'OUTPUT GAP GAP 'HP FILTER AND MULTIVARIATE HP FILTER close EMPlRICAL PROJECT_NWABISA.wf1 ' If such a workfile is open, it will be closed. (Useful if you wish to run this code multiple times and would like to avoid having opening multiple workfiles with the same name.) wfcreate(wf=EMPIRICAL PROJECT_NWABISA, page = Quarterly) q 1980 2025 ' ************** Reading data and setting some parameters ************** read(b6,s=Sheet1) "C:\Users\P519987\Desktop\CORVINUS\RESEARCH\RESEARCH PAPER_OUTPUT GAP\DATA AND RESULTS\QGDP_HPF.xls" 7 'SA = South Africa 'CHI= China 'BRA=Brazil '************generate log of GDP************** genr L_QGDP_SA = log(QGDP_SA) genr L_QGDP_CHI = log(QGDP_CHI) genr L_QGDP_BRA= log(QGDP_BRA) %first_available_observation = L_QGDP_SA.@first ' this is a string, its value will be 1980Q1 in the case of QGDP_SA %first_available_observation = L_QGDP_CHI.@first %first_available_observation = L_QGDP_BRA.@first %last_available_observation = L_QGDP_SA.@last ' this is a string, its value will be 2020Q4 %last_available_observation = L_QGDP_CHI.@last ' this is a string, its value will be 2020Q4 %last_available_observation = L_QGDP_BRA.@last ' this is a string, its value will be 2020Q4 smpl %first_available_observation %last_available_observation '----------------------------------------------------UNIVARIATE HP FILTER------------------------------------------------------------ hpf(lamba=1600) L_QGDP_SA L_QGDP_SA_HPT @ L_QGDP_SA_HPC '------------------------------------------------------------------------------------------------------------------------------------------------------------------- '------------------------------------------------------------------------------------------------------------------------------------------------------------------ 'STATE-SPACE MODEL - UNIVARIATE HP FILTER '------------------------------------------------------------------------------------------------------------------------------------------------------------------ 'HP filter smoothing parameter scalar lambda=1600 'Create the sspace object sspace hp_mod_SA ' Measurement equation hp_mod_SA.append @signal L_QGDP_SA= 1 * trend + 0 * gap+ eps hp_mod_SA.append @ename eps hp_mod_SA.append @evar var(eps) = 1 ' State equation (trend) hp_mod_SA.append @state trend = 1 * trend(-1) + 1 * gap(-1) + eta_trend hp_mod_SA.append @ename eta_trend hp_mod_SA.append @evar var(eta_trend) = 0 ' State equation (gap) hp_mod_SA.append @state gap = 0 * trend(-1) + 1 * gap(-1) + eta_gap hp_mod_SA.append @ename eta_gap hp_mod_SA.append @evar var(eta_gap) = 1 / lambda ' Estimate model by maximum likelihood hp_mod_SA.ml ' Create state estimates hp_mod_SA.makestates(t=smooth)*f1 hp_mod_SA.makestates(t=pred)*f2 hp_mod_SA.makestates(t=filt) *f3 ' Create gap estimates series CYCLE1 =L_QGDP_SA -trendf1 series CYCLE2 = L_QGDP_SA - trendf2 series CYCLE3 = L_QGDP_SA - trendf3 'run sperfectly ' ******************************************************************************************************************** ' Compare EViews built-in with State-Space Model ' ******************************************************************************************************************** show L_QGDP_SA_HPT trendf3'Trend comparison show L_QGDP_SA_HPC CYCLE3' Cycle comparison '----------------------------------------------------------------------------------------------------------------------------------------------------------------- 'MULTIVARIATE HP FILTER - using South African data only for now 'Extend the model with Output-inflation relationship / augmented Philips-Curve '------------------------------------------------------------------------------------------------------------------------------------------------------------------ 'STATE-SPACE MODEL '------------------------------------------------------------------------------------------------------------------------------------------------------------------ 'HP filter