代做program、Java/Python程序设计代写

日期：2023-12-05 10:40

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.

1

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.

2