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theil

Theil-Goldberger mixed estimator

CALLING SEQUENCE

[results]=theil(rvec,rmat,v,namey,arg1,...,argn)

PARAMETERS

Input

* rvec = a vector of prior mean values, (c in description)

* rmat = a matrix of rank(r) (R in description)

* v = prior variance-covariance (var-cov(U) in description)

* namey = a time series, a real (nx1) vector or a string equal to the name of a time series or a (nx1) real vector between quotes

* argi = arguments which can be:

  - a time series

  - a real (nx1) vector

  - a real (nxk) matrix

  - a string equal to the name of a time series or a (nxk) real vector or matrix between quotes

  - a list of such elements

  - the string 'noprint' if the user doesn't want to display the results of the regression

 

Output

* results = a results tlist with

  - results('meth') = 'Theil-Goldberger'

  - results('beta') = bhat

  - results('y') = y data vector

  - results('x') = x data matrix

  - results('nobs') = # observations

  - results('nvar') = # variables

  - results('yhat') = yhat

  - results('resid') = residuals

  - results('vcovar') = estimated variance-covariance matrix of beta

  - results('sige') = estimated variance of the residuals

  - results('sigu') = sum of squared residuals

  - results('ser') = standard error of the regression

  - results('tstat') = t-stats

  - results('pvalue') = pvalue of the betas

  - results('dw') = Durbin-Watson Statistic

  - results('condindex') = multicolinearity cond index

  - results('prescte') = boolean indicating the presence or absence of a constant in the regression

  - results('rsqr') = rsquared

  - results('rbar') = rbar-squared

  - results('f') = F-stat for the nullity of coefficients other than the constant

  - results('pvaluef') = its significance level

  - results('prests') = boolean indicating the presence or absence of a time series in the regression

  - results('namey') = name of the y variable

  - results('namex') = name of the x variables

  - results('bounds') = if there is a timeseries in the regression, the bounds of the regression

  - results('pmean') = prior means

  - results('pstd') = prior std deviations

DESCRIPTION

Computes Theil-Goldberger mixed estimator

y = X B + E, E = N(0,sige*IN)

c = R B + U, U = N(0,v)

EXAMPLE

xmat = rand(100,4,'n');
exo = [ones(100,1),xmat];
evec = rand(100,1,'n');
 
endo = exo*ones(5,1)+evec;
r = theil(ones(5,1),eye(5,5),0.1*eye(5,5),'endo','exo')
// This example shows the estimation of endogenous variables 'endo' on exogenous variables 'exo'
// (which should be a (nobsx5) constant matrix), with the relatively tight prior (v=0.1*eye(5,5))
// that each coefficient should be equal to 1 (since c=ones(5,1) and R=eye(5,5)).

AUTHOR

Eric Dubois 2002

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