Simulating Klein's Model I
/*--------------------------------------------------------------
SAS Sample Library
Name: simex01.sas
Description: Example program from SAS/ETS User's Guide,
The SIMLIN Procedure
Title: Simulating Klein's Model I
Product: SAS/ETS Software
Keys: structural equations
PROC: SIMLIN
Notes:
--------------------------------------------------------------*/
data klein;
input year c p w i x wp g t k wsum;
date=mdy(1,1,year);
format date year.;
y = c + i + g - t;
yr = year - 1931;
klag = lag( k );
plag = lag( p );
xlag = lag( x );
if year >= 1921;
label c ='consumption'
p ='profits'
w ='private wage bill'
i ='investment'
k ='capital stock'
y ='national income'
x ='private production'
wsum='total wage bill'
wp ='govt wage bill'
g ='govt demand'
t ='taxes'
klag='capital stock lagged'
plag='profits lagged'
xlag='private product lagged'
yr ='year-1931';
datalines;
1920 . 12.7 . . 44.9 . . . 182.8 .
1921 41.9 12.4 25.5 -0.2 45.6 2.7 3.9 7.7 182.6 28.2
1922 45.0 16.9 29.3 1.9 50.1 2.9 3.2 3.9 184.5 32.2
1923 49.2 18.4 34.1 5.2 57.2 2.9 2.8 4.7 189.7 37.0
1924 50.6 19.4 33.9 3.0 57.1 3.1 3.5 3.8 192.7 37.0
1925 52.6 20.1 35.4 5.1 61.0 3.2 3.3 5.5 197.8 38.6
1926 55.1 19.6 37.4 5.6 64.0 3.3 3.3 7.0 203.4 40.7
1927 56.2 19.8 37.9 4.2 64.4 3.6 4.0 6.7 207.6 41.5
1928 57.3 21.1 39.2 3.0 64.5 3.7 4.2 4.2 210.6 42.9
1929 57.8 21.7 41.3 5.1 67.0 4.0 4.1 4.0 215.7 45.3
1930 55.0 15.6 37.9 1.0 61.2 4.2 5.2 7.7 216.7 42.1
1931 50.9 11.4 34.5 -3.4 53.4 4.8 5.9 7.5 213.3 39.3
1932 45.6 7.0 29.0 -6.2 44.3 5.3 4.9 8.3 207.1 34.3
1933 46.5 11.2 28.5 -5.1 45.1 5.6 3.7 5.4 202.0 34.1
1934 48.7 12.3 30.6 -3.0 49.7 6.0 4.0 6.8 199.0 36.6
1935 51.3 14.0 33.2 -1.3 54.4 6.1 4.4 7.2 197.7 39.3
1936 57.7 17.6 36.8 2.1 62.7 7.4 2.9 8.3 199.8 44.2
1937 58.7 17.3 41.0 2.0 65.0 6.7 4.3 6.7 201.8 47.7
1938 57.5 15.3 38.2 -1.9 60.9 7.7 5.3 7.4 199.9 45.9
1939 61.6 19.0 41.6 1.3 69.5 7.8 6.6 8.9 201.2 49.4
1940 65.0 21.1 45.0 3.3 75.7 8.0 7.4 9.6 204.5 53.0
1941 69.7 23.5 53.3 4.9 88.4 8.5 13.8 11.6 209.4 61.8
1942 . . . . . 8.5 13.8 11.6 . .
1943 . . . . . 8.5 13.8 12.6 . .
1944 . . . . . 8.5 13.8 11.6 . .
1945 . . . . . 8.5 13.8 11.6 . .
1946 . . . . . 8.5 13.8 11.6 . .
1947 . . . . . 8.5 13.8 11.6 . .
;
title1 'Simulation of Klein''s Model I using SIMLIN';
proc syslin 3sls data=klein outest=a;
instruments klag plag xlag wp g t yr;
endogenous c p w i x wsum k y;
consume: model c = p plag wsum;
invest: model i = p plag klag;
labor: model w = x xlag yr;
product: identity x = c + i + g;
income: identity y = c + i + g - t;
profit: identity p = x - w - t;
stock: identity k = klag + i;
wage: identity wsum = w + wp;
run;
proc print data=a;
run;
title1 'Simulation of Klein''s Model I using SIMLIN';
proc simlin data=klein
est=a type=3sls
estprint
total interim=2
outest=b;
endogenous c p w i x wsum k y;
exogenous wp g t yr;
lagged klag k 1 plag p 1 xlag x 1;
id year;
output out=c p=chat phat what ihat xhat wsumhat khat yhat
r=cres pres wres ires xres wsumres kres yres;
run;
proc print data=b;
where _type_ = 'REDUCED' | _type_ = 'IMULT1';
run;
title2 'Plots of Simulation Results';
proc sgplot data=c;
scatter x=year y=c;
series x=year y=chat / markers markerattrs=(symbol=plus);
refline 1941.5 / axis=x;
run;
