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Assignment 2 (Updated)
November 30, 2023
Due Monday December 4. Please hand in individually and in-person (no electronic assignments will be accepted). Include all your codes in the file (copy and paste the Matlab code at
the end of the assignment). Please do not include the rest of the Matlab outputs other than
graphs and statistics you report in your table.
a) What is the Bank of Canada’s current policy mandate? Explain in words.
b) Given you answer to part (a), write down an interest rate rule for the Bank of Canada and explain
what parameters would you assign to the policy rule and why you chose those values.
c) For the remaining questions, you will simulate different models of the economy.
A typical macroeconomy is modelled as follow
xt = Etxt+1 −
1
σ
[it − Etπt+1]
πt = βEtπt+1 + κxt
it = ?
Assume σ = 1, β = 0.99, ω = 0.5, and κ =
(1−ω)(1−ωβ)
ω
.
Each period, assume that there are shocks to the economy given by the process
ut = 0.65ut−1 + ϵt
These could be shocks to aggregate demand (xt) or to inflation (πt).
Finally, assume that agents form rational expectations (Etπt+1 = πt+1 and Etxt+1 = xt+1).
Suppose the Bank of Canada went through a mandate renewal and could change their policy rule. They
have many options:
i) Flexible inflation targeting: it = ϕππt + ϕxxt
ii) Average inflation target over a 2 period horizon: i = ϕππ
A
t + ϕxxt where π
A
t = (πt + πt−1)/2
iii) Average inflation target over a 4 period horizon: i = ϕππ
A
t +ϕxxt where π
A
t = (πt+πt−1+πt−2+πt−3)/4
iv) Reacting to lagged inflation and output: i = ϕππt−1 + ϕxxt−1
Simulate the model for both a positive demand shock and a positive supply shock. In other words, do
the simulation first for a one-standard deviation positive demand shock and then again for a one-standard
deviation positive inflation shock.
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To do so, you must assume values for ϕπ and ϕx. Select values for each and keep the values constant for
the remainder of the assignment. Explain why you chose these values. Make sure ϕπ > 1 and ϕx ≥ 0.
In total, you should have 4 policy rules x 2 types of shocks = 8 simulations. To organize your results,
create a table summarizing your different findings. In that table, create columns for the standard deviation
of inflation, standard deviation of inflation, number of periods for output to return to steady state, number
of periods for inflation to return to steady state.
Dynare will produce you an impulse response for each simulation. Include each impulse response into
your assignment. Then explain in detail how AND why the shock transmits through the economy for EACH
simulation. Explain using insight from the household and firm’s optimization problems. Doing this detailed
explanation for each simulation may seem pedantic but it will help prepare you for the midterm.
d) Suppose the Bank of Canada wants to keep the economy as stable as possible. Given your results,
what policy framework would you recommend the Bank of Canada use for the next 5 years? Explain in detail
why.
Bonus question: Which of these frameworks would work best if people instead formed backward-looking
expectations, e.g. Etxt+1 = xt−1 and Etπt+1 = πt−1.
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