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paper_results.jl
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paper_results.jl
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using TypedTables, Plots
"""
get_figures_3_4(;TR::Int64 = 20, T::Int64 = 200, RChange::Float64 = -0.005)
Convenience function that replicates Figures 3 and 4 from the MNS paper.
Just running `get_figures_3_4()` will display equivalents to Figures 3 and 4 in the MNS paper.
The function relies on `set_parameters`, `get_steady_state`, `get_transition_full` and `get_transition_CompMkts`.
Optional argument: Time horizon of interest rate change (TR). Size of interest rate change (RChange)
"""
function get_figures_3_4(;TR::Int64 = 20, T::Int64 = 200, RChange::Float64 = -0.005)
p = set_parameters()
println("")
println("Solving for Steady State")
println("")
b,y,SS = get_steady_state(p,0.6,[0.95,0.99])
p.β = b
println("")
println("Solving for transition path")
println("")
tp = get_transition_full(TR,T,p,SS; RChange=RChange)
println("")
println("Solving for complete markets transition path")
println("")
tpc = get_transition_CompMkts(TR,T,p; RChange=RChange)
p1 = plot(0:2*TR-1,(tp.Y[1:2*TR]./SS.Y .- 1.0)*100.0, title="Figure 3: Output response",xlabel = "Quarter", ylabel = "Output",
label = "Incomplete Markets")
plot!(0:2*TR-1,tpc.Y[1:2*TR]*100.0,label = "Complete Markets" )
p2 = plot(0:2*TR-1,(tp.pΠ[1:2*TR] .- 1.0)*100.0,title = "Figure 4: Inflation Response",xlabel = "Quarter", ylabel = "Inflation",
label = "Incomplete Markets")
plot!(0:2*TR-1,tpc.pΠ[1:2*TR]*100.0,label = "Complete Markets" )
return plot(p1,p2, layout = (2,1))
end
"""
get_figures_5_6(; Horizon::StepRange{Int64,Int64} = 1:2:41, T::Int64 = 200, RChange::Float64 = -0.005)
Convenience function that replicates Figures 5 and 6 from the MNS paper.
Just running `get_figures_5_6()` will display equivalents to Figures 5 and 6 in the MNS paper.
The function relies on `set_parameters`, `get_steady_state`, `get_transition_full` and `get_transition_CompMkts`.
Optional argument:
..* Horizons of interest rate changes to consider (`Horizon`), to be supplied as `StepRange`.
..* Total length of transition period to compute (`T`), i.e. assuming that after T periods economy will be back in SS
..* Size of interest rate change (RChange).
All default values corresppond to the values used by MNS.
"""
function get_figures_5_6(; Horizon::StepRange{Int64,Int64} = 1:2:41, T::Int64 = 200, RChange::Float64 = -0.005)
TRs = collect(Horizon)
#pre-allocate vectors for results
Y_response = Array{Float64,1}(undef,length(TRs)); Π_response = Array{Float64,1}(undef,length(TRs))
Y_response_CM = Array{Float64,1}(undef,length(TRs)); Π_response_CM = Array{Float64,1}(undef,length(TRs))
#get initial steady state
p = set_parameters()
b, y , SS = get_steady_state(p,0.6,[0.95,0.99])
p.β = b #update beta
for horiz = 1:length(TRs)
println("")
println("Solving for transition path with horizon ",TRs[horiz])
println("")
tr = get_transition_full(TRs[horiz],T,p,SS; RChange = RChange)
Y_response[horiz] = tr.Y[1]
Π_response[horiz] = tr.pΠ[1]
println("")
println("Initial Output response: ",tr.Y[1]/SS.Y - 1.0," Initial Inflation response: ",tr.pΠ[1]-1.0)
println("")
trc = get_transition_CompMkts(TRs[horiz],T,p; RChange=RChange)
Y_response_CM[horiz] = trc.Y[1]
Π_response_CM[horiz] = trc.pΠ[1]
p = set_parameters(β = b,ψ1 = 1.0) #ensure par structure is stable
end
p1 = plot(Horizon, (Y_response/SS.Y .- 1.0)*100.0, title="Figure 5: Initial Output response",xlabel = "Horizon rate change", ylabel = "Output",
label = "Incomplete Markets")
plot!(Horizon, Y_response_CM*100.0, label = "Complete Markets")
p2 = plot(Horizon,(Π_response .- 1.0)*100.0,title = "Figure 6: Initial Inflation response",xlabel = "Horizon rate change", ylabel = "Inflation",
label = "Incomplete Markets")
#for baseline case, make it look like figure 6 in paper
if TRs[end] == 41
plot!(1:2:19, Π_response_CM[1:10]*100.0, label = "Complete Markets")
else #plot complete path
plot!(Horizon, Π_response_CM*100.0, label = "Complete Markets")
end
return plot(p1,p2, layout = (2,1))
end
"""
get_table_2(;Horizon::Int=20,T::Int=200,RChange::Float64 = -0.005)
Convenience function that replicates Table 2 from the MNS paper.
Just running `get_table_2()` will return an equivalent to Table 2 as a table object.
The function relies on `set_parameters`, `get_steady_state`, `get_transition_full` and `get_transition_CompMkts`.
Optional argument:
..* Time horizon of interest rate change (`TR`)
..* Total length of transition period to compute (`T`), i.e. assuming that after T periods economy will be back in SS
..* Size of interest rate change (`RChange`)
Default values correspond to the values chosen by MNS.
### Note: The returned values will not be identical to the ones obtained by MNS.
### However, notice that chosen unit is Basis Points (=0.01 percent), so the actual numerical difference between the MNS solution and ours is small.
"""
function get_table_2(;Horizon::Int=20,T::Int=200,RChange::Float64 = -0.005)
#arrays for results
resp_inflation = Array{Float64,1}(undef,5)
resp_output = Array{Float64,1}(undef,5)
cases = ["Baseline","High Risk","High Asset","High Risk and High Asset","Complete Markets"]
#output standard deviations for different cases:
σ2s = [0.01695,0.033,0.01695,0.024]
#aggregate assets for different cases
Bs = [5.5,5.5,15.15,15.15]
#loop over cases
for case = 1:4
#adjust guess for β range and range of asset grid depending on case
if Bs[case] == 15.15
βmin = 0.97 ; βmax = 0.995 ; a_max = 110.0
else
βmin = 0.95 ; βmax = 0.99 ; a_max = 75.0
end
#generate initial parameter vector
p = set_parameters(B = Bs[case], σ = σ2s[case]^0.5, a_max = a_max)
println("")
println("Solving for Steady State: ",cases[case]," Calibration")
println("")
#calibrate β and get steady state
β,y,SS = get_steady_state(p,0.6,[βmin,βmax])
p.β = β #update parameter structure
println("")
println("Solving for Transition path: ",cases[case]," Calibration")
println("")
tr = get_transition_full(Horizon,T,p,SS;RChange = RChange)
#save results - convert to basis points
resp_inflation[case] = (tr.pΠ[1] - 1.0)*10000.0
resp_output[case] = (tr.Y[1]/SS.Y - 1.0)*10000.0
end
p = set_parameters()
tpc = get_transition_CompMkts(Horizon,T,p;RChange = RChange)
resp_inflation[5] = tpc.pΠ[1]*10000.0
resp_output[5] = tpc.Y[1]*10000.0
return Table(Case = cases, initial_output_response = resp_output, initial_inflation_response= resp_inflation)
end