The document presents a New Keynesian model with a small open economy. It introduces the model, which includes Calvo staggered prices, perfect international financial markets, PPP in the long run, and identical preferences across countries. The model derives a two-equation system for inflation and output gaps, as well as characterizes monetary policy. It then calibrates the model under technology and cost-push shocks for closed, slightly open, and moderately open economies.

1. NewNew KeynesianKeynesian modelmodel withwith
small open Economysmall open Economy
Aliya Kenjegalieva
Giuseppe Caivano
Diego Ruge

2. IntroductionIntroduction
 Recent works in macroeconomics have shown that,
including imperfect competition and nominal rigidities,
monetary policy has nontrivial effects on real variables.
 With the extension of the New Keynesian Model in
open economy we can observe the impact of shocks on
economies with different degrees of openness.
 We focuse our analysis on the technology and cost-
push shocks.
 Our framework allow us to model monetary policy as
endogenous, with the interest rate as the instrument of
the policy.

3. ReferencesReferences
 Gali and Monacelli (2005): small open economy version
of Calvo sticky price model
 Obsfeld-Rogoff (1995): 2-country model in which firms
face monopolistic competition setting price one period
before the shock hits the economy
 Corsetti and Pesenti (2001), Betts and Devereux (2000):
Estensions to OR Model
 Clarida, Galì and Gertler (2001): cost-push shocks in the
model

4. The Model (assumptions)The Model (assumptions)
 Continuum of small open economies:
- home country vs. world economy
 Calvo staggered prices
 Perfect international financial markets:
- UIP condition holds
 PPP holds in the long run
 Identical preferences, market structure,
technologies over countries
 Law of one price holds

5. The model (introduction)The model (introduction)
 Two-equation dynamical system for
inflation and output gap:
 A IS-type equation is derived
 A new Keynesian Phillips curve
 A third equation to close the model, describing
how monetary policy is conducted

6. AgentsAgents
 Households
Economies are populated by a representative household
who maximizes utility from the consumption function
Subject to the budget constraint:
 The optimality conditions are:

7. International Risk Sharing
Under the assumption of complete securities markets, an
analogous FOC must hold for consumers in foreign
country:
 Firms
Each firm produces a differenciated good with linear
technology represented by the production function:
at ≡ logAt follows an AR(1) process
Firms set prices in a staggered fashion à la Calvo, so a 1-θ
fraction of firms sets new prices each period
Where μ is the (log of the)
mark-up in the steady state

8. EquilibriumEquilibrium
 To describe how output and consumption are determined
in the world economy we combine the log-linearized Euler
equation with the market clearing condition
Domestic output can be expressed as:
Where st is the terms of trade and ωα depends on the
degree of openness α of the economy
(New IS equation)
World Consumption and Output (the demand side)

9. EquilibriumEquilibrium
 Marginal Cost and Inflation Dynamics (the supply side)
 The dynamics of Inflation in the home economy:
where denotes the (log) real marginal cost,
expressed as a deviation from its steady state value ,
while the slope coefficient is given by
ut is the cost push shock which follows an AR(1) process
 The (log) real marginal cost:
where , with τ denoting a constant
employment subsidy.

10. EquilibriumEquilibrium
• The New Keynesian Phillips curve in the small open
economy can be written in terms of the output gap:
where output gap is defined as the difference between the
real output yt and the output obtained under flexible price
and
Also, the home log-linear Euler equation that relates the
output and the interest rate is:

11. EquilibriumEquilibrium
We can then derive a new IS equation in terms of the
output gap:
where the output gap can see also as the inverse (log) of
the gross markup, xt
and the natural interest rate for the small economy :

12. ResultsResults
 We calibrate two models regarding first a
technology shock, and second a cost push shock,
both under the next conditions:
 i) The NK model with closed economy
 ii) The NK model with open economy with a very
low degree of openness, i.e. α=0.0001
 iii) The NK model with open economy with a
degree of openness of α=0.4 which is according to
literature that develops the NK model in open
economy

13. CalibrationCalibration ofof thethe modelmodel
ParameterValues
β 0.99 Discount Factor
θ 0.75 Prob. of not changing prices
σ 1 Intertemporal elasticity of consumption
η 1 Elasticity of substitution between Home and Foreign goods
α 0.4 Degree of openness in open economy
ρa 0.9 Technology shock persistence
ρu 0.9 Cost push shock persistence
φ 3 Labor disutility
πt 0 CPI inflation targeting

14. IRF of a Technology ShockIRF of a Technology Shock
5 10 15 20
0
1
2
3
4
x 10
-3 y
5 10 15 20
-8
-6
-4
-2
0
x 10
-4 r
5 10 15 20
-5
0
5
10
15
x 10
-3 x
5 10 15 20
-15
-10
-5
0
5
x 10
-4 pi
5 10 15 20
0
0.2
0.4
0.6
0.8
1
y
5 10 15 20
0
0.2
0.4
0.6
0.8
1
y
5 10 15 20
-2
0
2
4
6
8
x 10
-5 x
5 10 15 20
-0.1
-0.08
-0.06
-0.04
-0.02
0
r
5 10 15 20
-10
-5
0
5
x 10
-5 pi
5 10 15 20
-0.05
0
0.05
0.1
0.15
r
5 10 15 20
-0.1
0
0.1
0.2
0.3
x
5 10 15 20
-0.4
-0.3
-0.2
-0.1
0
0.1
pi
y x
π
r

15. IRF of a Cost Push ShockIRF of a Cost Push Shock
5 10 15 20
-0.015
-0.01
-0.005
0
y
5 10 15 20
0
1
2
3
4
x 10
-3
r
5 10 15 20
0
0.005
0.01
0.015
0.02
x
5 10 15 20
-2
0
2
4
6
8
x 10
-3
pi
5 10 15 20
-0.8
-0.6
-0.4
-0.2
0
y
5 10 15 20
0
0.02
0.04
0.06
0.08
r
5 10 15 20
0
0.2
0.4
0.6
0.8
x
5 10 15 20
-2
0
2
4
6
8
x 10
-5
pi
5 10 15 20
-0.8
-0.6
-0.4
-0.2
0
y
5 10 15 20
-0.06
-0.04
-0.02
0
0.02
0.04
r
5 10 15 20
0
0.2
0.4
0.6
0.8
x
5 10 15 20
-0.1
0
0.1
0.2
0.3
pi
y r x π