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 0.015.

```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 29.10. 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 0.0104, which indicates that the hypothesis tested is almost but not quite rejected at the 0.01 level. See the section TEST Statement for details.

Figure 29.10: TEST Statement Results

The SYSLIN Procedure
Three-Stage Least Squares Estimation

 System Weighted MSE 0.5711 113 0.9627

Model DEMAND q Quantity

Parameter Estimates
Variable DF Parameter
Estimate
Standard
Error
t Value Pr > |t| Variable
Label
Intercept 1 1.980269 1.169176 1.69 0.0959 Intercept
p 1 -1.17654 0.605015 -1.94 0.0568 Price
y 1 0.404117 0.117179 3.45 0.0011 Income
s 1 0.359204 0.085077 4.22 <.0001 Price of Substitutes

Test Results
Num DF Den DF F Value Pr > F Label
1 113 6.79 0.0104 TEST_1

To test hypotheses that involve 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 0.01 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 29.11. The form and interpretation of the STEST statement results are like the TEST statement results. In this case, the F test produces a p value less than 0.0001, and strongly rejects the hypothesis tested. See the section STEST Statement for details.

Figure 29.11: STEST Statement Results

The SYSLIN Procedure
Three-Stage Least Squares Estimation

 System Weighted MSE 0.5711 113 0.9627

Model DEMAND q Quantity

Parameter Estimates
Variable DF Parameter
Estimate
Standard
Error
t Value Pr > |t| Variable
Label
Intercept 1 1.980269 1.169176 1.69 0.0959 Intercept
p 1 -1.17654 0.605015 -1.94 0.0568 Price
y 1 0.404117 0.117179 3.45 0.0011 Income
s 1 0.359204 0.085077 4.22 <.0001 Price of Substitutes

Model SUPPLY q Quantity

Parameter Estimates
Variable DF Parameter
Estimate
Standard
Error
t Value Pr > |t| Variable
Label
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
Num DF Den DF F Value Pr > F Label
1 113 22.46 0.0001 STEST1

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 depends on the correctness of any restrictions you impose on the estimates.