Aiyagari.yaml

name: Consumption Savings

symbols:
    states: [a]
    exogenous: [r, w, e]
    parameters: [β, B, a_max]
    controls: [i]


definitions: |
    c[t] = (1+r[t])*a[t] +  w[t]*exp(e[t]) - i[t]
equations:

    arbitrage: |
        1-β*(1+r[t+1])*c[t]/c[t+1] ⟂ -B <= i[t] <= (1+r[t])*a[t]+w[t]*exp(e[t])
    transition: |
        a[t] = i[t-1]
calibration:

    β: 0.99
    B: 1e-10
    a_max: 300.
    a: 1
    i: a
    K: 41.
    α: 0.36
    A: 1
    N: 1
    δ: 0.025
    r: α*(N/K)^(1-α) - δ
    w: (1-α)*(K/N)^(α)

domain:
    a: [-B, a_max]

exogenous:  
    r,w: !ConstantProcess
        μ: [r, w]
    e: !VAR1
        ρ: 0.95
        Σ: [[0.06^2]]

options:
    grid:
        !Cartesian
        orders: [30]

---

name: Ayiagari

symbols:
    exogenous: [z]
    aggregate: [K]
    parameters: [A, α, δ, N, ρ]

calibration:
    A: 1
    α: 0.36
    δ: 0.025
    N: 1.0
    K: 40
    z: 0
    ρ: 0.95
    σ: 0.025

exogenous: !VAR1
    ρ: 0.9
    Σ: [[ 0.02 ]]

projection: |
    r[t] = α*exp(z[t])*(N/K[t])^(1-α) - δ
    w[t] = (1-α)*exp(z[t])*(K[t]/N)^(α)
equilibrium: |
    K[t] = a[t]