation:

bt = bH;t + bSt bSt1 (7)

The uncovered interest-parity (UIP) condition:

bit bit = Etbect+1 bat + Etbt+1 (8)

The net-foreign-assets position (the current account):

byt bct = bat 1bat1 +

(1 )bqt (9)

Imported-good in
ation (based on the law of one price):

bF;t = bect + bt (10)

Monetary-policy (Taylor) rule:bit = ibit1 + bt + ybyt + ybyt + ebect "m;t (11)

Evolution of risk premium: bt = bt1 + ";t (12)

Evolution of foreign output:

byt = ybyt1 + "y;t (13)

Evolution of foreign in
ation:

bt = bt1 + ";t (14)

Evolution of foreign interest rate:bit = ibit1 + "i;t (15)

Evolution of preference shock:

g^t = g g^t1 + "g;t (16)

2

Denition of variables and shocks NOTE: all hatted variables are in terms of log or

percentage deviation from the steady-state value, except for bit, bt, bH;t, bF;t, bt , and bit ,

which are in terms of level deviation from the steady state (e.g. bit it i).

bct
consumption (per capita)bit nominal interest ratebt CPI in
ationbyt outputbSt terms of trade (price of exports in terms of
imports)bqt real exchange ratebH;t domestic-goods (PPI) in
ationbF;t imported-goods in
ationcmct real marginal costbat domestic-households' holding of foreign
assetsbect domestic-currency depreciation rate (% change in the exchange
rate)byt foreign outputbt foreign in
ationbit foreign interest ratebt relative risk premiumbgt consumer
preference

"m;t monetary-policy shock (i.i.d.)

";t risk-premium shock (i.i.d.)

"y;t foreign-output shock (i.i.d.)

";t foreign-in
ation shock (i.i.d.)

"i;t foreign interest-rate shock (i.i.d.)

"g;t preference shock (i.i.d.)

3

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4

The Questions

1. Solve the model described above using Dynare. Obtain the impulse response for 10

periods to a one-time 1% shock to

a. money supply or the domestic interest-rate shock ("m;t);

b. preference ("g;t);

c. foreign output ("y;t).

Analyze (i.e. explain the dynamics) and plot the eect of each of these shocks to

domestic output (byt), consumption (bct), interest rate (bit), in
ation (bt), domestic-currency

nominal depreciation (bect), and the "shocked" variable (e.g. if it's a foreign output shock,

plot byt ). Relate your analysis to what you have learned in the rst half of the course (the

"qualitative model"). For the money supply or the domestic interest-rate shock, do you

observe an overshooting of the nominal exchange rate?

[Extra points: (i) plot the six variables above in a 3x2 plot (with 3 rows and 2

columns); (ii) plot the evolution of the nominal exchange rate and the current account in

a separate gure and explain the dynamics.]

2. In the model above, we assume a fully-
exible (
oating) exchange rate system.

Suppose that the central bank also directly intervenes in the foreign exchange market, i.e.

it's operating under a managed oating exchange rate. This policy can be analyzed within

our model by assuming that

e = 0:65 > 0

Redo #(1.c) above, i.e. plot and analyze the impulse response to a 1% foreign-output shock,

under this alternative policy. Particularly, analyze the eect of this policy on the size of

the uctuations of CPI-in
ation, output, and the nominal exchange rate, in comparison to

the case with e = 0.

3. Now assume that the central bank is operating under a xed exchange-rate system.

Specically, the monetary policy rule in equation (11) is replaced with the following policy

rule: bect = 0

This policy rule eectively (and credibly) xes the nominal exchange rate at a specied

level. Redo #(1.c) above, i.e. plot and analyze the impulse response to a 1% foreign-

output shock, under this policy. Particularly, analyze the eect of this policy on the size

of the uctuations of CPI-in
ation, output, the nominal interest rate, and the nominal

5

exchange rate, in comparison to the oating exchange-rate system (both when e = 0 and

e = 0:65).

[Notes: (i) Dynare does not plot the impulse response of a variable if that variable is

always
constant (zero deviation from the steady state), (ii) since the
foreign-debt holding,bat, enters the UIP condition in equation (8), you
will generally not nd bit = bit , unless

= 0)]. [Extra points: plot the variables under the three policies in one gure, e.g. the

plot for output should include three dierent impulse responses.]

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References

[1] Gali, J. and T. Monacelli. 2005. "Monetary policy and exchange rate volatility in a

small open economy". Review of Economic Studies 72: 707-734.

[2] Justiniano, A. and B. Preston. 2010. "Monetary policy and uncertainty in an empirical

small open-economy model". Journal of Applied Econometrics 25: 93-128.

[3] Monacelli, T. 2005. "Monetary policy in a low pass-through environment". Journal of

Money, Credit, and Banking 37(6): 1019-1045.

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