Eco 3152 Team Assignment #2
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Eco 3152
Team Assignment #2
29/10/2022
Due date: 14 novembre 2022
Format:
● 1 assignment per team of 4, submitted through Brightspace
● Submit the R script used to do the various graphs/calculations. Provide your written answers as comments within the R script.
● Read the document Expectation Errors.pdf to help you answer the questions of the assignment.
Question 1
Assume the modified SIMEX model:
ydt = wt . nt _ rt (2)
rt = θ . wt . nt (3)
ydt(e) = ydt _ 1 (4)
ct = (1 _ β) . ct _ 1 + β . (α1 . ydt(e) + α2 . hh,t _ 1 ) (5)
hd,t = hh,t _ 1 + ydt(e) _ ct (6)
hh,t = hh,t _ 1 + ydt _ ct (7)
hs,t = hs,t _ 1 + gt _ rt (8)
nt = (9)
1e) Does the model with β = 0.85 need more or less time to reach the steady state, relative to the model with β = 0.5? How do you explain this difference?
Return now to the model with β = 0.5. Assume now that the government wishes to reduce the debt-to-GDP by permanently increasing θ from 0.25 to 0.30, starting from period r = 5, ie in sfcr skОco() use st_rt=5. 1f) Graph the variables ct and yt for the first 30 period of the simulation of the increase in θ . Plot the variables as % from their initial steady state value (% shk minus control) as explained in class. What is the
long run impact, on consumption, of increasing the tax rate on income? Explain briefly and intuitively why we find this result?
1g) Graph the debt to GDP ratio for the first 30 periods of the simulation. Is the government capable of achieving a lower debt to GDP?
Assume now that the income tax rate increase causes α 1 to simultaneously drop from 0.8 to 0.785. 1h) Explain intuitively why an increase in θ could simultaneously lead to a decline in α 1 .
1f) Plot the debt to GDP ratio for the first 30 periods of this alternative simulation. Can the government achieve a lower debt-to-GDP ratio? In your opinion, what explains this result?
1g) What lesson policymakers should learn from this experiment in formulating fiscal policy?
Question 2
Soit le modèle suivant:
ydt = yt + γt _ 1 bh,t _ 1 _ rt (11)
rt = θ(yt + γt _ 1 bh,t _ 1 ) (12)
ydt(e) = ydt _ 1 (13)
ct = α 1 . ydt(e) + α2 . tt _ 1 (14)
tt(e) = tt _ 1 + ydt(e) _ ct (15)
bh,t = bd,t (17)
hh,t = tt _ bh,t (18)
tt = tt _ 1 + ydt _ ct (19)
bs,t = bs,t _ 1 + (gt + γt _ 1 bs,t _ 1 ) _ (rt + γt _ 1 bcb,t _ 1 ) (20)
hs,t = hs,t _ 1 + bcb,t _ bcb,t _ 1 (21)
bcb,t = bs,t _ bd,t (22)
In this model, households base their consumption decision on expected disposable income and their gobernment
bill purchase decision on expected wealth and expected disposable income. The redundant equation is again hs = hh . We assume that the central bank sets the interest rate γt = 0.03 and that the government spends gt = 50 every period. Further assume that θ = 0.2, α 1 = 0.6﹐ α2 = 0.4﹐ λ0 = 0.635﹐ λ1 = 5 et λ2 = 0.01.
2a) In our opinion, what is the economic significance of the equation bh,t = bd,t in the model?
2b) If households make an expectational mistake, ie ydt(e) ydt , which asset will «buffer» the expectation error, government bills or money holdings?
2c) At the steady state, what is the level of GDP yt and consumption ct ? What is the debt-to-GDP ratio?
2d) At the steady state, what is the total amount of interest paid by the government? What is the amount of interest paid by the government to households?
2e) Define the effective interest rate of the government as the ratio of interest paid to households to the TOTAL amount of government debt. Calculate the effective interest rate of the government. Is it higher or lower than the official interest rate set by the central bank?
2f) Find the steady state level of GDP, consumption and the debt-to-GDP ratio assuming now that α 1 = 0.8 and α2 = 0.2. Is it different that what you found in 2c)?
Pour les reste de la question, assumons que α 1 = α 10 _ V . Tt _ 1 .
2g) Assume initially that α 10 = 0.75, V = 5, and α2 = 0.4. What is the value of α 1 at the steady state?
2h) Graph the response of consumption to an interest raate shock whereby the central bank permanently increases the interest rate from 3% to 3.5%. In sfcr skОco() use st_rt=5. Graph your response as percentage deviation from the initial steady state.
2i) Assume now that α 10 = 0.95, V = 5 and α2 = 0.2. What is the steady state value of α 1 ?
2j) Graph the response of consumption to an interest raate shock whereby the central bank permanently increases the interest rate from 3% to 3.5%. In sfcr skОco() use st_rt=5. Graph your response as percentage deviation from the initial steady state.
2k) In the same graph, plot the response of consumption you obtained in 2h) and 2j). You should find that depending on the value ofα1 , consumption responds more in one case than in the other, and that it takes longer for consumption to recover, even if the interest rate shock is the same. Explain intuitively why you obtain such a difference.
2022-12-13