Theil-Goldberger mixed estimator
[results]=theil(rvec,rmat,v,namey,arg1,...,argn)
* 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
* 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
y = X B + E, E = N(0,sige*IN)
c = R B + U, U = N(0,v)
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)). | ![]() | ![]() |