smoothing parameter scalar lambda=1600 'Create the sspace object sspace hp_mod_SA ' Measurement equation hp_mod_SA.append @signal L_QGDP_SA= 1 * trend + 0 * gap+ eps hp_mod_SA.append @ename eps hp_mod_SA.append @evar var(eps) = 1 ' State equation (trend) hp_mod_SA.append @state trend = 1 * trend(-1) + 1 * gap(-1) + eta_trend hp_mod_SA.append @ename eta_trend hp_mod_SA.append @evar var(eta_trend) = 0 ' State equation (gap) hp_mod_SA.append @state gap = 0 * trend(-1) + 1 * gap(-1) + eta_gap hp_mod_SA.append @ename eta_gap hp_mod_SA.append @evar var(eta_gap) = 1 / lambda 'EXTEND THE MODEL with Output-inflation relationship hp_mod_SA.append @signal infl_sa = c(1) +Inflex_sa+ c(2)*gap+c(3)*gap(-1)+eps_infl_sa 'T actual inflation rate p depends on inflation expectations (p^e) and the current and lagged output gap. hp_mod_SA.append @ename eps_infl_sa hp_mod_SA.append @evar var (eps_infl_sa)=1 ' Estimate model by maximum likelihood hp_mod_SA.ml ' Create state estimates hp_mod_SA.makestates(t=smooth)*f1 hp_mod_SA.makestates(t=pred)*f2 hp_mod_SA.makestates(t=filt) *f3 ' Create gap estimates series CYCLE1 =L_QGDP_SA -trendf1 series CYCLE2 = L_QGDP_SA - trendf2 series CYCLE3 = L_QGDP_SA - trendf3 'run sperfectly ' ******************************************************************************************************************** ' Compare EViews built-in with State-Space Model ' ******************************************************************************************************************** show L_QGDP_SA_HPT trendf3'Trend comparison show L_QGDP_SA_HPC CYCLE3' Cycle comparison '=========================================================================================== 'IGNORE THE CODE BELOW '----------------------------------------------------------------------------------------------------------------------------------------------------------------- 'MULTIVARIATE HP FILTER - using South African data only for now 'Extend the model with Output-inflation relationship / augmented Philips-Curve '------------------------------------------------------------------------------------------------------------------------------------------------------------------ 'STATE-SPACE MODEL '------------------------------------------------------------------------------------------------------------------------------------------------------------------ 'HP filter smoothing parameter scalar lambda=1600 'Create the sspace object sspace hp_mod_SA 'State equation (trend) hp_mod_SA.append @state trend11=c(1) + trend11(-1)+eta_trend11 hp_mod_SA.append @ename eta_trend11 hp_mod_SA.append @evar var(eta_trend11)=0 'State equation (gap) hp_mod_SA.append @state gap11= c(1)*gap11(-1)+eta_gap11 hp_mod_SA.append @ename eta_gap11 hp_mod_SA.append @evar var(eta_gap11)=1/lambda 'Measurement equation hp_mod_SA.append @signal L_QGDP_SA= trend11+ gap11 +eps hp_mod_SA.append @ename eps hp_mod_SA.append @evar var (eps)=1 'EXTEND THE MODEL with Output-inflation relationship hp_mod_SA.append @signal infl_sa = c(1) +Inflex_sa+ c(2)*gap11+eps_infl_sa 'The actual inflation rate p depends on inflation expectations (p^e) and the current and lagged output gap. hp_mod_SA.append @ename eps_infl_sa hp_mod_SA.append @evar var (eps_infl_sa)=1 'Estimate model by maximum likelihood hp_mod_SA.ml 'Create state estimates hp_mod_SA.makestates(t=filt)*f1 hp_mod_SA.makestates(t=smooth)*f2 hp_mod_SA.makestates(t=filtse)*f3 'Create gap estimate series cycle1=L_QGDP_SA - trend11f1 series cycle2=L_QGDP_SA - trend11f2 series cycle3=L_QGDP_SA - trend11f3 'compare trend and cycle from unvariate hp and multivariate hp show l_qgdp_sa_hp trend11f1 ' Trend comparison show L_QGDP_SA_gap cycle1 ' Cycle comparison ' ------------------------------------------------------------------------------------------------------------------- ' END OF PROGRAM ' -------------------------------------------------------------------------------------------------------------------