rbc_catastrophe.yaml

name: Real Business Cycle

model_type: dtcc

symbols:

   exogenous: [z, xi]
   states: [k]
   controls: [n, i]
   expectations: [m]
   values: [V]
   parameters: [beta, sigma, eta, chi, delta, alpha, rho, zbar, sig_z]
   rewards: [u]

definitions:
    y: exp(z-xi)*k^alpha*n^(1-alpha)
    c: y - i
    rk: alpha*y/k
    w: (1-alpha)*y/n

equations:

    arbitrage:
        - chi*n^eta*c^sigma - w                      | 0 <= n <= inf
        - 1 - beta*(c/c(1))^(sigma)*(1-delta+rk(1))  | 0 <= i <= inf
        # - V0 = c^(1-sigma)/(1-sigma) - chi*n^(1+eta)/(1+eta) + beta*V0(1) |  -100000<=V0<=100000

    transition:
        - k = (1-delta)*k(-1) + i(-1)

    value:
        - V = c^(1-sigma)/(1-sigma) - chi*n^(1+eta)/(1+eta) + beta*V(1)

    felicity:
        - u =  c^(1-sigma)/(1-sigma) - chi*n^(1+eta)/(1+eta)

    expectation:
        - m = beta/c(1)^sigma*(1-delta+rk(1))

    direct_response:
        - n = ((1-alpha)*exp(z-xi)*k^alpha*m/chi)^(1/(eta+alpha))
        - i = exp(z-xi)*k^alpha*n^(1-alpha) - (m)^(-1/sigma)

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
    m: 0
    V0: (c^(1-sigma)/(1-sigma) - chi*n^(1+eta)/(1+eta))/(1-beta)

    # endogenous variables
    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)
    xi: 0.0

domain:
    k: [k*0.5, k*1.5]

exogenous: !Product
    p1: !VAR1
         rho: 0.8
         Sigma: [[0.001]]
    p2: !MarkovChain
        values: [[0.0],[0.1]]
        transitions: [[0.97, 0.03], [0.1, 0.9]]

options:

    grid: !Cartesian
        orders: [50]