The MODEL Procedure

The INSTRUMENTS statement specifies the instrumental variables to be used in the N2SLS, N3SLS, IT2SLS, IT3SLS, GMM, and ITGMM estimation methods.

There are three ways of specifying the INSTRUMENTS statement. The first form of the INSTRUMENTS statement is declared before a FIT statement and defines the default instruments list. The items specified as instruments can be variables or the special keyword _EXOG_. The keyword _EXOG_ indicates that all the model variables declared EXOGENOUS are to be added to the instruments list. If a single INSTRUMENTS statement of the first form is declared before multiple FIT statements, then it serves as the default instruments list for each of the FIT statements. However, if any of these FIT statements are followed by separate INSTRUMENTS statement, then the latter take precedence over the default list. Hence, in the case of multiple FIT statements, the INSTRUMENTS statement for a particular FIT statement is written below the FIT statement if instruments other than the default are required. For a single FIT statement, you can declare the INSTRUMENTS statement of the first form either preceding or following the FIT statement.

The second form of the INSTRUMENTS statement is used only after the FIT statement and before the next RUN statement. The items specified as instruments for the second form can be variables, names of parameters to be estimated, or the special keyword _EXOG_. If you specify the name of a parameter in the instruments list, the partial derivatives of the equations with respect to the parameter (that is, the columns of the Jacobian matrix associated with the parameter) are used as instruments. The parameter itself is not used as an instrument. These partial derivatives should not depend on any of the parameters to be estimated. Only the names of parameters to be estimated can be specified.

Note that an INSTRUMENTS statement of only the first form declared before multiple FIT statements serves as the default instruments list. Hence, in the cases of multiple as well as single FIT statements, you can declare the second form of INSTRUMENTS statements only following the FIT statements.

In the case where a FIT statement is preceded by an INSTRUMENTS statement of the second form in error and not followed by any INSTRUMENTS statement, then the default list is used. This default list is given by the INSTRUMENTS statement of the first form as explained above. If such a list is not declared, all the model variables declared EXOGENOUS comprise the default.

A third form of the INSTRUMENTS statement is used to specify instruments for each equation. No explicit intercept is added, parameters cannot be specified to represent instruments, and the _EXOG_ keyword is not allowed. Equations not explicitly assigned instruments use all the instruments specified for the other equations as well as instruments not assigned specific equations. In the following statements, z1, z2, and z3 are instruments used with equation y1, and z2, z3, and z4 are instruments used with equation y2.

proc model data=data_sim;
   exogenous x1 x2;
   parms a b c d e f;

   y1 =a*x1**2 + b*x2**2 + c*x1*x2   ;
   y2 =d*x1**2 + e*x2**2 + f*x1*x2**2;

   fit y1 y2 / 3sls ;
   instruments (y1, z1 z2 z3) (y2,z2 z3 z4);
run;