Chapter Contents Previous Next
 The SYSLIN Procedure

## Example 19.2: 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 may 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| Unpublished thesis, Chicago, 1958                          |                      |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';
cards;
1935     33.1      1170.6    97.8      12.93     191.5     1.8
1936     45.0      2015.8    104.4     25.90     516.0     .8
1937     77.2      2803.3    118.0     35.05     729.0     7.4
1938     44.6      2039.7    156.2     22.89     560.4     18.1
1939     48.1      2256.2    172.6     18.84     519.9     23.5
1940     74.4      2132.2    186.6     28.57     628.5     26.5
1941     113.0     1834.1    220.9     48.51     537.1     36.2
1942     91.9      1588.0    287.8     43.34     561.2     60.8
1943     61.3      1749.4    319.9     37.02     617.2     84.4
1944     56.8      1687.2    321.3     37.81     626.7     91.2
1945     93.6      2007.7    319.6     39.27     737.2     92.4
1946     159.9     2208.3    346.0     53.46     760.5     86.0
1947     147.2     1656.7    456.4     55.56     581.4     111.1
1948     146.3     1604.4    543.4     49.56     662.3     130.6
1949     98.3      1431.8    618.3     32.04     583.8     141.8
1950     93.5      1610.5    647.4     32.24     635.2     136.7
1951     135.2     1819.4    671.3     54.38     723.8     129.7
1952     157.3     2079.7    726.1     71.78     864.1     145.5
1953     179.5     2371.6    800.3     90.08     1193.5    174.8
1954     189.6     2759.9    888.9     68.60     1188.9    213.5
;
```

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 19.2.1.

Output 19.2.1: 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 27.8827 R-Square 0.70531 Dependent Mean 102.29 Adj R-Sq 0.67064 Coeff Var 27.2585

 Parameter Estimates Variable DF ParameterEstimate Standard Error t Value Pr > |t| VariableLabel 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

 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 10.2131 R-Square 0.74445 Dependent Mean 42.8915 Adj R-Sq 0.71438 Coeff Var 23.8115

 Parameter Estimates Variable DF ParameterEstimate Standard Error t Value Pr > |t| VariableLabel 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

 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

 The SYSLIN Procedure Seemingly Unrelated Regression Estimation

 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 ParameterEstimate Standard Error t Value Pr > |t| VariableLabel 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

 The SYSLIN Procedure Seemingly Unrelated Regression Estimation

 Model WESTING Dependent Variable wh_i Label Gross Investment, WH

 Parameter Estimates Variable DF ParameterEstimate Standard Error t Value Pr > |t| VariableLabel 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

 Chapter Contents Previous Next Top