PROC SYSLIN: Grunfeld’s Model Estimated with SUR

The SYSLIN Procedure

Example 27.2 Grunfeld’s Model Estimated with SUR

The following example was used by Zellner in his classic 1962 paper on seemingly unrelated regressions. Different stock prices often move in the same direction at a given point in time. The SUR technique might provide more efficient estimates than OLS in this situation.

The following statements read the data. (The prefix GE stands for General Electric and WH stands for Westinghouse.)

*---------Zellner's Seemingly Unrelated Technique------------*
| A. Zellner, "An Efficient Method of Estimating Seemingly   |
| Unrelated Regressions and Tests for Aggregation Bias,"     |
| JASA 57(1962) pp.348-364                                   |
|                                                            |
| J.C.G. Boot, "Investment Demand: an Empirical Contribution |
| to the Aggregation Problem," IER 1(1960) pp.3-30.          |
|                                                            |
| Y. Grunfeld, "The Determinants of Corporate Investment,"   |
| Unpublished thesis, Chicago, 1958                          |
*------------------------------------------------------------*;

data grunfeld;
   input year ge_i ge_f ge_c wh_i wh_f wh_c;
   label ge_i = 'Gross Investment, GE'
         ge_c = 'Capital Stock Lagged, GE'
         ge_f = 'Value of Outstanding Shares Lagged, GE'
         wh_i = 'Gross Investment, WH'
         wh_c = 'Capital Stock Lagged, WH'
         wh_f = 'Value of Outstanding Shares Lagged, WH';
datalines;

   ... more lines ...

The following statements compute the SUR estimates for the Grunfeld model.

proc syslin data=grunfeld sur;
   ge:      model ge_i = ge_f ge_c;
   westing: model wh_i = wh_f wh_c;
run;

The PROC SYSLIN output is shown in Output 27.2.1 through Output 27.2.5.

Output 27.2.1 PROC SYSLIN Output for SUR

The SYSLIN Procedure

Ordinary Least Squares Estimation

Model	GE
Dependent Variable	ge_i
Label	Gross Investment, GE

Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	2	31632.03	15816.02	20.34	<.0001
Error	17	13216.59	777.4463
Corrected Total	19	44848.62

Root MSE	27.88272	R-Square	0.70531
Dependent Mean	102.29000	Adj R-Sq	0.67064
Coeff Var	27.25850

Parameter Estimates
Variable	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|	Variable Label
Intercept	1	-9.95631	31.37425	-0.32	0.7548	Intercept
ge_f	1	0.026551	0.015566	1.71	0.1063	Value of Outstanding Shares Lagged, GE
ge_c	1	0.151694	0.025704	5.90	<.0001	Capital Stock Lagged, GE

Output 27.2.2 PROC SYSLIN Output for SUR

The SYSLIN Procedure

Ordinary Least Squares Estimation

Model	WESTING
Dependent Variable	wh_i
Label	Gross Investment, WH

Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	2	5165.553	2582.776	24.76	<.0001
Error	17	1773.234	104.3079
Corrected Total	19	6938.787

Root MSE	10.21312	R-Square	0.74445
Dependent Mean	42.89150	Adj R-Sq	0.71438
Coeff Var	23.81153

Parameter Estimates
Variable	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|	Variable Label
Intercept	1	-0.50939	8.015289	-0.06	0.9501	Intercept
wh_f	1	0.052894	0.015707	3.37	0.0037	Value of Outstanding Shares Lagged, WH
wh_c	1	0.092406	0.056099	1.65	0.1179	Capital Stock Lagged, WH

Output 27.2.3 PROC SYSLIN Output for SUR

The SYSLIN Procedure

Seemingly Unrelated Regression Estimation

Cross Model Covariance
	GE	WESTING
GE	777.446	207.587
WESTING	207.587	104.308

Cross Model Correlation
	GE	WESTING
GE	1.00000	0.72896
WESTING	0.72896	1.00000

Cross Model Inverse Correlation
	GE	WESTING
GE	2.13397	-1.55559
WESTING	-1.55559	2.13397

Cross Model Inverse Covariance
	GE	WESTING
GE	0.002745	-.005463
WESTING	-.005463	0.020458

Output 27.2.4 PROC SYSLIN Output for SUR

System Weighted MSE	0.9719
Degrees of freedom	34
System Weighted R-Square	0.6284

Model	GE
Dependent Variable	ge_i
Label	Gross Investment, GE

Parameter Estimates
Variable	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|	Variable Label
Intercept	1	-27.7193	29.32122	-0.95	0.3577	Intercept
ge_f	1	0.038310	0.014415	2.66	0.0166	Value of Outstanding Shares Lagged, GE
ge_c	1	0.139036	0.024986	5.56	<.0001	Capital Stock Lagged, GE

Output 27.2.5 PROC SYSLIN Output for SUR

Model	WESTING
Dependent Variable	wh_i
Label	Gross Investment, WH

Parameter Estimates
Variable	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|	Variable Label
Intercept	1	-1.25199	7.545217	-0.17	0.8702	Intercept
wh_f	1	0.057630	0.014546	3.96	0.0010	Value of Outstanding Shares Lagged, WH
wh_c	1	0.063978	0.053041	1.21	0.2443	Capital Stock Lagged, WH

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