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blocks.py
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blocks.py
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import time
import numpy as np
import numba as nb
#######################
# auxiliary functions #
#######################
@nb.njit
def lag(inivalue,pathvalue):
output = np.empty_like(pathvalue)
output[0,:] = inivalue
output[1:,:] = pathvalue[:-1,:]
return output
@nb.njit
def lead(pathvalue,ssvalue):
output = np.empty_like(pathvalue)
output[:-1,:] = pathvalue[1:,:]
output[-1,:] = ssvalue
return output
@nb.njit
def next_period(x,t,ssvalue):
if t+1 < x.shape[0]:
return x[t+1]
else:
return np.repeat(ssvalue,x.shape[1])
@nb.njit
def prev_period(x,t,inivalue):
if t > 0:
return x[t-1]
else:
return np.repeat(inivalue,x.shape[1])
@nb.njit
def CES_Y(Xi,Xj,mui,sigma,Gamma=1.0):
muj = 1-mui
inv_sigma = 1/sigma
pow_sigma = (sigma-1)/sigma
inv_pow_sigma = sigma/(sigma-1)
part_i = mui**inv_sigma*Xi**pow_sigma
part_j = muj**inv_sigma*Xj**pow_sigma
return Gamma*(part_i+part_j)**inv_pow_sigma
@nb.njit
def CES_demand(Pi,P,mui,X,sigma,Gamma=1.0):
return mui*(Pi/P)**(-sigma)*X*Gamma**(sigma-1)
@nb.njit
def CES_P(Pi,Pj,mui,sigma,Gamma=1.0):
muj = 1-mui
part_i = mui*Pi**(1-sigma)
part_j = muj*Pj**(1-sigma)
return 1/Gamma*(part_i+part_j)**(1/(1-sigma))
@nb.njit
def adj_cost(iota,K_lag,Psi_0,delta_K):
return 0.5*Psi_0*(iota/K_lag-delta_K)**2*K_lag
@nb.njit
def adj_cost_iota(iota,K_lag,Psi_0,delta_K):
return Psi_0*(iota/K_lag-delta_K)
@nb.njit
def adj_cost_K(iota,K_lag,Psi_0,delta_K):
return 0.5*Psi_0*(iota/K_lag-delta_K)**2 - Psi_0*(iota/K_lag-delta_K)*iota/K_lag
##########
# blocks #
##########
@nb.njit
def repacking_firms_prices(par,ini,ss,sol):
# inputs
P_Y = sol.P_Y
P_M_C = sol.P_M_C
P_M_G = sol.P_M_G
P_M_I = sol.P_M_I
P_M_X = sol.P_M_X
# outputs
P_C = sol.P_C
P_G = sol.P_G
P_I = sol.P_I
P_X = sol.P_X
P_C[:] = CES_P(P_M_C,P_Y,par.mu_M_C,par.sigma_C, Gamma=1)
P_G[:] = CES_P(P_M_G,P_Y,par.mu_M_G,par.sigma_G, Gamma=1)
P_I[:] = CES_P(P_M_I,P_Y,par.mu_M_I,par.sigma_I, Gamma=1)
P_X[:] = CES_P(P_M_X,P_Y,par.mu_M_X,par.sigma_X, Gamma=1)
@nb.njit
def wage_determination(par,ini,ss,sol):
# inputs
P_C = sol.P_C
L = sol.L
# outputs
W = sol.W
real_wage_ss = ss.W/ss.P_C*(L/ss.L)**par.epsilon_w
W[:] = real_wage_ss*P_C
@nb.njit
def search_and_match(par,ini,ss,sol):
# inputs
L = sol.L
# outputs
curlyM = sol.curlyM
delta_L = sol.delta_L
L_a = sol.L_a
LH_a = sol.LH_a
L_ubar = sol.L_ubar
L_ubar_a = sol.L_ubar_a
m_s = sol.m_s
m_v = sol.m_v
