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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   | Unpublished thesis, Chicago, 1958                          |                      |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 27.88272 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

 
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

 
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 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

 
The SYSLIN Procedure
Seemingly Unrelated Regression Estimation

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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