ECON6008 International Money & Finance
International Money & Finance
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ECON6008 International Money & Finance
1 The model (equations and variables)
1.1 The model in brief
The model you will analyze is a simpli
ed version of the New-Keynesian small open-
economy (SOE) model in Justiniano and Preston (2010), which in turn is based on the
model in Monacelli (2005) and Gali and Monacelli (2005). Compared to Justiniano and
Prestons model, our simpli
ed model assumes that the law of one price (LoP) holds for
all imported retail goods and there is no price indexation for these imported goods. The
model is also extended to include labor-supply shocks, which could be used as a proxy
for the supply-side disruption of the COVID-19 pandemic. Aggregate uctuations in our
model model are driven by 7 exogenous shocks: risk premium, monetary policy (money
supply), preference (consumer spending), labor supply, foreign ination, foreign output,
and foreign interest rate.
The model can be derived from the ground up with micro-foundations, based on op-
timizing households, domestic
rms and importers, etc., resulting in a set of non-linear
equations. We will instead work directly with the log-linearized equilibrium equa-
tions, 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 ination (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 "^s;t (6)
The wedge between CPI- and PPI-ination:
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 ination (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 ination: 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)
Evolution of labor-supply shock:
"^s;t = s"^s;t1 + s;t (17)
2
De
nition 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 inationbyt outputbSt terms of trade (price of exports in terms of imports)bqt real exchange ratebH;t domestic-goods (PPI) inationbF;t imported-goods inationcmct real marginal costbat domestic-householdsholding of foreign assetsbect domestic-currency depreciation rate (% change in the exchange rate)byt foreign outputbt foreign inationbit foreign interest ratebt relative risk premiumbgt consumer preference
"^s;t exogenous labor-supply disruption
"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-ination shock (i.i.d.)
"i;t foreign interest-rate shock (i.i.d.)
"g;t preference shock (i.i.d.)
s;t labor-supply shock (i.i.d.)