*==========================================================================
*
*  C:\PROJECT\ERM\GDPPOP\IMPULSE.PRG
*
*  RATS code that graphs impulse response of GDP per capita given an ARMA.
*  Model identification from RATS program IDENTIFY.PRG.
*
*==========================================================================
*
cal 1947 1 4
compute t0 = 1947:1       ;* quarter of first observation
compute tf = 1997:4       ;* quarter of last observation
compute nstep = 16        ;* number of quarters to compute impulse responses
all tf+nstep
*
*  READ INPUT FILE AND COMPUTE PER CAPITA SERIES
*
open data gdppop.por
data(format=portable) / gdp pop p16
*
set gdp = gdp * 1000000000              ;* real GDP
set gdpall = gdp / (pop * 1000000)      ;* GDP / total population
set gdp16 = gdp / (p16 * 1000000)       ;* GDP / civilian noninstitutional pop
*
*  LOG TRANSFORMATIONS
*
set lgdpall = log(gdpall)
set lgdp16 = log(gdp16)
*
*  TIME TRENDS
*
set trend = t
set trend2 = (t ** 2)
*
*  TIME DETREND ALL SERIES
*
linreg gdpall
# constant trend trend2
prj fit
set dgdpall = gdpall - fit
*
linreg gdp16
# constant trend trend2
prj fit
set dgdp16 = gdp16 - fit
*
linreg lgdpall
# constant trend trend2
prj fit
set dlgdpall = lgdpall - fit
*
linreg lgdp16
# constant trend trend2
prj fit
set dlgdp16 = lgdp16 - fit
*
open plot impulse.plt
*
*  COMPUTE IMPULSE RESPONSES ON LEVEL TOTAL PER CAPITA SERIES
*
boxjenk(ar=2,diffs=0,ma=2,constant,iterations=50,define=eqn_dgdpall22) dgdpall
impulse(noprint) 1 nstep 1
# eqn_dgdpall22 impres
graph(nodates,header='Response: ARMA(2,2) on detrended total per capita levels') 1
# impres
*
boxjenk(ar=2,diffs=0,ma=1,constant,iterations=50,define=eqn_dgdpall21) dgdpall
impulse(noprint) 1 nstep 1
# eqn_dgdpall21 impres
graph(nodates,header='Response: ARMA(2,1) on detrended total per capita levels') 1
# impres
*
boxjenk(ar=3,diffs=0,ma=3,constant,iterations=50,define=eqn_dgdpall33) dgdpall
impulse(noprint) 1 nstep 1
# eqn_dgdpall33 impres
graph(nodates,header='Response: ARMA(3,3) on detrended total per capita levels') 1
# impres
*
boxjenk(ar=1,diffs=0,ma=1,constant,iterations=50,define=eqn_dgdpall11) dgdpall
impulse(noprint) 1 nstep 1
# eqn_dgdpall11 impres
graph(nodates,header='Response: ARMA(1,1) on detrended total per capita levels') 1
# impres
*
*  COMPUTE IMPULSE RESPONSES ON LEVEL 16+ PER CAPITA SERIES
*
boxjenk(ar=2,diffs=0,ma=2,constant,iterations=50,define=eqn_dgdp1622) dgdp16
impulse(noprint) 1 nstep 1
# eqn_dgdp1622 impres
graph(nodates,header='Response: ARMA(2,2) on detrended 16+ per capita levels') 1
# impres
*
boxjenk(ar=2,diffs=0,ma=1,constant,iterations=50,define=eqn_dgdp1621) dgdp16
impulse(noprint) 1 nstep 1
# eqn_dgdp1621 impres
graph(nodates,header='Response: ARMA(2,1) on detrended 16+ per capita levels') 1
# impres
*
boxjenk(ar=3,diffs=0,ma=3,constant,iterations=50,define=eqn_dgdp1633) dgdp16
impulse(noprint) 1 nstep 1
# eqn_dgdp1633 impres
graph(nodates,header='Response: ARMA(3,3) on detrended 16+ per capita levels') 1
# impres
*
boxjenk(ar=1,diffs=0,ma=1,constant,iterations=50,define=eqn_dgdp1611) dgdp16
impulse(noprint) 1 nstep 1
# eqn_dgdp1611 impres
graph(nodates,header='Response: ARMA(1,1) on detrended 16+ per capita levels') 1
# impres
*
*  COMPUTE IMPULSE RESPONSES ON LOGGED TOTAL PER CAPITA SERIES
*
boxjenk(ar=2,diffs=0,ma=2,constant,iterations=50,define=eqn_dlgdpall22) dlgdpall
impulse(noprint) 1 nstep 1
# eqn_dlgdpall22 impres
graph(nodates,header='Response: ARMA(2,2) on detrended total per capita logs') 1
# impres
*
boxjenk(ar=2,diffs=0,ma=1,constant,iterations=50,define=eqn_dlgdpall21) dlgdpall
impulse(noprint) 1 nstep 1
# eqn_dlgdpall21 impres
graph(nodates,header='Response: ARMA(2,1) on detrended total per capita logs') 1
# impres
*
boxjenk(ar=3,diffs=0,ma=3,constant,iterations=50,define=eqn_dlgdpall33) dlgdpall
impulse(noprint) 1 nstep 1
# eqn_dlgdpall33 impres
graph(nodates,header='Response: ARMA(3,3) on detrended total per capita logs') 1
# impres
*
boxjenk(ar=1,diffs=0,ma=1,constant,iterations=50,define=eqn_dlgdpall11) dlgdpall
impulse(noprint) 1 nstep 1
# eqn_dlgdpall11 impres
graph(nodates,header='Response: ARMA(1,1) on detrended total per capita logs') 1
# impres
*
*  COMPUTE IMPULSE RESPONSES ON LOGGED 16+ PER CAPITA SERIES
*
boxjenk(ar=2,diffs=0,ma=2,constant,iterations=50,define=eqn_dlgdp1622) dlgdp16
impulse(noprint) 1 nstep 1
# eqn_dlgdp1622 impres
graph(nodates,header='Response: ARMA(2,2) on detrended 16+ per capita logs') 1
# impres
*
boxjenk(ar=2,diffs=0,ma=1,constant,iterations=50,define=eqn_dlgdp1621) dlgdp16
impulse(noprint) 1 nstep 1
# eqn_dlgdp1621 impres
graph(nodates,header='Response: ARMA(2,1) on detrended 16+ per capita logs') 1
# impres
*
boxjenk(ar=3,diffs=0,ma=3,constant,iterations=50,define=eqn_dlgdp1633) dlgdp16
impulse(noprint) 1 nstep 1
# eqn_dlgdp1633 impres
graph(nodates,header='Response: ARMA(3,3) on detrended 16+ per capita logs') 1
# impres
*
boxjenk(ar=1,diffs=0,ma=1,constant,iterations=50,define=eqn_dlgdp1611) dlgdp16
impulse(noprint) 1 nstep 1
# eqn_dlgdp1611 impres
graph(nodates,header='Response: ARMA(1,1) on detrended 16+ per capita logs') 1
# impres