Solution plots for the SSY Model



In [1]:

    
include("src/utilities.jl")
include("src/ez_model.jl")
include("src/ssy_discretized.jl")









    Out[1]:





compute_fp_ssy



In [2]:

    
using PyPlot
plt = PyPlot









    Out[2]:





PyPlot

Default parameter values:



In [2]:

    
ez = EpsteinZinSSY()
ssy = SSY_default()









    Out[2]:





SSY{Float64}(0.987, 0.232, 0.0032, 1.0, 0.994, 0.06244997998398398, 0.991, 0.0938083151964686)



In [3]:

    
K = compute_K_ssy(ez, ssy);



In [4]:

    
compute_spec_rad(K)









    Out[4]:




1.0160552696073246

Spectral Radius Plot, SSY Parameters



In [7]:

    
J = 20 # grid size
R = Array{Float64}(J, J);



In [24]:

    
x_vals = linspace(1.25, 2.25, J)          # ψ
y_vals = linspace(0.0005, 0.008, J)        # μ`









    Out[24]:





0.0005:0.00039473684210526315:0.008



In [25]:

    
for (i, x) in enumerate(x_vals)
    for (j, y) in enumerate(y_vals)
        ez = EpsteinZinSSY(ψ=x)
        @assert ez.θ < 0 "Detected non-negative theta value"
        K = compute_K_ssy(ez, ssy, μ=y)
        R[i, j] = compute_spec_rad(K)
    end
end



In [26]:

    
ez = EpsteinZinSSY() # Get a fresh copy
μ=0.0016









    Out[26]:




0.0016



In [10]:

    
ez.ψ









    Out[10]:




1.93



In [29]:

    
fig, ax = plt.subplots(figsize=(10, 5.7))

#lvs = [0.0, 0.8, 1.0, 1.4, 1.8, 2.2, 4.4]
#cls = [cm.jet(i) for i in np.linspace(0.4, 1, len(lvs))]

cs1 = ax[:contourf](x_vals, 
                    y_vals, 
                    R',
                    alpha=0.6)
                    #levels=lvs,


ctr1 = ax[:contour](x_vals, 
                    y_vals, 
                    R', 
                    levels=[1.0])

plt.clabel(ctr1, inline=1, fontsize=13)
plt.colorbar(cs1, ax=ax)

ax[:set_title]("Spectral radius")
ax[:set_xlabel]("ψ", fontsize=16)
ax[:set_ylabel]("μ", fontsize=16)


ax[:annotate]("Schorfheide, Song and Yaron ", 
         xy=(ez.ψ - 0.024, μ - 0.0001),  
         xycoords="data",
         xytext=(-225, 30),
         textcoords="offset points",
         fontsize=12,
         arrowprops=Dict("arrowstyle" => "->"))

ax[:plot]([ez.ψ], [μ],  "ko", alpha=0.6)

plt.savefig("ssy_pm.pdf")
plt.show()

Let's try varying gamma



In [68]:

    
x_vals = linspace(4.0, 12.0, J)       # γ
y_vals = linspace(0.0005, 0.006, J)      # μ









    Out[68]:





0.0005:0.00028947368421052634:0.006



In [69]:

    
for (i, x) in enumerate(x_vals)
    for (j, y) in enumerate(y_vals)
        ez = EpsteinZinSSY(γ=x)
        @assert ez.θ < 0 "Detected non-negative theta value"
        K = compute_K_ssy(ez, ssy, μ=y)
        R[i, j] = compute_spec_rad(K)
    end
end



In [70]:

    
ez = EpsteinZinSSY() # Get a fresh copy
μ=0.0016









    Out[70]:




0.0016



In [71]:

    
ez.γ









    Out[71]:




8.6



In [72]:

    
fig, ax = plt.subplots(figsize=(10, 5.7))

#lvs = [0.0, 0.8, 1.0, 1.4, 1.8, 2.2, 4.4]
#cls = [cm.jet(i) for i in np.linspace(0.4, 1, len(lvs))]

cs1 = ax[:contourf](x_vals, 
                    y_vals, 
                    R',
                    alpha=0.6)
                    #levels=lvs,


ctr1 = ax[:contour](x_vals, 
                    y_vals, 
                    R', 
                    levels=[1.0])

plt.clabel(ctr1, inline=1, fontsize=13)
plt.colorbar(cs1, ax=ax)

ax[:set_title]("Spectral radius")
ax[:set_xlabel]("γ", fontsize=16)
ax[:set_ylabel]("μ", fontsize=16)


ax[:annotate]("Schorfheide, Song and Yaron ", 
         xy=(ez.γ - 0.084, μ - 0.0001),  
         xycoords="data",
         xytext=(-225, -30),
         textcoords="offset points",
         fontsize=12,
         arrowprops=Dict("arrowstyle" => "->"))

ax[:plot]([ez.γ], [μ],  "ko", alpha=0.6)

plt.savefig("ssy_gm.pdf")
plt.show()

And now mu and volatility



In [200]:

    
x_vals = linspace(0.0015, 0.004, J)          # sigma_bar
y_vals = linspace(0.0005, 0.005, J)         # μ









    Out[200]:





0.0005:0.00023684210526315788:0.005



In [201]:

    
ssy = SSY_default()









    Out[201]:





SSY{Float64}(0.987, 0.232, 0.0032, 1.0, 0.994, 0.06244997998398398, 0.991, 0.0938083151964686)



In [202]:

    
for (i, x) in enumerate(x_vals)
    for (j, y) in enumerate(y_vals)
        ez = EpsteinZinSSY()
        ssy.σ_bar = x
        @assert ez.θ < 0 "Detected non-negative theta value"
        K = compute_K_ssy(ez, ssy, μ=y)
        R[i, j] = compute_spec_rad(K)
    end
end



In [203]:

    
ez = EpsteinZinSSY() # Get a fresh copy
μ=0.0016
ssy = SSY_default()









    Out[203]:





SSY{Float64}(0.987, 0.232, 0.0032, 1.0, 0.994, 0.06244997998398398, 0.991, 0.0938083151964686)



In [204]:

    
ssy.σ_bar









    Out[204]:




0.0032



In [205]:

    
fig, ax = plt.subplots(figsize=(10, 5.7))

#lvs = [0.0, 0.8, 1.0, 1.4, 1.8, 2.2, 4.4]
#cls = [cm.jet(i) for i in np.linspace(0.4, 1, len(lvs))]

cs1 = ax[:contourf](x_vals, 
                    y_vals, 
                    R',
                    alpha=0.6)
                    #levels=lvs,


ctr1 = ax[:contour](x_vals, 
                    y_vals, 
                    R', 
                    levels=[1.0])

plt.clabel(ctr1, inline=1, fontsize=13)
plt.colorbar(cs1, ax=ax)

ax[:set_title]("Spectral radius")
ax[:set_xlabel]("σ_bar", fontsize=16)
ax[:set_ylabel]("μ", fontsize=16)

ax[:annotate]("Schorfheide, Song and Yaron ", 
         xy=(ssy.σ_bar - 0.000084, μ - 0.0001),  
         xycoords="data",
         xytext=(-175, -40),
         textcoords="offset points",
         fontsize=12,
         arrowprops=Dict("arrowstyle" => "->"))

ax[:plot]([ssy.σ_bar], [μ],  "ko", alpha=0.6)

plt.savefig("ssy_sbm.pdf")
plt.show()



In [ ]: