International Macroeconomics 6:
The Asset Approach, Dynare, and Computational
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Steady States
Graded Homework Problems∗
Francisco E. Ilabaca, Ph.D.
Johns Hopkins University
November 1, 2022
1. Consider the following planning problem (all non-price variables are normalized by
the aggregate population), where all notation is standard:
yt = Z̄ · ztnαt
In addition,
ln zt = χ+ ρ ln zt−1 + ξ
where ξzt ∼ N(0, η2ξ )
(a) a) Set up the current value Lagrangian using a single constraint.
(b) Derive the first-order conditions. Please show your work.
(c) Solve for the steady state values of c, n, z. Please show your work.
(d) d) Create a Dynare .mod file called RBC2 that simulates the model in the
previous problem for 1,065 periods assuming the following parameter values:
ε = 4, α = 2/3, γ = 0.0897. You should estimate the parameters Z̄, χ, ρ, η2ξ
using Stata and the data provided in the Excel file called ”HW6Data”. As
usual, all non-price variables should be normalized by the aggregate population
in accordance with the model’s statement.
∗These lecture notes closely follow sections from: Epstein, Brendan. Masters Level International
Macroeconomics, 2013 ; Feenstra, ., and . Taylor. International Economics, 2012.
2. Following as an example the development in this Lesson, create a Matlab .m file
called CONTROL HW6.m and a Matlab function called MODEL HW6.m that solve
computationally problems 8.b. ad 8.c from the practice problems with solutions
from Lesson 1, under the following parameter assumptions: It = 100, pc,t = 1, pg,t =
2, α = 0.5, β = 0.5
3. Use the FX market diagram to answer the following question. Consider the rela-
tionship between the Mexican peso and the Canadian dollar (C$). Let the exchange
rate be defined as Mexican pesos per Canadian dollar, Epesos/C$. For each of the
following cases, illustrate the effects on the FX market using graphs and state how
the following variables change: interest rates in Mexico (ipeso) and Canada (iC$),
the spot exchange rate (Epesos/C$), and the expected rate of return on Canadian and
Mexican deposits (from the perspective of a Mexican investor). Unless otherwise
noted, you may assume that the expected exchange rate is unchanged.
(a) Canada’s interest rate increases.
(a) Investors in the market anticipate an appreciation in the peso.
(a) Mexico’s interest rate decreases.
(a) Canada and Mexico decrease interest rates by the same amount.
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