### 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| Unpublished thesis, Chicago, 1958                          |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;
1935     33.1      1170.6    97.8      12.93     191.5     1.8

... 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 ge_i 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 R-Square 27.8827 0.70531 102.29 0.67064 27.2585

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 wh_i 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 R-Square 10.2131 0.74445 42.8915 0.71438 23.8115

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 34 0.6284

Model GE ge_i 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 wh_i 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