# The SYSLIN Procedure

### Computing Reduced Form Estimates

A system of structural equations with endogenous regressors can be represented as functions of only the predetermined variables. For this to be possible, there must be as many equations as endogenous variables. If there are more endogenous variables than regression models, you can use IDENTITY statements to complete the system. See the section Reduced Form Estimates for details.

The REDUCED option in the PROC SYSLIN statement prints reduced form estimates. The following statements show this by using the 3SLS estimates of the structural parameters.

```proc syslin data=in 3sls reduced;
endogenous  p;
instruments y u s;
demand: model q = p y s;
supply: model q = p u;
run;
```

The first four pages of this output were as shown previously and are not repeated here. (See Figure 29.3, Figure 29.4, Figure 29.5, and Figure 29.6.) The final page of the output from this example contains the reduced form coefficients from the 3SLS structural estimates, as shown in Figure 29.8.

Figure 29.8: Reduced Form 3SLS Results

The SYSLIN Procedure
Three-Stage Least Squares Estimation

Endogenous Variables
p q
DEMAND 1.176543 1
SUPPLY -1.33308 1

Exogenous Variables
Intercept y s u
DEMAND 1.980269 0.404117 0.359204 0
SUPPLY -0.51878 0 0 -1.14623

Inverse Endogenous Variables
DEMAND SUPPLY
p 0.398466 -0.39847
q 0.531187 0.468813

Reduced Form
Intercept y s u
p 0.995788 0.161027 0.143131 0.456735
q 0.808682 0.214662 0.190804 -0.53737