add fevd to generate plots script

Author: thorek1

docs/generate_plots.jl

@@ -972,3 +972,270 @@ plot_solution(Backus_Kehoe_Kydland_1992, "K{H}",
 
 # ![Backus IRF - E{H} shock with rename dictionary](../assets/rename_dict_irf__Backus_Kehoe_Kydland_1992__E{H}__1.png)
 
+
+# Conditional Variance Decomposition
+@model Smets_Wouters_2007_linear begin
+    a[0] = calfa * rkf[0] + (1 - calfa) * wf[0]
+    zcapf[0] = rkf[0] * 1 / (czcap / (1 - czcap))
+    rkf[0] = wf[0] + labf[0] - kf[0]
+    kf[0] = zcapf[0] + kpf[-1]
+    invef[0] = qs[0] + 1 / (1 + cgamma * cbetabar) * (pkf[0] * 1 / (csadjcost * cgamma ^ 2) + invef[-1] + invef[1] * cgamma * cbetabar)
+    pkf[0] = b[0] * (1 / ((1 - chabb / cgamma) / (csigma * (1 + chabb / cgamma)))) - rrf[0] + rkf[1] * (crk / (crk + (1 - ctou))) + pkf[1] * ((1 - ctou) / (crk + (1 - ctou)))
+    cf[0] = b[0] + cf[-1] * chabb / cgamma / (1 + chabb / cgamma) + cf[1] * 1 / (1 + chabb / cgamma) + (labf[0] - labf[1]) * ((csigma - 1) * cwhlc / (csigma  *(1 + chabb / cgamma))) - rrf[0] * (1 - chabb / cgamma) / (csigma * (1 + chabb / cgamma))
+    yf[0] = g[0] + cf[0] * ccy + invef[0] * ciy + zcapf[0] * crkky
+    yf[0] = cfc * (a[0] + calfa * kf[0] + (1 - calfa) * labf[0])
+    wf[0] = labf[0] * csigl + cf[0] * 1 / (1 - chabb / cgamma) - cf[-1] * chabb / cgamma / (1 - chabb / cgamma)
+    kpf[0] = kpf[-1] * (1 - cikbar) + invef[0] * cikbar + qs[0] * csadjcost * cgamma ^ 2 * cikbar
+    mc[0] = calfa * rk[0] + (1 - calfa) * w[0] - a[0]
+    zcap[0] = 1 / (czcap / (1 - czcap)) * rk[0]
+    rk[0] = w[0] + lab[0] - k[0]
+    k[0] = zcap[0] + kp[-1]
+    inve[0] = qs[0] + 1 / (1 + cgamma * cbetabar) * (pk[0] * 1 / (csadjcost * cgamma ^ 2) + inve[-1] + inve[1] * cgamma * cbetabar)
+    pk[0] = pinf[1] - r[0] + b[0] * 1 / ((1 - chabb / cgamma) / (csigma * (1 + chabb / cgamma))) + rk[1] * (crk / (crk + (1 - ctou))) + pk[1] * ((1 - ctou) / (crk + (1 - ctou)))
+    c[0] = b[0] + c[-1] * chabb / cgamma / (1 + chabb / cgamma) + c[1] * 1 / (1 + chabb / cgamma) + 
+    (lab[0] - lab[1]) * ((csigma - 1) * cwhlc / (csigma * (1 + chabb / cgamma))) - (r[0] - pinf[1]) * (1 - chabb / cgamma) / (csigma * (1 + chabb / cgamma))
+    y[0] = g[0] + c[0] * ccy + inve[0] * ciy + zcap[0] * crkky
+    y[0] = cfc * (a[0] + calfa * k[0] + (1 - calfa) * lab[0])
+    pinf[0] = spinf[0] + 1 / (1 + cindp * cgamma * cbetabar) * (cindp * pinf[-1] + pinf[1] * cgamma * cbetabar + mc[0] * (1 - cprobp) * (1 - cprobp * cgamma * cbetabar) / cprobp / (1 + (cfc - 1) * curvp))
+    w[0] = sw[0] + w[-1] * 1 / (1 + cgamma * cbetabar) + w[1] * cgamma * cbetabar / (1 + cgamma * cbetabar) + pinf[-1] * cindw / (1 + cgamma * cbetabar) - pinf[0] * (1 + cindw * cgamma * cbetabar) / (1 + cgamma * cbetabar) + pinf[1] * cgamma * cbetabar / (1 + cgamma * cbetabar) + (csigl * lab[0] + c[0] * 1 / (1 - chabb / cgamma) - c[-1] * chabb / cgamma / (1 - chabb / cgamma) - w[0]) * 1 / (1 + (clandaw - 1) * curvw) * (1 - cprobw) * (1 - cprobw * cgamma * cbetabar) / (cprobw * (1 + cgamma * cbetabar))
+    r[0] = pinf[0] * crpi * (1 - crr) + (1 - crr) * cry * (y[0] - yf[0]) + crdy * (y[0] - yf[0] - y[-1] + yf[-1]) + crr * r[-1] + ms[0]
+    a[0] = crhoa * a[-1] + z_ea * ea[x]
