Computing Reduced Form Estimates

The SYSLIN Procedure

Computing Reduced Form Estimates

A system of structural equations with endogenous regressors can be represented as functions only of 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 "Reduced Form Estimates" in the "Computational Details" section later in this chapter for details.

The REDUCED option on the PROC SYSLIN statement prints reduced form estimates. The following statements show this 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 19.3, Figure 19.4, Figure 19.5, and Figure 19.6.) The final page of the output from this example contains the reduced form coefficients from the 3SLS structural estimates, as shown in Figure 19.8.

The SYSLIN Procedure

Three-Stage Least Squares Estimation

Endogenous Variables
	p	q
DEMAND	1.176539	1
SUPPLY	-1.33308	1

Exogenous Variables
	Intercept	y	s	u
DEMAND	1.980261	0.404115	0.359204	0
SUPPLY	-0.51878	0	0	-1.14623

Inverse Endogenous Variables
	DEMAND	SUPPLY
p	0.398467	-0.39847
q	0.531188	0.468812

Reduced Form
	Intercept	y	s	u
p	0.995786	0.161027	0.143131	0.456736
q	0.80868	0.214661	0.190805	-0.53737

Figure 19.8: Reduced Form 3SLS Results

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