global modelnumber var a_j a_k a_me a_mh a_p a_z acdb acdh acke ackh acloeb acloee aclosb acloss cb ce ch cs ctot d data_CC data_II data_LO data_LOE data_LOH data_NN data_QQ data_TFP data_YY dke dkh he hh hs itot ke kh ktot lambdab lambdae lambdas loe los nh ns ntot q re rh rk rm rs rv ucb uce uch ucs wh ws y zke zkh pi ; varexo eps_j eps_k eps_me eps_mh eps_p eps_z eps_r; parameters ALPHA BETAB BETAE BETAH BETAS DELTA ECH FIDB FIDH FIKE FIKH FILOEB FILOEE FILOSB FILOSS GAMMAE GAMMAS JEI MH MS MIU MK MN NU RHOD RHOE RHOS SIG_J SIG_K SIG_R SIG_ME SIG_MH SIG_P SIG_Z SIGMA SIGMAB SIGMAE SIGMAH TAUH TAUS ZETAE ZETAH ZRHO_AJ ZRHO_AK ZRHO_AME ZRHO_AMH ZRHO_AP ZRHO_AZ rR rY rpi ; ALPHA = 0.35; //Total capital share in production BETAB = 0.945; //Bankers discount factor BETAE = 0.94; //Entrepreneurs discount factor BETAH = 0.9925; //Patient hh discount factor BETAS = 0.94; //Impatient hh discount factor DELTA = 0.035; //deprecitation rates deltake deltakh %GAMMAE = 0.9; //liabilities to assets ratio for Bankers %GAMMAS = 0.9; //liabilities to assets ratio for Bankers GAMMAE = 0.5; //%Not binding capital adequacy constraint? GAMMAS = 0.5; %JEI = 0.075; //Housing preference share JEI = 0.2; //iac2005 MH = 0.9; //LTV on housing, E MK = 0.9; //LTV on capital, E MS = 0.9; //LTV on housing, H MN = 1; //Wage bill paid in advance SIGMAB = 1; SIGMAE = 1; SIGMAH = 1; TAUH = 2; //Labour supply parameter TAUS = 2; SIG_J = 0.0348377631969606; //st.dev., housing demand shock SIG_K = 0.00726749042971863; //investment shock SIG_ME = 0.0180901014471815; //LTV shock, E SIG_MH = 0.0115559596659929; //LTV shock, impatient hh SIG_P = 0.0199390346980942; //preference shock SIG_Z = 0.00701598674399746; //technology shock SIG_R = 0.013; //monetary policy shock ECH = 0.45550721335391; //habit in consumption FIDB = 0.134965498268201; //D adj. cost, Banks FIDH = 0.178577119853786; //D adj. cost, patient hh FIKE = 0.492786343143027; //K adj. cost, E FIKH = 1.79002530669715; //K adj. cost, impatient hh FILOEB = 0.0976660264503774; //Loan to E adj. cost, B FILOEE = 0.140767700365659; //Loan to E adj. cost, E FILOSB = 0.39701402874408; //Loan to hh adj. cost, B FILOSS = 0.341804130203978; //Loan