#!/usr/bin/env python # coding: utf-8 # # Monetary Economics: Chapter 11 # ### Preliminaries # In[1]: # This line configures matplotlib to show figures embedded in the notebook, # instead of opening a new window for each figure. More about that later. # If you are using an old version of IPython, try using '%pylab inline' instead. get_ipython().run_line_magic('matplotlib', 'inline') from pysolve.model import Model from pysolve.utils import is_close,round_solution import matplotlib.pyplot as plt # ### Model GROWTH # > Changes to the model: # > In the GROWTH model, I've used the definition of the Tobin's Q from the INSOUT model in Chapter 10 # > # > Original: Q = (Eks*Pe)/(K + IN + Lfd) # > # > Corrected : Q = (Eks*Pe + Lfd)/(K + IN) # In[2]: def create_growth_model(): model = Model() model.set_var_default(0) model.var('ADDl', desc='Spread between interest rate on loans and rate on deposits') model.var('Bbd', desc='Government bills demanded by commercial banks') model.var('Bbs', desc='Government bills supplied to commercial banks') model.var('Bcbd', desc='Government bills demanded by Central bank') model.var('Bcbs', desc='Government bills supplied by Central bank') model.var('Bhd', desc='Demand for government bills from households') model.var('Bhs', desc='Government bills supplied to households') model.var('Bs', desc='Supply of government bills') model.var('BLd', desc='Demand for government bonds') model.var('BLs', desc='Supply of government bonds') model.var('BLR', desc='Gross bank liquidity ratio') model.var('BUR', desc='Burden of personal debt') model.var('Ck', desc='Real consumption') model.var('CAR', desc='Capital adequacy ratio of banks') model.var('CG', desc='Capital gains on government bonds') model.var('CONS', desc='Consumption at current prices') model.var('Ekd', desc='Number of equities demanded') model.var('Eks', desc='Number of equities supplied by firms') model.var('ER', desc='Employment rate') model.var('Fb', desc='Realized banks profits') model.var('Fbt', desc='Target profits of banks') model.var('Fcb', desc='Central bank "profits"') model.var('Ff', desc='Realized entrepreneurial profits') model.var('Fft', desc='Planned entrepreneurial profits') model.var('FDb', desc='Dividends of banks') model.var('FDf', desc='Dividends of firms') model.var('FUb', desc='Retained earnings of banks') model.var('FUbt', desc='Targt retained earnings of banks') model.var('FUf', desc='Retained earnings of firms') model.var('FUft', desc='Planned retained earnings of firms') model.var('G', desc='Government expenditures') model.var('Gk', desc='Real government expenditures') model.var('GD', desc='Government debt') model.var('GL', desc='Gross amount of new personal loans') model.var('GRk', desc='growth_mod of real capital stock') model.var('Hbd', desc='Cash required by banks') model.var('Hbs', desc='Cash supplied to banks') model.var('Hhd', desc='Households demand for cash') model.var('Hhs', desc='Cash supplied to households') model.var('Hs', desc='Total supply of cash') model.var('HCe', desc='Expected historical costs') model.var('INV', desc='Gross investment') model.var('Ik', desc='Gross investment in real terms') model.var('IN', desc='Stock of inventories at current costs') model.var('INk', desc='Real inventories') model.var('INke', desc='Expected real inventories') model.var('INkt', desc='Target level of real inventories') model.var('K', desc='Capital stock') model.var('Kk', desc='Real capital stock') model.var('Lfd', desc='Demand for loans by firms') model.var('Lfs', desc='Supply of loans to firms') model.var('Lhd', desc='Demand for loans by households') model.var('Lhs', desc='Loans supplied to households') model.var('Md', desc='Deposits demanded by households') model.var('Ms', desc='Deposits supplied by banks') model.var('N', desc='Employment level') model.var('Nt', desc='Desired employment level') model.var('NHUC', desc='Normal historic unit cost') model.var('NL', desc='Net flow of new loans to the household sector') model.var('NLk', desc='Real flow of new loans to the household sector') model.var('NPL', desc='Non-Performing loans') model.var('NPLke', desc='Expected proportion of Non-Performing Loans') model.var('NUC', desc='Normal unit cost') model.var('OFb', desc='Own funds of banks') model.var('OFbe', desc='Short-run target for banks own funds') model.var('OFbt', desc='Long-run target for banks own funds') model.var('omegat', desc='Target real wage for workers') model.var('P', desc='Price level') model.var('Pbl', desc='Price of government bonds') model.var('Pe', desc='Price of equities') model.var('PE', desc='Price earnings ratio') model.var('PI', desc='Price inflation') model.var('PR', desc='Lobor productivity') model.var('PSBR', desc='Government deficit') model.var('Q', desc="Tobin's Q") model.var('Rb', desc='Interest rate on government bills') model.var('Rbl', desc='Interest rate on bonds') model.var('Rk', desc='Dividend yield of firms') model.var('Rl', desc='Interest rate on loans') model.var('Rm', desc='Interest rate on deposits') model.var('REP', desc='Personal loans repayments') model.var('RRl', desc='Real interest rate on loans') model.var('S', desc='Sales at current prices') model.var('Sk', desc='Real sales') model.var('Ske', desc='Expected real sales') model.var('T', desc='Taxes') model.var('U', desc='Capital utilization proxy') model.var('UC', desc='Unit costs') model.var('V', desc='Wealth of households') model.var('Vk', desc='Real wealth of households') model.var('Vfma', desc='Investible wealth of households') model.var('W', desc='Wage rate') model.var('WB', desc='The wage bill') model.var('Y', desc='Output at current prices (nominal GDP)') model.var('Yk', desc='Real output') model.var('YDhs', desc='Haig-Simons measure of disposable income') model.var('YDr', desc='Regular disposable income') model.var('YDkr', desc='Regular real disposable income') model.var('YDkre', desc='Expected regular real disposable income') model.var('YP', desc='Personal income') model.var('eta', desc='Ratio of new loans to personal income') model.var('phi', desc='Mark-up on unit costs') model.var('phit', desc='Ideal mark-up on unit costs') model.var('z1a', desc='Is one if bank liquidity ratio is below bottom range') model.var('z1b', desc='Is one if bank liquidity ratio is below bottom range') model.var('z2a', desc='Is one if bank liquidity ratio is above top range') model.var('z2b', desc='Is one if bank liquidity ratio is above top range') model.var('z3', desc='Parameter in wage aspiration equation') model.var('z4', desc='Parameter in wage aspiration equation') model.var('z5', desc='Parameter in wage aspiration equation') model.var('sigmase', desc='Opening inventories to expected sales ratio') model.param('alpha1', desc='Propensity to consume out of income') model.param('alpha2', desc='Propensity to consume out of wealth') model.param('beta', desc='Parameter in expectation formations on real sales') model.param('betab', desc='Spped of adjustment of banks own funds') model.param('bot', desc='Bottom value for bank net liquidity ratio') model.param('delta', desc='Rate of depreciation of fixed capital') model.param('deltarep', desc='Ratio of personal loans repayments to stock of loans') model.param('eps', desc='Parameter in expectation formations on real disposable income') model.param('eps2', desc='Speed of