Example 29.2 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| Unpublished thesis, Chicago, 1958                          |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 29.2.1 through Output 29.2.5.

Output 29.2.1 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 29.2.2 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 29.2.3 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 29.2.4 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 29.2.5 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