Opening Economy Extension

Business Cycles and Fluctuations - AE2E6

Using Dynare:

  • get familiar with the structure of a modfile
  • interpret results
    • compare moments with the data
  • edit a model
    • fix steady-state
    • extend a model (in particular recheck/rederive first order conditions)

Uncomment the following lines to install needed packages (if not already present).

# uncomment the next lines, the first time you run
# import Pkg; Pkg.add(["Dynare", "DataFrames"])

Small Open Economy

Start from the same rbc model as in last tutorial session. Assume the representative agent can save \(b^{\star}_t\) as foreign assets, remunerated at a constant interest rate \(r^{\star}-1\).

Write the new budget constraint for the representative household.

Write the new optimality condition.

What is the long run constraint on interest rate \(r^{\star}\)?

Update the modfile (set \(\overline{b^{\star}}=0\))

Print theoretical moments. Comment.

Simulate the model over 100 periods. Comment.

Assume the foreign interest rate depends on the amount of foreign assets

\[r^{\star}_t=\frac{1}{\beta} + exp(-\kappa b^{\star}_t) - 1\]

with \(\kappa=0.001\). How do you interpret the equation for \(r^{\star}_t\). How should you modify the model equations?

Update the modfile and comment on the generated moments. Do they depend on the choice of \(\kappa\)?