rbc.yaml

name: Real Business Cycle

symbols:

   exogenous: [e_z]
   states: [z, k]
   controls: [n, i]
   parameters: [beta, sigma, eta, chi, delta, alpha, rho, zbar, sig_z]

definitions: |
    y[t] = exp(z[t])*k[t]^alpha*n[t]^(1-alpha)
    c[t] = y[t] - i[t]
    rk[t] = alpha*y[t]/k[t]
    w[t] = (1-alpha)*y[t]/n[t]

equations:

    arbitrage: |
        chi*n[t]^eta*c[t]^sigma - w[t]                     ⟂ 0.0 <= n[t] <= inf
        1 - beta*(c[t]/c[t+1])^(sigma)*(1-delta+rk[t+1])   ⟂ 0.20 <= i[t] <= inf

    transition: |
        z[t] = rho*z[t-1] + e_z
        k[t] = (1-delta)*k[t-1] + i[t-1]

calibration:

    # parameters
    beta : 0.99
    phi: 1
    delta : 0.025
    alpha : 0.33
    rho : 0.8
    sigma: 5
    eta: 1
    sig_z: 0.016
    zbar: 0
    chi : w/c^sigma/n^eta
    c_i: 1.5
    c_y: 0.5
    e_z: 0.0
    n: 0.33
    z: zbar
    rk: 1/beta-1+delta
    w: (1-alpha)*exp(z)*(k/n)^(alpha)
    k: n/(rk/alpha)^(1/(1-alpha))
    y: exp(z)*k^alpha*n^(1-alpha)
    i: delta*k
    c: y - i
    V: log(c)/(1-beta)
    u: c^(1-sigma)/(1-sigma) - chi*n^(1+eta)/(1+eta)
    m: beta/c^sigma*(1-delta+rk)
    kss: 10

exogenous: !UNormal
    sigma: 0.01

domain:
    z: [-2*sig_z/(1-rho^2)^0.5,  2*sig_z/(1-rho^2)^0.5]
    k: [ kss*0.5, kss*1.5]

options:
    grid: !Cartesian
        n: [100, 100]
    discrete_choices: [n]