+    b[0] = crhob * b[-1] + z_eb * eb[x]
+    g[0] = crhog * g[-1] + z_eg * eg[x] + z_ea * ea[x] * cgy
+    qs[0] = crhoqs * qs[-1] + z_eqs * eqs[x]
+    ms[0] = crhoms * ms[-1] + z_em * em[x]
+    spinf[0] = crhopinf * spinf[-1] + epinfma[0] - cmap * epinfma[-1]
+    epinfma[0] = z_epinf * epinf[x]
+    sw[0] = crhow * sw[-1] + ewma[0] - cmaw * ewma[-1]
+    ewma[0] = z_ew * ew[x]
+    kp[0] = kp[-1] * (1 - cikbar) + inve[0] * cikbar + qs[0] * csadjcost * cgamma ^ 2 * cikbar
+    dy[0] = ctrend + y[0] - y[-1]
+    dc[0] = ctrend + c[0] - c[-1]
+    dinve[0] = ctrend + inve[0] - inve[-1]
+    pinfobs[0] = constepinf + pinf[0]
+    robs[0] = r[0] + conster
+    dwobs[0] = ctrend + w[0] - w[-1]
+    labobs[0] = lab[0] + constelab
+end
+
+@parameters Smets_Wouters_2007_linear begin
+    ctou = .025
+    clandaw = 1.5
+    cg = 0.18
+    curvp = 10
+    curvw = 10
+    calfa = .24
+    csigma = 1.5
+    cfc = 1.5
+    cgy = 0.51
+    csadjcost = 6.0144
+    chabb = 0.6361
+    cprobw = 0.8087
+    csigl = 1.9423
+    cprobp = 0.6
+    cindw = 0.3243
+    cindp = 0.47
+    czcap = 0.2696
+    crpi = 1.488
+    crr = 0.8762
+    cry = 0.0593
+    crdy = 0.2347
+    crhoa = 0.9977
+    crhob = 0.5799
+    crhog = 0.9957
+    crhoqs = 0.7165
+    crhoms = 0
+    crhopinf = 0
+    crhow = 0
+    cmap = 0
+    cmaw = 0
+    constelab = 0
+    constepinf = 0.7
+    constebeta = 0.7420
+    ctrend = 0.3982
+    z_ea	= 0.4618
+    z_eb	= 1.8513
+    z_eg	= 0.6090
+    z_em	= 0.2397
+    z_ew	= 0.2089
+    z_eqs	= 0.6017
+    z_epinf	= 0.1455
+    cpie 	= 1 + constepinf / 100         							# gross inflation rate
+    cgamma 	= 1 + ctrend / 100          							# gross growth rate
+    cbeta 	= 1 / (1 + constebeta / 100)    						# discount factor
+    clandap = cfc                									# fixed cost share/gross price markup
+    cbetabar= cbeta * cgamma ^ (-csigma)   							# growth-adjusted discount factor in Euler equation
+    cr 		= cpie / cbetabar  										# steady state gross real interest rate
+    crk 	= 1 / cbetabar - (1 - ctou) 							# steady state rental rate
+    cw 		= (calfa ^ calfa * (1 - calfa) ^ (1 - calfa) / (clandap * crk ^ calfa)) ^ (1 / (1 - calfa))	# steady state real wage
+    cikbar 	= 1 - (1 - ctou) / cgamma								# (1-k_1) in equation LOM capital, equation (8)
+    cik 	= cikbar * cgamma										# i_k: investment-capital ratio
+    clk 	= (1 - calfa) / calfa * crk / cw						# labor to capital ratio
+    cky 	= cfc * clk ^ (calfa - 1)								# k_y: steady state output ratio
+    ciy 	= cik * cky												# investment-output ratio
+    ccy 	= 1 - cg - cik * cky									# consumption-output ratio
+    crkky 	= crk * cky												# z_y=R_{*}^k*k_y
+    cwhlc 	= (1 / clandaw) * (1 - calfa) / calfa * crk * cky / ccy	# W^{h}_{*}*L_{*}/C_{*} used in c_2 in equation (2)
+    conster = (cr - 1) * 100										# steady state federal funds rate ($\bar r$)
+end
+
+
+plot_conditional_variance_decomposition(Smets_Wouters_2007_linear,
+	save_plots = true, save_plots_format = :png, save_plots_path = "./docs/src/assets")
+
+
+plot_fevd(Smets_Wouters_2007_linear, periods = 12,
