The PANEL Procedure

INSTRUMENTS Statement

INSTRUMENTS options;

The INSTRUMENTS statement selects variables to be used in the moment condition equations of the dynamic panel estimator. It is also used to specify variables that are correlated with individual effects during Hausman-Taylor (HTAYLOR) or Amemiya-MaCurdy (AMACURDY) estimation.

You can specify the following options:

CONSTANT: includes an intercept (column of ones) as an uncorrelated exogenous instrument.
CORRELATED=(variable variable … variable): specifies a list of variables correlated with the unobserved individual effects. These variables are correlated with the error terms in the level equations, so they are not used in forming moment conditions from those equations.
DEPVAR<(LEVEL | DIFF | DIFFERENCE | BOTH )>: specifies instruments related to the dependent variable. With LEVEL, the lagged dependent variables are included as instruments for differenced equations. With DIFFERENCE, the differenced dependent variable is included as instruments for equations. With BOTH or nothing specified, both level and differenced dependent variables are included in the instrument matrix.
DIFFEQ=(variable variable … variable) DIFFERENCEDEQ=(variable variable … variable): specifies a list of variables that can be used as standard instruments for the differenced equations.
EXOGENOUS=(variable variable … variable): specifies a list of variables that are not correlated with the disturbances given the unobserved individual effects.
LEVELEQ=(variable variable … variable) LEVELSEQ=(variable variable … variable): specifies a list of variables that can be used as standard instruments for the level equations.
PREDETERMINED=(variable variable … variable): specifies a list of variables whose future realizations can be correlated with the disturbances but whose present and past realizations are not conditional on the individual effects.

For estimation with dynamic panels, because a variable can be used as an instrument only if it is either exogenous or predetermined, the variables listed in the CORRELATED= option must be included in either the EXOGENOUS= list or the PREDETERMINED= list. If a variable listed in the EXOGENOUS= list is not included in the CORRELATED= list, then it is considered to be uncorrelated to the error term in the level equations, which consist only of the individual effects and the disturbances. Moreover, it is uncorrelated with the error term in the differenced equations, which consist only of the disturbances. For example, in the following statements, the exogenous instruments are Z1, Z2, and X1. Because Z1 is an instrument that is correlated with the individual fixed effects, it is included in the differenced equations but not in the level equations. Because Z2 is not correlated with either the individual effects or the disturbances, it is included in both the level equations and the differenced equations.

   proc panel data=a;
      instruments exogenous = (Z1 Z2 X1) correlated = (Z1) constant depvar;
      model Y = X1 X2 X3 / gmm1;
   run;

For a detailed discussion of the model set up and the use of the INSTRUMENTS statement for dynamic panels, see Dynamic Panel Estimators.

For Hausman-Taylor or Amemiya-MaCurdy estimation, you specify which variables are correlated with the individual effects by using the CORRELATED= option. All other options are ignored. For these estimators, the specified variables are not instruments—they are merely designated as correlated. The instruments are determined by the method; for more information, see the section Hausman-Taylor Estimation.

   proc panel data=a;
      instruments correlated = (X2 Z2);
      model Y = X1 X2 Z1 Z2 / htaylor;
   run;

One INSTRUMENT statement is required for each MODEL statement. For example, if there are two models to be estimated by using GMM1 within one PANEL procedure, then there should be two INSTRUMENT statements, as follows:

    proc panel data=test;
      id cs ts;
      instruments depvar predetermined = (x1 x2)
                         exogenous     = (x3 x4 x5)
                         correlated    = (x3 x4 x5);
      model y = y_1 x1 x2 / gmm1;
      instruments        predetermined = (x2 x4)
                         exogenous     = (x3 x5)
                         correlated    = (x3 x4);
      model y = y_1 x2 / gmm1;
    run;