' Article explaining Simultaneous Equation Models (SEM) applied to e-Views: ' http://davegiles.blogspot.com/2012/05/estimating-simulating-sem.html '-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' A. SETTING UP EXOGENOUS AND SYSTEM EQUATIONS ' Open spread-sheet wfopen "{' PLEASE INSERT HERE THE PATH TO THE FILE}\G4 dataset.xlsx" range=eViews smpl @first+1 @last ' Setting up the system of equations with AR(1) components: system _sys_3sls _sys_3sls.append DE_LR = C(1) + C(2)*DE_GDP + C(3)*DE_INF + C(4)*DE_SR + C(5)*DE_LRS + [AR(1)=c(6)] @ JP_GDP JP_INF JP_SR UK_GDP UK_INF UK_SR US_GDP US_INF US_SR DE_SR(-1) DE_INF(-1) DE_GDP _sys_3sls.append JP_LR = C(7) +C(8)* JP_GDP +C(9)*JP_INF + C(10)* JP_SR+C(11)* JP_LRS + [AR(1)=c(12)] @ DE_GDP DE_INF DE_SR UK_GDP UK_INF UK_SR US_GDP US_INF US_SR JP_SR(-1) JP_GDP JP_INF(-1) _sys_3sls.append UK_LR =C(13) +C(14)*UK_GDP +C(15)*UK_INF+C(16)*UK_SR +C(17)*UK_LRS + [AR(1)=c(18)] @ DE_GDP DE_INF DE_SR JP_GDP JP_INF JP_SR UK_GDP US_GDP US_INF US_SR UK_SR(-1) UK_INF _sys_3sls.append US_LR = C(19) +C(20)* US_GDP +C(21)*US_INF+C(22)* US_SR +C(23)*US_LRS +[AR(1)=c(24)] @ DE_GDP DE_INF DE_SR JP_GDP JP_INF JP_SR UK_GDP UK_INF UK_SR US_GDP US_INF US_SR(-1) '-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' ' A.1 {INPUT VARIABLES IN SCENARIO 1 to 3} ARIMA (p,q) models for endogenour variables ' First, we estimate the ARIMA models ' GERMANY equation _f_degdp.LS DE_GDP C AR(1) equation _f_deinf.LS DE_INF C DE_INF(-1) equation _f_delrs.LS(DERIV=AA) DE_LRS C AR(1) MA(1) equation _f_desr.LS(DERIV=AA) DE_SR C AR(1) AR(2) MA(1) ' JAPAN equation _f_jpgdp.LS JP_GDP C AR(1) equation _f_jpinf.LS JP_INF C AR(1) equation _f_jplrs.LS(DERIV=AA) JP_LRS C AR(1) MA(1) equation _f_jpsr.LS JP_SR C AR(1) AR(2) MA(1) 'UK equation _f_ukgdp.LS UK_GDP C AR(1) equation _f_ukinf.LS UK_INF C AR(1) equation _f_uklrs.LS(DERIV=AA) UK_LRS C AR(1) MA(1) equation _f_uksr.LS UK_SR C AR(1) AR(2) 'US equation _f_usgdp.LS US_GDP C AR(1) equation _f_usinf.LS US_INF C AR(1) equation _f_uslrs.LS US_LRS C AR(1) AR(2) equation _f_ussr.LS(DERIV=AA) US_SR C AR(1) AR(2) MA(1) ' Second, we obtain forecast using model specification estimated above. pagestruct(end=@last+24) ' The pagestruct command extend the sample size to include the period we want to forecasts, i.e. 24 months. smpl @last-23 @last+24 For !i=1 to 3 _f_degdp.forecast de_gdp_{!i} _f_deinf.forecast de_inf_{!i} _f_delrs.forecast de_lrs_{!i} _f_desr.forecast de_sr_{!i} _f_jpgdp.forecast jp_gdp_{!i} _f_jpinf.forecast jp_inf_{!i} _f_jplrs.forecast jp_lrs_{!i} _f_jpsr.forecast jp_sr_{!i} _f_ukgdp.forecast uk_gdp_{!i} _f_ukinf.forecast uk_inf_{!i} _f_uklrs.forecast uk_lrs_{!i} _f_uksr.forecast uk_sr_{!i} _f_usgdp.forecast us_gdp_{!i} _f_usinf.forecast us_inf_{!i} _f_uslrs.forecast us_lrs_{!i} _f_ussr.forecast us_sr_{!i} next smpl @first+1 @last '-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 'A.2 {INPUT VARIABLES IN SCENARIO 4} ' In this scenario, the user can choose to input the forecast of her choice. ' The tab "FcastInput" tab in the Excecl template is prepared for this. Select the variable to be tested (same for all four countries). 