S = sol.S
S_a = sol.S_a
x_a = sol.x_a
U = sol.U
U_a = sol.U_a
v = sol.v
H_a = sol.H_a
LH = sol.LH
H = sol.H
# evaluations
for t in range(par.T):
# a. lagged employment
L_lag = prev_period(L,t,ini.L)
# b. searchers and employed before matching
S_a[0,t] = 1.0
L_ubar_a[0,t] = 0.0
x_a[0,t] = 0
for a in range(1,par.work_life_span):
L_a_lag = prev_period(L_a[a-1],t,ini.L_a[a-1])
x_a_lag = prev_period(x_a[a-1],t,ini.x_a[a-1])
S_a[a,t] = (1-par.zeta_a[a])*((par.N_a[a-1]-L_a_lag) + par.delta_L_a[a]*L_a_lag)
L_ubar_a[a,t] = (1-par.zeta_a[a])*((1-par.delta_L_a[a])*L_a_lag)
x_a[a,t] = x_a_lag + (L_a_lag/par.N_a[a-1])**par.Phi * (ss.L_a[a-1]/par.N_a[a-1])**(1-par.Phi)
S_a[par.work_life_span:,t] = 0.0
L_ubar_a[par.work_life_span:,t] = 0.0
x_a[par.work_life_span:,t] = 0.0
H_a[:,t] = 1 + par.rho_1*x_a[:,t] - par.rho_2*x_a[:,t]**2
S[t] = 0.0
L_ubar[t] = 0.0
for a in range(par.life_span):
S[t] += S_a[a,t]
L_ubar[t] += L_ubar_a[a,t]
# c. aggregate separation rate
delta_L[t] = (L_lag-L_ubar[t])/L_lag
# d. matching
curlyM[t] = L[t]-L_ubar[t]
m_s[t] = curlyM[t]/S[t]
v[t] = (curlyM[t]**(1/par.sigma_m)/(1-m_s[t]**(1/par.sigma_m)))**par.sigma_m
m_v[t] = curlyM[t]/v[t]
# e. emplolyment and unemployment
U[t] = 0.0
LH[t] = 0.0
for a in range(par.life_span):
L_a[a,t] = L_ubar_a[a,t] + m_s[t]*S_a[a,t]
LH_a[a,t] = H_a[a,t]*L_a[a,t]
if a < par.work_life_span:
U_a[a,t] = par.N_a[a] - sol.L_a[a,t]
else:
U_a[a,t] = 0.0
LH[t] += LH_a[a,t]
U[t] += U_a[a,t]
H[t] = LH[t]/L[t]
@nb.njit
def labor_agency(par,ini,ss,sol):
# inputs
delta_L = sol.delta_L
L = sol.L
m_v = sol.m_v
v = sol.v
W = sol.W
H = sol.H
# outputs
ell = sol.ell
r_ell = sol.r_ell
# evaluations
ell[:] = H*L-par.kappa_L*v
for k in range(par.T):
t = par.T-1-k
r_ell_plus = next_period(r_ell,t,ss.r_ell)
delta_L_plus = next_period(delta_L,t,ss.delta_L)
m_v_plus = next_period(m_v,t,ss.m_v)
fac = 1/(H[t]-par.kappa_L/m_v[t])
term = r_ell_plus*(1-delta_L_plus)/(1+par.r_firm)*par.kappa_L/m_v_plus
r_ell[t] = fac*(W[t]*H[t]-term)
@nb.njit
def production_firm(par,ini,ss,sol):
# inputs
ell = sol.ell
Gamma = sol.Gamma
K = sol.K
r_K = sol.r_K
r_ell = sol.r_ell
# outputs
P_Y_0 = sol.P_Y_0
Y = sol.Y
# targets
FOC_K_ell = sol.FOC_K_ell
# evaluations
K_lag = lag(ini.K,K)
Y[:] = CES_Y(K_lag,ell,par.mu_K,par.sigma_Y,Gamma=Gamma)
P_Y_0[:] = CES_P(r_K,r_ell,par.mu_K,par.sigma_Y,Gamma=Gamma)
FOC_K_ell[:] = K_lag/ell - par.mu_K/(1-par.mu_K)*(r_ell/r_K)**par.sigma_Y
@nb.njit
def phillips_curve(par,ini,ss,sol):
# inputs
P_Y_0 = sol.P_Y_0
Y = sol.Y
# outputs
P_Y = sol.P_Y
