# ### Incumbent Firms' Decision Rule (Tauchen's method first usage)
# In[47]:
### k_grid
k_low = k_ss - 0.5
k_high = k_ss + 0.5
k_grid = np.linspace(k_low, k_high, N_k)
### eps_grid using Tauchen
## https://lectures.quantecon.org/jl/finite_markov.html
trans_eps_MC = tauchen(rho, sigma, n=N_eps).P
sigma_y = np.sqrt( sigma ** 2 / (1 - rho ** 2) )
eps_grid = np.zeros(N_eps)
eps_grid[0] = -m * sigma_y
eps_grid[N_eps-1] = m * sigma_y
s = (eps_grid[N_eps-1] - eps_grid[0]) / (N_eps - 1)
for i in range(1, N_eps-1):
eps_grid[i] = eps_grid[i-1] + s
# Now we initialize the value function:
V_init = np.zeros((N_eps, N_k))
# In[48]:
agrid = curvedspace(amin, amax, acurve, num_a)
kapgrid = curvedspace(kapmin, kapmax, kapcurve, num_kap)
# productivity shock
rho_z = 0.7
sig_z = 0.1
num_z = 5
rho_eps = 0.70446 # Estimates based on:
sig_eps = 0.1598256 # Low, Meghir, Pistaferri (2011)
num_eps = 5
mc_z = tauchen(rho=rho_z, sigma_u=sig_z, m=3, n=num_z) # discretize z
mc_eps = tauchen(rho=rho_eps, sigma_u=sig_eps, m=3,
n=num_eps) # discretize eps
# prob_z_filepath = './DeBacker/debacker_prob_z.csv'
# prob_eps_filepath = './DeBacker/debacker_prob_eps.csv'
# prob_z = np.loadtxt(prob_z_filepath)# read transition matrix from DeBacker
# prob_eps = np.loadtxt(prob_eps_filepath) # read transition matrix from DeBacker
prob_z = np.array([[
6.115186988266497758e-01, 1.704010286422269760e-01,
9.831623067597275445e-02, 6.450040495404339713e-02,
5.526363690110723537e-02
],
[
1.722564529992201832e-01, 5.509025811996880462e-01,
