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 1, and the output for the supply equation is shown in Figure 2.

Figure 1: OLS Results for Demand Equation

The SYSLIN Procedure
Ordinary Least Squares Estimation

ModelDEMAND
Dependent Variableq
LabelQuantity

Analysis of Variance
SourceDFSum of SquaresMean SquareF ValuePr > F
Model39.5879013.195967398.31<.0001
Error560.4493380.008024  
Corrected Total5910.03724   

Root MSE0.08958R-Square0.95523
Dependent Mean1.30095Adj R-Sq0.95283
Coeff Var6.88542  

Parameter Estimates
VariableDFParameter
Estimate
Standard
Error
t ValuePr > |t|Variable
Label
Intercept1-0.476770.210239-2.270.0272Intercept
p10.1233260.1051771.170.2459Price
y10.2012820.0324036.21<.0001Income
s10.1672580.0240916.94<.0001Price of Substitutes


Figure 2: OLS Results for Supply Equation

The SYSLIN Procedure
Ordinary Least Squares Estimation

ModelSUPPLY
Dependent Variableq
LabelQuantity

Analysis of Variance
SourceDFSum of SquaresMean SquareF ValuePr > F
Model29.0339024.516951256.61<.0001
Error571.0033370.017602  
Corrected Total5910.03724   

Root MSE0.13267R-Square0.90004
Dependent Mean1.30095Adj R-Sq0.89653
Coeff Var10.19821  

Parameter Estimates
VariableDFParameter
Estimate
Standard
Error
t ValuePr > |t|Variable
Label
Intercept1-0.303890.471397-0.640.5217Intercept
p11.2187430.05391422.61<.0001Price
u1-1.077570.234150-4.60<.0001Unit Cost


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 squared error, dependent variable mean and coefficient of variation, and the upper R squared and adjusted upper R squared 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 (0.1233) has a positive sign. This could be caused by simultaneous equation bias.

Last updated: June 19, 2025