+	save_plots = true, save_plots_format = :png, save_plots_path = "./docs/src/assets", save_plots_name = :short_period)
+
+
+plot_fevd(Smets_Wouters_2007_linear,
+    variables = [:inve, :c, :y, :pinf, :w, :lab],
+	save_plots = true, save_plots_format = :png, save_plots_path = "./docs/src/assets", save_plots_name = :var_select)
+
+
+
+@model FS2000 begin
+    dA[0] = exp(gam + z_e_a  *  e_a[x])
+    log(m[0]) = (1 - rho) * log(mst)  +  rho * log(m[-1]) + z_e_m  *  e_m[x]
+    - P[0] / (c[1] * P[1] * m[0]) + bet * P[1] * (alp * exp( - alp * (gam + log(e[1]))) * k[0] ^ (alp - 1) * n[1] ^ (1 - alp) + (1 - del) * exp( - (gam + log(e[1])))) / (c[2] * P[2] * m[1])=0
+    W[0] = l[0] / n[0]
+    - (psi / (1 - psi)) * (c[0] * P[0] / (1 - n[0])) + l[0] / n[0] = 0
+    R[0] = P[0] * (1 - alp) * exp( - alp * (gam + z_e_a  *  e_a[x])) * k[-1] ^ alp * n[0] ^ ( - alp) / W[0]
+    1 / (c[0] * P[0]) - bet * P[0] * (1 - alp) * exp( - alp * (gam + z_e_a  *  e_a[x])) * k[-1] ^ alp * n[0] ^ (1 - alp) / (m[0] * l[0] * c[1] * P[1]) = 0
+    c[0] + k[0] = exp( - alp * (gam + z_e_a  *  e_a[x])) * k[-1] ^ alp * n[0] ^ (1 - alp) + (1 - del) * exp( - (gam + z_e_a  *  e_a[x])) * k[-1]
+    P[0] * c[0] = m[0]
+    m[0] - 1 + d[0] = l[0]
+    e[0] = exp(z_e_a  *  e_a[x])
+    y[0] = k[-1] ^ alp * n[0] ^ (1 - alp) * exp( - alp * (gam + z_e_a  *  e_a[x]))
+    gy_obs[0] = dA[0] * y[0] / y[-1]
+    gp_obs[0] = (P[0] / P[-1]) * m[-1] / dA[0]
+    log_gy_obs[0] = log(gy_obs[0])
+    log_gp_obs[0] = log(gp_obs[0])
+end
+
+@parameters FS2000 begin
+    alp     = 0.356
+    bet     = 0.993
+    gam     = 0.0085
+    mst     = 1.0002
+    rho     = 0.129
+    psi     = 0.65
+    del     = 0.01
+    z_e_a   = 0.035449
+    z_e_m   = 0.008862
+end
+
+plot_fevd(FS2000,
+	variables = :all_excluding_obc,
+	save_plots = true, save_plots_format = :png, save_plots_path = "./docs/src/assets", save_plots_name = :aux)
+
+
+plot_fevd(Smets_Wouters_2007_linear,
+    parameters = :constebeta => 1,
+	save_plots = true, save_plots_format = :png, save_plots_path = "./docs/src/assets", save_plots_name = :param_change)
+
+
+plot_fevd(Smets_Wouters_2007_linear,
+    parameters = (:constebeta => 1.5, :crpi => 1.75),
+	save_plots = true, save_plots_format = :png, save_plots_path = "./docs/src/assets", save_plots_name = :param_change_2)
+
+
+ec_color_palette =
+[
+	"#FFD724", 	# "Sunflower Yellow"
+	"#353B73", 	# "Navy Blue"
+	"#2F9AFB", 	# "Sky Blue"
+	"#B8AAA2", 	# "Taupe Grey"
+	"#E75118", 	# "Vermilion"
+	"#6DC7A9", 	# "Mint Green"
+	"#F09874", 	# "Coral"
+	"#907800"  	# "Olive"
+]
+
+
+plot_fevd(Smets_Wouters_2007_linear,
+    plot_attributes = Dict(:palette => ec_color_palette),
+	save_plots = true, save_plots_format = :png, save_plots_path = "./docs/src/assets", save_plots_name = :color_palette)
+
+
+
+plot_fevd(Smets_Wouters_2007_linear,
+    plot_attributes = Dict(:fontfamily => "computer modern"),
+    save_plots = true, save_plots_format = :png, save_plots_path = "./docs/src/assets", save_plots_name = :font_family)
+
+
+plot_fevd(Smets_Wouters_2007_linear,
+    plot_attributes = Dict(:fillalpha => .5),
+    save_plots = true, save_plots_format = :png, save_plots_path = "./docs/src/assets", save_plots_name = :fill_alpha)