to hh adj. cost, hh MIU = 0.480393235385172; //capital share of E NU = 0.0319371884502803; //Housing share of E RHOD = 0.233704970097865; //inertia in capital adequacy constraint RHOE = 0.630714695022202; //inertia in E borrowing constraint RHOS = 0.710795535781382; //inertia in hh borrowing constraint SIGMA = 0.327274221745279; //wage share impatient hh ZETAE = 0.380069681903693; //curvature for utilization rate E ZETAH = 0.374431387407989; //curvature for utilization rate patient HH ZRHO_AJ = 0.991154920014142; //autocorr. housing demand shock ZRHO_AK = 0.918228805520155; //investment shock ZRHO_AME = 0.872348385798409; //LTV shock, E ZRHO_AMH = 0.84636409040358; //LTV shcok, hh ZRHO_AP = 0.995276908247411; //preference shock ZRHO_AZ = 0.990219844054634; //technology shock rR = 0.8; rY = 0.5; rpi = 1.5; %rpi = 1.65; model; # zzGAMMAE=GAMMAE; # zzGAMMAS=GAMMAS; # zzrh = 1/BETAH; # zzrm = zzrh - (1-DELTA); # zzlambdab = (1-BETAB*zzrh)/(1-BETAB*RHOD); # zzre = (1/BETAB)*(1-((1-BETAB)*RHOD+(1-RHOD)*GAMMAE)*zzlambdab); # zzrs = (1/BETAB)*(1-((1-BETAB)*RHOD+(1-RHOD)*GAMMAS)*zzlambdab); # zzlambdae = (1-BETAE*zzre)/(1-BETAE*RHOE) ; # zzlambdas = (1-BETAS*zzrs)/(1-BETAS*RHOS) ; # zzrk = 1/BETAE*(1-zzlambdae*(1-RHOE)*MK) - (1-DELTA) ; # zzrv = 1/BETAE*(1-zzlambdae*MH/zzre*(1-RHOE)) - 1 ; # oo1 = JEI/(1-BETAH) ; # oo2 = JEI/(1-BETAS-zzlambdas*(1-RHOS)*MS/zzrs); # oo3 = 1/(1+(1-1/zzrs)*MS*oo2); # oo4 = GAMMAE*(zzrh-1)*(MH*NU/(zzre*zzrv)+MK*ALPHA*MIU/(zzrk)-MN*(1-ALPHA-NU)/(1+MN*(1-RHOE)*zzlambdae)) ; # oo5 = GAMMAS*MS/zzrs*(oo2*(zzrh-1))*oo3 ; # oo7 = zzrm - DELTA ; # oo8 = (1-ALPHA-NU)*(1-SIGMA)/((1+MN*(1-RHOE)*zzlambdae)) ; # oo9 = (1-MIU)*ALPHA/(zzrm) ; # zzns = 1/(1+oo3*TAUS) ; # zzzeta1 = oo7*oo9/oo8 + 1 + oo4/oo8 + oo5*SIGMA/(1-SIGMA) ; # zznh = 1/(1+TAUH*zzzeta1) ; # zzctoys = oo3*(1-ALPHA-NU)/(1+MN*(1-RHOE)*zzlambdae)*SIGMA ; # zzctoyh = zzzeta1*oo8 ; # zziktoye = DELTA*ALPHA*MIU/(zzrk) ; # zziktoyh = DELTA*ALPHA*(1-MIU)/(zzrm) ; # zzdenh = oo1*zzctoyh + oo2*zzctoys + NU/(zzrv) ; # zzhh = oo1*zzctoyh / zzdenh ; # zzhs = oo2*zzctoys / zzdenh ; # zzhe = (NU/(zzrv)) / zzdenh ; # zzy = (ALPHA*(1-MIU)/(zzrm))^(ALPHA*(1-MIU)/(1-ALPHA))* (ALPHA*MIU/(zzrk))^(ALPHA*MIU/(1-ALPHA))* zzhe^(NU/(1-ALPHA))* (zznh^(1-SIGMA)*zzns^SIGMA)^((1-ALPHA-NU)/(1-ALPHA)) ; # zzkh = ALPHA*(1-MIU)*zzy/(zzrm) ; # zzke = ALPHA*MIU*zzy/(zzrk) ; # zzq = NU*zzy/(zzrv)/zzhe ; # zzloe = MH*zzq/zzre*zzhe + MK*zzke - MN*(1-ALPHA-NU)/(1+MN*(1-RHOE)*zzlambdae)*zzy ; # zzwh = ((1-SIGMA)*(1-ALPHA-NU)/(1+MN*(1-RHOE)*zzlambdae))*zzy/zznh ; # zzws = (SIGMA*(1-ALPHA-NU)/(1+MN*(1-RHOE)*zzlambdae))*zzy/zzns; # zzlos = MS/zzrs*oo2*oo3*zzws*zzns ; # zzd = zzGAMMAE*zzloe + zzGAMMAS*zzlos ; # zzch = (zzrm-DELTA)*zzkh + (zzrh-1)*zzd + zzwh*zznh ; # zzcb = ((zzre-1)*zzloe + (zzrs-1)*zzlos - (zzrh-1)*zzd); # zzmu = zzcb^(-SIGMAB) ; # zzce = zzy - DELTA*zzke - (zzre-1)*zzloe - zzwh*zznh - zzws*zzns - zzrm*zzkh ; # zzcs = oo3*zzws*zzns ; # zzame = 0 ; # zzamh = 0 ; # zzab = 0 ; # zzas = 0 ; # zzak = 0 ; # zzcumloss = 0; # zzctot = zzch + zzcs + zzce + zzcb; # zzitot = DELTA*(zzkh+zzke) ; # zzkb = zzloe + zzlos - zzd; # zzspread_re_rh = 4*(zzre-zzrh); # zzspread_rs_rh = 4*(zzrs-zzrh); # zzktot = zzke+zzkh; # zzntot = zznh^(1-SIGMA)*zzns^SIGMA ; # zzytot = zzitot+zzctot; # Y_SS = (zzy); # ITOT_SS = (zzitot); # CTOT_SS = (zzctot); # Q_SS = (zzq); # LTOT_SS = zzloe+zzlos; # NTOT_SS = zzntot; # KE_SS = zzke; # KH_SS = zzkh; # RK_SS = zzrk; # D_SS = zzd; # LOE_SS = zzloe; # LOS_SS = zzlos; # zzloetoy=zzloe/4/zzy; # zzlostoy=zzlos/4/zzy; # zzlotoy=(zzloe+zzlos)/4/zzy; # zzcbtoy = zzcb/zzy ; # zzcetoy = zzce/zzy ; # zzchtoy = zzch/zzy ; # zzcstoy = zzcs/zzy ; # zzkab=1-(zzd/(zzloe+zzlos)); # CE_SS = zzce; # RE_SS = zzre; # LE_SS = zzlambdae; # LB_SS = zzlambdab; # CB_SS = zzcb; # R_SS = zzrh; % Household Savers 1-5 ((ch) + kh/exp(a_k) + (q)*((hh)-(hh(-1))) + (d) - ((rh(-1))*(d(-1)))/(pi) - (rm*zkh+(1-dkh)/exp(a_k))*kh(-1) - (wh)*(nh) ) = 0 ; (1+acdh)*(uch*exp(a_p)) - BETAH*(uch(+1)*exp(a_p(+1)))*(rh)/(pi(+1)) = 0 ; (wh)*uch*exp(a_p) - TAUH/(1-(nh)) = 0 ; (1/exp(a_k)+ackh)*(uch*exp(a_p)) = BETAH*(uch(+1)*exp(a_p(+1)))*((rm(+1)*zkh(+1)+(1-dkh(+1))/exp(a_k(+1)))) ; (q)*uch*exp(a_p) = JEI*exp(a_j)*exp(a_p)/hh + BETAH*(q(+1))*(uch(+1)*exp(a_p(+1))) ; //% Household Borrowers 6-10 (cs) + ((rs(-1))*(los(-1)))/(pi) + (q)*((hs)-(hs(-1))) = (los) + (ws)*(ns) ; (los) = RHOS*(los(-1)) + (1-RHOS)*MS*exp(a_mh)*((q(+1))*(hs)*(pi(+1))/(rs(+1))) ; (1-acloss-(lambdas))*(ucs*exp(a_p)) = BETAS*(rs-RHOS*(lambdas(+1)))*(ucs(+1)*exp(a_p(+1))) ; (ws)*(ucs*exp(a_p)) - TAUS/(1-(ns)) = 0 ; (q)*(ucs*exp(a_p)) = JEI*exp(a_j)*exp(a_p)/hs + BETAS*(q(+1))*(ucs(+1)*exp(a_p)) + (lambdas)*(1-RHOS)*(ucs*exp(a_p))*MS*exp(a_mh)*(q(+1))*(pi(+1))/((rs(+1))) ; //% BANK 11-15 (cb) + ((rh(-1))*(d(-1)))/(pi) + (loe) + (los) - ((re)*(loe(-1)))/(pi) - ((rs(-1))*(los(-1)))/(pi) - (d) = 0 ; (d)-RHOD*( d(-1)-(loe(-1))-(los(-1)) ) -(1-(1-RHOD)*(1-GAMMAE))*(loe) -(1-(1-RHOD)*(1-GAMMAS))*(los) = 0; (1-acdb-(lambdab))*ucb - BETAB*ucb(+1)*((rh)/(pi(+1))-RHOD*lambdab(+1)) = 0; (1+aclosb-(RHOD+(1-RHOD)*GAMMAS)*(lambdab))*ucb - BETAB*ucb(+1)*((rs)/(pi(+1))-RHOD*lambdab(+1)) = 0; (1+acloeb-(RHOD+(1-RHOD)*GAMMAE)*(lambdab))*ucb - BETAB*ucb(+1)*((re(+1)/(pi(+1)))-RHOD*lambdab(+1)) = 0; //% Entre 16-21 (ce) + (ke)/exp(a_k) + (q)*(he) + ((re)*loe(-1))/(pi) + (wh)*(nh) + (ws)*(ns) + (rm)*zkh*kh(-1) = (y) + (1-dke)*ke(-1)/exp(a_k) + (q)*(he(-1)) + (loe); (y) = exp(a_z)*(zke*(ke(-1)))^(MIU*ALPHA)*(zkh*(kh(-1)))^((1-MIU)*ALPHA)* (he(-1)^NU)*(ntot)^(1-ALPHA-NU) ; (loe) = RHOE*(loe(-1)) + (1-RHOE)*( MH*exp(a_me)*(q(+1))*(he)*(pi(+1))/(re(+1)) + MK*exp(a_me)*(ke) - MN*((wh)*(nh) + (ws)*(ns)) ) ; (1-acloee-(lambdae))*uce = BETAE*((re(+1)/(pi(+1))-RHOE*lambdae(+1))*uce(+1)) ; (1/exp(a_k)+acke-(lambdae)*(1-RHOE)*MK*exp(a_me))*uce = BETAE*(rk(+1)*zke(+1)+(1-dke(+1))/exp(a_k(+1)))*uce(+1) ; (q)*uce = BETAE*(q(+1))*(1+rv(+1))*uce(+1) + (lambdae)*(1-RHOE)*uce*MH*exp(a_me)*(q(+1))*(pi(+1))/((re(+1))) ; //% Factor demand 22-26 ALPHA*MIU*(y) = (rk)*zke*(ke(-1)) ; ALPHA*(1-MIU)*(y) = (rm)*zkh*(kh(-1)) ; NU*(y) = (rv)*(q)*(he(-1)) ; (1-ALPHA-NU)*(1-SIGMA)*(y)/(1+MN*exp(a_me)*(1-RHOE)*lambdae) = (wh)*(nh) ; (1-ALPHA-NU)*SIGMA*(y)/(1+MN*exp(a_me)*(1-RHOE)*lambdae) = (ws)*(ns) ; //% Housing 27-27 (hh) + (hs) + (he) = 1; //% Utilization rate dke = DELTA + (RK_SS) * ( (ZETAE/(1-ZETAE)*zke^2)/2 + (1-ZETAE/(1-ZETAE))*zke + .5*ZETAE/(1-ZETAE) - 1 ) ; dkh = DELTA + (1/BETAH-1+DELTA) * ( (ZETAH/(1-ZETAH)*zkh^2)/2 + (1-ZETAH/(1-ZETAH))*zkh + .5*ZETAH/(1-ZETAH) - 1 ) ; rk = (RK_SS)*( ZETAE/(1-ZETAE)*zke + 1-ZETAE/(1-ZETAE) ) ; rm = (1/BETAH-1+DELTA)*( ZETAH/(1-ZETAH)*zkh + 1-ZETAH/(1-ZETAH) ) ; //%Monetary policy %pi =1; %rh = (rh(-1))^rR*((pi(-1))^(1-rpi)*(y(-1)/Y_SS)^rY*R_SS)^(1-rR)*exp(eps_r); //iac2005 %rh/R_SS = (rh(-1)/R_SS)^rR*(pi^rpi*(y/Y_SS)^rY)^(1-rR)*exp(eps_r); %rh = ((pi(-1))^(1+rpi))*exp(eps_r); rh = R_SS^(1-rR)*(rh(-1))^rR*(pi)^(rpi*(1-rR))*(y/y(-1))^(rY*(1-rR))*exp(eps_r); //% Auxiliary vars (ktot) = (ke)+(kh) ; ntot = nh^(1-SIGMA)*ns^SIGMA ; (ctot) = (ce)+(ch)+(cb)+(cs) ; (itot) = (ke)+(kh)-(1-dke)*(ke(-1))-(1-dkh)*(kh(-1)) ; a_j = ZRHO_AJ*a_j(-1) + eps_j ; a_k = ZRHO_AK*a_k(-1) + eps_k ; a_me = ZRHO_AME*a_me(-1) + eps_me ; a_mh = ZRHO_AMH*a_mh(-1) + eps_mh ; a_p = ZRHO_AP*a_p(-1) + eps_p ; a_z = ZRHO_AZ*a_z(-1) + eps_z ; acdb = FIDB*((d)-(d(-1)))/D_SS ; acdh = FIDH*((d)-(d(-1)))/D_SS ; acke = FIKE*((ke)-(ke(-1)))/KE_SS ; ackh = FIKH*((kh)-(kh(-1)))/KH_SS ; acloeb = FILOEB*((loe)-(loe(-1)))/LOE_SS ; aclosb = FILOSB*((los)-(los(-1)))/LOS_SS ; acloee = FILOEE*((loe)-(loe(-1)))/LOE_SS ; acloss = FILOSS*((los)-(los(-1)))/LOS_SS ; data_TFP = a_z ; data_YY = (ctot+itot)/Y_SS-1; data_CC = (ctot/CTOT_SS-1) ; data_II = (itot/ITOT_SS-1) ; data_LO = ((loe+los)/LTOT_SS-1) ; data_LOE = ((loe)/LOE_SS-1) ; data_LOH = ((los)/LOS_SS-1) ; data_QQ = (q/Q_SS-1) ; data_NN = ntot/NTOT_SS-1 ; //% HABITS //% 25 ucb = (1-ECH)*( cb - ECH*cb(-1))^(-SIGMAB) ; uce = (1-ECH)*( ce - ECH*ce(-1))^(-SIGMAE) ; uch = (1-ECH)*( ch - ECH*ch(-1))^(-SIGMAH) ; ucs = (1-ECH)*( cs - ECH*cs(-1))^(-SIGMAH) ; end; shocks; var eps_j; stderr 100*SIG_J ; var eps_k; stderr 100*SIG_K ; var eps_me; stderr 100*SIG_ME ; var eps_mh; stderr 100*SIG_MH ; var eps_p; stderr 100*SIG_P ; var eps_z; stderr 100*SIG_Z ; var eps_r; stderr 100*SIG_R ; end; //% Optimal policy %optim_weights; %y 1; %pi 1; %end; //% Initial values for parameters in Taylor rule %rR = 0.1; //Monetary policy parameters taken from GNSS %rY = 0.1; %rpi = 1.2; %osr_params rY; %osr(order=1, irf=20) data_YY data_CC data_II data_LO data_QQ ; //% caluclulation of steady state steady(nocheck); %stoch_simul(order=1,irf=20) y cs los q pi rh ; stoch_simul(order=1,irf=20) data_YY data_CC data_II data_LO data_QQ pi ; %model_diagnostics;