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EFIMM0099

Public Finance and Monetary Policy

2021

Question 1

Consider a household with the preferences over consumption c and labour supply l given by

log 、c . α _ ,

where α and ε are positive scalars. The household faces a wage rate w and a labour income tax T (y) = τ > y + T0, where y is the labour income. The only income the household receives is from labour.

a. Set up the maximisation problem of the household. Find the optimal labour sup- ply and provide the ‘marginal cost / marginal beneﬁt’ interpretation of the optimality condition.

(10 marks)

b. How does labour supply depend on the tax rate? Explain using the income and the substitution effects.

(8 marks)

c. Suppose that T0 is ﬁxed at 0 and cannot be changed. Instead, the government chooses the income tax rate τ to maximise the tax revenue from the household. There is a single parameter of the household problem which determines the revenue- maximising tax rate. Which parameter is it? Explain and provide intuition.

(7 marks)

d. Now suppose that instead of a single household, there is a distribution of households with identical preferences but different wage rates. In particular, half of households has wage rate wH and the other half a wage rate wL , where wH > wL . The gov- ernment is maximising the Utilitarian notion of social welfare and chooses τ and T0 . There is no tax revenue requirement. Explain carefully whether this government has any motive to conduct income redistribution. Argue what will be the signs of τ and T0 in the optimal allocation.

(7 marks) Total: 32 marks

Question 2

Under which conditions would the optimal ﬁscal policy involve issuing government debt? Provide two examples which we analysed in the lectures and explain them carefully.

Total: 18 marks

Question 3

A researcher at the Treasury wants to model the dynamics of output, yt .

A simple AR(1) model

In a ﬁrst instance, the researcher considers the following AR(1) model,

yt = ayt-1 + vt , where E(vt) = 0, E(vt(2)) = σ 2 .

a. Derive the condition(s) under which this AR(1) process is covariance-stationary.

(4 marks)

b. What is the impulse response IR(s) = aa(/)从t(t＋)s for any s ≥ 0? Explain carefully.

(3 marks)

c. The researcher estimates this baseline model in the data with OLS and inadvertently adds controls in one speciﬁcation (i.e., contemporary and past money supply). A t-test shows that these controls do have an effect on output. What is the economic interpretation, and what does this imply for her modeling of output dynamics?

(3 marks)

A SVAR model

The researcher now considers the following SVAR of order 1 for xt = [yt; pt; it; mt] where the components represent, in order, output, prices, interest rates and money:

A0xt = A1xt-1 + ut , where E(ut) = 0, E(utut(l)) = Ωu . This SVAR(1) has the corresponding reduced-form VAR(1),

xt = Φxt-1 + εt , where E(εt) = 0, E(εtεt(l)) = Ωe .

d. Show how Φ and Ωe are calculated from parameters of the SVAR(1) model (A0, A1 , Ωu).

(4 marks)

e. How many restrictions does the researcher need to identify the parameters of the SVAR? Explain carefully.

(3 marks)

f. The researcher has access to quarterly data and assumes that it takes longer than one quarter for output to react to shocks in the remaining variables. The structural errors in the four variables are also assumed to be independent of each other. Write down what restrictions this implies for the structural coefﬁcients (elements of matrices A0 and Ωu respectively). Do we have enough restrictions to identify the parameters?

(4 marks)

g. A colleague suggests that, in addition to the previous restrictions, the researcher should assume that pt, it and mt do not Granger-cause yt. Write down the model for yt when imposing these additional restrictions, and explain why the researcher may not want to impose these restrictions.

(3 marks)

h. Describe how you would (i) identify/estimate the model and (ii) analyse the effect of shocks (and which shocks?) in the model.

(4 marks) Total: 28 marks

Question 4

The same researcher at the Treasury is asked to give policy advice to the Chancellor of the Exchequer, Rishi Sunak. She has to answer three questions. Your task is to help her answer these questions. Here are the three questions of Mr. Sunak.

a. In all your SVAR estimations, you are obsessed with ﬁnding purely exogenous shocks to policy. How is it useful for me who needs to design an effective policy response to the current huge drop in economic activity?

(4 marks)

b. I would like to boost output and increase investment as we are getting out of the pandemic. I consider a large cut in value-added taxes or a huge public infrastructure investment project. Given the benchmark results of Blanchard and Perotti (Quarterly Journal of Economics, 2002), which policy should I choose? Also, in what sense should I be careful using this paper’s prediction for my policy design?

(10 marks)

c. Can we rely on monetary policy instead? What does the paper by Christiano, Eichen- baum and Evans (Review of Economic Studies, 1996) suggest? Can we use their suggestions regarding interest rate policy in the current situation? Given this, what are the caveats of this approach?