Fiscal Policy (Pt.2)

Question 1

Can you write an econometric equation to show how the response to fiscal policy shocks is identified using Narrative shocks?

Answer 1

[from application of Econometrics]
Yt = α0 + α1Yt−1 + α2Yt−2 + … + γ0Dt + γ1Dt−1 + … + µt
where we control for the past of the variable Yt, Dt are dummies representing whether a narrative event happened at time t and µt is a shock.

Question 2

What is the implication of falling long-term Government Bond Yields for the primary deficit?

Answer 2

[from slide 10] Remember that Gt − Tt = Bt − qtBt+1. A fall in rt ⇒ a rise in qt ⇒ easier access to financial markets, but no particular implication for the primary deficit.

Question 3

Carbon taxes: how does “green” energy affect the coefficients
(1 − ds )?

Answer 3

[from slide 25] past energy enters the carbon stock with larger coefficients when (1 − ds ) is higher:
St = S¯ + (t+T) Xigma s=0 (1 − ds )Et−s
Therefore, if energy is produced with “cleaner” technology, the coefficients (1 − ds ) will be lower.

Question 4

What is the derivative of St (t = 1, 2, …, ∞) with respect to a particular Et (t = 1)?

Answer 4

[from slide 25]
∂St = (1 − dt−1)
∂E1 1
Therefore, the effect of energy created in period 1 (E1), on stock of carbon in different time periods t (St) is:
t = 1 →(1 − d0) = φL + (1 − φL)φ0
t = 2 →(1 − d1) = φL + (1 − φL)φ0(1 − φ)
t = 3 →(1 − d2) = φL + (1 − φL)φ0(1 − φ)^2
Emissions have persistent effects!!!

Question 5

Write the problem of the Social Planner for the Carbon Taxes exercise (in Lagrangian form).

Answer 5

Slide 9/10 Tutorial 6 solutions

Question 6

Prescott (2004): How can you account for social security payments and redistribution in this simple model?

Answer 6

[from slide 33] H is all income that is not labor income, therefore socialsecurity payments and other form of redistribution can be included in there!

Question 7

Prescott (2004): What happens to the solution of the problem if H = 0? Why?

Answer 7

[from slide 33] without H, the budget constraint becomes:
c = (1 − τ )wl
Rewrite the problem only as function of l by substituting BC into objective:
max log((1 − τ )wl) + α log(1 − l)
l

which can be rewritten as
max log((1 − τ )w) + log(l) + α log(1 − l)
l

In the final solution, τ and w don’t matter without H! This is because, with log utility from consumption, substitution and income effect exactly cancel each other out and the level of wages (gross or net) does not matter for the optimal allocation.