Solutions for http://quant-econ.net/py/odu.html
In [1]:
%matplotlib inline
In [2]:
import numpy as np
import matplotlib.pyplot as plt
from quantecon import compute_fixed_point
from quantecon.models import SearchProblem
This code solves the "Offer Distribution Unknown" model by iterating on a guess of the
reservation wage function. You should find that the run time is much shorter than that of the value function approach in odu_vfi.py
In [3]:
sp = SearchProblem(pi_grid_size=50)
phi_init = np.ones(len(sp.pi_grid))
w_bar = compute_fixed_point(sp.res_wage_operator, phi_init)
fig, ax = plt.subplots(figsize=(9, 7))
ax.plot(sp.pi_grid, w_bar, linewidth=2, color='black')
ax.set_ylim(0, 2)
ax.grid(axis='x', linewidth=0.25, linestyle='--', color='0.25')
ax.grid(axis='y', linewidth=0.25, linestyle='--', color='0.25')
ax.fill_between(sp.pi_grid, 0, w_bar, color='blue', alpha=0.15)
ax.fill_between(sp.pi_grid, w_bar, 2, color='green', alpha=0.15)
ax.text(0.42, 1.2, 'reject')
ax.text(0.7, 1.8, 'accept')
plt.show()
The next piece of code is not one of the exercises from quant-econ, it's just a fun simulation to see what the effect of a change in the underlying distribution on the unemployment rate is.
At a point in the simulation, the distribution becomes significantly worse. It takes a while for agents to learn this, and in the meantime they are too optimistic, and turn down too many jobs. As a result, the unemployment rate spikes.
The code takes a few minutes to run.
In [4]:
from scipy import interp
# Set up model and compute the function w_bar
sp = SearchProblem(pi_grid_size=50, F_a=1, F_b=1)
pi_grid, f, g, F, G = sp.pi_grid, sp.f, sp.g, sp.F, sp.G
phi_init = np.ones(len(sp.pi_grid))
w_bar_vals = compute_fixed_point(sp.res_wage_operator, phi_init)
w_bar = lambda x: interp(x, pi_grid, w_bar_vals)
class Agent(object):
"""
Holds the employment state and beliefs of an individual agent.
"""
def __init__(self, pi=1e-3):
self.pi = pi
self.employed = 1
def update(self, H):
"Update self by drawing wage offer from distribution H."
if self.employed == 0:
w = H.rvs()
if w >= w_bar(self.pi):
self.employed = 1
else:
self.pi = 1.0 / (1 + ((1 - self.pi) * g(w)) / (self.pi * f(w)))
num_agents = 5000
separation_rate = 0.025 # Fraction of jobs that end in each period
separation_num = int(num_agents * separation_rate)
agent_indices = list(range(num_agents))
agents = [Agent() for i in range(num_agents)]
sim_length = 600
H = G # Start with distribution G
change_date = 200 # Change to F after this many periods
unempl_rate = []
for i in range(sim_length):
if i % 20 == 0:
print("date =", i)
if i == change_date:
H = F
# Randomly select separation_num agents and set employment status to 0
np.random.shuffle(agent_indices)
separation_list = agent_indices[:separation_num]
for agent_index in separation_list:
agents[agent_index].employed = 0
# Update agents
for agent in agents:
agent.update(H)
employed = [agent.employed for agent in agents]
unempl_rate.append(1 - np.mean(employed))
fig, ax = plt.subplots(figsize=(9, 7))
ax.plot(unempl_rate, lw=2, alpha=0.8, label='unemployment rate')
ax.axvline(change_date, color="red")
ax.legend()
plt.show()