def Qfunc(theta):
'''
This is a function that calculates the distance between simulated moments
and the actual moments for the setup used for table 2
'''
import kgrid
import zgrid
import z_markov
import simulate as sim
import VFI
# getting the grid space for capital
kgrid, sizek = kgrid.main(params,w,a_k)
# getting the grid space for shocks
z_grid, pi = zgrid.main(sigma, mu, rho, sizez)
# getting firm's optimal decision rule
V, PF = VFI.main(theta, params, z_grid, kgrid, sizek, sizez,
pi, a_k, w, psi)
# simulate the data
k_sim, I_sim, V_sim, pi_sim = sim.main(theta, params, kgrid,
pi, V, PF, N, T, z_grid)
# define variables of interest
I_K = (I_sim/k_sim).reshape((N*T, 1))
Qav = (V_sim/k_sim).reshape((N*T, 1))
PI_K = (pi_sim/k_sim).reshape((N*T, 1))
# get the necessary statistics
I_Kr = I_K.reshape((1, N*T))
sc = np.corrcoef(I_Kr[0][1:], I_Kr[0][:N*T-1])[0,1]
sd = np.std(PI_K)
qbar = V_sim.sum() / k_sim.sum()
# run the q-regression
Y = np.matrix(I_K)
X = np.matrix(np.concatenate((np.ones((N*T, 1)), Qav, PI_K), axis = 1))
a0, a1, a2 = np.linalg.inv(X.T * X) * X.T * Y
# construct the vectors
mu_sim = np.array((a1[0, 0], a2[0, 0], sc, sd, qbar))
mu_real = np.array((.03, .24, .4, .25, 3))
# identity matrix
Wmat = np.eye(len(mu_sim))
# get the distance between simulated statistics and the actual statistics
dist = np.matrix((mu_real - mu_sim)) * np.linalg.inv(Wmat) * np.matrix((mu_real - mu_sim)).T
return dist
def get_sim(theta):
'''
This is a function that returns the simulated moments
to be used to obtain the standard errors
'''
import kgrid
import zgrid
import z_markov
import simulate as sim
import VFI
# getting the grid space for capital
kgrid, sizek = kgrid.main(params,w,a_k)
# getting the grid space for shocks
z_grid, pi = zgrid.main(sigma, mu, rho, sizez)
# getting firm's optimal decision rule
V, PF = VFI.main(theta, params, z_grid, kgrid, sizek, sizez,
pi, a_k, w, psi)
# simulate the data
k_sim, I_sim, V_sim, pi_sim = sim.main(theta, params, kgrid,
pi, V, PF, N, T, z_grid)
# define variables of interest
I_K = (I_sim/k_sim).reshape((N*T, 1))
Qav = (V_sim/k_sim).reshape((N*T, 1))
PI_K = (pi_sim/k_sim).reshape((N*T, 1))
# get the necessary statistics
I_Kr = I_K.reshape((1, N*T))
sc = np.corrcoef(I_Kr[0][1:], I_Kr[0][:N*T-1])[0,1]
sd = np.std(PI_K)
qbar = V_sim.sum() / k_sim.sum()
# run the q-regression
Y = np.matrix(I_K)
X = np.matrix(np.concatenate((np.ones((N*T, 1)), Qav, PI_K), axis = 1))
a0, a1, a2 = np.linalg.inv(X.T * X) * X.T * Y
# construct the vectors
mu_sim = np.array((a1[0, 0], a2[0, 0], sc, sd, qbar))
return mu_sim
def sim_moments(theta):
import numpy as np
import time
import numba
import zgrid
import kgrid
import zshocks
import simul
import VFI
# params
#sigma = 0.213 # struct param to be estimated
mu = 0 # fixed param
#rho = 0.7605 # struct param to be estimated
sizez = 9 # fixed param
#ak = .297 # struct param to be estimated
al = .650 # fixed
delta = 0.15 # fixed
betaf = .95 # fixed
#psi = 1.080 # struct param to be estimated
params = (mu, sizez, al, delta, betaf)
T = 250 # number of years simulated
N = 1000 # number of firms simulated
kgrid, sizek = kgrid.main(params)
z_grid, pi = zgrid.main(sigma, mu, rho, sizez)
# E = earnings.main(theta, params, kgrid, sizek, z_grid)
Vnext, loc = VFI.main(theta, params, z_grid, kgrid, sizek, sizez, pi)
k_sim, I_sim, V_sim, prof_sim = simul.main(theta, params, kgrid, pi, Vnext,
loc, T, N, z_grid)
def moments(k_sim, I_sim, V_sim, prof_sim):
IoverK = (I_sim / k_sim).reshape((N * 50, 1))
avgQ = (V_sim / k_sim).reshape((N * 50, 1))
PIoverK = (prof_sim / k_sim).reshape((N * 50, 1))
y = np.matrix(IoverK)
X = np.matrix(
np.concatenate((np.ones((N * 50, 1)), avgQ, PIoverK), axis=1))
a0, a1, a2 = np.linalg.inv(X.T * X) * X.T * y # reg coeffs
ik = IoverK.reshape((1, N * 50)) # I over K reshaped for corrcoef()
sc_ik = np.corrcoef(ik[0][1:], ik[0][:50000 - 1])[0, 1] # sc_
sd_piK = np.std(PIoverK)
qbar = V_sim.sum() / k_sim.sum()
U_sim = np.array((a1[0, 0], a2[0, 0], sc_ik, sd_piK, qbar))
return U_sim
U_sim = moments(k_sim, I_sim, V_sim, prof_sim)
return U_sim
delta = .154 # Depreciation
psi = 1.080 # Coeff on quadratic adj costs
wage = .7 # wage rate
r = .040 # Int rate
betaf = 1 / (1 + r) # discount factor
sigma = .213 # Std. Deviation of z shockkgrid
mu = 0 # mean of z AR1
rho = .7605 # Persistance of z shock
sizez = 9 # size of z grid
h = 6.616
# parameters that occur in any state of the model (Gen or Partial equilibrium)
params = (ak, al, delta, psi, wage, r, betaf, sigma, mu, rho, sizez)
# calls the kgrid function to return the grid of k values and size of kgrid
kgrid, sizek = kgrid.main(params)
# calls the z_grid function to caluclate the zgrid given sizez
z_grid, pi = zgrid.main(params)
# free parameters in the Gen eq (not including wage since it is endog.)
eq_params = (ak, al, delta, psi, r, betaf, sigma, mu, rho, sizez, h)
wage_initial = .89 # initialize a wage guess.
# cal the optimizer routine of the equil function which determines equlibrium
# for a given wage and param values
OPTWAGE = opt.minimize(equil.main,
wage_initial, (eq_params, sizek, kgrid, z_grid, pi),
method='Nelder-Mead',
tol=1e-5,