adjustment of mark-up') model.param('epsb', desc='Speed of adjustment in expected proportion of non-performing loans') model.param('epsrb', desc='Speed of adjustment in the real interest rate on bills') model.param('eta0', desc='Ratio of new loans to personal income - exogenous component') model.param('etan', desc='Speed of adjustment of actual employment to desired employment') model.param('etar', desc='Relation between the ratio of new loans to personal income and the interest rate on loans') model.param('gamma', desc='Speed of adjustment of inventories to the target level') model.param('gamma0', desc='Exogenous growth_mod in the real stock of capital') model.param('gammar', desc='Relation between the real interest rate and growth_mod in the stock of capital') model.param('gammau', desc='Relation between the utilization rate and growth_mod in the stock of capital') model.param('lambda20', desc='Parameter in households demand for bills') model.param('lambda21', desc='Parameter in households demand for bills') model.param('lambda22', desc='Parameter in households demand for bills') model.param('lambda23', desc='Parameter in households demand for bills') model.param('lambda24', desc='Parameter in households demand for bills') model.param('lambda25', desc='Parameter in households demand for bills') model.param('lambda30', desc='Parameter in households demand for bonds') model.param('lambda31', desc='Parameter in households demand for bonds') model.param('lambda32', desc='Parameter in households demand for bonds') model.param('lambda33', desc='Parameter in households demand for bonds') model.param('lambda34', desc='Parameter in households demand for bonds') model.param('lambda35', desc='Parameter in households demand for bonds') model.param('lambda40', desc='Parameter in households demand for equities') model.param('lambda41', desc='Parameter in households demand for equities') model.param('lambda42', desc='Parameter in households demand for equities') model.param('lambda43', desc='Parameter in households demand for equities') model.param('lambda44', desc='Parameter in households demand for equities') model.param('lambda45', desc='Parameter in households demand for equities') model.param('lambdab', desc='Parameter determining dividends of banks') model.param('lambdac', desc='Parameter in households demand for cash') model.param('psid', desc='Ratio of dividends to gross profits') model.param('psiu', desc='Ratio of retained earnings to investments') model.param('ro', desc='Reserve requirement parameter') model.param('sigman', desc='Parameter of influencing normal historic unit costs') model.param('theta', desc='Income tax rate') model.param('top', desc='Top value for bank net liquidity ratio') model.param('xim1', desc='Parameter in the equation for setting interest rate on deposits') model.param('xim2', desc='Parameter in the equation for setting interest rate on deposits') model.param('omega0', desc='Parameter influencing the target real wage for workers') model.param('omega1', desc='Parameter influencing the target real wage for workers') model.param('omega2', desc='Parameter influencing the target real wage for workers') model.param('omega3', desc='Speed of adjustment of wages to target value') model.param('ADDbl', desc='Spread between long-term interest rate and rate on bills') model.param('BANDb', desc='Lower range of the flat Phillips curve') model.param('BANDt', desc='Upper range of the flat Phillips curve') model.param('GRg', desc='growth_mod of real government expenditures') model.param('GRpr', desc='growth_mod rate of productivity') model.param('NCAR', desc='Normal capital adequacy ratio of banks') model.param('Nfe', desc='Full employment level') model.param('NPLk', desc='Proportion of Non-Performing loans') model.param('RA', desc='Random shock to expectations on real sales') model.param('Rbbar', desc='Interest rate on bills, set exogenously') model.param('Rln', desc='Normal interest rate on loans') model.param('RRb', desc='Real interest rate on bills') model.param('sigmas', desc='Realized inventories to sales ratio') model.param('sigmat', desc='Target inventories to sales ratio') # Box 11.1 : Firms' equations # --------------------------- model.add('Yk = Ske + INke - INk(-1)') # 11.1 : Real output model.add('Ske = beta*Sk + (1-beta)*Sk(-1)*(1 + (GRpr + RA))') # 11.2 : Expected real sales model.add('INke = INk(-1) + gamma*(INkt - INk(-1))') # 11.3 : Long-run inventory target model.add('INkt = sigmat*Ske') # 11.4 : Short-run inventory target model.add('INk - INk(-1) = Yk - Sk - NPL/UC') # 11.5 : Actual real inventories model.add('Kk = Kk(-1)*(1 + GRk)') # 11.6 : Real capital stock model.add('GRk = gamma0 + gammau*U(-1) - gammar*RRl') # 11.7 : Growth of real capital stock model.add('U = Yk/Kk(-1)') # 11.8 : Capital utilization proxy model.add('RRl = ((1 + Rl)/(1 + PI)) - 1') # 11.9 : Real interest rate on loans model.add('PI = (P - P(-1))/P(-1)') # 11.10 : Rate of price inflation model.add('Ik = d(Kk) + delta*Kk(-1)') # 11.11 : Real gross investment # Box 11.2 : Firms' equations # --------------------------- model.add('Sk = Ck + Gk + Ik') # 11.12 : Actual real sales model.add('S = Sk*P') # 11.13 : Value of realized sales model.add('IN = INk*UC') # 11.14 : Inventories valued at current cost model.add('INV = Ik*P') # 11.15 : Nominal gross investment model.add('K = Kk*P') # 11.16 : Nomincal value of fixed capital model.add('Y = Sk*P + d(INk)*UC') # 11.17 : Nomincal GDP # Box 11.3 : Firms' equations # --------------------------- # 11.18 : Real wage aspirations model.add('omegat = exp(omega0 + omega1*log(PR) + omega2*log(ER + z3*(1 - ER) - z4*BANDt + z5*BANDb))') model.add('ER = N(-1)/Nfe(-1)') # 11.19 : Employment rate # 11.20 : Switch variables model.add('z3 = if_true(ER > (1-BANDb)) * if_true(ER <= (1+BANDt))') model.add('z4 = if_true(ER > (1+BANDt))') model.add('z5 = if_true(ER < (1-BANDb))') model.add('W - W(-1) = omega3*(omegat*P(-1) - W(-1))') # 11.21 : Nominal wage model.add('PR = PR(-1)*(1 + GRpr)') # 11.22 : Labor productivity model.add('Nt = Yk/PR') # 11.23 : Desired employment model.add('N - N(-1) = etan*(Nt - N(-1))') # 11.24 : Actual employment model.add('WB = N*W') # 11.25 : Nominal wage bill model.add('UC = WB/Yk') # 11.26 : Actual unit cost model.add('NUC = W/PR') # 11.27 : Normal unit cost model.add('NHUC = (1 - sigman)*NUC + sigman*(1 + Rln(-1))*NUC(-1)') # 11.28 : Normal historic unit cost # Box 11.4 : Firms' equations # --------------------------- model.add('P = (1 + phi)*NHUC') # 11.29 : Normal-cost pricing model.add('phi - phi(-1) = eps2*(phit(-1) - phi(-1))') # 11.30 : Actual mark-up # 11.31 : Ideal mark-up model.add('phit = (FDf + FUft + Rl(-1)*(Lfd(-1) - IN(-1)))/((1 - sigmase)*Ske*UC + (1 + Rl(-1))*sigmase*Ske*UC(-1))') model.add('HCe = (1 - sigmase)*Ske*UC + (1 + Rl(-1))*sigmase*Ske*UC(-1)') # 11.32 : Expected historical costs model.add('sigmase = INk(-1)/Ske') # 11.33 : Opening inventories to expected sales ratio model.add('Fft = FUft + FDf + Rl(-1)*(Lfd(-1) - IN(-1))') # 11.34 : Planned entrepeneurial profits of firmss model.add('FUft = psiu*INV(-1)') # 11.35 : Planned retained earnings of firms model.add('FDf = psid*Ff(-1)') # 11.36 : Dividends of firms # Box 11.5 : Firms' equations # --------------------------- model.add('Ff = S - WB + d(IN) - Rl(-1)*IN(-1)') # 11.37 : Realized entrepeneurial profits model.add('FUf = Ff - FDf - Rl(-1)*(Lfd(-1) - IN(-1)) + Rl(-1)*NPL') # 11.38 : Retained earnings of firms # 11.39 : Demand for loans by firms model.add('Lfd - Lfd(-1) = INV + d(IN) - FUf - d(Eks)*Pe - NPL') model.add('NPL = NPLk*Lfs(-1)') # 11.40 : Defaulted loans model.add('Eks - Eks(-1) = ((1 - psiu)*INV(-1))/Pe') # 11.41 : Supply of equities issued by firms model.add('Rk = FDf/(Pe(-1)*Ekd(-1))') # 11.42 : Dividend yield of firms model.add('PE = Pe/(Ff/Eks(-1))') # 11.43 : Price earnings ratio model.add('Q = (Eks*Pe + Lfd)/(K + IN)') # 11.44 : Tobin's Q ratio # Box 11.6 : Households' equations # -------------------------------- model.add('YP = WB + FDf + FDb + Rm(-1)*Md(-1) + Rb(-1)*Bhd(-1) + BLs(-1)') # 11.45 : Personal income model.add('T = theta*YP') # 11.46 : Income taxes model.add('YDr = YP - T - Rl(-1)*Lhd(-1)') # 11.47 : Regular disposable income model.add('YDhs = YDr + CG') # 11.48 : Haig-Simons disposable income # !1.49 : Capital gains model.add('CG = d(Pbl)*BLd(-1) + d(Pe)*Ekd(-1) + d(OFb)') # 11.50 : Wealth model.add('V - V(-1) = YDr - CONS + d(Pe)*Ekd(-1) + d(Pbl)*BLs(-1) + d(OFb)') model.add('Vk = V/P') # 11.51 : Real staock of wealth model.add('CONS = Ck*P') # 11.52 : Consumption model.add('Ck = alpha1*(YDkre + NLk) + alpha2*Vk(-1)') # 11.53 : Real consumption model.add('YDkre = eps*YDkr + (1 - eps)*YDkr(-1)*(1 + GRpr)') # 11.54 : Expected real regular disposable income model.add('YDkr = YDr/P - d(P)*Vk(-1)/P') # 11.55 : Real regular disposable income # Box 11.7 : Households' equations # -------------------------------- model.add('GL = eta*YDr') # 11.56 : Gross amount of new personal loans model.add('eta = eta0 - etar*RRl') # 11.57 : New loans to personal income ratio model.add('NL = GL - REP') # 11.58 : Net amount of new personal loans model.add('REP = deltarep*Lhd(-1)') # 11.59 : Personal loans repayments model.add('Lhd - Lhd(-1) = GL - REP') # 11.60 : Demand for personal loans model.add('NLk = NL/P') # 11.61 : Real amount of new personal loans model.add('BUR = (REP + Rl(-1)*Lhd(-1))/YDr(-1)') # 11.62 : Burden of personal debt # Box 11.8 : Households equations - portfolio decisions # ----------------------------------------------------- # 11.64 : Demand for bills model.add('Bhd = Vfma(-1)*(lambda20 + lambda22*Rb(-1) - lambda21*Rm(-1) - lambda24*Rk(-1) - lambda23*Rbl(-1) - lambda25*YDr/V)') # 11.65 : Demand for bonds model.add('BLd = Vfma(-1)*(lambda30 - lambda32*Rb(-1) - lambda31*Rm(-1) - lambda34*Rk(-1) + lambda33*Rbl(-1) - lambda35*YDr/V)/Pbl') # 11.66 : Demand for equities - normalized to get the price of equitities model.add('Pe = Vfma(-1)*(lambda40 - lambda42*Rb(-1) - lambda41*Rm(-1) + lambda44*Rk(-1) - lambda43*Rbl(-1) - lambda45*YDr/V)/Ekd') model.add('Md = Vfma - Bhd - Pe*Ekd - Pbl*BLd + Lhd') # 11.67 : Money deposits - as a residual model.add('Vfma = V - Hhd - OFb') # 11.68 : Investible wealth model.add('Hhd = lambdac*CONS') # 11.69 : Households' demand for cash model.add('Ekd = Eks') # 11.70 : Stock market equilibrium # Box 11.9 : Government's equations # --------------------------------- model.add('G = Gk*P') # 11.71 : Pure government expenditures model.add('Gk = Gk(-1)*(1 + GRg)') # 11.72 : Real government expenditures model.add('PSBR = G + BLs(-1) + Rb(-1)*(Bbs(-1) + Bhs(-1)) - T') # 11.73 : Government deficit # 11.74 : New issues of bills model.add('Bs - Bs(-1) = G - T - d(BLs)*Pbl + Rb(-1)*(Bhs(-1) + Bbs(-1)) + BLs(-1)') model.add('GD = Bbs + Bhs + BLs*Pbl + Hs') # 11.75 : Government debt # Box 11.10 : The Central bank's equations # ---------------------------------------- model.add('Fcb = Rb(-1)*Bcbd(-1)') # 11.76 : Central bank profits model.add('BLs = BLd') # 11.77 : Bonds are supplied on demand model.add('Bhs = Bhd') # 11.78 : Household bills supplied on demand model.add('Hhs = Hhd') # 11.79 : Cash supplied on demand model.add('Hbs = Hbd') # 11.80 : Reserves supplied on demand model.add('Hs = Hbs + Hhs') # 11.81 : Total supply of cash model.add('Bcbd = Hs') # 11.82 : Central bankd model.add('Bcbs = Bcbd') # 11.83 : Supply of bills to Central bank model.add('Rb = Rbbar') # 11.84 : Interest rate on bills set exogenously model.add('Rbl = Rb + ADDbl') # 11.85 : Long term interest rate model.add('Pbl = 1/Rbl') # 11.86 : Price of long-term bonds # Box 11.11 : Commercial Bank's equations # --------------------------------------- model.add('Ms = Md') # 11.87 : Bank deposits supplied on demand model.add('Lfs = Lfd') # 11.88 : Loans to firms supplied on demand model.add('Lhs = Lhd') # 11.89 : Personal loans supplied on demand model.add('Hbd = ro*Ms') # 11.90 : Reserve requirements of banks # 11.91 : Bills supplied to banks model.add('Bbs - Bbs(-1) = d(Bs) - d(Bhs) - d(Bcbs)') # 11.92 : Balance sheet constraint of banks model.add('Bbd = Ms + OFb - Lfs - Lhs - Hbd') model.add('BLR = Bbd/Ms') # 11.93 : Bank liquidity ratio # 11.94 : Deposit interest rate model.add('Rm - Rm(-1) = z1a*xim1 + z1b*xim2 - z2a*xim1 - z2b*xim2') # 11.95-97 : Mechanism for determining changes to the interest rate on deposits model.add('z2a = if_true(BLR(-1) > (top + .05))') model.add('z2b = if_true(BLR(-1) > top)') model.add('z1a = if_true(BLR(-1) <= bot)') model.add('z1b = if_true(BLR(-1) <= (bot -.05))') # Box 11.12 : Commercial bank's equations # --------------------------------------- model.add('Rl = Rm + ADDl') # 11.98 : Loan interest rate model.add('OFbt = NCAR*(Lfs(-1) + Lhs(-1))') # 11.99 : Long-run own funds target model.add('OFbe = OFb(-1) + betab*(OFbt - OFb(-1))') # 11.100 : Short-run own funds target model.add('FUbt = OFbe - OFb(-1) + NPLke*Lfs(-1)') # 11.101 : Target retained earnings of banks model.add('NPLke = epsb*NPLke(-1) + (1 - epsb)*NPLk(-1)') # 11.102 : Expected proportion of non-performaing loans model.add('FDb = Fb - FUb') # 11.103 : Dividends of banks model.add('Fbt = lambdab*Y(-1) + (OFbe - OFb(-1) + NPLke*Lfs(-1))') # 11.104 : Target profits of banks # 11.105 : Actual profits of banks model.add('Fb = Rl(-1)*(Lfs(-1) + Lhs(-1) - NPL) + Rb(-1)*Bbd(-1) - Rm(-1)*Ms(-1)') # 11.106 : Lending mark-up over deposit rate model.add('ADDl = (Fbt - Rb(-1)*Bbd(-1) + Rm*(Ms(-1) - (1 - NPLke)*Lfs(-1) - Lhs(-1)))/((1 - NPLke)*Lfs(-1) + Lhs(-1))') model.add('FUb = Fb - lambdab*Y(-1)') # 11.107 : Actual retained earnings model.add('OFb - OFb(-1) = FUb - NPL') # 11.108 : Own funds of banks model.add('CAR = OFb/(Lfs + Lhs)') # 11.109 : Actual capital capacity ratio return model growth_parameters = {'alpha1': 0.75, 'alpha2': 0.064, 'beta': 0.5, 'betab': 0.4, 'gamma': 0.15, 'gamma0': 0.00122, 'gammar': 0.1, 'gammau': 0.05, 'delta': 0.10667, 'deltarep': 0.1, 'eps': 0.5, 'eps2': 0.8, 'epsb': 0.25, 'epsrb': 0.9, 'eta': 0.04918, 'eta0': 0.07416, 'etan': 0.6, 'etar': 0.4, 'theta': 0.22844, 'lambda20': 0.25, 'lambda21': 2.2, 'lambda22': 6.6, 'lambda23': 2.2, 'lambda24': 2.2, 'lambda25': 0.1, 'lambda30': -0.04341, 'lambda31': 2.2, 'lambda32': 2.2, 'lambda33': 6.6, 'lambda34': 2.2, 'lambda35': 0.1, 'lambda40': 0.67132, 'lambda41': 2.2, 'lambda42': 2.2, 'lambda43': 2.2, 'lambda44': 6.6, 'lambda45': 0.1, 'lambdab': 0.0153, 'lambdac': 0.05, 'xim1': 0.0008, 'xim2': 0.0007, 'ro': 0.05, 'sigman': 0.1666, 'sigmase': 0.16667, 'sigmat': 0.2, 'phi': 0.26417, 'phit': 0.26417, 'psid': 0.15255, 'psiu': 0.92, 'omega0': -0.20594, 'omega1': 1, 'omega2': 2, 'omega3': 0.45621 } growth_exogenous = [('ADDbl', 0.02), ('BANDt', 0.01), ('BANDb', 0.01), ('bot', 0.05), ('GRg', 0.03), ('GRpr', 0.03), ('Nfe', 87.181), ('NCAR', 0.1), ('NPLk', 0.02), ('Rbbar', 0.035), ('Rln', 0.07), ('RA', 0), ('top', 0.12), ('ADDl', 0.04592), ('BLR', 0.1091), ('BUR', 0.06324), ('Ck', 7334240), ('CAR', 0.09245), ('CONS', 52603100), ('ER', 1), ('Fb', 1744130), ('Fbt', 1744140), ('Ff', 18081100), ('Fft', 18013600), ('FDb', 1325090), ('FDf', 2670970), ('FUb', 419039), ('FUf', 15153800), ('FUft', 15066200), ('G', 16755600), ('Gk', 2336160), ('GL', 2775900), ('GRk', 0.03001), ('INV', 16911600), ('Ik', 2357910), ('N', 'Nfe'), ('Nt', 'Nfe'), ('NHUC', 5.6735), ('NL', 683593), ('NLk', 95311), ('NPL', 309158), ('NPLke', 0.02), ('NUC', 5.6106), ('omegat', 112852), ('P', 7.1723), ('Pbl', 18.182), ('Pe', 17937), ('PE', 5.07185), ('PI', 0.0026), ('PR', 138659), ('PSBR', 1894780), ('Q', 0.77443), ('Rb', 0.035), ('Rbl', 0.055), ('Rk', 0.03008), ('Rl', 0.06522), ('Rm', 0.0193), ('REP', 2092310), ('RRb', 0.03232), ('RRl', 0.06246), ('S', 86270300), ('Sk', 12028300), ('Ske', 'Sk'), ('T', 17024100), ('U', 0.70073), ('UC', 5.6106), ('W', 777968), ('WB', 67824000), ('Y', 86607700), ('Yk', 12088400), ('YDr', 56446400), ('YDkr', 7813270), ('YDkre', 7813290), ('YP', 73158700), ('z1a', 0), ('z1b', 0), ('z2a', 0), ('z2b', 0), ] growth_variables = [('Bbd', 4388930), ('Bbs', 4389790), ('Bcbd', 4655690), ('Bcbs', 4655690), ('Bhd', 33396900), ('Bhs', 'Bhd'), ('Bs', 42484800), ('BLd', 840742), ('BLs', 'BLd'), ('GD', 57728700), ('Ekd', 5112.6001), ('Eks', 'Ekd'), ('Hbd', 2025540), ('Hbs', 'Hbd'), ('Hhd', 2630150), ('Hhs', 'Hhd'), ('Hs', 'Hbd + Hhd'), ('IN', 11585400), ('INk', 2064890), ('INke', 2405660), ('INkt', 'INk'), ('K', 127444000), ('Kk', 17768900), ('Lfd', 15962900), ('Lfs', 'Lfd'), ('Lhd', 21606600), ('Lhs', 'Lhd'), ('Md', 40510800), ('Ms', 'Md'), ('OFb', 3473280), ('OFbe', 3782430), ('OFbt', 3638100), ('V', 165395000), ('Vfma', 159291000), ('Vk', 22576100), ] # ### Scenario: Model GROWTH, baseline # In[3]: baseline = create_growth_model() baseline.set_values(growth_parameters) baseline.set_values(growth_exogenous) baseline.set_values(growth_variables) for _ in range(100): baseline.solve(iterations=200, threshold=1e-6) # ### Scenario: Model GROWTH, Increase in the target real wage rate # In[4]: omega0 = create_growth_model() omega0.set_values(growth_parameters) omega0.set_values(growth_exogenous) omega0.set_values(growth_variables) for _ in range(10): omega0.solve(iterations=200, threshold=1e-6) omega0.set_values({'omega0': -0.15}) for _ in range(90): omega0.solve(iterations=200, threshold=1e-6) # ###### Figure 11.2A # In[5]: caption = ''' Figure 11.2A Evolution of wage inflation and price inflation, following an autonomous increase in the target real wage''' pidata = list() widata = list() for i in range(5, 80): s = omega0.solutions[i] s_1 = omega0.solutions[i-1] pidata.append(s['PI']*100) widata.append((s['W']/s_1['W'] - 1)*100) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) #axes.set_ylim(0.975, 1.034) axes.plot(pidata, linestyle='-', color='b') axes.plot(widata, linestyle='--', color='g') # add labels plt.text(12, 2.1, 'Price inflation percentage rate') plt.text(12, 5.5, 'Wage inflation percentage rate') fig.text(0.1, -.05, caption); # ###### Figure 11.2B # In[6]: caption = ''' Figure 11.2B Evolution of real gross fixed investment, real output and real consumption, all relative to the base line solution, following an autonomous increase in the target real wage''' idata = list() ydata = list() cdata = list() for i in range(5, 80): s = omega0.solutions[i] base = baseline.solutions[i] idata.append(s['Ik']/base['Ik']) ydata.append(s['Yk']/base['Yk']) cdata.append(s['Ck']/base['Ck']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) #axes.set_ylim(0.975, 1.034) axes.plot(idata, linestyle='-', color='b') axes.plot(ydata, linestyle='--', color='g') axes.plot(cdata, linestyle=':', linewidth=2, color='r') # add labels plt.text(30, 1.005, 'Real fixed investment') plt.text(30, 0.975, 'Real output') plt.text(30, 0.945, 'Real consumption') fig.text(0.1, -.1, caption); # ### Scenario: Model GROWTH, increase in target real wage rate which does not affect long-run real interest rate on bills # In[7]: omega0_rbbar = create_growth_model() omega0_rbbar.set_values(growth_parameters) omega0_rbbar.set_values(growth_exogenous) omega0_rbbar.set_values(growth_variables) for _ in range(10): omega0_rbbar.solve(iterations=200, threshold=1e-6) omega0_rbbar.set_values({'omega0': -.15, 'Rbbar': 'Rbbar+.011'}) for _ in range(90): omega0_rbbar.solve(iterations=200, threshold=1e-6) # ###### Figure 11.2C # In[8]: caption = ''' Figure 11.2C Evolution of the real interest rate on bills, following an autonomous increase in inflation, when the nominal bill rate is set so as to ensure a long-run real rate which is no different from the real rate of the baseline solution''' data = [s['Rb'] - s['PI'] for s in omega0_rbbar.solutions[3:70]] fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) #axes.set_ylim(0.975, 1.034) axes.plot(data, linestyle='-', color='b') # add labels plt.text(20, .035, 'Real interest rate on bills') fig.text(0.1, -.1, caption); # ###### Figure 11.2D # In[9]: caption = ''' Figure 11.2D Evolution of real output, relative to the baseline solution, following an autonomous increase in inflation, when the nominal bill rate is set as to ensure a long-run real rate which is no different from the real rate of the baseline solution''' data = list() for i in range(5, 70): s = omega0_rbbar.solutions[i] base = baseline.solutions[i] data.append(s['Yk']/base['Yk']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.94, 1.01) axes.plot(data, linestyle='-', color='b') # add labels plt.text(20, 0.975, 'Real output') fig.text(0.1, -.1, caption); # ### Scenario: Model GROWTH, an increase in the growth rate of government expenditure for one year # In[10]: grg_one = create_growth_model() grg_one.set_values(growth_parameters) grg_one.set_values(growth_exogenous) grg_one.set_values(growth_variables) for _ in range(10): grg_one.solve(iterations=200, threshold=1e-6) saved_grg = grg_one.parameters['GRg'].value grg_one.set_values({'GRg': 0.035}) grg_one.solve(iterations=200, threshold=1e-6) grg_one.set_values({'GRg': saved_grg}) for _ in range(89): grg_one.solve(iterations=200, threshold=1e-6) # ###### Figure 11.3A # In[11]: caption = ''' Figure 11.3A Evolution of real output and real government expenditures, relative to the baseline solution, following an increase in the rate of growth of real pure government expenditures for only one year''' ydata = list() gdata = list() for i in range(5, 80): s = grg_one.solutions[i] base = baseline.solutions[i] ydata.append(s['Yk']/base['Yk']) gdata.append(s['Gk']/base['Gk']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.975, 1.034) axes.plot(ydata, linestyle='--', color='g') axes.plot(gdata, linestyle='-', color='b') # add labels plt.text(30, 1.00, 'real pure government expenditure') plt.text(30, 1.01, 'real output') fig.text(0.1, -.1, caption); # ###### Figure 11.3B # In[12]: caption = ''' Figure 11.3B Evolution of the employment rate, assumed to be at unity in the baseline solution, following an increase in the rate of growth of real pure government expenditures for only one year''' data = list() for