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The SYSLIN Procedure

OLS Estimation

PROC SYSLIN performs OLS regression if you do not specify a method of estimation in the PROC SYSLIN statement. OLS does not use instruments, so the ENDOGENOUS and INSTRUMENTS statements can be omitted.

The following statements estimate the supply and demand model shown previously:


   proc syslin data=in;
      demand: model q = p y s;
      supply: model q = p u;
   run;

The PROC SYSLIN output for the demand equation is shown in Figure 19.1, and the output for the supply equation is shown in Figure 19.2.

 
The SYSLIN Procedure
Ordinary Least Squares Estimation

Model DEMAND
Dependent Variable q
Label Quantity
 
Analysis of Variance
Source DF Sum of Squares Mean Square F Value Pr > F
Model 3 9.587891 3.195964 398.31 <.0001
Error 56 0.449336 0.008024    
Corrected Total 59 10.03723      
 
Root MSE 0.08958 R-Square 0.95523
Dependent Mean 1.30095 Adj R-Sq 0.95283
Coeff Var 6.88541    
 
Parameter Estimates
Variable DF Parameter
Estimate
Standard Error t Value Pr > |t| Variable
Label
Intercept 1 -0.47677 0.210239 -2.27 0.0272 Intercept
p 1 0.123324 0.105177 1.17 0.2459 Price
y 1 0.201282 0.032403 6.21 <.0001 Income
s 1 0.167258 0.024091 6.94 <.0001 Price of Substitutes
Figure 19.1: OLS Results for Demand Equation

 
The SYSLIN Procedure
Ordinary Least Squares Estimation

Model SUPPLY
Dependent Variable q
Label Quantity
 
Analysis of Variance
Source DF Sum of Squares Mean Square F Value Pr > F
Model 2 9.033890 4.516945 256.61 <.0001
Error 57 1.003337 0.017602    
Corrected Total 59 10.03723      
 
Root MSE 0.13267 R-Square 0.90004
Dependent Mean 1.30095 Adj R-Sq 0.89653
Coeff Var 10.19821    
 
Parameter Estimates
Variable DF Parameter
Estimate
Standard Error t Value Pr > |t| Variable
Label
Intercept 1 -0.30390 0.471397 -0.64 0.5217 Intercept
p 1 1.218743 0.053914 22.61 <.0001 Price
u 1 -1.07757 0.234150 -4.60 <.0001 Unit Cost
Figure 19.2: OLS Results for Supply Equation

For each MODEL statement, the output first shows the model label and dependent variable name and label. This is followed by an Analysis of Variance table for the model, which shows the model, error, and total mean squares, and an F test for the no-regression hypothesis. Next, the procedure prints the root mean square error, dependent variable mean and coefficient of variation, and the R2 and adjusted R2 statistics.

Finally, the table of parameter estimates shows the estimated regression coefficients, standard errors, and t-tests. You would expect the price coefficient in a demand equation to be negative. However, note that the OLS estimate of the price coefficient P in the demand equation (.1233) has a positive sign. This could be caused by simultaneous equation bias.

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