+
+
+
+plot_fevd(Smets_Wouters_2007_linear,
+    variables = [:inve, :c, :y, :pinf, :w, :lab],
+    plots_per_page = 4,
+    save_plots = true, save_plots_format = :png, save_plots_path = "./docs/src/assets", save_plots_name = :four_per_page)
+
+
+
+plot_fevd(Smets_Wouters_2007_linear,
+    rename_dictionary = Dict(:y => "Output", :pinfobs => "Inflation", :robs => "Interest Rate", :inve => "Investment", :c => "Consumption", :w => "Wages", :lab => "Labor"),
+    save_plots = true, save_plots_format = :png, save_plots_path = "./docs/src/assets", save_plots_name = :rename_dict_fevd)
+
+@model Backus_Kehoe_Kydland_1992 begin
+    for co in [H, F]
+        Y{co}[0] = ((LAMBDA{co}[0] * K{co}[-4]^theta{co} * N{co}[0]^(1-theta{co}))^(-nu{co}) + sigma{co} * Z{co}[-1]^(-nu{co}))^(-1/nu{co})
+        K{co}[0] = (1-delta{co})*K{co}[-1] + S{co}[0]
+        X{co}[0] = for lag in (-4+1):0 phi{co} * S{co}[lag] end
+        A{co}[0] = (1-eta{co}) * A{co}[-1] + N{co}[0]
+        L{co}[0] = 1 - alpha{co} * N{co}[0] - (1-alpha{co})*eta{co} * A{co}[-1]
+        U{co}[0] = (C{co}[0]^mu{co}*L{co}[0]^(1-mu{co}))^gamma{co}
+        psi{co} * mu{co} / C{co}[0]*U{co}[0] = LGM[0]
+        psi{co} * (1-mu{co}) / L{co}[0] * U{co}[0] * (-alpha{co}) = - LGM[0] * (1-theta{co}) / N{co}[0] * (LAMBDA{co}[0] * K{co}[-4]^theta{co}*N{co}[0]^(1-theta{co}))^(-nu{co})*Y{co}[0]^(1+nu{co})
+
+        for lag in 0:(4-1)  
+            beta{co}^lag * LGM[lag]*phi{co}
+        end +
+        for lag in 1:4
+            -beta{co}^lag * LGM[lag] * phi{co} * (1-delta{co})
+        end = beta{co}^4 * LGM[+4] * theta{co} / K{co}[0] * (LAMBDA{co}[+4] * K{co}[0]^theta{co} * N{co}[+4]^(1-theta{co})) ^ (-nu{co})* Y{co}[+4]^(1+nu{co})
+
+        LGM[0] = beta{co} * LGM[+1] * (1+sigma{co} * Z{co}[0]^(-nu{co}-1)*Y{co}[+1]^(1+nu{co}))
+        NX{co}[0] = (Y{co}[0] - (C{co}[0] + X{co}[0] + Z{co}[0] - Z{co}[-1]))/Y{co}[0]
+    end
+
+    (LAMBDA{H}[0]-1) = rho{H}{H}*(LAMBDA{H}[-1]-1) + rho{H}{F}*(LAMBDA{F}[-1]-1) + Z_E{H} * E{H}[x]
+    (LAMBDA{F}[0]-1) = rho{F}{F}*(LAMBDA{F}[-1]-1) + rho{F}{H}*(LAMBDA{H}[-1]-1) + Z_E{F} * E{F}[x]
+
+    for co in [H,F] C{co}[0] + X{co}[0] + Z{co}[0] - Z{co}[-1] end = for co in [H,F] Y{co}[0] end
+end
+
+@parameters Backus_Kehoe_Kydland_1992 begin
+    K_ss = 11
+    K[ss] = K_ss | beta
+    
+    mu      =    0.34
+    gamma   =    -1.0
+    alpha   =    1
+    eta     =    0.5
+    theta   =    0.36
+    nu      =    3
+    sigma   =    0.01
+    delta   =    0.025
+    phi     =    1/4
+    psi     =    0.5
+
+    Z_E = 0.00852
+    
+    rho{H}{H} = 0.906
+    rho{F}{F} = rho{H}{H}
+    rho{H}{F} = 0.088
+    rho{F}{H} = rho{H}{F}
+end
+
+# Backus model example showing String to String mapping
+plot_fevd(Backus_Kehoe_Kydland_1992,
+    rename_dictionary = Dict("K{H}" => "Capital (Home)", 
+                             "K{F}" => "Capital (Foreign)",
+                             "Y{H}" => "Output (Home)",
+                             "Y{F}" => "Output (Foreign)"),
+    save_plots = true, save_plots_format = :png, save_plots_path = "./docs/src/assets", save_plots_name = :rename_dict_string)