help for tgmixed

Perform Theil-Goldberger mixed estimation of regression equation

tgmixed varlist [if exp] [in range],
prior(string) [
cov(string) quietly]

varlist may not contain time-series operators nor factor variables; see help varlist.

Description

tgmixed estimates a regression equation subject to stochastic linear
constraints, using the Theil-Goldberger (1961) mixed estimation technique. This estimator
is a generalization of cnsreg, which applies exact linear constraints to a regression
equation. In the Theil-Goldberger technique, the constraints hold with some degree of subjective
belief. The routine computes the Theil compatibility statistic (Theil, 1963) for the null
hypothesis that the sample and non-sample information are compatible. Under the null, this
statistic is distributed Chi-squared, with degrees of freedom equal to the number of
stochastic constraints.

Options

prior(string) is a required option. It must contain triples of
varname prior_value prior_se where varname must be a regressor in the varlist. The
stochastic constraint indicates that this regressor has a prior_value and a prior_se.
If multiple regressors have priors, each should be listed within the prior() option.
Note that at present tgmixed does not support stochastic constraints involving multiple
variables (e.g., adding-up or equality constraints).

cov(string) may be used to specify prior covariances between pairs of
coefficients included in the prior() option.

quietly may be used to suppress the listing of the unconstrained OLS regression
estimates.

Saved results

tgmixed saves the following scalars:

e(rmse) : the root mean squared error of the mixed estimates

e(r2) : the R-squared of the mixed estimates

e(N): the number of observations in the estimation sample

e(df_r) : the number of degrees of freedom of the residual sum of squares

e(compat) : the Theil compatibility statistic

e(vrank) : the rank of the matrix of stochastic constraints

e(pvalue) : the p-value of the compatibility statistic

e(frac_sample) : the proportion of precision due to sample information

e(frac_prior) : the proportion of precision due to prior information

tgmixed saves the following macros:

e(cmd) : tgmixed

e(predict) : regres_p

e(depvar) : the name of the dependent variable

e(marginsok) : XB default

e(cmdline) : the command line used for estimation

e(prior) : the content of the prior() option

e(properties) : b V

tgmixed saves the following matrices:

e(b) : the vector of mixed coefficient estimates

e(V) : the VCE of mixed coefficient estimates

e(Vprior) : the VCE of stochastic prior estimates

tgmixed saves the following function:

e(sample) : indicator for inclusion in the estimation sample

References

Theil, H. and A.S. Goldberger, On pure and mixed statistical information in economics.
International Economic Review, 2:1, 65-78, 1961.

Theil, H., On the Use of Incomplete Prior Information in Regression Analysis.
Journal of the American Statistical Association, 58:302, 401-414, 1963.

For more information, see the Stata Conference 2011 presentation at
http://econpapers.repec.org/paper/bocchic11/14.htm

Example: reproduce textile example in Theil, 1963

. use http://fmwww.bc.edu/ec-p/data/micro/theiltextile

. tgmixed lconsump lincome lprice, prior(lprice -0.7 0.15 lincome 1 0.15) cov(lprice lincome -0.01)

Acknowledgements

The Mata code for tgmixed includes a copy of Ben Jann's mm_posof() from
his moremata package.

Author

Christopher F Baum, Boston College, USA

baum@bc.edu