def makeTargetMfig(Rfree, DiscFac, CRRA, permShkStd, TranShkStd): inf_hor = IndShockConsumerType(quietly=True, **base_params) inf_hor.Rfree = Rfree inf_hor.DiscFac = DiscFac inf_hor.CRRA = CRRA inf_hor.permShkStd = [permShkStd] inf_hor.TranShkStd = [TranShkStd] inf_hor.update_income_process() mPlotMin = 0 mPlotMax = 250 inf_hor.aXtraMax = mPlotMax inf_hor.solve(quietly=True, messaging_level=logging.CRITICAL) soln = inf_hor.solution[0] Bilt, cFunc = soln.Bilt, soln.cFunc cPlotMin = 0, cFunc(mPlotMax) if Bilt.GICNrm: # tattle soln.check_GICNrm(soln, quietly=False, messaging_level=logging.WARNING) mBelwStE = np.linspace(mPlotMin, mPlotMax, 1000) EPermGroFac = inf_hor.PermGroFac[0] def EmDelEq0(mVec): return (EPermGroFac / Rfree) + (1.0 - EPermGroFac / Rfree) * mVec cBelwStE_Best = cFunc(mBelwStE) # "best" = optimal c cBelwStE_Sstn = EmDelEq0(mBelwStE) # "sustainable" c mNrmStE = Bilt.mNrmStE plt.figure(figsize=(12, 8)) plt.plot(mBelwStE, cBelwStE_Best, label="$c(m_{t})$") plt.plot(mBelwStE, cBelwStE_Sstn, label="$\mathsf{E}_{t}[\Delta m_{t+1}] = 0$") plt.xlim(mPlotMin, mPlotMax) plt.ylim(cPlotMin, cFunc(mPlotMax)) plt.plot( [mNrmStE, mNrmStE], [0, 2.5], color="black", linestyle="--", ) plt.tick_params( # labelbottom=False, # labelleft=False, # left="off", right="off", # bottom="off", top="off", ) plt.text(0, 1.47, r"$c$", fontsize=26) plt.text(3.02, 0, r"$m$", fontsize=26) plt.text(mNrmStE - 0.05, -0.1, "m̌", fontsize=26) plt.legend(fontsize='x-large') plt.show() return None
def makeConvergencePlot(DiscFac, CRRA, Rfree, permShkStd): # Construct finite horizon agent with baseline parameters baseAgent_Fin = IndShockConsumerType(quietly=True, messaging_level=logging.CRITICAL, **base_params) baseAgent_Fin.DiscFac = DiscFac baseAgent_Fin.CRRA = CRRA baseAgent_Fin.Rfree = Rfree baseAgent_Fin.permShkStd = [permShkStd] baseAgent_Fin.cycles = 100 baseAgent_Fin.solve(quietly=True, messaging_level=logging.CRITICAL) baseAgent_Fin.unpack('cFunc') # figure plot limits mMin, mMax, cPlotMin, cPlotMax = 0, 7, 0, 7 mPlotMin = 0 mLocCLabels = 5.6 # Defines horizontal limit of figure mPlotTop = 6.5 # 3.5 # 6.5 # Defines maximum m value where functions are plotted mPts = 100 # Number of points at which functions are evaluated plt.figure(figsize=(12, 8)) plt.ylim([cPlotMin, cPlotMax]) plt.xlim([mMin, mMax]) mBelwLabels = np.linspace(mPlotMin, mLocCLabels - 0.1, mPts) # Range of m below loc of labels m_FullRange = np.linspace(mPlotMin, mPlotTop, mPts) # Full plot range # c_Tm0 defines the last period consumption rule (c=m) c_Tm0 = m_FullRange # c_Tm1 defines the second-to-last period consumption rule c_Tm1 = baseAgent_Fin.cFunc[-2](mBelwLabels) c_Tm5 = baseAgent_Fin.cFunc[-6]( mBelwLabels) # c_Tm5 defines the T-5 period consumption rule # c_Tm10 defines the T-10 period consumption rule c_Tm10 = baseAgent_Fin.cFunc[-11](mBelwLabels) # c_Limt defines limiting infinite-horizon consumption rule c_Limt = baseAgent_Fin.cFunc[0](mBelwLabels) plt.plot(mBelwLabels, c_Limt, label="$c(m)$") plt.plot(mBelwLabels, c_Tm1, label="$c_{T-1}(m)$") plt.plot(mBelwLabels, c_Tm5, label="$c_{T-5}(m)$") plt.plot(mBelwLabels, c_Tm10, label="$c_{T-10}(m)$") plt.plot(m_FullRange, c_Tm0, label="$c_{T}(m) = 45$ degree line") plt.legend(fontsize='x-large') plt.tick_params(labelbottom=False, labelleft=False, left="off", right="off", bottom="off", top="off") plt.show() return None
