EFIMM0099 Public Finance and Monetary Policy 2020
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EFIMM0099
Public Finance and Monetary Policy
2020
Question 1
Consider a household which lives for 2 periods. In the first period it chooses labour supply l and savings s given a wage rate w and an interest rate r. The household receives no other income. Household preferences over consumption in the first period c1 and consumption in the second period c2 and labour supply l are given by log(c1 ) − l2 + β log(c2 ), where β > 0 is the discount factor.
1. Set up the maximization problem of the household. (5 marks)
2. Derive the first-order condition with respect to the labour supply and interpret it.
(5 marks)
3. Derive the first-order condition with respect to savings (the Euler equation) and inter- pret it.
(5 marks) Total 15 marks
Question 2
Consider a government with outstanding debt b. The government decides whether to repay it or to default on it. In the case of repayment, the government needs to pay b to interna- tional investors. In the case of default, the government repays nothing, but a fraction γ of current output is destroyed. There is no other cost of default.
1. Show how incentives to default depend on the values of debt b and current output y.
(5 marks)
2. Suppose that output can take two values: yL with probability ⇡L and yH with proba- bility ⇡H , where yH > yL . Recall that the government bond price q(b) satisfies
q(b) = Prob{debt b is repayed} ⇥ q⇤ ,
where q⇤ is a price of a risk-free bond. Derive the government bond price schedule q(b).
(5 marks)
3. Discuss whether the possibility of default leads to lower debt issuance by the govern- ment.
(5 marks) Total 15 marks
Question 3
Decide whether each of statements is true or false.
Write answers in your answer notebook. Do not explain your choice.
1. An increase of wage rate in general generates both income and substitution effects in labour supply. (2 marks)
2. An increase of wage rate generates only income effect when utility from consumption is linear. (2 marks)
3. An increase of interest rate does not always lead to higher savings. (2 marks)
4. Tax smoothing means that the tax rates should increase smoothly over time.
(2 marks)
5. According to Ramsey taxation we should not tax capital income. (2 marks)
6. In the Diamond model, a golden rule level of capital maximises the resources for consumption.
(2 marks)
7. In the Diamond model, a steady state equilibrium is efficient if the capital stock is equal to or lower than the golden rule level of capital. (2 marks)
8. Issuing government debt always leads to lower capital stock. (2 marks)
9. Ricardian equivalence means that labour income taxes are equivalent to capital in- come taxes.
(2 marks)
10. No European country defaulted on its debt in the XXI century. (2 marks)
Total 20 marks
Question 4
Consider a SVAR(1) for Yt = [GDPt;pt;it;Mt] where the components represent, in order, output, prices, interest rates and money:
A0Yt = A1Yt−1 + ut, E(utut(0)) = ⌦u
and consider the corresponding reduced-form VAR(1)
Yt = ΦYt−1 + ✏t, E(✏t✏t(0)) = ⌦ ✏
a) Show how Φ and ⌦ ✏ are calculated from the SVAR(1) model.
b) Suppose you have quarterly data and that you can plausibly assume that it takes longer than one quarter for output to react to shocks in the remaining variables. Write down what restrictions this implies for the structural coefficients (elements of matrix A0).
c) How many more restrictions besides those considered in questions 4.b do you need to identify the parameters of the SVAR?
d) In addition to the restrictions in question 4.c, suppose pt,it and Mt do not Granger- cause GDPt: Write down the model for GDPt when imposing these additional re- strictions.
e) Can we use the reduced-form error, ✏t, for policy analysis? Explain.
Total 25 marks
Question 5
Set up a simple VAR model with GDP (Y), GDP deflator (P), an index for commodity prices (PCOM), non-borrowed reserve (NBRD), federal fund rate (FF), total reserve (TR), to study the impact of federal funds rate on real output.
Total 25 marks
2022-05-17