These questions should be answered using the rbc_benchmark_HW.mod
file included with your lab materials.
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
from mpl_toolkits.mplot3d import Axes3D
from scipy import linalg, interpolate, io
The only difference between the rbc_benchmark_HW.mod
file and the rbc_benchmark.mod
file that we used in the lab is that in rbc_benchmark_HW.mod
I have set $\theta = 1.0$ and $\gamma=1.0$. What does this parameterization imply about the preferences of the representative household?
Using Dynare++
solve for a first-order approximation of the household decision rules (you should also specify the same command line options that we used in the lab) and load the resulting rbc_benchmark_HW.mat
file in a Python.
# insert your code here!
Using code provided in the lab, plot impulse response functions (IRFs) for output, consumption, and investment in response to a negative productivity shock. Discuss the economic mechanisms at work. You may wish to refer to the discussion of IRFs in Romer Chapter 5 and/or your lecture notes.
# insert your code here!
Using code provided in the lab, plot IRFs for labor supply and the real wage for the model in response to a positive productivity shock. Discuss the economic mechanisms at work. You may wish to refer to the discussion of IRFs in Romer Chapter 5 and/or your lecture notes.
# insert your code here!
Using code provided in the lab, construct the correlation matrix for the model's endogenous variables. What is the correlation between the real wage and the labor supply? How does your result compare to results reported in Romer and discussed in your lecture notes?
# insert your code here!
Open the rbc_benchmark_HW.mod
file and change the value of $\theta$ to $\theta = 2.5$. Discuss the impact of this change on household preferences.
Using Dynare++
solve for a first-order approximation of the household decision rules (you should also specify the same command line options that we used in the lab) and load the resulting rbc_benchmark_HW.mat
file into Python.
# insert your code here!
Using code provided in the lab, plot IRFs for labor supply and the real wage for the model in response to a positive productivity shock. Discuss. Discuss the economic mechanisms at work. You may wish to refer to the discussion of IRFs in Romer Chapter 5 and/or your lecture notes.
# insert your code here!
Using code provided in the lab, construct the correlation matrix for the model's endogenous variables. What is the correlation between the real wage and the labor supply? How does your result compare to results reported in Romer and discussed in your lecture notes? Compare/contrast this result with your result from Question 1, Part e.
# insert your code here!