/* Data: Taken from FRED data base on the Federal Reserve Bank of St. Louis website. The data span
the period 1978:01 - 2010:10. The two series are the Consumer Sentiment Index (NSA), Survey Research
Center, University of Michigan and the Conference Board and Total Industrial Production (SA). The
estimation of the below model was done using EVIEWS 6 and a program called csi_a_new.wf1. */
/* This program is intended to demonstrate the effects of a pulse change in x(t)
on the industrial production annual growth regression. The ARDL model is
growa(t) = -6.990220 + 0.100663*growa(t-1) + 0.186323*growa(t-2) + 0.116898*growa(t-3)
0.414086*csi(t-1) - 0.318151*csi(t-3) */
/* Holding csi at its mean of 86.18604 indefinitely gives rise to the steady state (equilibrium) of growa:
growa(steady state) = -6.990220/(1 - 0.100663 - 0.186323 - 0.116898) + (0.414086 - 0.318151)*86.18604/(1 - 0.100663 - 0.186323 - 0.116898)
= 2.143941.
*/
/* Here we examine the effect of keeping csi at its mean = 86.18604 for t = -20, -19,
... -1 and then at time t = 0 make x(t) = 86.18604 + 1 = 87.18604 and then in time = 1 return csi back to 86.18604.
This will allow us to plot the dynamic multipiers associated with a PULSE change in csi on the dependent variable of the model.
In a subsequent set of graphs we look at the effect of a STEP change in csi on the dependent variable. */
/* Looking at the step function results, the interim multipliers are as follows:
t = 0: 2.14394 - 2.14394 = 0 i.e. there is no immediate impact
t = 1: 2.23988 - 2.14394 = 0.09594
t = 2: 2.27862 - 2.23988 = 0.03874
t = 3: 2.29427 - 2.27862 = 0.01565
t = 4: 2.30059 - 2.29427 = 0.00632
t = 5: 2.30315 - 2.30059 = 0.00256
t = 6: 2.30418 - 2.30315 = 0.00103
t = 7: 2.30459 - 2.30418 = 0.00041
t = 8: 2.30476 - 2.30459 = 0.00017
t = 9: 2.30483 - 2.30476 = 0.00007
t = 10: 2.30486 - 2.30483 = 0.00003
t = 11: 2.30487 - 2.30486 = 0.00001
t = 12: 2.30487 - 2.30487 = 0
The total multiplier is the sum of the interim multipliers above or can alternatively be calculated
as 2.30487 - 2.14394 = 0.16093.
*/
Options Nodate;
data dynamic;
yt=2.143941;
yt1=2.143941;
yt2=2.143941;
yt3=2.143941;
xt=86.18604;
xt1=86.18604;
xt2=86.18604;
xt3=86.18604;
do t = -20 to 20;
if t = 0 then xt = 87.18604;
if t = 1 then xt = 86.18604;
if t = 2 then xt1 = 86.18604;
if t = 3 then xt2 = 86.18604;
if t = 4 then xt3 = 86.18604;
yt = -6.990220 + 0.100663*yt1 + 0.186323*yt2 + 0.116898*yt3 +
0.414086*xt1 - 0.318151*xt3;
output;
yt1=yt;
yt2=yt1;
yt3=yt2;
xt1=xt;
xt2=xt1;
xt3=xt2;
end;
run;
title 'Pulse change in x(t) at time t = 0';
proc plot data=dynamic;
plot xt*t;
run;
title 'Effect of Pulse Change in x(t) on y(t)';
proc plot data=dynamic;
plot yt*t;
run;
proc print data=dynamic;
run;
data dynamic;
yt=2.143941;
yt1=2.143941;
yt2=2.143941;
yt3=2.143941;
xt=86.18604;
xt1=86.18604;
xt2=86.18604;
xt3=86.18604;
do t = -20 to 20;
if t = 0 then xt = 87.18604;
if t = 1 then xt = 87.18604;
if t = 2 then xt1 = 87.18604;
if t = 3 then xt2 = 87.18604;
if t = 4 then xt3 = 87.18604;
yt = -6.990220 + 0.100663*yt1 + 0.186323*yt2 + 0.116898*yt3 +
0.414086*xt1 - 0.318151*xt3;
output;
yt1=yt;
yt2=yt1;
yt3=yt2;
xt1=xt;
xt2=xt1;
xt3=xt2;
end;
run;
title 'Step change in x(t) at time t = 0';
proc plot data=dynamic;
plot xt*t;
run;
title 'Effect of Step Change in x(t) on y(t)';
proc plot data=dynamic;
plot yt*t;
run;
proc print data=dynamic;
run;