ECON 6002 Problem Set 2 (RBC)
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Problem Set 2 (RBC)
ECON 6002
1. Abstracting from long-run growth by setting n = g = 0 nd from persistent shocks by setting ρA = ρtt = 0, with A˜t ≡ lnAt − lnA¯ and tt˜t ≡ lnttt − lntt¯, and normalizing the population to N = 1, the following nine equations describe the “baseline” RBC model in Chapter 5:
Yt = Ct + It + ttt (1)
Yt = Kα (AtLt)1−α (2)
Kt = Kt−1 + It − δKt−1 (3)
A˜t = ϵA,t (4)
tt˜t = ϵtt,t (5)
rt = α(AtLt/Kt−1)1−α − δ (6)
wt = (1 − α)(Kt−1/AtLt)αAt (7)
where e−ρ = β.
1
Ct
Ct
1 − Lt
= βEt
= wt b
1 (1 + r Ct+1
t+1
)Σ (8)
(9)
(a) Find the steady state for this economy under the following calibration: α = 1/3, δ = 0.05,
r¯ = 0.025, A¯ = 1, and L¯
= 0.5 and tt¯
such that tt¯/Y¯
= 0.2. In particular, find the
remaining parameter values b and ρ that are consistent with steady state and determine
steady-state values for the endogenous variables, Y¯ , C¯, I¯, tt¯, K¯ , and w¯.
(b) Log-linearize the seven equations above excluding equations (4) and (5) for A˜t and tt˜t.
(c) Write a Dynare .mod file to simulate this economy. Assume that A˜t = ρAA˜t−1 + ϵA,t and
tt˜t = ρtttt˜t−1 + ϵtt,t are the log-linearized shocks. Set α = 1/3, δ = 0.05, ρA = ρtt = .8,
e−ρ = 0.99, σϵ = σϵ = 1, and b = 1. Provide a graph of the impulse response of one
G
standard deviation shock to technology and government spending. (Hint: This model is nearly identical to the one we went over in class. Rather than start from scratch try modifying the Dynare .mod I have provided on Canvas. Also, you need to use tt¯/Y¯ = 0.2 to figure out the steady parameter values needed to do your simulation.)
(d) What is the effect of a positive government spending shock on the real wage? Explain.
2022-10-11