The AUTOREG Procedure

The RESTRICT statement provides constrained estimation and places restrictions on the parameter estimates for covariates in the preceding MODEL statement. The AR, GARCH, and HETERO parameters are also supported in the RESTRICT statement when you specify the GARCH= option. Any number of RESTRICT statements can follow a MODEL statement. To specify more than one restriction in a single RESTRICT statement, separate them with commas.

Each restriction is written as a linear equation composed of constants and parameter names. Refer to model parameters by the name of the corresponding regressor variable. Each name that is used in the equation must be a regressor in the preceding MODEL statement. Use the keyword INTERCEPT to refer to the intercept parameter in the model. For the names of these parameters, see the section OUTEST= Data Set. Inequality constraints are supported only when you specify the GARCH= option. For non-GARCH models, if inequality signs are specified, they are treated as equality signs.

The following is an example of a RESTRICT statement:

model y = a b c d;
restrict a+b=0, 2*d-c=0;

When restricting a linear combination of parameters to be 0, you can omit the equal sign. For example, the following RESTRICT statement is equivalent to the preceding example:

restrict a+b, 2*d-c;

The following RESTRICT statement constrains the parameters estimates for three regressors (X1, X2, and X3) to be equal:

restrict x1 = x2, x2 = x3;

The preceding restriction can be abbreviated as follows:

restrict x1 = x2 = x3;

The following example shows how to specify AR, GARCH, and HETERO parameters in the RESTRICT statement:

model y = a b / nlag=2 garch=(p=2,q=3,mean=sqrt);
hetero c d;
restrict _A_1=0,_AH_2=0.2,_HET_2=1,_DELTA_=0.1;

You can specify only simple linear combinations of parameters in RESTRICT statement expressions. You cannot specify complex expressions that involve parentheses, division, functions, or complex products.