Generated on 2023-07-10 01:35:08 by gEcon ver. 1.2.2 (2023-07-10) http://gecon.r-forge.r-project.org/ Model name: rbc_hf Variables selected for reduction: L_d[], K_d[], pi[] Block: CONSUMER Definitions: u[] = (1 - eta)^-1 * ((1 - L_s[])^(1 - mu) * (C[] - pers * H[])^mu)^(1 - eta) Controls: K_s[], C[], L_s[], I[], H[] Objective: U[] = beta * E[][U[1]] + (1 - eta)^-1 * ((1 - L_s[])^(1 - mu) * (C[] - pers * H[])^mu)^(1 - eta) Constraints: pi[] - C[] - I[] + K_s[-1] * r[] + L_s[] * W[] = 0 (lambda__CONSUMER_1[]) I[] - K_s[] + K_s[-1] * (1 - delta) = 0 (lambda__CONSUMER_2[]) C[-1] - H[] = 0 (lambda__CONSUMER_3[]) First order conditions: -lambda__CONSUMER_2[] + beta * ((1 - delta) * E[][lambda__CONSUMER_2[1]] + E[][lambda__CONSUMER_1[1] * r[1]]) = 0 (K_s[]) -lambda__CONSUMER_1[] + beta * E[][lambda__CONSUMER_3[1]] + mu * (1 - L_s[])^(1 - mu) * (C[] - pers * H[])^(-1 + mu) * ((1 - L_s[])^(1 - mu) * (C[] - pers * H[])^mu)^(-eta) = 0 (C[]) lambda__CONSUMER_1[] * W[] + (-1 + mu) * (1 - L_s[])^(-mu) * (C[] - pers * H[])^mu * ((1 - L_s[])^(1 - mu) * (C[] - pers * H[])^mu)^(-eta) = 0 (L_s[]) -lambda__CONSUMER_1[] + lambda__CONSUMER_2[] = 0 (I[]) -lambda__CONSUMER_3[] - mu * pers * (1 - L_s[])^(1 - mu) * (C[] - pers * H[])^(-1 + mu) * ((1 - L_s[])^(1 - mu) * (C[] - pers * H[])^mu)^(-eta) = 0 (H[]) Block: FIRM Controls: K_d[], L_d[], Y[] Objective: pi[] = Y[] - L_d[] * W[] - r[] * K_d[] Constraints: -Y[] + Z[] * K_d[]^alpha * L_d[]^(1 - alpha) = 0 (lambda__FIRM_1[]) First order conditions: -r[] + alpha * lambda__FIRM_1[] * Z[] * K_d[]^(-1 + alpha) * L_d[]^(1 - alpha) = 0 (K_d[]) -W[] + lambda__FIRM_1[] * Z[] * (1 - alpha) * K_d[]^alpha * L_d[]^(-alpha) = 0 (L_d[]) 1 - lambda__FIRM_1[] = 0 (Y[]) First order conditions after reduction: -r[] + alpha * Z[] * K_d[]^(-1 + alpha) * L_d[]^(1 - alpha) = 0 (K_d[]) -W[] + Z[] * (1 - alpha) * K_d[]^alpha * L_d[]^(-alpha) = 0 (L_d[]) Block: EQUILIBRIUM Identities: K_s[-1] - K_d[] = 0 -L_d[] + L_s[] = 0 Block: EXOG Identities: -Z[] + exp(epsilon_Z[] + phi * log(Z[-1])) = 0 Variables (11): lambda__CONSUMER_2[], r[], C[], H[], I[], K_s[], L_s[], U[], W[], Y[], Z[] Shocks (1): epsilon_Z[] Parameters (7): alpha, beta, delta, eta, mu, pers, phi Free parameters (6): beta, delta, eta, mu, pers, phi Calibrated