# targets
PC = sol.PC
# evaluations
P_Y_lag = lag(ini.P_Y,P_Y)
P_Y_lag_lag = lag(ini.P_Y,P_Y_lag)
P_Y_plus = lead(P_Y,ss.P_Y)
Y_plus = lead(Y,ss.Y)
eta = par.theta*par.gamma
LHS = P_Y
RHS_0 = (1+par.theta)*P_Y_0
fac_lag = P_Y/P_Y_lag/(P_Y_lag/P_Y_lag_lag)
RHS_1 = -eta*(fac_lag-1)*fac_lag*P_Y
fac = P_Y_plus/P_Y/(P_Y/P_Y_lag)
RHS_2 = 2/(1+par.r_firm)*eta*Y_plus/Y*(fac-1)*fac*P_Y_plus
PC[:] = LHS - RHS_0 - RHS_1 - RHS_2
@nb.njit
def foreign_economy(par,ini,ss,sol):
# inputs
P_F = sol.P_F
chi = sol.chi
P_X = sol.P_X
# outputs
X = sol.X
# evaluations
for t in range(par.T):
X_lag = prev_period(X,t,ini.X)
X[t] = par.gamma_X*X_lag + (1-par.gamma_X)*chi[t]*(P_X[t]/P_F[t])**(-par.sigma_F)
@nb.njit
def capital_agency(par,ini,ss,sol):
# inputs
K = sol.K
P_I = sol.P_I
r_K = sol.r_K
# outputs
I = sol.I
iota = sol.iota
# targets
FOC_capital_agency = sol.FOC_capital_agency
# evaluations
K_lag = lag(ini.K,K)
P_I_plus = lead(P_I,ss.P_I)
r_K_plus = lead(r_K,ss.r_K)
iota[:] = K - (1-par.delta_K)*K_lag
I[:] = iota + adj_cost(iota,K_lag,par.Psi_0,par.delta_K)
iota_plus = lead(iota,ss.iota)
term_a = -P_I*(1+adj_cost_iota(iota,K_lag,par.Psi_0,par.delta_K))
term_b = (1-par.delta_K)*P_I_plus*(1+adj_cost_iota(iota_plus,K,par.Psi_0,par.delta_K))
term_c = -P_I_plus*adj_cost_K(iota_plus,K,par.Psi_0,par.delta_K)
FOC_capital_agency[:] = term_a + 1/(1+par.r_firm)*(r_K_plus + term_b + term_c)
@nb.njit
def government(par,ini,ss,sol):
# inputs
G = sol.G
P_G = sol.P_G
U = sol.U
W = sol.W
LH = sol.LH
# outputs
B = sol.B
tau = sol.tau
# evaluations
for t in range(par.T):
B_lag = prev_period(B,t,ini.B)
expenditure = par.r_b*B_lag + P_G[t]*G[t] + par.W_U*ss.W*U[t] + par.W_R*ss.W*(par.N-par.N_work)
taxbase = W[t]*LH[t] + par.W_U*ss.W*U[t] + par.W_R*ss.W*(par.N-par.N_work)
B_tilde = B_lag + expenditure - ss.tau*taxbase
tau[t] = ss.tau + par.epsilon_B*(B_tilde-ss.B)/taxbase
B[t] = B_lag + expenditure - tau[t]*taxbase
@nb.njit(parallel=True)
def household_income(par,ini,ss,sol):
# inputs
Aq = sol.Aq
LH_a = sol.LH_a
tau = sol.tau
U_a = sol.U_a
W = sol.W
L_a = sol.L_a
# outputs
inc_a = sol.inc_a
for t in nb.prange(par.T):
for a in range(par.life_span):
inc_a[a,t,:] = (1-tau[t])*W[t]*LH_a[a,t,:]/par.N_a[a] + (1-tau[t])*par.W_U*ss.W*U_a[a,t,:]/par.N_a[a] + Aq[t]/par.N
if a >=par.work_life_span:
inc_a[a,t,:] += (1-tau[t])*par.W_R*ss.W
@nb.njit(parallel=True)
def household_consumption_HtM(par,ini,ss,sol):
# inputs
P_C = sol.P_C
inc_a = sol.inc_a
# outputs
C_HtM_a = sol.C_HtM_a
A_HtM_a = sol.A_HtM_a