'For the other variable, the model takes the latest realised value for all the forecast period. ' Text box to be desplayed when running the Code: %choice ="SR" %list ="SR GDP INF LRS" @uilist(%choice,"Please select the exogenous variable that you want to use for the scenario analysis",%list) statusline %choice If %choice = "SR" then group gr1 DE_SR JP_SR UK_SR US_SR group gr2 DE_LRS DE_GDP DE_INF JP_GDP JP_INF JP_LRS UK_GDP UK_INF UK_LRS US_GDP US_INF US_LRS else If %choice = "GDP" then group gr1 DE_GDP JP_GDP UK_GDP US_GDP group gr2 DE_LRS DE_INF JP_INF JP_LRS UK_INF UK_LRS US_INF US_LRS DE_SR JP_SR UK_SR US_SR else If %choice = "INF" then group gr1 DE_INF JP_INF UK_INF US_INF group gr2 DE_LRS DE_GDP JP_GDP JP_LRS UK_GDP UK_LRS US_GDP US_LRS DE_SR JP_SR UK_SR US_SR else If %choice = "LRS" then group gr1 DE_LRS JP_LRS UK_LRS US_LRS group gr2 DE_GDP DE_INF JP_GDP JP_INF UK_GDP UK_INF US_GDP US_INF DE_SR JP_SR UK_SR US_SR Endif Endif Endif Endif ' The following step construct the data series for scenario 4. ' GROUP 1 Variables smpl @all For !i=1 to gr1.@count %name=gr1.@seriesname(!i) ' Obtaining the names ("strings") of the endogenous variables smpl @first @last-24 ' For the realised observation, scenario 4 and 5 are the same and equal to the realised values. series {%name}_4 =gr1(!i) series {%name}_5 ={%name}_4 smpl @last-23 @last+24 ' For the forecast period, the values are imported from Excel, "FcastInput" tab. import(mode=u) "{' PLEASE INSERT HERE THE PATH TO THE FILE}\G4 dataset.xlsx" range=FcastInput series {%name}_5 ={%name}_4 Next smpl @all ' GROUP 2 Variables smpl @all For !i=1 to gr2.@count %name=gr2.@seriesname(!i) ' Obtaining the names ("strings") of the endogenous variables smpl @first @last-24 series {%name}_4 =gr2(!i) series {%name}_5 ={%name}_4 smpl @last-23 @last+24 ' For the forecast period, we use the last realised value. series {%name}_4 ={%name}_4(-1) series {%name}_5 ={%name}_4 Next smpl @all '-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- '-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 'B. SOLVING THE SYSTEM AND CREATING MODEL. ' Solving the system with Three Stage Least Square: _sys_3sls.3sls ' Creating the model : _sys_3sls.makemodel(_m_3sls) _sys_3sls.output freeze(coef_tbl) _sys_3sls.output ' Model statistics (optional) '_sys_3sls.qstats ' residual autorcorrelation Portmanteau test '_sys_3sls.cov ' residual covariance matrix '_sys_3sls.correl(12, graph) ' residuals correlations '-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- '-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 'C. SOLVING THE MODEL ' 1. a FITTED VALUES: Stochastic Valuation with full sample values estimation. smpl @first+1 @last-24 _m_3sls.scenario(n,a=_0) "Fitted Values" _m_3sls.stochastic _m_3sls.solve(s=s,d=d) ' stochastic and dynamic options 'smpl @all '_m_3sls.makegraph(s=s, a) grph_lr @endog ' a = include actuals, s= plots stochastics and std. deviation 'show grph_lr '1.b Fitted Value Forecasts smpl @first+1 @last+24 _m_3sls.scenario(n,a=_1) "Fitted Values & Forecasts" _m_3sls.override DE_LRS DE_SR DE_GDP DE_INF JP_GDP JP_INF JP_LRS JP_SR UK_GDP UK_INF UK_LRS UK_SR US_GDP US_INF US_LRS US_SR ' Replaces the exogenoous variables with the extended variables that include the forecasts as estimated in A.1 above _m_3sls.stochastic _m_3sls.solve(s=s,d=d) ' stochastic and dynamic options smpl @last-240 @last ' Charts showing 10 years of data points 'smpl @all _m_3sls.scenario "Fitted Values & Forecasts" 'ARMA forecasts _m_3sls.makegraph(s=s, a) grph_Fitted @endog ' a = include actuals, s= plots stochastics and std. deviation show grph_Fitted ' 2. OUT-OF-SAMPLE FORECASTS. The exogenous variables used are the ls estimates of the ARMA models computed above. '2.a Stochastic forecasting smpl @last-23 @last+24 _m_3sls.scenario "actuals" _m_3sls.scenario(n, a=_2) "Out-of-Sample Forecasts - ARMA inputs" ' Stochastic estimations _m_3sls.override DE_LRS DE_SR DE_GDP DE_INF JP_GDP JP_INF JP_LRS JP_SR UK_GDP UK_INF UK_LRS UK_SR US_GDP US_INF US_LRS US_SR _m_3sls.solve(s=s,d=d) ' stochastic and dynamic options smpl @last-240 @last ' Charts showing 10 years of data points _m_3sls.makegraph(s=s, a) grph_OOS @endog ' a = include actuals, s= plots stochastics and std. deviation show grph_OOS '' 2.b Deterministic Forecasts. '' Generating override variables for scenario 2 'smpl @last-23 @last+24 '_m_3sls.scenario "actuals" '_m_3sls.scenario(n,a=_3) "Out-of-Sample Forecasts - Deterministic" ''_m_3sls.scenario(n, i="Out-of-Sample Forecasts") "Out-of-Sample Forecasts - Deterministic" ' Stochastic estimations '_m_3sls.override DE_LRS DE_SR DE_GDP DE_INF JP_GDP JP_INF JP_LRS JP_SR UK_GDP UK_INF UK_LRS UK_SR US_GDP US_INF US_LRS US_SR '_m_3sls.solve(s=d,d=d) ' stochastic and dynamic options ' 'smpl @last-240 @last ' Charts showing 10 years of data points '_m_3sls.makegraph(a) grph_Det @endog ' a = include actuals, s= plots stochastics and std. deviation 'show grph_Det '-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- '3. SCENARIO ANALYSIS: Exogenous variables are the original data. The forecast for the exogenous variables are the last observations and "our" own expected values. '3.a. Fitted Values & Scenario Forecasts smpl @first+1 @last _m_3sls.scenario "Fitted Values" _m_3sls.scenario(n,a=_4) "Scenario Input: SR" _m_3sls.override DE_LRS DE_SR DE_GDP DE_INF JP_GDP JP_INF JP_LRS JP_SR UK_GDP UK_INF UK_LRS UK_SR US_GDP US_INF US_LRS US_SR _m_3sls.stochastic _m_3sls.solve(s=s,d=d) ' stochastic and dynamic options smpl @last-240 @last ' Charts showing 10 years of data points _m_3sls.makegraph(s=s, a) grph_scen @endog ' a = include actuals, s= plots stochastics and std. deviation '_m_3sls.makegraph(s=s, a) grph_JP_lrscen jp_lr show grph_scen '3.b. smpl @last-23 @last+24 _m_3sls.scenario "actuals" _m_3sls.scenario(n, a=_5) "Out-of-Sample Forecasts - Scenario Inputs" ' Stochastic estimations _m_3sls.override DE_LRS DE_SR DE_GDP DE_INF JP_GDP JP_INF JP_LRS JP_SR UK_GDP UK_INF UK_LRS UK_SR US_GDP US_INF US_LRS US_SR _m_3sls.solve(s=s,d=d) ' stochastic and dynamic options smpl @last-240 @last ' Charts showing 10 years of data points _m_3sls.makegraph(s=s, a) grph_scft @endog ' a = include actuals, s= plots stochastics and std. deviation show grph_scft group excel_series *_lr *lr_4m *4s '-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- '-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 'line de_lr_1m de_lr_4m 'line jp_lr_1m jp_lr_4m 'line uk_lr_1m uk_lr_4m 'line us_lr_1m us_lr_4m '---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- '---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ' Half Life group gr3 de_lr jp_lr uk_lr us_lr smpl @all For !i=1 to gr3.@count %name=gr3.@seriesname(!i) ' Obtaining the names ("strings") of the endogenous variables equation ls{%name}.ls(COV=HAC) {%name} c {%name}(-1) scalar LAMBDA_{%name}= c(2) ' Speed of Mean Reversion scalar mu_{%name}= c(1)/lambda_{%name} 'Mean scalar sigma_{%name}= @stdev(resid) ' Volatility scalar half_life__{%name} = log(0.5)/log(abs(lambda_{%name})) Next '' Transforming series to levels from logs (logs= 100*LN(1+lr/100), levels = (EXP(lr/100)-1)*100) 'series lev_de_lr_1 = (@exp(de_lr_1m/100)-1)*100 'series lev_jp_lr_1 = (@exp(jp_lr_1m/100)-1)*100