SECTION A Answer ALL questions. Indicate whether the statements are True, False or Uncertain and give a brief reason for your answer.
1. Policymakers should act in a certainty equivalent manner if there is parameter uncertainty.
2. Aggregate demand channel is the only monetary transmission mech- anism channel.
3. An increase in the net worth of a firm would increase the impact of the financial accelerator.
4. Large differences in fundamentals distinguish countries that face sovereign default from those that do not.
5. An increase in the real rate of interest makes the rate of search un- employment rise.
6. Incentives to innovate depend on the size of the market.
SECTION B: Answer ALL questions.
7. New Keynesian model with technology shocks: Consider a New Keynesian economy with equilibrium conditions given by
yt = Et {yt+1} - 1/σ (it - Et {πt+1} - ρ) ,
πt = βEt {πt+1} + κxt
where πt and yt are inflation and aggregate output in period t, xt = yt - ytn is the output gap, ytn is the natural rate of output, ρ is the exogenous discount rate, and σ > 0, κ > 0, and 0 < β < 1. Monetary policy is described by a simple rule of the form
it = ρ + φππt
with φπ > 1. Labour productivity is given by
yt - nt = at
where nt is employment and at is an exogenous technology parame- ter that evolves according to
at = ρaat-1 + εt
where εt is a mean-zero i.i.d. process and persistence parameter ρa ∈ [0, 1). The underlying RBC model is assumed to imply a natural output level proportional to technology
ytn = ψyat
where ψy > 1.
(a) Discuss the real output and inflation expressions verbally.
(b) Determine the equilibrium response of output, employment and inflation to a technology shock.
(c) Describe how these responses depend on the value of φπ and κ. Provide economic intuition. What happens when φπ → ∞? What happens when the elasticity of labour supply (HINT: one of the ingredients of parameter κ) increases ?
(d) Analyse the joint response of employment and output to a tech-nology shock and discuss briefly the implications of the role of technology as the source of business cycles.
(e) (NONCOMPULSORY-BONUS QUESTION) Simulate the model with technology, inflation and aggregate demand shocks with the help of Matlab/Dynare programme.
8. Home Production: Consider a macro model where the representative consumer derives utility not only from market-based consump- tion (CM ) and leisure (L) but also from "home-based" consumption (CH):
Ut = 1/e ln [a(CtM)e + (1 - a) (CtH)e] + ηlnLt.
where Lt represents the leisure defined as Lt = 1 - NtH - NtM, where NtH is the hours worked at home and NtM is the hours worked in the market. Parameter e governs the elasticity of substitution between market-based and home-based consumption. The budget constraint of the consumer is given by:
CtM + CtH + Bt/Pt = WtM/Pt.NtM + ( 1 + it-1) Bt-1/Pt
where B is the nominal bond holdings, (1 + i) represents the gross rate of return on bond holdings, WM/P represents the "market" real wage rate only paid when the consumer offers labour supply for the production of the market-based goods and P the aggregate price index. The consumer produces the home-based good only for her own consumption, CtH. Therefore there is a second constraint which denotes the home-based production such that CtH = sHNtH, with sH ≥ 1. The market-based good is produced by using market labour supply and the production of this good takes the form YtM = sMNtM with sM ≥ 1. Finally, assume that the transversality condition holds.
(a) Define decision and state variables.
(b) State the value function and the associated Lagrangian. Derive the first-order conditions for the consumer with respect to bond holdings, labor supplies and consumption.
(c) Derive the consumption Euler equation and the intratemporal labour supply condition between hours worked at home and in the market. Provide intuition to your results.
(d) Suppose that the consumer is subject to
i. a liquidity constraint such that she cannot borrow in the financial market in the current period only. How do your results change? Explain.
ii. a liquidity constraint such that she cannot borrow in the market both in the current and future periods. How do your results change? Explain.
SECTION C: Answer ALL questions.
9. Output Y us a positive function of capital K, productivity A, popu- lation L and education E:
Yt = Ktα (At, Lt G(E))1-α
G(E) = eφE
with φ > 0. Assume that the economy is closed so that savings equal investment. Investment is denoted by I, the exogenous saving rate is s and depreciation is denoted by δ. Furthermore, there is population growth n and technical progress g:
K? = sYt - δKt
A? = aAt
L? = nLt
Finally, the length of an individuals lifespan is T, the individual spends time E acquiring education and T - E in the labour market.
At each point in time there are Bt new born individuals being added to total population N of which L participate in the labour market.
(a) Solve the model for steady state, in particular the steady-state level of output per member of the labour force (Y/L) and output per capita (Y/N)?
(b) Find the optimal length of education E that maximises output per capita (Y/N) in steady state (the Golden rule level of educa- tion). Is it possible that under certain parameter configurations it becomes optimal for individuals to acquire no education?
(c) What is the impact of a longer life expectancy (T) on the optimal length of education? Explain!
(d) What is the impact of better schools on the optimal length of education? Explain!
10. A government has quantity D of debt coming due next year. The interest on the debt is r so that the interest factor R = 1 + r. There is uncertainty about next years tax revenues T; if they exceed debt repayments RD the government will not default on its obligations while if they fall short; R < RD, it will default and creditors will not get anything back. The uncertainty regarding future tax revenues is described by the cumulative distribution function F(x) which gives the probability that x < T. The minimum possible level of T is de- noted by T and the maximum possible level of T is denoted by T. The probability of default is denoted by π.
(a) Describe the equilibrium in the model where the expected re- turn on the sovereigns debt is equal to the riskless interest rate (riskless interest factor R') and the probability of default is the one implied by the equilibrium interest rate. Show how multi- ple equilibria can arise in the model and discuss their stability properties.
(b) Describe the effects of the following changes on the equilibrium probability of default; i. An increase in the level of debt D. ii. Higher rate of riskless interest rate. iii. A fall in the minimum possible level of tax revenues T.
(c) Describe using the model how a sovereign default can occur due to a self-fulfilling prophecy.
(d) Discuss the Eurozone crisis that started in the spring of 2010 in the light of this model