Instrumental Variables Options

Instrumental variables estimation or related computations are supported by the instructions AR1, CMOMENT, LINREG, NLLS, NLSYSTEM, SUR, and SWEEP. The list of instruments is maintained by the instruction INSTRUMENTS separate from the actual estimation instructions and must be set prior to doing the estimation.

For the linear model \({\bf{y}} = {\bf{X}}\beta + {\bf{u}}\) with instruments \({\bf{Z}}\), \(\beta \) is estimated by

\({\left( {{\bf{X'ZWZ'X}}} \right)^{ - 1}}\left( {{\bf{X'ZWZ'y}}} \right)\)

where, by default, \({\bf{W}}\) is \({\left( {{\bf{Z'Z}}} \right)^{ - 1}}\). This minimizes over \(\beta \)

\({\bf{u'ZWZ'u}}\)

The following options are available on most of the instructions listed above:

INSTRUMENTS/[NOINSTRUMENTS]

This tells RATS to use instrumental variables.

WMATRIX=weighting matrix [\({\left( {{\bf{Z'Z}}} \right)^{ - 1}}\)]

OPTIMALWEIGHTS/[NOOPTIMALWEIGHTS]

UPDATE=NONE/ONCE/CONTINUOUS

This controls the updating of the weighting matrix. You can directly input a weight matrix with the WMATRIX option. If you don’t, the weight matrix is initialized as the \({\left( {{\bf{Z'Z}}} \right)^{ - 1}}\) matrix which gives two-stage least squares. If you use OPTIMALWEIGHTS or UPDATE=CONTINUOUS (they’re synonyms), the weight matrices are recomputed after every iteration using the choices you have made from the next group of options. Note, however, that the default number of iterations (governed by the ITERATIONS option) is just one. For a linear model, the coefficients can be solved without iterations given a weight matrix, so an iteration here means another calculation of the weight matrix.

[ZUDEP]/NOZUDEP

LAGS=correlated lags [0]

LWINDOW=NEWEYWEST/BARTLETT/DAMPED/PARZEN/QUADRATIC/[FLAT]/PANEL/WHITE

DAMP=value of \(\gamma\) for LWINDOW=DAMPED [0.0]

LWFORM=VECTOR with the lag window form [not used]

CLUSTER=SERIES with category values for clustered calculation

Use these to select the type of correlation assumed for the \({{\bf{Z'u}}}\) process. See the description of MCOV for more information.

ITERATIONS=iteration limit [1]

CVCRIT=convergence limit [.00001]

TRACE/[NOTRACE]

ITERATIONS sets the maximum number of iterations, which here means recalculations of weighting matrices. The default is to do just one recalculation.

ZUMEAN=VECTOR of means of moment conditions [zeros]

This allows you to supply a VECTOR (with dimensions equal to the number of instruments) with a set of known (non-zero) means for \(E\left( {{\bf{Z'u}}} \right)\). By default, RATS sets these to zero.

CENTER/[NOCENTER]

CENTER adjusts the formula for the weight matrix to subtract off the (sample) means of \({{\bf{Z'u}}}\), which may be non-zero for an overidentified model. See the description of MCOV for more information.

JROBUST=STATISTIC/[DISTRIBUTION]

You can use this option to adjust the J-statistic specification test when the weighting matrix used is not the optimal one.

Variables Defined for Instrumental Variables/GMM

%JSTAT	test statistics for overidentification (for instrumental variables regressions) (REAL)
%JSIGNIF	significance level of %JSTAT (REAL)
%NDFJ	degrees of freedom for %JSTAT (INTEGER)
%UZWZU	\({\bf{u'}}{\kern 1pt} {\bf{Z}}{\kern 1pt} {\bf{W}}{\kern 1pt} {\bf{Z'u}}\) (REAL)
%WMATRIX	final weight matrix for GMM (SYMMETRIC)