Monetary Economics Exam 2023 - PDF

Monetary economics Exam: March 2023 Prof. Giuliano Curatola Submission (via email) deadline : Tuesday March 21, 12:00 (noon). Late submissions (at time 18 : xx, ∀ xx > 0) will not be accepted. Copy-paste answers from the slides result in zero...

Monetary economics Exam: March 2023 Prof. Giuliano Curatola Submission (via email) deadline : Tuesday March 21, 12:00 (noon). Late submissions (at time 18 : xx, ∀ xx > 0) will not be accepted. Copy-paste answers from the slides result in zero points. Copy-paste answers from other students result in zero points. Arbitrary changes of assumptions result in zero points. Prepare 2 files: i) one PDF (only one !!) which includes your answers and the Matlab generated figures and ii) The Matlab file. Make sure the m-file runs smoothly without errors. Non-running files result in zero points. Name the submitted files using your family name; Add name and matriculation number in the submitted files. The total number of points is 30 +2. Passing score: 18 (if you fail you cannot take the oral exam. You will be informed before the oral exam). Exam solution will not be posted/distributed online but can be discussed during the office hours. Name: Matriculation number: 1. Equilibrium asset pricing (Total: 12 Points) Consider a Lucas economy where the representative agent is equipped with exponential utility function of consump- tion, U(c) = − e −γC γ Assume that aggregate consumption follows Ct+1 = a + bCt + εt+1 where εt+1 ∼ N(0, σ), a > 0 and −1 < b < 1. (a) Compute the equilibrium risk-free rate at time t. What happens to the risk-free rate if γ increases? Explain (4 Points). (b) The representative agent can also buy a risky asset which pays a random div- idend in one period from now. The dividend D follows log Dt+1 = d0 + log Dt + εt+1 + ǫt+1 where ǫt+1 ∼ N(0, χ) and is uncorrelated with ε. Compute the price-dividend ratio of the one-period asset. What happens to the price-divided ratio if γ increases? Explain (4 Points) (c) Compute the expected return of the one-period asset. What happens to ex- pected returns if a increases? Explain. (4 Points) 2. Real effects of monetary policy (Total: 10 Points) Assume you want to esti- mate the effect of monetary policy on output and, thus, run the following regressions ! ! ! ! yt+1 a1,1 a1,2 yt uy,t+1 = + (1) xt+1 a2,1 a2,2 xt ux,t+1 where y is the log of real output and x represents short-term interest rates. Moreover, the assumed structure of the error terms is given by ! ! ! uy,t+1 b11 b12 ey,t+1 = ux,t+1 b21 b22 ex,t+1 (a) Derive the system to be solved to estimate parameters bij. (3 Points) (b) Set b12 = 0 and estimate b11 , b21 and b22. Explain the economic meaning of the identification assumption (4 Points) (c) What is the contemporaneous impact of ex on output? What is the lagged impact of ex on output? Explain and discuss conditions such that the impact is positive or negative. (3 Points) 3. Solving models with Matlab (Total: 10 Points) Assume you solve your DSGE model and find the following optimality conditions describing output growth (ỹt = Page 1 of 2 yt − ȳ) and interest rates (ĩt = it − ī) ỹt+1 = β ỹt + δ ĩt+1 (2) ĩt+1 = +γ ỹt+1 + λĩt + νt+1 (3) where yt and it represent the log of output and interest rates at time t, x̄ is the steady-state value of x, ν captures monetary policy shocks and t represents the time in years. (a) Assume β = −.1, δ =.2, γ =.1 and λ =.4. Set νt+1 = 0 and plot ỹt+1 and ĩt+1 as a function of ĩt. Explain (include the answer in the PDF file). (5 Points) (b) What is the effect of a unit expansionary monetary policy shock? Plot output growth as a function of νt+1 for νt+1 = [−.5,...,.5]. Under which condition the expansionary shock has a positive impact on output (include the answer in the PDF file)? (5 Points) Page 2 of 2