# a. HtM
for t in nb.prange(par.T):
for a in range(par.life_span):
C_HtM_a[a,t,:] = inc_a[a,t,:]/P_C[t]
A_HtM_a[a,t,:] = 0.0
@nb.njit(parallel=True)
def household_consumption_R(par,ini,ss,sol):
# inputs
A_R_death = sol.A_R_death
P_C = sol.P_C
W = sol.W
inc_a = sol.inc_a
r_hh = sol.r_hh
# outputs
pi_hh = sol.pi_hh
real_r_hh = sol.real_r_hh
real_W = sol.real_W
A_R_a = sol.A_R_a
C_R_a = sol.C_R_a
# evaluations
P_C_lag = lag(ini.P_C,P_C)
pi_hh[:] = P_C/P_C_lag-1
pi_hh_plus = lead(pi_hh,ss.pi_hh)
real_W[:] = W/P_C
real_r_hh[:] = (1+r_hh)/(1+pi_hh_plus)-1
# Ricardian
for t0 in nb.prange(-par.life_span+1,par.T): # birthcohort
C_R_a_plus = np.zeros(C_R_a.shape[2])
for i in range(par.life_span):
a = par.life_span - 1 - i
t = t0 + a
if t < 0: continue
if t > par.T-1: continue
# i. now and plus
if a == par.life_span-1:
A_R_a[a,t,:] = A_R_death[t]
else:
if t == par.T-1:
A_R_a[a,t,:] = ss.A_R_a[a]
C_R_a_plus[:] = ss.C_R_a[a+1]
else:
C_R_a_plus[:] = C_R_a[a+1,t+1,:]
# # ii. consumption
RHS = par.zeta_a[a]*par.mu_Aq*(A_R_a[a,t,:]/P_C[t])**(-par.sigma)
if a < par.life_span-1:
RHS += (1-par.zeta_a[a])*par.beta*(1+real_r_hh[t])*C_R_a_plus**(-par.sigma)
C_R_a[a,t,:] = RHS**(-1/par.sigma)
# iii. lagged assets
if a > 0 and t > 0:
A_R_a[a-1,t-1,:] = (A_R_a[a,t,:] + P_C[t]*C_R_a[a,t,:] - inc_a[a,t,:])/(1+r_hh[t])
@nb.njit
def household_A_R_ini_error(par,ini,ss,sol):
# inputs
A_R_death = sol.A_R_death
P_C = sol.P_C
inc_a = sol.inc_a
r_hh = sol.r_hh
real_r_hh = sol.real_r_hh
A_R_a = sol.A_R_a
C_R_a = sol.C_R_a
# outputs
# targets
A_R_ini_error = sol.A_R_ini_error
for t0 in range(-par.life_span+1,par.T): # birthcohort
for i in range(par.life_span):
a = par.life_span - 1 - i
t = t0 + a
if t < 0: continue
if t > par.T-1: continue
if not (a > 0 and t > 0):
A_R_a_lag = (A_R_a[a,t,:] + P_C[t]*C_R_a[a,t,:] - inc_a[a,t,:])/(1+r_hh[t])
if t0 < 0:
A_R_ini_error[t0-(-par.life_span+1),:] = A_R_a_lag-ini.A_R_a[a-1]
elif t0 <= par.T-1-par.life_span+1:
A_R_ini_error[t0-(-par.life_span+1),:] = A_R_a_lag-0.0
@nb.njit(parallel=True)
def household_aggregate(par,ini,ss,sol):
# inputs
inc_a = sol.inc_a
A_a = sol.A_a
Aq = sol.Aq
C_HtM_a = sol.C_HtM_a
C_R_a = sol.C_R_a
C_a = sol.C_a
pi_hh = sol.pi_hh
real_r_hh = sol.real_r_hh
real_W = sol.real_W
A_HtM_a = sol.A_HtM_a
A_R_a = sol.A_R_a
A_a = sol.A_a
C_HtM_a = sol.C_HtM_a
C_R_a = sol.C_R_a
C_a = sol.C_a
# outputs
A = sol.A
C = sol.C
C_R = sol.C_R
C_HtM = sol.C_HtM
inc = sol.inc
r_hh = sol.r_hh
# targets
Aq_diff = sol.Aq_diff
# calculations
C_HtM[:] = 0
C_R[:] = 0
C[:] = 0
A[:] = 0
