PROC SYSLIN: OLS Estimation :: SAS/ETS(R) 9.22 User's Guide

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 27.1, and the output for the supply equation is shown in Figure 27.2.

Figure 27.1 OLS Results for Demand Equation

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	9.587901	3.195967	398.31	<.0001
Error	56	0.449338	0.008024
Corrected Total	59	10.03724

Root MSE	0.08958	R-Square	0.95523
Dependent Mean	1.30095	Adj R-Sq	0.95283
Coeff Var	6.88542

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	0.123326	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 27.2 OLS Results for Supply 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	9.033902	4.516951	256.61	<.0001
Error	57	1.003337	0.017602
Corrected Total	59	10.03724

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	-0.30389	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

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 $\text{[math]}$ and adjusted $\text{[math]}$ 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.

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