i in range(5, 80): s = grg_one.solutions[i] base = baseline.solutions[i] data.append(s['ER'] - base['ER'] + 1) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.975, 1.03) axes.plot(data, linestyle='--', color='g') # add labels plt.text(30, 1.00, 'employment rate') plt.hlines(0.99, 0, 80, linestyle=':') plt.hlines(1.01, 0, 80, linestyle=':') fig.text(0.1, -.1, caption); # ###### Figure 11.3C # In[13]: caption = ''' Figure 11.3C Evolution of the government deficit and of the government debt, relative to the baseline solution, following an increase in the rate of growth of real pure government expenditures for only one year''' psbrdata = list() gdata = list() for i in range(5, 80): s = grg_one.solutions[i] base = baseline.solutions[i] psbrdata.append(s['PSBR']/base['PSBR']) gdata.append(s['GD']/base['GD']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.965, 1.05) axes.plot(psbrdata, linestyle='-', color='b') axes.plot(gdata, linestyle='--', color='g') # add labels plt.text(12, 1.03, 'Government deficit') plt.text(40, 1.0, 'Government debt') fig.text(0.1, -.1, caption); # ###### Figure 11.3D # In[14]: caption = ''' Figure 11.3D Evolution of the bank liquidity ratio and of the loan to inventories ratio of firms, relative to the baseline solution, following an increase in the rate of growth of real pure government expenditures for only one year''' blrdata = list() lidata = list() for i in range(5, 80): s = grg_one.solutions[i] base = baseline.solutions[i] blrdata.append(s['BLR']/base['BLR']) lidata.append((s['Lfd']/s['IN'])/(base['Lfd']/base['IN'])) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.5, 1.5) axes.plot(blrdata, linestyle='-', color='b') axes.plot(lidata, linestyle='--', color='g') # add labels plt.text(30, 1.2, 'Bank liquidity ratio') plt.text(39, 0.92, 'Loans to inventories ratio of firms') fig.text(0.1, -.1, caption); # ### Scenario: Model GROWTH, Decrease in the income tax rate # In[15]: theta = create_growth_model() theta.set_values(growth_parameters) theta.set_values(growth_exogenous) theta.set_values(growth_variables) for _ in range(10): theta.solve(iterations=200, threshold=1e-6) theta.set_values({'theta': 0.21844}) for _ in range(89): theta.solve(iterations=200, threshold=1e-6) # ###### Figure 11.3E # In[16]: caption = ''' Figure 11.3E Evolution of real consumption and real output, relative to the baseline solution, following a permanent one-shot decrease in the income tax rate''' ydata = list() ckdata = list() for i in range(5, 80): s = theta.solutions[i] base = baseline.solutions[i] ydata.append(s['Yk']/base['Yk']) ckdata.append(s['Ck']/base['Ck']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.99, 1.03) axes.plot(ydata, linestyle='-', color='b') axes.plot(ckdata, linestyle='--', color='g') # add labels plt.text(40, 1.019, 'Real output') plt.text(40, 1.026, 'Real consumption') fig.text(0.1, -.1, caption); # ### Scenario: Model GROWTH, Permanent increase in the growth rate of government expenditure # In[17]: grg = create_growth_model() grg.set_values(growth_parameters) grg.set_values(growth_exogenous) grg.set_values(growth_variables) for _ in range(10): grg.solve(iterations=200, threshold=1e-6) grg.set_values({'GRg': 0.035}) for _ in range(90): grg.solve(iterations=200, threshold=1e-6) # ###### Figure 11.4A # In[18]: caption = ''' Figure 11.4A Evolution of the employment rate and of the inflation rate, with the growth rate of real pure government expenditure being forever higher than in the baseline solution''' erdata = [s['ER'] for s in grg.solutions[5:80]] pidata = [s['PI'] for s in grg.solutions[5:80]] fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.set_ylim(0.99, 1.09) axes.plot(erdata, linestyle='-', color='b') plt.text(13, 1.03, 'Employment') plt.text(13, 1.026, 'rate') axes2 = axes.twinx() axes2.spines['top'].set_visible(False) axes2.set_ylim(0, 0.095) axes2.plot(pidata, linestyle='--', color='g') plt.text(65, 0.065, 'Inflation') plt.text(65, 0.061, 'rate') # add labels fig.text(0.1, 1.24, 'Employment rate') fig.text(1.05, 1.24, 'Inflation rate') fig.text(0.1, -.1, caption); # ###### Figure 11.4B # In[19]: caption = ''' Figure 11.4B Evolution of the real rate of capital accumulation and of the growth rate of real output, with the growth rate of real pure government expenditures being forever higher than the baseline solution.''' grgdata = list() grkdata = list() ykdata = list() for i in range(5, 80): s = grg.solutions[i] s_1 = grg.solutions[i-1] grgdata.append(s['GRg']) grkdata.append(s['GRk']) ykdata.append((s['Yk']/s_1['Yk'])-1) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.029, 0.036) axes.plot(grgdata, linestyle='-', color='b') axes.plot(grkdata, linestyle='--', color='g') axes.plot(ykdata, linestyle=':', linewidth=2, color='r') # add labels plt.text(15, 0.0353, 'Real pure government expenditures growth rate') plt.text(40, 0.033, 'Real rate of capital') plt.text(40, 0.0327, 'accumulation') plt.text(40, 0.0307, 'Real output growth rate') fig.text(0.1, -.1, caption); # ###### Figure 11.4C # In[20]: caption = ''' Figure 11.4C Evolution of the government deficit to GDP ratio and of the government debt to GDP ratio, with the growth rate of real pure government expenditures being forever higher than in the baseline solution.''' gddata = [s['GD']/s['Y'] for s in grg.solutions[5:80]] psbrdata = [s['PSBR']/s['Y'] for s in grg.solutions[5:80]] fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.014, 0.09) axes.plot(psbrdata, linestyle='--', color='g') plt.text(14, 0.04, 'Debt to GDP ratio') axes2 = axes.twinx() axes2.spines['top'].set_visible(False) axes2.set_ylim(0.66, 0.78) axes2.plot(gddata, linestyle='-', color='b') plt.text(45, 0.695, 'Real output growth rate') # add labels fig.text(0, 1.28, 'Deficit to GDP ratio') fig.text(1.1, 1.28, 'Debt to GDP ratio') fig.text(0.1, -.1, caption); # ### Scenario: Model GROWTH, an increase in four steps in the nominal interest rate on government bills # In[21]: rbbar_step = create_growth_model() rbbar_step.set_values(growth_parameters) rbbar_step.set_values(growth_exogenous) rbbar_step.set_values(growth_variables) for _ in range(15): rbbar_step.solve(iterations=200, threshold=1e-6) for rate_step in [0.0375, 0.04, 0.0425, 0.045]: rbbar_step.set_values({'Rbbar': rate_step}) for _ in range(2): rbbar_step.solve(iterations=200, threshold=1e-6) for _ in range(77): rbbar_step.solve(iterations=200, threshold=1e-6) # ###### Figure 11.5A # In[22]: caption = ''' Figure 11.5A Evolution of the lending rate, the deposit rate, and the bond rate, when the (nominal) bill rate is being hiked up in steps and then kept at this higher level.''' rmdata = [s['Rm'] for s in rbbar_step.solutions[5:80]] rbdata = [s['Rb'] for s in rbbar_step.solutions[5:80]] rbldata = [s['Rbl'] for s in rbbar_step.solutions[5:80]] rldata = [s['Rl'] for s in rbbar_step.solutions[5:80]] fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.014, 0.09) axes.plot(rmdata, linestyle='-', color='k') axes.plot(rbdata, linestyle='--', color='g') axes.plot(rbldata, linestyle=':', linewidth=2, color='b') axes.plot(rldata, linestyle='-.', color='r') # add labels plt.text(30, 0.032, 'Deposit rate') plt.text(30, 0.048, 'Bill rate') plt.text(30, 0.06, 'Bond rate') plt.text(30, 0.077, 'Lending rate') fig.text(0.1, -.1, caption); # ###### Figure 11.5B # In[23]: caption = ''' Figure 11.5B Evolution of the real rate of capital accumulation and of the growth rate of real output, with the growth rate of real pure government expenditures being forever higher than the baseline solution.''' ykdata = list() ckdata = list() for i in range(5, 80): s = rbbar_step.solutions[i] base = baseline.solutions[i] ykdata.append(s['Yk']/base['Yk']) ckdata.append(s['Ck']/base['Ck']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.97, 1.05) axes.plot(ykdata, linestyle='-', color='b') axes.plot(ckdata, linestyle='--', color='g') # add labels plt.text(45, 1.022, 'Real output') plt.text(45, 1.039, 'Real consumption') fig.text(0.1, -.1, caption); # ###### Figure 11.5C # In[24]: caption = ''' Figure 11.5C Evolution of the government debt to GDP ratio, when the (nominal) bill rate is set to a higher level''' gddata = [s['GD']/s['Y'] for s in rbbar_step.solutions[5:80]] fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.plot(gddata, linestyle='-', color='b') # add labels plt.text(35, 0.71, 'Government debt to GDP ratio') fig.text(0.1, -.05, caption); # ###### Figure 11.5D # In[25]: caption = ''' Figure 11.5D Evolution of the personal loans to regular disposable income ratio, when the (nominal) bill rate is set at a higher level.''' data = [s['Lhs']/s['YDr'] for s in rbbar_step.solutions[5:80]] fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.35, 0.395) axes.plot(data, linestyle='-', color='b') # add labels plt.text(25, 0.37, 'Personal loans to regular disposable income ratio') fig.text(0.1, -.05, caption); # ###### Figure 11.5E # In[26]: caption = ''' Figure 11.5E Evolution of the burden of personal debut (the weight of interest payments and principal repayment, as a fraction of personal income), when the (nominal) bill rate is set at a higher level.''' data = [s['BUR'] for s in rbbar_step.solutions[5:80]] fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.plot(data, linestyle='-', color='b') # add labels plt.text(25, 0.064, 'The burden of personal debt') fig.text(0.1, -.1, caption); # ### Scenario: Model GROWTH, Increase in the rate of growth in government expenditures # In[27]: alpha1 = create_growth_model() alpha1.set_values(growth_parameters) alpha1.set_values(growth_exogenous) alpha1.set_values(growth_variables) for _ in range(10): alpha1.solve(iterations=200, threshold=1e-6) alpha1.set_values({'alpha1': 0.8}) for _ in range(90): alpha1.solve(iterations=200, threshold=1e-6) # ###### Figure 11.7A # In[28]: caption = ''' Figure 11.7A Evolution of real consumption and real output, relative to the baseline solution, following a one-step permanent increase in the propensity to consume out of regular income.''' ykdata = list() ckdata = list() for i in range(5, 80): s = alpha1.solutions[i] base = baseline.solutions[i] ykdata.append(s['Yk']/base['Yk']) ckdata.append(s['Ck']/base['Ck']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.99, 1.08) axes.plot(ykdata, linestyle='-', color='b') axes.plot(ckdata, linestyle='--', color='g') # add labels plt.text(19, 1.005, 'Real output') plt.text(11, 1.06, 'Real consumption') fig.text(0.1, -.1, caption); # ###### Figure 11.7B # In[29]: caption = ''' Figure 11.7B Evolution of real household wealth, relative to the baseline solution, following a one-step permanent increase in the propensity to consume out of regular income.''' data = list() for i in range(5, 80): s = alpha1.solutions[i] base = baseline.solutions[i] data.append(s['Vk']/base['Vk']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.7, 1.05) axes.plot(data, linestyle='-', color='b') # add labels plt.text(15, 0.9, 'Real household wealth') fig.text(0.1, -.1, caption); # ###### Figure 11.7C # In[30]: caption = ''' Figure 11.7C Evolution of the inflation rate, following a one-step permanent increase in the propensity to consume out of regular income.''' data = [s['PI'] for s in alpha1.solutions[5:80]] fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.plot(data, linestyle='-', color='b') # add labels plt.text(12, 0.028, 'Inflation rate') fig.text(0.1, -.05, caption); # ###### Figure 11.7D # In[31]: caption = ''' Figure 11.7D Evolution of the costing margin of firms and of their normal historic unit costs, relative to the baseline solution, following a one-step permanent increase in the propensity to consume out of regular income.''' nhucdata = list() phidata = list() for i in range(5, 80): s = alpha1.solutions[i] base = baseline.solutions[i] nhucdata.append(s['NHUC']/base['NHUC']) phidata.append(s['phi']/base['phi']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.9, 1.35) axes.plot(nhucdata, linestyle='-', color='b') axes.plot(phidata, linestyle='--', color='g') # add labels plt.text(20, 1.18, 'Normal historic unit costs') plt.text(20, 1.03, 'Costing margin') fig.text(0.1, -.1, caption); # ###### Figure 11.7E # In[32]: caption = ''' Figure 11.7E Evolution of the retained earnings to gross fixed investment ratio and of real inventories, relative to the baseline solution, following a one-step permanent increase in the propensity to consume out of regular income.''' indata = list() fudata = list() for i in range(5, 80): s = alpha1.solutions[i] base = baseline.solutions[i] indata.append(s['INk']/base['INk']) fudata.append((s['FUf']/s['INV']) / (base['FUf']/base['INV'])) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) #axes.set_ylim(0.9, 1.35) axes.plot(indata, linestyle='-', color='b') axes.plot(fudata, linestyle='--', color='g') # add labels plt.text(15, 1.05, 'Real inventories') plt.text(10, 1.08, 'Retained earnings to gross fixed investment ratio') fig.text(0.1, -.1, caption); # ###### Figure 11.7F # In[33]: caption = ''' Figure 11.7F Evolution of government deficit to GDP ratio and of the government debt to GDP ratio, relative to the baseline solution, following a one-step permanent increase in the propensity to consume out of regular income.''' gddata = list() psbrdata = list() for i in range(5, 80): s = alpha1.solutions[i] base = baseline.solutions[i] gddata.append((s['GD']/s['Y'])/(base['GD']/base['Y'])) psbrdata.append((s['PSBR']/s['Y'])/(base['PSBR']/base['Y'])) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.35, 1.05) axes.plot(gddata, linestyle='-', color='b') axes.plot(psbrdata, linestyle='--', color='g') # add labels plt.text(15, 0.8, 'Government debt to GDP ratio') plt.text(20, .5, 'Government deficit to GDP ratio') fig.text(0.1, -.1, caption); # ###### Figure 11.7G # In[34]: caption = ''' Figure 11.7G Evolution of Tobin's q ratio and of the price-earnings ratio, relative to the baseline solution, following a one-step permanent increase in the propensity to consume out of regular income.''' qdata = list() pedata = list() for i in range(5, 80): s = alpha1.solutions[i] base = baseline.solutions[i] qdata.append(s['Q']/base['Q']) pedata.append(s['PE']/base['PE']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.plot(qdata, linestyle='-', color='b') axes.plot(pedata, linestyle='--', color='g') # add labels plt.text(10, 1, "Tobin's q ratio") plt.text(15, .9, 'Price earnings ratio') fig.text(0.1, -.1, caption); # ### Scenario: Model GROWTH, an increase in the ratio of new loans to personal income # In[35]: eta0 = create_growth_model() eta0.set_values(growth_parameters) eta0.set_values(growth_exogenous) eta0.set_values(growth_variables) for _ in range(10): eta0.solve(iterations=200, threshold=1e-6) eta0.set_values({'eta0': 0.08416}) for _ in range(90): eta0.solve(iterations=200, threshold=1e-6) # ###### Figure 11.8A # In[36]: caption = ''' Figure 11.8A Evolution of the personal loans to personal income ratio and of the burden of personal debt, following an increase in the gross new loans to personal income ratio.''' data = list() burdata = list() for i in range(5, 80): s = eta0.solutions[i] base = baseline.solutions[i] data.append((s['Lhd']/s['YP'])) burdata.append(s['BUR']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.061, 0.082) axes.plot(burdata, linestyle='--', color='g') plt.text(30, 0.0753, 'Debt burden ratio') axes2 = axes.twinx() axes2.spines['top'].set_visible(False) axes2.set_ylim(0.28, 0.37) axes2.plot(data, linestyle='-', color='b') plt.text(30, 0.361, 'Personal loans to personal income ratio') # add labels fig.text(0.05, 1.25, 'Burden') fig.text(1.1, 1.25, 'Loans to income ratio') fig.text(0.1, -.1, caption); # ###### Figure 11.8B # In[37]: caption = ''' Figure 11.8B Evolution of real output and real consumption, relative to the baseline solution, following an increase int the groww new loans to personal income ratio.''' ykdata = list() ckdata = list() for i in range(5, 80): s = eta0.solutions[i] base = baseline.solutions[i] ykdata.append(s['Yk']/base['Yk']) ckdata.append(s['Ck']/base['Ck']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.plot(ykdata, linestyle='-', color='b') axes.plot(ckdata, linestyle='--', color='g') # add labels plt.text(35, 0.997, 'Real output') plt.text(40, 0.991, 'Real consumption') fig.text(0.1, -.05, caption); # ###### Figure 11.8C # In[38]: caption = ''' Figure 11.8C Evolution of the bank capital adequacy ratio and of the bank liquidity ratio, relative to the baseline solution, following an increase in the groww new loans to personal income ratio.''' blrdata = list() cardata = list() for i in range(5, 80): s = eta0.solutions[i] base = baseline.solutions[i] blrdata.append(s['BLR']/base['BLR']) cardata.append(base['CAR']/base['CAR']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.plot(blrdata, linestyle='-', color='b') axes.plot(cardata, linestyle='--', color='g') # add labels plt.text(45, 0.9, 'Bank liquidity ratio') plt.text(33, 1.01, 'Bank capital adequacy ratio') fig.text(0.1, -.1, caption); # ###### Figure 11.8D # In[39]: caption = ''' Figure 11.8D Evolution of the lending rate set by banks, following an increase in the gross new loans to personal income ratio.''' data = [s['Rl'] for s in eta0.solutions[5:80]] fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.plot(data, linestyle='-', color='b') # add labels plt.text(14, 0.062, 'Interest rate on loans') fig.text(0.1, -.1, caption); # ###### Figure 11.8E # In[40]: caption = ''' Figure 11.8E Evolution of the government deficit to GDP ratio and of the government debt to GDP ratio, relative to the baseline solution, following an increase in the gross new loans to personal income ratio.''' gddata = list() psbrdata = list() for i in range(5, 80): s = eta0.solutions[i] base = baseline.solutions[i] gddata.append((s['GD']/s['Y'])/(base['GD']/base['Y'])) psbrdata.append((s['PSBR']/s['Y'])/(base['PSBR']/base['Y'])) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.plot(gddata, linestyle='-', color='b') axes.plot(psbrdata, linestyle='--', color='g') # add labels plt.text(40, 0.97, 'Debt to GDP ratio') plt.text(18, 0.92, 'Deficit to GDP ratio') fig.text(0.1, -.1, caption); # ### Scenario: Model GROWTH, an increase in the desire to hold equities, offset by a drop in the desire to hold deposits # In[41]: lambda40 = create_growth_model() lambda40.set_values(growth_parameters) lambda40.set_values(growth_exogenous) lambda40.set_values(growth_variables) for _ in range(10): lambda40.solve(iterations=200, threshold=1e-6) lambda40.set_values({'lambda40': 0.77132}) for _ in range(90): lambda40.solve(iterations=200, threshold=1e-6) # ###### Figure 11.9A # In[42]: caption = ''' Figure 11.9A Evolution of Tobin's q ratio, the price-earnings ratio and the share of equities in household wealth held in the form of financial market assets, all relative to the baseline solution, following an increase in the household desire to hold stock market equities.''' eqdata = list() qdata = list() pedata = list() for i in range(5, 80): s = lambda40.solutions[i] base = baseline.solutions[i] eqdata.append((s['Pe']*s['Ekd']/s['Vfma'])/(base['Pe']*base['Ekd']/base['Vfma'])) qdata.append(s['Q']/base['Q']) pedata.append(s['PE']/base['PE']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.98, 1.3) axes.plot(eqdata, linestyle='-', color='b') axes.plot(qdata, linestyle='--', color='g') axes.plot(pedata, linestyle=':', linewidth=2, color='r') # add labels plt.text(30, 1.05, 'Share of equities in financial market assets') plt.text(40, 1.17, "Tobin's q ratio") plt.text(35, 1.11, 'Price-earnings ratio') fig.text(0.1, -.15, caption); # ###### Figure 11.9B # In[43]: caption = ''' Figure 11.9B Evolution of real wealth, real consumption, real output and real gross investment, all relative to the baseline solution, following an increase in the household desire to hold stock market equities.''' ykdata = list() ckdata = list() ikdata = list() vkdata = list() for i in range(5, 80): s = lambda40.solutions[i] base = baseline.solutions[i] ykdata.append(s['Yk']/base['Yk']) ckdata.append(s['Ck']/base['Ck']) ikdata.append(s['Ik']/base['Ik']) vkdata.append(s['Vk']/base['Vk']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.92, 1.17) axes.plot(ykdata, linestyle='-', color='b') axes.plot(ckdata, linestyle='--', color='g') axes.plot(ikdata, linestyle=':', linewidth=2, color='r') axes.plot(vkdata, linestyle='-.', color='k') # add labels plt.text(40, 0.98, 'Real output') plt.text(28, 1.015, 'Real consumption') plt.text(20, 0.96, 'Real gross') plt.text(21, 0.95, 'investment') plt.text(11, 1.15, 'Real wealth') fig.text(0.1, -.15, caption); # ###### Figure 11.9C # In[44]: caption = ''' Figure 11.9C Evolution of the lending rate and the deposit rate, following an increase in the household desire to hold stock market equities, when this desire is offset by a drop in the desire to hold bank deposits.''' rldata = [s['Rl'] for s in lambda40.solutions[5:80]] rmdata = [s['Rm'] for s in lambda40.solutions[5:80]] fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.plot(rldata, linestyle='-', color='b') axes.plot(rmdata, linestyle='--', color='g') # add labels plt.text(30, 0.078, 'Lending rate') plt.text(30, 0.04, 'Deposit rate') fig.text(0.1, -.1, caption); # ### Scenario: Model GROWTH, an increase in the desire to hold equities, offset by a drop in the desire to hold bills and bonds # In[45]: lambdax0 = create_growth_model() lambdax0.set_values(growth_parameters) lambdax0.set_values(growth_exogenous) lambdax0.set_values(growth_variables) for _ in range(10): lambdax0.solve(iterations=200, threshold=1e-6) lambdax0.set_values({'lambda20': 0.20, 'lambda30': -0.04341 - 0.05, 'lambda40': 0.77132}) for _ in range(90): lambdax0.solve(iterations=200, threshold=1e-6) # ###### Figure 11.9D # In[46]: caption = ''' Figure 11.9D Evolution of the lending rate and the deposit rate, following an increase in the household desire to hold stock market equities, when this desire is offset by a