inc[:] = 0
Aq_diff[:] = Aq[:]
for t in nb.prange(par.T):
for a in range(par.life_span):
C_a[a,t,:] = par.Lambda*C_HtM_a[a,t,:]+(1-par.Lambda)*C_R_a[a,t,:]
A_a[a,t,:] = par.Lambda*A_HtM_a[a,t,:]+(1-par.Lambda)*A_R_a[a,t,:]
C_HtM[t] += par.N_a[a]*C_HtM_a[a,t,:]
C_R[t] += par.N_a[a]*C_R_a[a,t,:]
C[t] += par.N_a[a]*C_a[a,t,:]
A[t] += par.N_a[a]*A_a[a,t,:]
inc[t] += par.N_a[a]*inc_a[a,t,:]
if t == 0:
Aq_diff[t] -= (1+r_hh[t])*par.zeta_a[a]*par.N_a[a]*ss.A_a[a]
else:
Aq_diff[t] -= (1+r_hh[t])*par.zeta_a[a]*par.N_a[a]*A_a[a,t,:]
@nb.njit
def repacking_firms_components(par,ini,ss,sol):
# inputs
C = sol.C
G = sol.G
I = sol.I
P_M_C = sol.P_M_C
P_M_G = sol.P_M_G
P_M_I = sol.P_M_I
P_M_X = sol.P_M_X
P_C = sol.P_C
P_G = sol.P_G
P_I = sol.P_I
P_X = sol.P_X
P_Y = sol.P_Y
X = sol.X
# outputs
C_M = sol.C_M
C_Y = sol.C_Y
G_M = sol.G_M
G_Y = sol.G_Y
I_M = sol.I_M
I_Y = sol.I_Y
X_M = sol.X_M
X_Y = sol.X_Y
# evaluations
C_M[:] = CES_demand(P_M_C,P_C,par.mu_M_C,C,par.sigma_C,Gamma=1)
G_M[:] = CES_demand(P_M_G,P_G,par.mu_M_G,G,par.sigma_G,Gamma=1)
I_M[:] = CES_demand(P_M_I,P_I,par.mu_M_I,I,par.sigma_I,Gamma=1)
X_M[:] = CES_demand(P_M_X,P_X,par.mu_M_X,X,par.sigma_X,Gamma=1)
C_Y[:] = CES_demand(P_Y,P_C,1-par.mu_M_C,C,par.sigma_C,Gamma=1)
G_Y[:] = CES_demand(P_Y,P_G,1-par.mu_M_G,G,par.sigma_G,Gamma=1)
I_Y[:] = CES_demand(P_Y,P_I,1-par.mu_M_I,I,par.sigma_I,Gamma=1)
X_Y[:] = CES_demand(P_Y,P_X,1-par.mu_M_X,X,par.sigma_X,Gamma=1)
@nb.njit
def goods_market_clearing(par,ini,ss,sol):
# inputs
C_M = sol.C_M
C_Y = sol.C_Y
G_M = sol.G_M
G_Y = sol.G_Y
I_M = sol.I_M
I_Y = sol.I_Y
X_M = sol.X_M
X_Y = sol.X_Y
Y = sol.Y
# outputs
M = sol.M
# targets
mkt_clearing = sol.mkt_clearing
# evalautions
M[:] = C_M + G_M + I_M + X_M
mkt_clearing[:] = Y - (C_Y + G_Y + I_Y + X_Y)
@nb.njit
def real_productivity(par,ini,ss,sol):
# inputs
r_K = sol.r_K
r_ell = sol.r_ell
P_Y = sol.P_Y
P_C = sol.P_C
inc = sol.inc
Aq = sol.Aq
# outputs
real_r_K = sol.real_r_K
real_r_ell = sol.real_r_ell
real_inc = sol.real_inc
real_Aq = sol.real_Aq
#evaluations
real_r_K[:] = r_K/P_Y
real_r_ell[:] = r_ell/P_Y
real_inc[:] = inc/P_C
real_Aq[:] = Aq/P_C
@nb.njit
def ratios(par,ini,ss,sol):
# inputs
Y = sol.Y
C = sol.C
G = sol.G
I = sol.I
K = sol.K
L = sol.L
M = sol.M
X = sol.X
# outputs
C_ratio = sol.C_ratio
G_ratio = sol.G_ratio
I_ratio = sol.I_ratio
K_ratio = sol.K_ratio
L_ratio = sol.L_ratio
M_ratio = sol.M_ratio
X_ratio = sol.X_ratio
#evaluations
C_ratio = C/Y
G_ratio = G/Y
I_ratio = I/Y
K_ratio = K/Y
L_ratio = L/par.N
M_ratio = M/Y
X_ratio = X/Y