Dolo.jl code for a simple example

[azev77]

Hi and thank you for this package! In this post I compare many different ways of solving economic models in the Julia ecosystem. Would it be at all possible for you to provide simple Dolo.jl code to solve this model?

[albop]

Thanks for the interest! From a very quick look at your post, it looks like the Euler equation version (augmented with the occasionally binding constraints) should be solvable with Dolo easily. @gabriellequeran : do you want to have a look at it ?

[azev77]

Awesome, is it possible to also solve the dynamic programming version w VFI?

[albop]

It is possible to formulate the bellman problem and in principle it is possible to apply VFI methods to it, but the solution method hasn't received much love since its initial implementation.

[azev77]

Hey @albop & @gabriellequeran has there been any luck solving these problems w/ Dolo.jl?

[albop]

Hey @azev77! We haven't had time yet, but we plan to look into it next week

On Tue, Jan 18, 2022 at 10:46 PM azev77 @.***> wrote:

Hey @albop https://github.com/albop & @gabriellequeran https://github.com/gabriellequeran has there been any luck solving these problems w/ Dolo.jl?

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[azev77]

Hey @albop & @gabriellequeran has there been any luck solving these problems w/ Dolo.jl?

[gabriellequeran]

Hello @azev77, I have just started working on your example and have added a new constraint on the investment for the case in which k is small. I will send you the implementation of that next week.

[azev77]

Awesome. I look forward to it. btw, if you’d like feel free to post on the Discourse post (link above) to showcase & get exposure for Dolo

[azev77]

Here is my attempt:

YAML:

name: Investment

symbols:
    states: [k]
    controls: [i]
    exogenous: [z]
    rewards: [u]
    parameters: [delta, r, zz]

equations:
    transition:
        - k[t] = (1-delta)*k[t-1] + i[t-1]
    arbitrage:
        - i[t] - ((r+delta-zz)/(1-delta)) - ((1+r)/(1-delta))*i[t-1]
    felicity:
        - u[t] = zz*k[t] -i[t] -.5*(i[t]^2)

############################
calibration:

    ## exogenous state
    z: 0

    # controls
    i: (zz-r-delta)/(r+delta)

    # states
    k: i/delta

    u: zz*k -i -.5*(i^2)

    # parameters:
    delta: 0.1
    r: 0.15
    zz: 0.27

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

exogenous: 
    z: !VAR1
        ρ: r
        Σ: [[ 0.00001 ]]

Now in Julia: the perturb(model) solution works

using Dolo, Plots;
model = yaml_import("inv.yaml");
dr_pert    = perturb(model) # linear solution WORKS! 
tab_pert   = tabulate(model, dr_pert.dr,   :k)
p1 = plot()
plot!(tab_pert[V=:k],tab_pert[V=:i],label = "Perturbation", title = "Investment", xlabel = "k", ylabel = "i")

time_iteration(model) gives an error

julia> dr_global  = time_iteration(model)
---------------------------------------------------------------------
Time Iteration
---------------------------------------------------------------------
       n | ϵₙ=|F(xₙ,xₙ)| | ηₙ=|xₙ-xₙ₋₁| |   λₙ=ηₙ/ηₙ₋₁ |         Time
---------------------------------------------------------------------
ERROR: UndefVarError: i_m1_ not defined
Stacktrace:
 [1] macro expansion
   @ C:\Users\azevelev\.julia\packages\Dolang\FoOif\src\compiler.jl:391 [inlined]
 [2] macro expansion
   @ .\simdloop.jl:77 [inlined]
 [3] macro expansion
   @ C:\Users\azevelev\.julia\packages\Dolang\FoOif\src\compiler.jl:388 [inlined]
 [4] arbitrage(::Model{Symbol("##569"), Dolo.ContinuousProcess}, m::StaticArrays.SVector{1, Float64}, s::Vector{StaticArrays.SVector{1, Float64}}, x::SubArray{StaticArrays.SVector{1, Float64}, 1, Vector{StaticArrays.SVector{1, Float64}}, Tuple{UnitRange{Int64}}, true}, M::StaticArrays.SVector{1, Float64}, S::Vector{StaticArrays.SVector{1, Float64}}, X::Vector{StaticArrays.SVector{1, Float64}}, p::StaticArrays.SVector{3, Float64}, out::Nothing) (repeats 2 times)
   @ Dolo C:\Users\azevelev\.julia\packages\Dolang\FoOif\src\compiler.jl:443
 [5] euler_residuals(F::Dolo.Euler{Symbol("##569"), 1, 1, 1, Dolo.UCGrid{1}, Dolo.UCGrid{1}}, s::Vector{StaticArrays.SVector{1, Float64}}, x::Dolo.MSM{StaticArrays.SVector{1, Float64}}, dr::Dolo.CachedDecisionRule{Dolo.CubicDR{Dolo.UCGrid{1}, Dolo.UCGrid{1}, 1, 2}, Dolo.DiscretizedProcess{Dolo.UCGrid{1}}}, dprocess::Dolo.DiscretizedProcess{Dolo.UCGrid{1}}, parms::StaticArrays.SVector{3, Float64}; keep_J_S::Bool, out::Dolo.MSM{StaticArrays.SVector{1, Float64}})
   @ Dolo C:\Users\azevelev\.julia\packages\Dolo\RlF3H\src\algos\time_iteration_helpers.jl:174
 [6] (::Dolo.Euler{Symbol("##569"), 1, 1, 1, Dolo.UCGrid{1}, Dolo.UCGrid{1}})(x0::Dolo.MSM{StaticArrays.SVector{1, Float64}}, x1::Dolo.MSM{StaticArrays.SVector{1, Float64}}; set_future::Bool, ignore_constraints::Bool, out::Nothing, p::StaticArrays.SVector{3, Float64})
   @ Dolo C:\Users\azevelev\.julia\packages\Dolo\RlF3H\src\algos\time_iteration_helpers.jl:200
 [7] time_iteration(model::Model{Symbol("##569"), Dolo.ContinuousProcess}; dr0::Dolo.ConstantDecisionRule{1}, discretization::Dict{Any, Any}, interpolation::Symbol, verbose::Bool, details::Bool, ignore_constraints::Bool, trace::Bool, tol_η::Float64, tol_ε::Float64, maxit::Int64)
   @ Dolo C:\Users\azevelev\.julia\packages\Dolo\RlF3H\src\algos\time_iteration.jl:240
 [8] time_iteration(model::Model{Symbol("##569"), Dolo.ContinuousProcess})
   @ Dolo C:\Users\azevelev\.julia\packages\Dolo\RlF3H\src\algos\time_iteration.jl:203
 [9] top-level scope
   @ REPL[10]:1

julia> 

Is it bc Dolo.jl isn't meant for models w/o uncertainty?

Update: it seems to work if the exogenous variable z[t] is in the arbitrage equation

    arbitrage:
        - i[t+1] - ((r+delta-zz - .00001*z[t])/(1-delta)) - ((1+r)/(1-delta))*i[t]