% "Asset Price Channels and Macroeconomic Fluctuations" % XXX % Changes from v14: Testing file % % Code by Jacob Smith and Diego Vilán %---------------------------------------------------------------- % 0. Housekeeping: %---------------------------------------------------------------- close all; //clc; %---------------------------------------------------------------- % 1. Define variables: %---------------------------------------------------------------- var gmuhhat, chhat, ghatlambda, what, nhat, qlhat, lhhat, rhat, gmuehat, cehat, yhat, qkhat, gmubhat, ghatq, lehat, khat, ghatz, ihat, bhat, glambdaahat, glambdaqhat, glambdazhat, gpsihat, gthetahat, gvarphihat, gnuqhat, gnuzhat, chat, obs1, obs2, obs3, obs4, obs5, obs6; varexo ez, enuz, eq, enuq, ea, evarphi, epsi, etheta; parameters gbeta, galpha, glambdaq, glambdaa, ggammah, ggammae, geta, gOmega, gOmegah, gOmegae, gtheta, gdelta, gphi qlLeOY, CeOY, ChOY, qlLeOB, iy, ky, gmuboe, by, r, lbar, LhOLe, Le, Lh, grhoz, grhonuz, grhoq, grhonuq, grhoa, grhovarphi, grhopsi, grhotheta, sigma, qlLhOY, COY, CeOC, ChOC, glambdastar, n_bar, ik, glambdaK; %---------------------------------------------------------------- % 2. Calibration - Deep parameters: %---------------------------------------------------------------- gbeta = 0.98; geta = 0.0; r = 1.01; by = 2.52; ky = 5.40; ik = 0.148/4; qlLeOY = 2.60; qlLhOY = 4.5664; n_bar = 0.22; lbar = 1; //sigma = 0.1; //g = 1.005; //yk = 1/ky; //glambdaq = 1.01; //ggammah = 0.7; //ggammae = 0.7; //glambdastar = 1.0045; //gOmega = 2.0; //grhoz = 0.1; //grhonuz = 0.9; //grhoq = 0.1; //grhonuq = 0.9; //grhoa = 0.9; //grhovarphi = 0.9; //grhopsi = 0.9; //grhotheta = 0.9; %---------------------------------------------------------------- % 3. Calibration - Parameters: %---------------------------------------------------------------- glambdaK = glambdaq*glambdastar; gtheta = by/(glambdastar*qlLeOY+ky/glambdaq); // gtheta = 0.3166; gdelta = 1-(1-ik)*glambdastar*glambdaq; glambdaa = glambdastar/(gbeta*r)-1; //glambdaa = 0.00154; galpha = (1-gbeta-gbeta*glambdaa*gtheta)*qlLeOY/gbeta + (1-gbeta*glambdaa*gtheta/glambdaK-gbeta*(1-gdelta)/glambdaK)*ky/gbeta; //galpha = 0.3246; gphi = qlLeOY*(1-gbeta*(1+glambdaa*gtheta))/(gbeta*galpha); //gphi = 0.1245; iy = ik*ky; //iy = 0.1998; CeOY = galpha-iy-by*(1-gbeta*(1+glambdaa))/glambdastar; //CeOY = 0.0784; ChOY = 1-CeOY-iy; //ChOY = 0.7218; COY = CeOY + ChOY; CeOC = CeOY/COY; ChOC = ChOY/COY; gmuboe = gbeta*glambdaa/glambdastar; //gmuboe = 0.0015; LhOLe = qlLhOY/qlLeOY; qlLeOB = qlLeOY/by; //qlLeOB = 1.0317; Le = 1/(1+LhOLe); Lh = 1-Le; gOmegah = (glambdastar-gbeta*(1+glambdaa)*ggammah)*(glambdastar-ggammah); //gOmegah = 0.0970; gOmegae = (glambdastar-gbeta*ggammae)*(glambdastar-ggammae); //gOmegae = 0.0973; %---------------------------------------------------------------- % 4. The Model: %---------------------------------------------------------------- model(linear); gOmegah * gmuhhat = -(glambdastar^2+ggammah^2*gbeta*(1+glambdaa))*chhat+glambdastar*ggammah*(chhat(-1) - ghatlambda)-gbeta*glambdaa*ggammah*(glambdastar-ggammah)*glambdaahat(+1)+gbeta*(1+glambdaa)*glambdastar*ggammah*(chhat(+1)+ghatlambda(+1)); what + gmuhhat = gpsihat + geta*nhat; qlhat + gmuhhat = gbeta*(1+glambdaa)*(gmuhhat(+1)+qlhat(+1))+(1-gbeta*(1+glambdaa))*(gvarphihat-lhhat)+gbeta*glambdaa*glambdaahat(+1); gmuhhat - rhat = gmuhhat(+1)+ (glambdaa/(1+glambdaa))*glambdaahat(+1) - ghatlambda(+1); gOmegae * gmuehat = -(glambdastar^2 + gbeta*ggammae^2)*cehat + glambdastar*ggammae*(cehat(-1)-ghatlambda)+gbeta*glambdastar*ggammae*(cehat(+1)+ghatlambda(+1)); what = yhat - nhat; qkhat = (1 + gbeta)*gOmega*glambdastar^2*ihat*glambdaq^2 - gOmega*glambdastar^2*ihat(-1)*glambdaq^2 + gOmega*glambdastar^2*glambdaq^2*(ghatlambda + ghatq) - gbeta*gOmega*glambdastar^2*glambdaq^2*(ihat(+1)+ghatlambda(+1)+ghatq(+1)); qkhat + gmuehat = gmuboe*(gtheta/glambdaq)*(gmubhat + gthetahat)+((gbeta*(1-gdelta))/glambdastar*glambdaq)*(qkhat(+1)+ ghatq(+1)+ghatlambda(+1))+(1-gmuboe*(gtheta/glambdaq))*gmuehat(+1)+ gmuboe*(gtheta/glambdaq)*(qkhat(+1)-ghatq(+1))+gbeta*galpha*(1-gphi)*(1/ky)*(yhat(+1)-khat); qlhat + gmuehat = gmuboe*glambdastar*gtheta*(gthetahat + gmubhat)+(1-gmuboe*glambdastar*gtheta)*gmuehat(+1)+ gmuboe*glambdastar*gtheta*(qlhat(+1)+ghatlambda(+1))+gbeta*qlhat(+1)+(1-gbeta-gbeta*gtheta*glambdaa)*(yhat(+1)-lehat); gmuehat - rhat = (1/(1+glambdaa))*(gmuehat(+1)-ghatlambda(+1)+glambdaa*gmubhat); yhat = galpha*gphi*lehat(-1)+ galpha*(1-gphi)*khat(-1)+ (1-galpha)*nhat - (ghatq + ghatz)*((1-gphi)*galpha/(1-(1-gphi)*galpha)); khat = ((1-gdelta)/(glambdastar*glambdaq))*(khat(-1)- ghatlambda - ghatq)+(1-((1-gdelta)/(glambdastar*glambdaq)))*ihat; yhat = ChOY*chhat + CeOY*cehat + iy*ihat; 0 = (Lh/lbar)*lhhat + (Le/lbar)*lehat; galpha*yhat = CeOY*cehat + iy*ihat + qlLeOY*(lehat-lehat(-1))+(1/glambdastar)*by*(bhat(-1)-ghatlambda)- (1/r)*by*(bhat-rhat); bhat = gthetahat + glambdastar*gtheta*qlLeOB*(qlhat(+1)+ lehat - ghatlambda(+1)) + (1 - glambdastar*gtheta*qlLeOB)*(qkhat(+1)+khat-ghatq(+1)); ghatz = glambdazhat + gnuzhat - gnuzhat(-1); ghatq = glambdaqhat + gnuqhat - gnuqhat(-1); ghatlambda = (1/(1-(1-gphi)*galpha))*ghatz + (((1-gphi)*galpha)/((1-(1-gphi)*galpha)))*ghatq; glambdazhat = grhoz*glambdazhat(-1)+ ez; gnuzhat = grhonuz*gnuzhat(-1)+ enuz; glambdaqhat = grhoq*glambdaqhat(-1) + eq; gnuqhat = grhonuq*gnuqhat(-1) + enuq; glambdaahat = grhoa*glambdaahat(-1) + ea; gvarphihat = grhovarphi*gvarphihat(-1) + evarphi; gpsihat = grhopsi*gpsihat(-1)+ epsi; gthetahat = grhotheta*gthetahat(-1)+ etheta; chat = CeOC* cehat + ChOC*chhat; obs1 = log(glambdastar)+ bhat - bhat(-1)+ (1/1 -(1 - gphi)*galpha)*(glambdazhat + gnuzhat - gnuzhat(-1) + (1 - gphi)*galpha*(glambdaqhat + gnuqhat - gnuqhat(-1))); //(nonfinancial business debt per capita) obs2 = log(glambdastar)+ (ihat - ihat(-1)) + (1/1 -(1 - gphi)*galpha)*(glambdazhat + gnuzhat - gnuzhat(-1) + (1 - gphi)*galpha*(glambdaqhat + gnuqhat - gnuqhat(-1))); //(investment (in consumption units) per capita) obs3 = log(glambdastar) + (qlhat - qlhat(-1)) + (1/1 -(1 - gphi)*galpha)*(glambdazhat + gnuzhat - gnuzhat(-1) + (1 - gphi)*galpha*(glambdaqhat + gnuqhat - gnuqhat(-1))); //(land price) obs4 = log(glambdaq) + glambdaqhat + gnuqhat - gnuqhat(-1); //(inverse of the relative price of investment) obs5 = (ChOY/COY)*(chhat - chhat(-1))+ (CeOY/COY)*(cehat - cehat(-1)) + (1/1 -(1 - gphi)*galpha)*(glambdazhat + gnuzhat - gnuzhat(-1) + (1 - gphi)*galpha*(glambdaqhat + gnuqhat - gnuqhat(-1))); //(consumption per capita) obs6 = log(n_bar)+ nhat; //(hours (percent of 24 hours) per capita) end; varobs obs1, obs2, obs3, obs4, obs5, obs6; %---------------------------------------------------------------- % 5. Computation: %---------------------------------------------------------------- initval; lhhat = (4.5664/4)*yhat; lehat = (2.60/4)*yhat; khat = (5.40/4)*yhat; ihat = yhat*(0.148/4); bhat = (2.52/4)*yhat; nhat = 0.22; gmuhhat = 0.1; chhat = 0.1; ghatlambda = 0.1; what = 0.1; qlhat = 0.1; rhat = 1.01; gmuehat = 0.1; cehat = 0.1; qkhat = 0.1; gmubhat = 0.1; ghatq = 0.1; ghatz = 0.1; glambdaahat = 0.1; glambdaqhat = 0.1; glambdazhat = 0.1; gpsihat = 0.1; gthetahat = 0.1; gvarphihat = 0.1; gnuqhat = 0.1; gnuzhat = 0.1; ez = 0; enuz = 0; eq = 0; enuq = 0; ea = 0; evarphi = 0; epsi = 0; etheta = 0; //yhat = 0.1; end; steady; check; %---------------------------------------------------------------- % 6. Estimation: %---------------------------------------------------------------- estimated_params; glambdaq, gamma_pdf, 1.816, 3.0112; glambdastar, gamma_pdf, 1.816, 3.0112; ggammah, beta_pdf, 1.0, 2.0; ggammae, beta_pdf, 1.0, 2.0; gOmega, gamma_pdf, 1.0, 0.5; grhoz, gamma_pdf, 1.0, 2.0; grhonuz, gamma_pdf, 1.0, 2.0; grhoq, gamma_pdf, 1.0, 2.0; grhonuq, gamma_pdf, 1.0, 2.0; grhoa, gamma_pdf, 1.0, 2.0; grhovarphi, gamma_pdf, 1.0, 2.0; grhopsi, gamma_pdf, 1.0, 2.0; grhotheta, gamma_pdf, 1.0, 2.0; stderr ez, inv_gamma_pdf, 0.0016, inf; stderr enuz, inv_gamma_pdf, 0.0016, inf; stderr eq, inv_gamma_pdf, 0.0016, inf; stderr enuq, inv_gamma_pdf, 0.0016, inf; stderr ea, inv_gamma_pdf, 0.0016, inf; stderr evarphi, inv_gamma_pdf, 0.0016, inf; stderr epsi, inv_gamma_pdf, 0.0016, inf; stderr etheta, inv_gamma_pdf, 0.0016, inf; end; estimated_params_init; glambdaq, 1.2789945000; glambdastar, 0.6031216600; ggammah, 0.3998073600; ggammae, 0.6574084000; gOmega, 0.2936255400; grhoa, 0.9158842800; grhoz, 0.4480247600; grhonuz, 0.4371422800; grhoq, 0.7512594000; grhonuq, 0.7512221300; grhovarphi, 0.9997822800; grhopsi, 0.9834809400; grhotheta, 0.9802902600; stderr ea, 0.1074987400; stderr ez, 0.0032192108; stderr enuz, 0.0043396775; stderr eq, 0.0029014840; stderr enuq, 0.0037502963; stderr evarphi, 0.0632112430; stderr epsi, 0.0069516930; stderr etheta, 0.0130274290; end; estimated_params_bounds; glambdastar, 0, r; end; %---------------------------------------------------------------- % 7. Results: %---------------------------------------------------------------- estimation(datafile=data_tao, mh_replic=2000, mh_nblocks=2, mh_drop=0.5, mh_jscale=0.60, forecast=12) chat qkhat ihat qlhat nhat yhat; //historicdec4 chat qkhat ihat qlhat nhat yhat +12;