Dynare/Matlab Project
International Finance (Open Economy Macroeconomics)
NOTE: “Handing in solutions to this project” involves scanning and emailing your analytical
solutions (to be written in directly in this handout), emailing me the Dynare code(.mod file),
1 The project is due on Thursday, August 8, 2019 at 6 pm (of course,
you are welcome to send me your solutions earlier). This project has a total of 100 points.
Late projects will not be accepted (except in the case of a reasonable excuse, such as, for
instance, justified medical issues).
Dynare留学生作业代做、代写Matlab Project作业、代做Matlab编程语言作业
Please make sure to print your name and sign the ”honor code” statement below. Any
projects returned without a name and signature will earn a grade of zero.
My name is:
I sign my name as a witness that I have not engaged in any form of academic misconduct
and abided by Johns Hopkins University’s honor code in solving this project. I also confirm
that each group member made honest and equal contributions to the project.
Group member 1:
Group member 2:
Group member 3:
Signature1: Date:
Signature2: Date:
Signature3: Date:
1ALTERNATIVELY, YOU CAN TYPE YOUR SOLUTIONS AND ATTACH YOUR ANSWERS TO
THIS PDF.
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Consider two large open economies, home and foreign (foreign variables that need not
be equal to home variables are denoted by an asterisk. Each economy is inhabited by a
continuum of identical individuals grouped into an aggregate risk sharing household. In
each country there is also a representative final goods producing firm. International trade
occurs in this final good. Lifetime utility is given by:
where: Et
is the expectation operator, β ∈ (0, 1) is the (constant) subjective discount factor,
C and C denote consumption, γ > 0 and γ > 0 are parameters, η > 0 is the Frisch
(marginal value of real wealth held constant) elasticity of labor supply, and N and N denote labor.
Production in each country is determined by:
where: A and A are stochastic technology processes; α ∈ (0, 1); K and K? denote capital;
and Z and Z are scaling parameters. Furthermore:
where: ρ, ρ > 0; v, v > 0; Et (εt) = Et (εt) = 0; and the standard deviations of ε and εare, respectively, σε and σε . In the preceding, all variables are normalized by the world
population, which consists of a unit mass. Also, the evolution of capital in each country is
given by:
Kt+1 = It + (1δ) Kt
where I and I
denote investment and δ and δ
are capital depreciation rates. Finally,
changing capital holdings involves a real adjustment cost of the form
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for the foreign country, where κ and κ
are positive parameters; this adjustment cost means
that the faster adjustments in the capital stock are the more expensive they are. Furthermore,
these costs are symmetric, so that reducing capital is as expensive as expanding it. The way
adjustment costs are written here, replacing depreciated capital does not generate adjustment
costs.
A benevolent world social planner solves the following problem:
max
. In addition, ψ is the fraction of the world population that
lives in the home country. So, the benevolent world social planner is weighting the utility of
each country by their relative size in the world economy. Finally, G and G? are exogenous
government consumption.
1) Set up the benevolent world social planner’s current value Lagrangian using one constraint,
only, and using λt to denote the time t Lagrange multiplier. Please write your answer
below. (10 points total)
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2) State the corresponding first-order conditions for consumption, labor, and capital. Please
write your answer below. (15 points total)
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3) Using your answer to (2) write down the system of 18 equations in the 18 unknowns, C,C
that jointly solve the
model (note: in all cases you should substitute out the Lagrange multiplier and combine the
first order conditions as needed). Please write down your answer below. (15 points
total)
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4) Assume the following parameter values: ψ = 0.5; η = 4; α = 2/3; β = 0.988; δ =δ = 0.025; γ = 10.7863; γ = 10.5256; G = 0.1017; G? = 0.0760; Z = 1; Z = 0.9283.
Of note, γ such that in steady state N = 1700/8760 (1700 is average hours worked in the
United States per year and 8760 is total hours available per year); γ
is such that in steady
state N = 1200/8760 (1200 is average hours worked in the euro area per year); G is such
that in steady state G/Y = 0.175, which is the average ratio of government consumption
to output in the United States; G?
is such that G?/Y = 0.207, which is the average ratio
of government consumption to output in the euro area; and Z
is such that in steady state
C/Y = 0.76, which is the average ratio of private consumption to output in the euro area.
Also, assume that ρ = ρ = 0.906; v = v = 0.088; σε = σε = 0.00852; κ = κ = 0; and that
the contemporaneous correlation of the structural shocks is given by:
corr (εt, εt) = 0.258.
These parameter values are roughly consistent with the following steady state values:2
Variable Rough Steady State Value
2Please fill in the missing ones.
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Given these steady state values, what is the intuition behind: C and C
being equal K
and K being different I and I
being different Y and Y
being different NX and NX
being different BE VERY EXPLICIT ABOUT THE INTUITIONS!
You can write down your answers below, but I prefer you typinge your answers
and attaching it. (15 points total)
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5) Given all of the information you have been provided with and/or arrived at, generate
simulated data for all model variables for 500 periods and impulse response functions for 50
periods using Dynare’s stoch simul command. Print impulse response functions for the U.S.
(home country) in percent deviations from steady state, given a NEGATIVE 1 standard
deviation orthogonalized shock to the euro area’s (the foreign country’s) productivity. In
other words, you are giving a negative productivity shock to the foreign economy and analyzing
the effects on home country variables.
Send your impulse response figures in a Word file called ”IRF Figure” along
with your relevant Dynare code to generate those. (25 points total).
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6) Analyzing dynare’s output (IRFs, moments, correlations and autocorrelations), discuss
which of the 10 business cycle facts are consistent with your model. Which fact(s) does your
model fail to deliver? Especially, what does your model say regarding the CA? (We cannot
study some of the facts with this model, so skip them). Again, I encourage you to type your
answers and attach it to the pdf, rather than writing by hand. (10 points total).
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7) Read the material posted under the folder ”Term Project”. What are the 3 main puzzles
coming from business-cycle models? How researchers resolve these puzzles? Once again,
you are encouraged to type your answers and attach it to the pdf, rather than writing by
hand.(10 points total).
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