def makeBoundsFigure(UnempPrb, permShkStd, TranShkStd, DiscFac, CRRA): inf_hor = IndShockConsumerType(quietly=True, messaging_level=logging.CRITICAL, **base_params) inf_hor.UnempPrb = UnempPrb inf_hor.permShkStd = [permShkStd] inf_hor.TranShkStd = [TranShkStd] inf_hor.DiscFac = DiscFac inf_hor.CRRA = CRRA inf_hor.update_income_process() inf_hor.solve(quietly=True, messaging_level=logging.CRITICAL) soln = inf_hor.solution[0] Bilt, Pars = soln.Bilt, soln.Pars cFunc = soln.cFunc mPlotMin, mPlotMax = 0, 25 inf_hor.aXtraMax = mPlotMax # Retrieve parameters (makes code more readable) Rfree, EPermGroFac = Pars.Rfree, Pars.PermGroFac κ_Min = 1.0 - (Rfree**(-1.0)) * (Rfree * DiscFac)**(1.0 / CRRA) h_inf = (1.0 / (1.0 - EPermGroFac / Rfree)) def cFunc_Uncnst(mVec): return (h_inf - 1) * κ_Min + κ_Min * mVec def cFunc_TopBnd(mVec): return (1 - UnempPrb**(1.0 / CRRA) * (Rfree * DiscFac)**(1.0 / CRRA) / Rfree) * mVec def cFunc_BotBnd(mVec): return (1 - (Rfree * DiscFac)**(1.0 / CRRA) / Rfree) * mVec # Plot the consumption function and its bounds cPlotMaxLabel = r"c̅$(m) = (m-1+h)κ̲$" # Use unicode kludge cPlotMinLabel = r"c̲$(m)= (1-\Phi_{R})m = κ̲ m$" # mKnk is point where the two upper bounds meet mKnk = ((h_inf - 1) * κ_Min) / ( (1 - UnempPrb**(1.0 / CRRA) * (Rfree * DiscFac)**(1.0 / CRRA) / Rfree) - κ_Min) mBelwKnkPts, mAbveKnkPts = 50, 100 mBelwKnk = np.linspace(mPlotMin, mKnk, mBelwKnkPts) mAbveKnk = np.linspace(mKnk, mPlotMax, mAbveKnkPts) mFullPts = np.linspace(mPlotMin, mPlotMax, mBelwKnkPts + mAbveKnkPts) plt.figure(figsize=(12, 8)) plt.plot(mFullPts, cFunc(mFullPts), label=r'$c(m)$') plt.plot(mBelwKnk, cFunc_Uncnst(mBelwKnk), label=cPlotMaxLabel, linestyle="--") plt.plot( mAbveKnk, cFunc_Uncnst(mAbveKnk), label= r'Upper Bound $ = $ Min $[\overline{\overline{c}}(m),\overline{c}(m)]$', linewidth=2.5, color='black') plt.plot(mBelwKnk, cFunc_TopBnd(mBelwKnk), linewidth=2.5, color='black') plt.plot(mAbveKnk, cFunc_TopBnd(mAbveKnk), linestyle="--", label=r"$\overline{\overline{c}}(m) = κ̅m = (1 - ℘^{1/ρ}Φᵣ)m$") plt.plot(mBelwKnk, cFunc_BotBnd(mBelwKnk), color='red', linewidth=2.5) plt.plot(mAbveKnk, cFunc_BotBnd(mAbveKnk), color='red', label=cPlotMinLabel, linewidth=2.5) plt.tick_params(labelbottom=False, labelleft=False, left='off', right='off', bottom='off', top='off') plt.xlim(mPlotMin, mPlotMax) plt.ylim(mPlotMin, 1.12 * cFunc_Uncnst(mPlotMax)) plt.text(mPlotMin, 1.12 * cFunc_Uncnst(mPlotMax) + 0.05, "$c$", fontsize=22) plt.text(mPlotMax + 0.1, mPlotMin, "$m$", fontsize=22) plt.legend(fontsize='x-large') plt.show() return None