parameters (1): alpha Equations (11): (1) C[-1] - H[] = 0 (2) -lambda__CONSUMER_2[] + beta * ((1 - delta) * E[][lambda__CONSUMER_2[1]] + E[][lambda__CONSUMER_2[1] * r[1]]) = 0 (3) -r[] + alpha * Z[] * K_s[-1]^(-1 + alpha) * L_s[]^(1 - alpha) = 0 (4) -W[] + Z[] * (1 - alpha) * K_s[-1]^alpha * L_s[]^(-alpha) = 0 (5) -Y[] + Z[] * K_s[-1]^alpha * L_s[]^(1 - alpha) = 0 (6) -Z[] + exp(epsilon_Z[] + phi * log(Z[-1])) = 0 (7) lambda__CONSUMER_2[] * W[] + (-1 + mu) * (1 - L_s[])^(-mu) * (C[] - pers * H[])^mu * ((1 - L_s[])^(1 - mu) * (C[] - pers * H[])^mu)^(-eta) = 0 (8) -lambda__CONSUMER_2[] - beta * mu * pers * E[][(1 - L_s[1])^(1 - mu) * (C[1] - pers * H[1])^(-1 + mu) * ((1 - L_s[1])^(1 - mu) * (C[1] - pers * H[1])^mu)^(-eta)] + mu * (1 - L_s[])^(1 - mu) * (C[] - pers * H[])^(-1 + mu) * ((1 - L_s[])^(1 - mu) * (C[] - pers * H[])^mu)^(-eta) = 0 (9) -C[] - I[] + Y[] = 0 (10) I[] - K_s[] + K_s[-1] * (1 - delta) = 0 (11) U[] - beta * E[][U[1]] - (1 - eta)^-1 * ((1 - L_s[])^(1 - mu) * (C[] - pers * H[])^mu)^(1 - eta) = 0 Steady state equations (11): (1) C[ss] - H[ss] = 0 (2) -lambda__CONSUMER_2[ss] + beta * (lambda__CONSUMER_2[ss] * r[ss] + lambda__CONSUMER_2[ss] * (1 - delta)) = 0 (3) -r[ss] + alpha * Z[ss] * K_s[ss]^(-1 + alpha) * L_s[ss]^(1 - alpha) = 0 (4) -W[ss] + Z[ss] * (1 - alpha) * K_s[ss]^alpha * L_s[ss]^(-alpha) = 0 (5) -Y[ss] + Z[ss] * K_s[ss]^alpha * L_s[ss]^(1 - alpha) = 0 (6) -Z[ss] + exp(phi * log(Z[ss])) = 0 (7) lambda__CONSUMER_2[ss] * W[ss] + (-1 + mu) * (1 - L_s[ss])^(-mu) * (C[ss] - pers * H[ss])^mu * ((1 - L_s[ss])^(1 - mu) * (C[ss] - pers * H[ss])^mu)^(-eta) = 0 (8) -lambda__CONSUMER_2[ss] + mu * (1 - L_s[ss])^(1 - mu) * (C[ss] - pers * H[ss])^(-1 + mu) * ((1 - L_s[ss])^(1 - mu) * (C[ss] - pers * H[ss])^mu)^(-eta) - beta * mu * pers * (1 - L_s[ss])^(1 - mu) * (C[ss] - pers * H[ss])^(-1 + mu) * ((1 - L_s[ss])^(1 - mu) * (C[ss] - pers * H[ss])^mu)^(-eta) = 0 (9) -C[ss] - I[ss] + Y[ss] = 0 (10) I[ss] - K_s[ss] + K_s[ss] * (1 - delta) = 0 (11) U[ss] - beta * U[ss] - (1 - eta)^-1 * ((1 - L_s[ss])^(1 - mu) * (C[ss] - pers * H[ss])^mu)^(1 - eta) = 0 Calibrating equations (1): (1) -0.36 * Y[ss] + r[ss] * K_s[ss] = 0 Parameter settings (6): (1) beta = 0.99 (2) delta = 0.025 (3) eta = 2 (4) mu = 0.3 (5) pers = 0.57 (6) phi = 0.95