% ================================================================================ % Project: "Oil Prices and Trend Growth" % Authors: Carlos de Resende and Philipp Maier % Purpose of this code: model simulation / estimation % by Carlos de Resende (July, 2008) % ================================================================================ % periods 10000; % Declare variables % ================= var xt, yhat, gTt, pt, st, pit, piTt, Rt, Rstar, pistar, ystar, gt, rr, rrstar, Rn, obsR, obsystar, obss, obspi, obsp, obspistar, obsRstar, obsyUS, mu;%, obspiT; % Declare shocks % ============== varexo eg, v, ep, eps, eR, emu, eystar, epistar, eRstar, epiT; % Declare parameters % ================== parameters rhog, rhopiT, rhop, rhopistar, rhoRstar, rhoystar, rhomu, lambdag, alpha, betay, betapi, betapi2, betap, gammap, gammay, gammar, gammas, gammaystar, rhoR, rhopi, rhoy, gTss, pss, piss, piTss, Rss, pistarss, Rstarss, ystarss, yhatss, xss, sss, g, gss, rrss, rrstarss, muss, Rnss; % Parameter calibration 1: Parameters to be estimated % =================================================== rhog = 0.4000; % GDP trend growth rate: persistence sigmag = 0.0070; % GDP trend growth rate: volatility rhopiT = 0.9900; % target inflation rate: persistence sigmapiT = 0.0001; % target inflation rate: volatility rhop = 0.7500; % oil price shock: persistence sigmap = 0.1200; % oil price shock: volatility rhopistar = 0.2200; % foreign inflation rate: persistence sigmapistar = 0.0040; % foreign inflation rate: volatility rhoRstar = 0.8000; % foreign nominal interest rate: persistence sigmaRstar = 0.0010; % foreign nominal interest rate: volatility rhoystar = 0.8000; % foreign output: persistence sigmaystar = 0.0070; % foreign output: volatility rhomu = 0.7500; % UIP shock: persistence sigmamu = 0.0060; % UIP shock: volatility sigmav = 0.0050; % Phillips curve (supply) shock: volatility sigmaeps = 0.0001; % IS curve (demand) shock: volatility sigmaR = 0.0020; % Monetary policy shock: volatility lambdag = -0.0121; % GDP trend growth rate: sensitivy to oil prices betay = 0.005; % Phillips curve: output gap parameter betapi = 0; % Phillips curve: past inflation parameter betapi2 = 0; % Phillips curve: expected inflation parameter betap = 0;%0.005; % Phillips curve: oil prices parameter gammay = 0; % IS curve: past output gap parameter gammar = -0.25; % IS curve: real interest rate parameter gammas = 0.050; % IS curve: real exchange rate parameter gammaystar = 0.200; % IS curve: foreign output parameter gammap = 0.000; % IS curve: past output gap parameter rhoR = 0.8000; % mon. policy rule: smoothing rhopi = 0.1000; % mon. policy rule: reaction to inflation rhoy = 0.3000; % mon. policy rule: reaction to output gap % Parameter calibration (Steady-State values) % =========================================== rrss = 1/0.991; % real interest rate gTss = 0.007673; % GDP treng growth gss = gTss; % Actual (observable) GDP growth pss = 1; % oil prices (real, relative to CPI, normalized to 1) piss = 1.011442; % domestic inflation rate piTss = piss; % domestic target for the inflation rate Rss = piss*rrss; % domestic nominal interest rate pistarss = 1.011228; % foreign inflation rate Rstarss = 1.018422; % foreign nominal interest rate yhatss = 0; % output gap excluding irregular component xss = exp(yhatss);% output gap including irregular component muss = 1 - (Rss/piss)*(pistarss/Rstarss); % UIP shock rrstarss = Rstarss/pistarss; % foreign real interest rate g = gTss - (lambdag/(1-rhog))*pss; ystarss = 1; sss = -(gammar/gammas)*(Rss/piss) - ((gammaystar*ystarss+gammap)/gammas); alpha = 1-betapi-betapi2-betay-betap; % Phillips curve: intercept Rnss = Rss; % The Model: system of equations % ============================== model; Rn = rrss*piTt; % Rn = Rss xt = exp(yhat); gTt = (1-rhog)*g + rhog*gTt(-1) + lambdag*pt + eg; 1 + gt = (1 + gTt) * (xt/xt(-1)); pit/piTt = alpha + betay*exp(yhat) + betapi*(pit(-1)/piTt(-1)) + betapi2*(pit(+1)/piTt(+1)) + betap*pt + v; yhat = gammay*yhat(-1) + gammar*(Rt/pit(+1)) + gammas*st + gammaystar*ystar + gammap*pt + eps; Rt/Rn =(Rt(-1)/Rn)^rhoR*(pit/piTt)^rhopi*(xt)^rhoy*exp(eR); rr = Rt/pit(+1); rrstar = Rstar/pistar(+1); st(+1)/st = (rr/rrstar) + mu; log(piTt) = (1-rhopiT)*log(piTss)+ rhopiT*log(piTt(-1)) + epiT; log(pt) = (1-rhop)*log(pss) + rhop*log(pt(-1)) + ep; log(pistar) = (1-rhopistar)*log(pistarss) + rhopistar*log(pistar(-1)) + epistar; log(Rstar) = (1-rhoRstar)*log(Rstarss) + rhoRstar*log(Rstar(-1)) + eRstar; log(ystar) = (1-rhoystar)*log(ystarss) + rhoystar*log(ystar(-1)) + eystar; mu = (1-rhomu)*muss + rhomu*mu(-1) + emu; % observed data % ------------- obspi = log(pit) - log(piTt); obsp = log(pt) - log(pss); obsR = log(Rt) - log(Rn); % deviations wrt Rn = rr*piTt or Rn = Rss obspistar= log(pistar) - log(pistarss); obsRstar = log(Rstar) - log(Rstarss); obsystar = log(ystar) - log(ystarss); obsyUS = log(ystar) - log(ystarss); obss = log(st) - log(sss); %obspiT = log(piTt) - log(piTss); end; % Initial values = SS values % ========================== initval; xt = xss; yhat = yhatss; gTt = gss; mu = muss; pt = pss; pit = piss; gt = gss; Rt = Rss; st = sss; piTt = piTss; rrstar = rrstarss; rr = rrss; ystar = ystarss; Rstar = Rstarss; pistar = pistarss; Rn = Rnss; eg = 0.00; v = 0.00; ep = 0.00; eps = 0.00; eR = 0.00; emu = 0.00; eystar = 0.00; epistar = 0.00; eRstar = 0.00; epiT = 0.00; obsR = 0.00; obsp = 0.00; obsystar = 0.00; obss = 0.00; obspi = 0.00; obspistar = 0.00; obsRstar = 0.00; obsyUS = 0.00; %obspiT = 0.00; end; % Shock processes % =============== shocks; var epiT; stderr sigmapiT; var eg; stderr sigmag; var v; stderr sigmav; var ep; stderr sigmap; var eps; stderr sigmaeps; var eR; stderr sigmaR; var emu; stderr sigmamu; var epistar; stderr sigmapistar; var eRstar; stderr sigmaRstar; var eystar; stderr sigmaystar; end; % rand('state',0) check; steady; stoch_simul(periods=1000,irf=10); // % Estimation % ========== % estimated_params; % % % 1) Monetary policy rule: % % ------------------------ % rhopi, 0.1, 0.01, 1; % rhoy, 0.3, 0.01, 1; % rhoR, 0.8, 0.01, 1; % % % 2) AR coefficients (** = calibrated): % % ------------------------------------- % rhop, 0.75; % relative price of oil % rhog, 0.40; % trend growth % rhoystar, 0.80; % foreign output % rhopistar, 0.22; % foreign inflation % rhoRstar, 0.80; % foreign interest rate % rhomu, 0.75; % UIP shock % % %rhopiT, 0.8530, 0.001, 0.999; % inflation target ** % % % % 3) Phillips Curve: % % ------------------ % betay, 0.0050, 0.0001, 5.000; % %betap, 0.0050, 0.004, 0.006; % %betapi2, 0.0000, 0.000, 5.000; % %betapi, 0.0000;%, -0.999, 0.999; % % % % 4) IS Curve (** = calibrated): % % ------------------------------ % gammar, -0.2500, -5.000, -0.0001; % gammas, 0.0500, 0.001, 5.000; % gammaystar, 0.2000, 0.001, 5.000; % %gammap, 0.0010;%, 0.001, 5.000; % % %gammay, 0.001, 0.001, 0.999; % % % 5) Sensitivity of trend growth to oil prices: % % --------------------------------------------- % lambdag, -0.0121; % % % 6) standard deviations (** = calibrated): % % ------------------------------------------ % stderr ep, 0.1200, 0.001, 0.5; % stderr eg, 0.0100, 0.001, 0.5; % stderr v, 0.0050, 0.001, 0.5; % stderr eR, 0.0020, 0.001, 0.5; % stderr eystar, 0.0070, 0.001, 0.5; % stderr epistar, 0.0040, 0.001, 0.5; % stderr eRstar, 0.0010, 0.001, 0.5; % stderr emu, 0.0060, 0.001, 0.5; % % %stderr eps, 0.0001, 0.000, 0.5; % ** % %stderr epiT, 0.0001, 0.000, 0.5; % ** % % muss, -0.0020; % end; % % % estimated_params_init; % rhopi, 0.0947; % rhoy, 0.2957; % rhoR, 0.8034; % rhop, 0.7474; % rhog, 0.4228; % rhoystar, 0.8200; % rhopistar, 0.2195; % rhoRstar, 0.8297; % rhomu, 0.7629; % betay, 0.0050; % betapi, 0.0040; % gammar, -0.2247; % gammas, 0.0612; % gammaystar, 0.1628; % lambdag, -0.0121; % % ep, 0.1202; % eg, 0.0073; % v, 0.0054; % eR, 0.0020; % eystar, 0.0074; % epistar, 0.0042; % eRstar, 0.0014; % emu, 0.0059; % end; % % % %oo_.mle_mode.parameters oo_.mle_mode.shocks_std % % varobs gt obspi obsp obsR obss obsyUS obsRstar obspistar; % obspiT; % % % estimation(datafile=CAN_data_input,nobs=149,periods=149,mode_check); % estimation(datafile=CAN_data_input,nobs=149,mode_check); % % % % % % % % % % % % % % % % % % % % % % %stoch_simul(order=1,irf=20, periods = 149) yhat gt gTt pit Rt rr st; % % %varexo ey, eg, v, ep, eps, eR, emu, eystar, epistar, eRstar, epiT; % % % Save inpulse responses % % ====================== % % % Growth shocks % %mat_eg=[yhat_eg pit_eg]; % % % Oil price shocks % %mat_ep=[yhat_ep gt_ep gTt_ep pit_ep Rt_ep rr_ep st_ep]; % % % % %forecast yhat gt gTt pit piTt; % % // %