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 The SYSLIN Procedure

## Two-Stage Least Squares Estimation

In the supply and demand model, P is an endogenous variable, and consequently the OLS estimates are biased. The following example estimates this model using two-stage least squares:

```
proc syslin data=in 2sls;
endogenous  p;
instruments y u s;
demand: model q = p y s;
supply: model q = p u;
run;
```

The 2SLS option on the PROC SYSLIN statement specifies the two-stage least-squares method. The ENDOGENOUS statement specifies that P is an endogenous regressor for which first-stage predicted values are substituted. You only need to declare an endogenous variable in the ENDOGENOUS statement if it is used as a regressor; thus although Q is endogenous in this model, it is not necessary to list it in the ENDOGENOUS statement.

Usually, all predetermined variables that appear in the system are used as instruments. The INSTRUMENTS statement specifies that the exogenous variables Y, U, and S are used as instruments for the first-stage regression to predict P.

The 2SLS results are shown in Figure 19.3 and Figure 19.4. The first-stage regressions are not shown. To see the first-stage regression results, use the FIRST option on the MODEL statement.

 The SYSLIN Procedure Two-Stage 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 9.670882 3.223627 115.58 <.0001 Error 56 1.561944 0.027892 Corrected Total 59 10.03723

 Root MSE 0.16701 R-Square 0.86095 Dependent Mean 1.30095 Adj R-Sq 0.85350 Coeff Var 12.8374

 Parameter Estimates Variable DF ParameterEstimate Standard Error t Value Pr > |t| VariableLabel Intercept 1 1.901040 1.171224 1.62 0.1102 Intercept p 1 -1.11518 0.607391 -1.84 0.0717 Price y 1 0.419544 0.117954 3.56 0.0008 Income s 1 0.331475 0.088472 3.75 0.0004 Price of Substitutes
Figure 19.3: 2SLS Results for Demand Equation

 The SYSLIN Procedure Two-Stage 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 9.646098 4.823049 253.96 <.0001 Error 57 1.082503 0.018991 Corrected Total 59 10.03723

 Root MSE 0.13781 R-Square 0.89910 Dependent Mean 1.30095 Adj R-Sq 0.89556 Coeff Var 10.5929

 Parameter Estimates Variable DF ParameterEstimate Standard Error t Value Pr > |t| VariableLabel Intercept 1 -0.51878 0.490999 -1.06 0.2952 Intercept p 1 1.333080 0.059271 22.49 <.0001 Price u 1 -1.14623 0.243491 -4.71 <.0001 Unit Cost
Figure 19.4: 2SLS Results for Supply Equation

The 2SLS output is similar in form to the OLS output. However, the 2SLS results are based on predicted values for the endogenous regressors from the first stage instrumental regressions. This makes the analysis of variance table and the R2 statistics difficult to interpret. See the sections "ANOVA Table for Instrumental Variables Methods" and "The R2 Statistics" later in this chapter for details.

Note that, unlike the OLS results, the 2SLS estimate for the P coefficient in the demand equation (-1.115) is negative.

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