MacroModelling.jl

MacroModelling.jl - fast prototyping of dynamic stochastic general equilibrium (DSGE) models

MacroModelling.jl currently supports dicsrete-time DSGE models and the timing of a variable reflects when the variable is decided (end of period for stock variables).

As of now MacroModelling.jl can:

• parse a model written with user friendly syntax (variables are followed by time indices ...[2], [1], [0], [-1], [-2]..., or [x] for shocks)
• (tries to) solve the model only knowing the model equations and parameter values (no steady state file needed)
• calculate first, second, and third order perturbation solutions using (forward) automatic differentiation (AD)
• calculate (generalised) impulse response functions, and simulate the model
• calibrate parameters using (non stochastic) steady state relationships
• match model moments
• estimate the model on data (kalman filter using first order perturbation)
• differentiate (forward AD) the model solution (first order perturbation), kalman filter loglikelihood, model moments, steady state, with respect to the parameters

MacroModelling.jl helps the modeller:

• Syntax makes variable and parameter definitions obsolete
• MacroModelling.jl applies symbolic and numerical tools to solve for the steady state (and mostly succeeds without much help)

julia> using MacroModelling
julia> @model RBC_estim begin
           # c[0]^(-sigma)=beta/gammax*c(+1)^(-sigma)*(alpha*exp(z(+1))*(k/l(+1))^(alpha-1)+(1-delta))
           c[0]^(-sigma) = beta * c[1]^(-sigma) * (alpha * exp(z[1]) * (k[0] / l[1])^(alpha - 1) + (1 - delta))
           psi * c[0]^sigma * 1 / (1 - l[0]) = w[0]
           k[0] = (1 - delta) * k[-1] + invest[0]
           y[0] = invest[0] + c[0] + gshare * y[ss] * exp(ghat[0])
           y[0] = exp(z[0]) * k[-1]^alpha * l[0]^(1 - alpha)
           w[0] = (1 - alpha) * y[0] / l[0]
           r[0] = 4 * alpha * y[0] / k[-1]
           z[0] = rhoz * z[-1] + std_z * eps_z[x]
           ghat[0] = rhog * ghat[-1] + std_g * eps_g[x]
           c_obs[0] = log(c[0]) - log(c[-1])
           y_obs[0] = log(y[0]) - log(y[-1])
           g_obs[0] = ghat[0] - ghat[-1]
       endModel: RBC_estim
Variables: 12
Shocks: 2
Parameters: 10
Auxiliary variables: 0
julia> @parameters RBC_estim begin
           std_g  = 0.0105
           std_z  = 0.0068
           sigma  = 1
           alpha  = 0.33
           rhoz   = 0.97
           rhog   = 0.989
           gshare = 0.2038
           delta  = 0.024038461538461536
           beta   = 0.9923664122137404
       
           psi | l[ss] = .33
           w > 0
           l > 0
           y > 0
           k > 0
           c > 0
           invest > 0
       
           psi > 0
       end
julia> get_solution(RBC_estim)2-dimensional KeyedArray(NamedDimsArray(...)) with keys:
↓   Steady_state__States__Shocks ∈ 8-element Vector{Symbol}
→   Variable ∈ 12-element Vector{Symbol}
And data, 8×12 adjoint(::Matrix{Float64}) with eltype Float64:
                   (:c)          (:c_obs)      …  (:y_obs)     (:z)
  (:Steady_state)   0.571206      0.0              0.0          0.0
  (:c₍₋₁₎)          0.0          -1.75068          0.0          0.0
  (:ghat₍₋₁₎)      -0.102612     -0.17964          0.146327    -6.32705e-17
  (:k₍₋₁₎)          0.0314001     0.0549716        0.0102794   -6.53931e-17
  (:y₍₋₁₎)         -2.47039e-17  -4.32487e-17  …  -0.956223     2.68323e-18
  (:z₍₋₁₎)          0.342423      0.599475         1.27181      0.97
  (:eps_g₍ₓ₎)      -0.0010894    -0.0019072        0.00155352  -0.0
  (:eps_z₍ₓ₎)       0.00240049    0.0042025        0.0089158    0.0068