Specifying the Regression Model

Next, specify the linear regression model with a MODEL statement, as shown in the following statements.

```   proc tscsreg data=a;
id state date;
model y = x1 x2;
run;
```

The MODEL statement in PROC TSCSREG is specified like the MODEL statement in other SAS regression procedures: the dependent variable is listed first, followed by an equal sign, followed by the list of regressor variables.

The reason for using PROC TSCSREG instead of other SAS regression procedures is that you can incorporate a model for the structure of the random errors. It is important to consider what kind of error structure model is appropriate for your data and to specify the corresponding option in the MODEL statement.

The error structure options supported by the TSCSREG procedure are FIXONE, FIXTWO, RANONE, RANTWO, FULLER, PARKS, and DASILVA. See Details: The TSCSREG Procedure for more information about these methods and the error structures they assume.

By default, the two-way random-effects error model structure is used while Fuller-Battese and Wansbeek-Kapteyn methods are used for the estimation of variance components in balanced data and unbalanced data, respectively. Thus, the preceding example is the same as specifying the RANTWO option, as shown in the following statements:

```   proc tscsreg data=a;
id state date;
model y = x1 x2 / rantwo;
run;
```

You can specify more than one error structure option in the MODEL statement; the analysis is repeated using each method specified. You can use any number of MODEL statements to estimate different regression models or estimate the same model by using different options.

In order to aid in model specification within this class of models, the procedure provides two specification test statistics. The first is an F statistic that tests the null hypothesis that the fixed-effects parameters are all zero. The second is a Hausman m-statistic that provides information about the appropriateness of the random-effects specification. It is based on the idea that, under the null hypothesis of no correlation between the effects variables and the regressors, OLS and GLS are consistent, but OLS is inefficient. Hence, a test can be based on the result that the covariance of an efficient estimator with its difference from an inefficient estimator is zero. Rejection of the null hypothesis might suggest that the fixed-effects model is more appropriate.

The procedure also provides the Buse R-square measure, which is the most appropriate goodness-of-fit measure for models estimated by using GLS. This number is interpreted as a measure of the proportion of the transformed sum of squares of the dependent variable that is attributable to the influence of the independent variables. In the case of OLS estimation, the Buse R-square measure is equivalent to the usual R-square measure.