The SYSLIN Procedure

Example 36.2 Grunfeld’s Model Estimated with SUR

(View the complete code for this example.)

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| Unpublished thesis, Chicago, 1958                          |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 36.2.1 through Output 36.2.5.

Output 36.2.1: PROC SYSLIN Output for SUR

The SYSLIN Procedure
Ordinary Least Squares Estimation

ModelGE
Dependent Variablege_i
LabelGross Investment, GE

Analysis of Variance
SourceDFSum of SquaresMean SquareF ValuePr > F
Model231632.0315816.0220.34<.0001
Error1713216.59777.4463  
Corrected Total1944848.62   

Root MSE27.88272R-Square0.70531
Dependent Mean102.29000Adj R-Sq0.67064
Coeff Var27.25850  

Parameter Estimates
VariableDFParameter
Estimate
Standard
Error
t ValuePr > |t|Variable
Label
Intercept1-9.9563131.37425-0.320.7548Intercept
ge_f10.0265510.0155661.710.1063Value of Outstanding Shares Lagged, GE
ge_c10.1516940.0257045.90<.0001Capital Stock Lagged, GE


Output 36.2.2: PROC SYSLIN Output for SUR

The SYSLIN Procedure
Ordinary Least Squares Estimation

ModelWESTING
Dependent Variablewh_i
LabelGross Investment, WH

Analysis of Variance
SourceDFSum of SquaresMean SquareF ValuePr > F
Model25165.5532582.77624.76<.0001
Error171773.234104.3079  
Corrected Total196938.787   

Root MSE10.21312R-Square0.74445
Dependent Mean42.89150Adj R-Sq0.71438
Coeff Var23.81153  

Parameter Estimates
VariableDFParameter
Estimate
Standard
Error
t ValuePr > |t|Variable
Label
Intercept1-0.509398.015289-0.060.9501Intercept
wh_f10.0528940.0157073.370.0037Value of Outstanding Shares Lagged, WH
wh_c10.0924060.0560991.650.1179Capital Stock Lagged, WH


Output 36.2.3: PROC SYSLIN Output for SUR

The SYSLIN Procedure
Seemingly Unrelated Regression Estimation

Cross Model Covariance
 GEWESTING
GE777.446207.587
WESTING207.587104.308

Cross Model Correlation
 GEWESTING
GE1.000000.72896
WESTING0.728961.00000

Cross Model Inverse Correlation
 GEWESTING
GE2.13397-1.55559
WESTING-1.555592.13397

Cross Model Inverse Covariance
 GEWESTING
GE0.002745-.005463
WESTING-.0054630.020458


Output 36.2.4: PROC SYSLIN Output for SUR

System Weighted MSE0.9719
Degrees of freedom34
System Weighted R-Square0.6284

ModelGE
Dependent Variablege_i
LabelGross Investment, GE

Parameter Estimates
VariableDFParameter
Estimate
Standard
Error
t ValuePr > |t|Variable
Label
Intercept1-27.719329.32122-0.950.3577Intercept
ge_f10.0383100.0144152.660.0166Value of Outstanding Shares Lagged, GE
ge_c10.1390360.0249865.56<.0001Capital Stock Lagged, GE


Output 36.2.5: PROC SYSLIN Output for SUR

ModelWESTING
Dependent Variablewh_i
LabelGross Investment, WH

Parameter Estimates
VariableDFParameter
Estimate
Standard
Error
t ValuePr > |t|Variable
Label
Intercept1-1.251997.545217-0.170.8702Intercept
wh_f10.0576300.0145463.960.0010Value of Outstanding Shares Lagged, WH
wh_c10.0639780.0530411.210.2443Capital Stock Lagged, WH


Last updated: August 25, 2017