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. For more information, see the section Reduced Form Estimates.

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 3, Figure 4, Figure 5, and Figure 6.) The final page of the output from this example contains the reduced form coefficients from the 3SLS structural estimates, as shown in Figure 8.

Figure 8: Reduced Form 3SLS Results

The SYSLIN Procedure
Three-Stage Least Squares Estimation

Endogenous Variables
 pq
DEMAND1.1765431
SUPPLY-1.333081

Exogenous Variables
 Interceptysu
DEMAND1.9802690.4041170.3592040
SUPPLY-0.5187800-1.14623

Inverse Endogenous Variables
 DEMANDSUPPLY
p0.398466-0.39847
q0.5311870.468813

Reduced Form
 Interceptysu
p0.9957880.1610270.1431310.456735
q0.8086820.2146620.190804-0.53737


Last updated: June 19, 2025