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 The SYSLIN Procedure

## Testing Parameters

You can test linear hypotheses about the model parameters with TEST and STEST statements. The TEST statement tests hypotheses about parameters in the equation specified by the preceding MODEL statement. The STEST statement tests hypotheses that relate parameters in different models.

For example, the following statements test the hypothesis that the price coefficient in the demand equation is equal to .015.

```
proc syslin data=in 3sls;
endogenous  p;
instruments y u s;
demand: model q = p y s;
test_1: test p = .015;
supply: model q = p u;
run;
```

The TEST statement results are shown in Figure 19.10. This reports an F-test for the hypothesis specified by the TEST statement. In this case the F statistic is 6.79 (3.879/.571) with 1 and 113 degrees of freedom. The p-value for this F statistic is .0104, which indicates that the hypothesis tested is almost but not quite rejected at the .01 level. See the section "TEST Statement" for more information.

 The SYSLIN Procedure Three-Stage Least Squares Estimation

 System Weighted MSE 0.5711 Degrees of freedom 113 System Weighted R-Square 0.9627

 Model DEMAND Dependent Variable q Label Quantity

 Parameter Estimates Variable DF ParameterEstimate Standard Error t Value Pr > |t| VariableLabel Intercept 1 1.980261 1.169169 1.69 0.0959 Intercept p 1 -1.17654 0.605012 -1.94 0.0568 Price y 1 0.404115 0.117179 3.45 0.0011 Income s 1 0.359204 0.085077 4.22 <.0001 Price of Substitutes

 Test Results for Variable TEST_1 Num DF Den DF F Value Pr > F 1 113 6.79 0.0104
Figure 19.10: TEST Statement Results

To test hypotheses involving parameters in different equations, use the STEST statement. Specify the parameters in the linear hypothesis as model-label.regressor-name. (If the MODEL statement does not have a label, you can use the dependent variable name as the label for the model, provided the dependent variable uniquely labels the model.)

For example, the following statements test the hypothesis that the income coefficient in the demand equation is .01 times the unit cost coefficient in the supply equation:

```
proc syslin data=in 3sls;
endogenous  p;
instruments y u s;
demand: model q = p y s;
supply: model q = p u;
stest1: stest demand.y = .01 * supply.u;
run;
```

The STEST statement results are shown in Figure 19.11. The form and interpretation of the STEST statement results is like the TEST statement results. In this case, the F-test produces a p-value less than .0001, and strongly rejects the hypothesis tested. See the section "STEST Statement" for more information.

 The SYSLIN Procedure Three-Stage Least Squares Estimation

 System Weighted MSE 0.5711 Degrees of freedom 113 System Weighted R-Square 0.9627

 Model DEMAND Dependent Variable q Label Quantity

 Parameter Estimates Variable DF ParameterEstimate Standard Error t Value Pr > |t| VariableLabel Intercept 1 1.980261 1.169169 1.69 0.0959 Intercept p 1 -1.17654 0.605012 -1.94 0.0568 Price y 1 0.404115 0.117179 3.45 0.0011 Income s 1 0.359204 0.085077 4.22 <.0001 Price of Substitutes

 Model SUPPLY Dependent Variable q Label Quantity

 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

 Test Results for Variable STEST1 Num DF Den DF F Value Pr > F 1 113 22.46 0.0001
Figure 19.11: STEST Statement Results

You can combine TEST and STEST statements with RESTRICT and SRESTRICT statements to perform hypothesis tests for restricted models. Of course, the validity of the TEST and STEST statement results will depend on the correctness of any restrictions you impose on the estimates.

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