drop in the desire to hold bills and bonds.''' rldata = [s['Rl'] for s in lambdax0.solutions[5:80]] rmdata = [s['Rm'] for s in lambdax0.solutions[5:80]] rbdata = [s['Rb'] for s in lambdax0.solutions[5:80]] fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.plot(rldata, linestyle='-', color='b') axes.plot(rmdata, linestyle='--', color='g') axes.plot(rbdata, linestyle=':', linewidth=2, color='r') # add labels plt.text(30, 0.066, 'Lending rate') plt.text(30, 0.021, 'Deposit rate') plt.text(30, 0.037, 'Bill rate') fig.text(0.1, -.1, caption); # ### Scenario: Model GROWTH, an increase in the target proportion of gross investment financed by retained earnings # In[47]: psiu = create_growth_model() psiu.set_values(growth_parameters) psiu.set_values(growth_exogenous) psiu.set_values(growth_variables) for _ in range(10): psiu.solve(iterations=200, threshold=1e-6) psiu.set_values({'psiu': 1}) for _ in range(90): psiu.solve(iterations=200, threshold=1e-6) # ###### Figure 11.10A # In[48]: caption = ''' Figure 11.10A Evolution of the costing margin of firms, following an increase in the target proportion of gross investment being financed by gross retained earnings.''' data = [s['phi'] for s in psiu.solutions[5:80]] fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.plot(data, linestyle='-', color='b') # add labels plt.text(30, 0.307, 'Costing margin') fig.text(0.1, -.05, caption); # ###### Figure 11.10B # In[49]: caption = ''' Figure 11.10B Evolution of the wage inflation rate, following an increase in the target proportion of gross investment being financed by gross retained earnings.''' data = list() for i in range(5, 80): s = psiu.solutions[i] s_1 = psiu.solutions[i-1] data.append(((s['W']/s_1['W']) - 1)*100) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.plot(data, linestyle='-', color='b') # add labels plt.text(25, 4.2, 'Wage inflation rate') fig.text(0.1, -.05, caption); # ###### Figure 11.10C # In[50]: caption = ''' Figure 11.10C Evolution of the employment rate and of real consumption, relative to the baseline solution, following an increase in the target proportion of gross investment being financed by gross retained earnings.''' ckdata = list() erdata = list() for i in range(5, 80): s = psiu.solutions[i] base = baseline.solutions[i] ckdata.append(s['Ck']/base['Ck']) erdata.append(s['ER']/base['ER']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.943, 1.003) axes.plot(ckdata, linestyle='-', color='b') axes.plot(erdata, linestyle='--', color='g') # add labels plt.text(30, 0.97, 'Real consumption') plt.text(13, 0.985, 'Employment rate') fig.text(0.1, -.1, caption); # ###### Figure 11.10D # In[51]: caption = ''' Figure 11.10D Evolution of Tobin's q ratio and of the price-earnings ratio, relative to the baseline solution, following an increase in the target proportion of gross investment being financed by gross retained earnings, which also corresponds to a decrease in the proportion of investment being financed by new equity issues.''' qdata = list() pedata = list() for i in range(5, 80): s = psiu.solutions[i] base = baseline.solutions[i] qdata.append(s['Q']/base['Q']) pedata.append(s['PE']/base['PE']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.97, 1.11) axes.plot(qdata, linestyle='-', color='b') axes.plot(pedata, linestyle='--', color='g') # add labels plt.text(40, 1.08, "Tobin's q ratio") plt.text(40, 1.03, 'Price-earnings ratio') fig.text(0.1, -.2, caption); # ###### Figure 11.10E # In[52]: caption = ''' Figure 11.10E Evolution of the deflated averaged growth rate of the entrepreneurial profits of firms and of the deflated growth rate of equity prices, following an increase in the target proportion of gross investment being financed by gross retained earnings and no new equity issues.''' pedata = list() prdata = list() for i in range(5, 80): s = psiu.solutions[i] s_1 = psiu.solutions[i-1] pedata.append(((s['Pe']/s['P'])/(s_1['Pe']/s_1['P'])) - 1) prdata.append(((s['Ff']/s['P'])/(s_1['Ff']/s_1['P'])) - 1) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.plot(pedata, linestyle='-', color='b') axes.plot(prdata, linestyle='--', color='g') # add labels plt.text(30, 0.032, 'Growth rate of equiity prices (deflated)') plt.text(15, 0.05, 'Growth rate of firms profits (deflated)') fig.text(0.1, -.15, caption); # ### Scenario: Model GROWTH, an increase in the percentage of defaulting loans # In[53]: nplk = create_growth_model() nplk.set_values(growth_parameters) nplk.set_values(growth_exogenous) nplk.set_values(growth_variables) for _ in range(10): nplk.solve(iterations=200, threshold=1e-6) nplk.set_values({'NPLk': 0.05}) for _ in range(90): nplk.solve(iterations=200, threshold=1e-6) # ###### Figure 11.11A # In[54]: caption = ''' Figure 11.11A Evolution of the actual bank capital adequacy ratio, following an increase in the percentage of non-performing loans (defaulting loans).''' data = [s['CAR'] for s in nplk.solutions[5:80]] fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.plot(data, linestyle='-', color='b') # add labels plt.text(30, 0.091, 'Bank capital adequacy ratio') fig.text(0.1, -.05, caption); # ###### Figure 11.11B # In[55]: caption = ''' Figure 11.11B Evolution of the lending rate and deposit rate, relative to the baseline solution, following an increase in the percentage of non-performing loans (defaulting loans).''' rmdata = list() rldata = list() for i in range(5, 80): s = nplk.solutions[i] base = baseline.solutions[i] rmdata.append(s['Rm']/base['Rm']) rldata.append(s['Rl']/base['Rl']) fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.plot(rmdata, linestyle='-', color='b') axes.plot(rldata, linestyle='--', color='g') # add labels plt.text(40, 0.81, 'Deposit rate') plt.text(40, 1.25, 'Lending rate') fig.text(0.1, -.1, caption); # ### Scenario: Model GROWTH, an increase in the normal adequacy ratio # In[56]: ncar = create_growth_model() ncar.set_values(growth_parameters) ncar.set_values(growth_exogenous) ncar.set_values(growth_variables) for _ in range(10): ncar.solve(iterations=200, threshold=1e-6) ncar.set_values({'NCAR': 0.11}) for _ in range(90): ncar.solve(iterations=200, threshold=1e-6) # ###### Figure 11.11C # In[57]: caption = ''' Figure 11.11C Evolution of the actual bank capital adequacy ratio, following a one-time permanent increase in the normal capital adequacy ratio.''' ncardata = [s['NCAR'] for s in ncar.solutions[5:80]] cardata = [s['CAR'] for s in ncar.solutions[5:80]] fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.set_ylim(0.09, 0.113) axes.plot(ncardata, linestyle='-', color='b') axes.plot(cardata, linestyle='--', color='g') # add labels plt.text(25, 0.111, 'Normal capital adequacy ratio') plt.text(24, 0.102, 'Actual capital adequacy ratio') fig.text(0.1, -.05, caption); # ###### Figure 11.11D # In[58]: caption = ''' Figure 11.11D Evolution of the interest rate on loans set by banks, following a one-time permanent increase in the normal capital adequacy ratio.''' data = [s['Rl'] for s in ncar.solutions[5:80]] fig = plt.figure() axes = fig.add_axes([0.1, 0.1, 1.1, 1.1]) axes.tick_params(top='off', right='off') axes.spines['top'].set_visible(False) axes.spines['right'].set_visible(False) axes.plot(data, linestyle='-', color='b') # add labels plt.text(10, 0.067, 'Interest rate on loans') fig.text(0.1, -.05, caption); # In[ ]: