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More example GCNs
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@jessegrabowski
jessegrabowski committed Nov 2, 2024
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177 changes: 177 additions & 0 deletions GCN Files/RBC_two_household.gcn
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assumptions
{
positive
{
Y[], K[], C_NR[], C_R[],
w[], r[], mc_L[],
L[], L_NR[], L_R[],
TFP[],
alpha, alpha_L, beta, sigma_C, sigma_L, delta;
};
};

tryreduce
{
U_NR[], U_R[], TC[];
};

block STEADY_STATE
{
definitions
{
f1[ss] = (r[ss] / (r[ss] - alpha * delta));
f2[ss] = (alpha_L * (1 - alpha_L) * (1 - alpha)) ^ (-sigma_L / sigma_C);
f3[ss] = alpha_L ^ (sigma_L / sigma_C) +
(1 - alpha_L) ^ (sigma_L / sigma_C);

};
identities
{
TFP[ss] = 1.0;
shock_beta_R[ss] = 1.0;

r[ss] = 1 / beta - (1 - delta);
w[ss] = (1 - alpha) * alpha_L ^ alpha_L * (1 - alpha_L) ^ (1 - alpha_L) *
(r[ss] / alpha) ^ (alpha / (alpha - 1));
mc_L[ss] = w[ss] / alpha_L ^ alpha_L / (1 - alpha_L) ^ (1 - alpha_L);
Y[ss] = (f1[ss] * f2[ss] * f3[ss] * w[ss] ^ ((1 + sigma_L) / sigma_C)) ^
(sigma_C / (sigma_L + sigma_C));

L[ss] = (1 - alpha) * Y[ss] / mc_L[ss];

L_R[ss] = alpha_L * L[ss] * mc_L[ss] / w[ss];
L_NR[ss] = (1 - alpha_L) * L[ss] * mc_L[ss] / w[ss];

C_R[ss] = w[ss] ^ (1/sigma_C) * L_R[ss] ^ (-sigma_L / sigma_C);
C_NR[ss] = w[ss] ^ (1/sigma_C) * L_NR[ss] ^ (-sigma_L / sigma_C);

K[ss] = alpha * Y[ss] / r[ss];
I[ss] = delta * K[ss];

lambda_R[ss] = C_R[ss] ^ -sigma_C;
q[ss] = lambda_R[ss];
lambda_NR[ss] = C_NR[ss] ^ -sigma_C;

};
};

block RICARDIAN_HOUSEHOLD
{
definitions
{
u_R[] = shock_beta_R[] * (C_R[] ^ (1 - sigma_C) / (1 - sigma_C) -
L_R[] ^ (1 + sigma_L) / (1 + sigma_L));
};

controls
{
C_R[], L_R[], I[], K[];
};

objective
{
U_R[] = u_R[] + beta * E[][U_R[1]];
};

constraints
{
@exclude
C_R[] + I[] = r[] * K[-1] + w[] * L_R[] : lambda_R[];

K[] = (1 - delta) * K[-1] + I[]: q[];
};

identities
{
log(shock_beta_R[]) = rho_beta_R * log(shock_beta_R[-1]) + epsilon_beta_R[];
};

shocks
{
epsilon_beta_R[];
};

calibration
{
beta = 0.99;
delta = 0.02;
sigma_C = 1.5;
sigma_L = 2.0;
rho_beta_R = 0.95;
};
};

block NON_RICARDIAN_HOUSEHOLD
{
definitions
{
u_NR[] = (C_NR[] ^ (1 - sigma_C) / (1 - sigma_C) -
L_NR[] ^ (1 + sigma_L) / (1 + sigma_L));
};

controls
{
C_NR[], L_NR[];
};

objective
{
U_NR[] = u_NR[] + beta * E[][U_NR[1]];
};

constraints
{
@exclude
C_NR[] = w[] * L_NR[]: lambda_NR[];
};
};


block FIRM
{
controls
{
K[-1], L[], L_R[], L_NR[];
};

objective
{
TC[] = -(r[] * K[-1] + w[] * L_R[] + w[] * L_NR[]);
};

constraints
{
L[] = L_R[] ^ alpha_L * L_NR[] ^ (1 - alpha_L) : mc_L[];
Y[] = TFP[] * K[-1] ^ alpha * L[] ^ (1 - alpha) : mc[];
};

identities
{
# Perfect competition
mc[] = 1;

# Exogenous technology process
log(TFP[]) = rho_TFP * log(TFP[-1]) + epsilon_TFP[];
};

shocks
{
epsilon_TFP[];
};

calibration
{
alpha = 0.35;
alpha_L = 0.5;

rho_TFP = 0.95;
};
};

block EQULIBRIUM
{
identities
{
Y[] = C_R[] + C_NR[] + I[];
};
};
183 changes: 183 additions & 0 deletions GCN Files/RBC_two_household_additive.txt
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assumptions
{
positive
{
Y[], K[], C_NR[], C_R[],
w[], r[], mc_L[],
L[], L_NR[], L_R[],
TFP[],
alpha, alpha_L, beta, sigma_C, sigma_L, delta, omega;
};
};

tryreduce
{
U_NR[], U_R[], TC[];
};

# block STEADY_STATE
# {
# definitions
# {
# f1[ss] = (r[ss] / (r[ss] - alpha * delta));
# f2[ss] = (alpha_L * (1 - alpha_L) * (1 - alpha)) ^ (-sigma_L / sigma_C);
# f3[ss] = alpha_L ^ (sigma_L / sigma_C) +
# (1 - alpha_L) ^ (sigma_L / sigma_C);

# };
# identities
# {
# TFP[ss] = 1.0;
# shock_beta_R[ss] = 1.0;

# r[ss] = 1 / beta - (1 - delta);
# w[ss] = (1 - alpha) * alpha_L ^ alpha_L * (1 - alpha_L) ^ (1 - alpha_L) *
# (r[ss] / alpha) ^ (alpha / (alpha - 1));
# mc_L[ss] = w[ss] / alpha_L ^ alpha_L / (1 - alpha_L) ^ (1 - alpha_L);
# Y[ss] = (f1[ss] * f2[ss] * f3[ss] * w[ss] ^ ((1 + sigma_L) / sigma_C)) ^
# (sigma_C / (sigma_L + sigma_C));

# L[ss] = (1 - alpha) * Y[ss] / mc_L[ss];

# L_R[ss] = alpha_L * L[ss] * mc_L[ss] / w[ss];
# L_NR[ss] = (1 - alpha_L) * L[ss] * mc_L[ss] / w[ss];

# C_R[ss] = w[ss] ^ (1/sigma_C) * L_R[ss] ^ (-sigma_L / sigma_C);
# C_NR[ss] = w[ss] ^ (1/sigma_C) * L_NR[ss] ^ (-sigma_L / sigma_C);

# K[ss] = alpha * Y[ss] / r[ss];
# I[ss] = delta * K[ss];

# lambda_R[ss] = C_R[ss] ^ -sigma_C;
# q[ss] = lambda_R[ss];
# lambda_NR[ss] = C_NR[ss] ^ -sigma_C;

# };
# };

block RICARDIAN_HOUSEHOLD
{
definitions
{
u_R[] = shock_beta_R[] * (C_R[] ^ (1 - sigma_C) / (1 - sigma_C) -
L_R[] ^ (1 + sigma_L) / (1 + sigma_L));

Phi_I[] = (1 - gamma_I / 2 * (I[] / I[-1] - 1) ^ 2);
};

controls
{
C_R[], L_R[], I[], K[];
};

objective
{
U_R[] = u_R[] + beta * E[][U_R[1]];
};

constraints
{
@exclude
C_R[] + I[] = r[] * K[-1] + w[] * L_R[] : lambda_R[];

K[] = (1 - delta) * K[-1] + Phi_I[] * I[]: q[];
};

identities
{
log(shock_beta_R[]) = rho_beta_R * log(shock_beta_R[-1]) + epsilon_beta_R[];
};

shocks
{
epsilon_beta_R[];
};

calibration
{
beta = 0.99;
delta = 0.02;
sigma_C = 1.5;
sigma_L = 2.0;
rho_beta_R = 0.95;
gamma_I = 5;
};
};

block NON_RICARDIAN_HOUSEHOLD
{
definitions
{
u_NR[] = (C_NR[] ^ (1 - sigma_C) / (1 - sigma_C) -
L_NR[] ^ (1 + sigma_L) / (1 + sigma_L));
};

controls
{
C_NR[], L_NR[];
};

objective
{
U_NR[] = u_NR[] + beta * E[][U_NR[1]];
};

constraints
{
C_NR[] = w[] * L_NR[]: lambda_NR[];
};
};


block FIRM
{
controls
{
K[-1], L[];
};

objective
{
TC[] = -(r[] * K[-1] + w[] * L[]);
};

constraints
{
Y[] = TFP[] * K[-1] ^ alpha * L[] ^ (1 - alpha) : mc[];
};

identities
{
# Perfect competition
mc[] = 1;

# Exogenous technology process
log(TFP[]) = rho_TFP * log(TFP[-1]) + epsilon_TFP[];
};

shocks
{
epsilon_TFP[];
};

calibration
{
alpha = 0.35;
rho_TFP = 0.95;
};
};

block EQULIBRIUM
{
identities
{
L[] = omega * L_R[] + (1 - omega) * L_NR[];
C[] = omega * C_R[] + (1 - omega) * C_NR[];
Y[] = C[] + I[];
};

calibration
{
omega = 0.5;
};
};
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