New New Keynesian Keynesian modelmodel with with small open Economysmall open Economy

Aliya KenjegalievaGiuseppe CaivanoDiego Ruge

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 inopen economy we can observe the impact of shocks oneconomies with different degrees of openness.

We focuse our analysis on the technology and cost-push shocks.

Our framework allow us to model monetary policy asendogenous, with the interest rate as the instrument ofthe policy.

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

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

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

AgentsAgents

HouseholdsEconomies are populated by a representative household who maximizes utility from the consumption function

Subject to the budget constraint:

The optimality conditions are:

International Risk SharingUnder the assumption of complete securities markets, ananalogous FOC must hold for consumers in foreigncountry:

FirmsEach firm produces a differenciated good with lineartechnology 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-θfraction of firms sets new prices each period

Where μ is the (log of the) mark-up in the steady state

EquilibriumEquilibrium

To describe how output and consumption are determinedin the world economy we combine the log-linearized Eulerequation with the market clearing condition

Domestic output can be expressed as:

Where st is the terms of trade and ωα depends on thedegree of openness α of the economy

(New IS equation)

World Consumption and Output (the demand side)

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 byut is the cost push shock which follows an AR(1) process

The (log) real marginal cost:

where , with τ denoting a constant employment subsidy.

EquilibriumEquilibrium• The New Keynesian Phillips curve in the small openeconomy can be written in terms of the output gap:

where output gap is defined as the difference between thereal output yt and the output obtained under flexible price

and

Also, the home log-linear Euler equation that relates theoutput and the interest rate is:

EquilibriumEquilibriumWe can then derive a new IS equation in terms of theoutput gap:

where the output gap can see also as the inverse (log) ofthe gross markup, xt

and the natural interest rate for the small economy :

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 toliterature that develops the NK model in open economy

CalibrationCalibration ofof the the modelmodelParameterValues

β 0.99 Discount Factorθ 0.75 Prob. of not changing pricesσ 1 Intertemporal elasticity of consumptionη 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 persistenceφ 3 Labor disutilityπt 0 CPI inflation targeting

IRF of a Technology ShockIRF of a Technology Shock

5 10 15 200

1

2

3

4x 10-3 y

5 10 15 20-8

-6

-4

-2

0x 10-4 r

5 10 15 20-5

0

5

10

15x 10-3 x

5 10 15 20-15

-10

-5

0

5x 10-4 pi

5 10 15 200

0.2

0.4

0.6

0.8

1y

5 10 15 200

0.2

0.4

0.6

0.8

1y

5 10 15 20-2

0

2

4

6

8x 10-5 x

5 10 15 20-0.1

-0.08

-0.06

-0.04

-0.02

0r

5 10 15 20-10

-5

0

5x 10-5

pi

5 10 15 20-0.05

0

0.05

0.1

0.15r

5 10 15 20-0.1

0

0.1

0.2

0.3x

5 10 15 20-0.4

-0.3

-0.2

-0.1

0

0.1pi

y x

π

rC

losed

Eco.

α=0.0001

α=0.4

IRF of a Cost Push ShockIRF of a Cost Push Shock

5 10 15 20-0.015

-0.01

-0.005

0y

5 10 15 200

1

2

3

4x 10

-3 r

5 10 15 200

0.005

0.01

0.015

0.02x

5 10 15 20-2

0

2

4

6

8x 10-3 pi

5 10 15 20-0.8

-0.6

-0.4

-0.2

0y

5 10 15 200

0.02

0.04

0.06

0.08r

5 10 15 200

0.2

0.4

0.6

0.8x

5 10 15 20-2

0

2

4

6

8x 10-5 pi

5 10 15 20-0.8

-0.6

-0.4

-0.2

0y

5 10 15 20-0.06

-0.04

-0.02

0

0.02

0.04r

5 10 15 200

0.2

0.4

0.6

0.8x

5 10 15 20-0.1

0

0.1

0.2

0.3pi

C

losed

Eco.

α=0.0001

α=0.4

y r x π