Create a list of control pararameters for function systemfit
.
All control parameters that are not passed to this function
are set to default values.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 
maxiter 
maximum number of iterations for WLS, SUR, W2SLS and 3SLS estimations. 
tol 
tolerance level indicating when to stop the iteration (only WLS, SUR, W2SLS and 3SLS estimations). 
methodResidCov 
method for calculating the estimated residual covariance matrix, one of "noDfCor", "geomean", "max", or "Theil" (see details). 
centerResiduals 
logical. Subtract the means from the residuals of each equation before calculating the estimated residual covariance matrix. 
residCovRestricted 
logical. If 'FALSE' the residual covariance matrix for a WLS, SUR, W2SLS, or 3SLS estimation is obtained from an unrestricted firststep estimation. 
residCovWeighted 
logical. If 'TRUE' the residual covariance matrix for a SUR or 3SLS estimation is obtained from a WLS or W2SLS estimation. 
method3sls 
method for calculating the 3SLS estimator, one of "GLS", "IV", "GMM", "Schmidt", or "EViews" (see details). 
singleEqSigma 
logical. use different σ^2s for each
single equation to calculate the covariance matrix and the
standard errors of the coefficients (only OLS and 2SLS)?
If 
useMatrix 
logical. Use package 
solvetol 
tolerance level for detecting linear dependencies
when inverting a matrix or calculating a determinant (see

model, x, y, z 
logical. If 'TRUE' the corresponding components of the fit (the model frame, the model matrix, the response, and the matrix of instruments, respectively) are returned. 
If the estimation is iterated
(WLS, SUR, W2SLS or 3SLS estimation with maxiter
>1),
the convergence criterion is
√{ \frac{ ∑_i (b_{i,g}  b_{i,g1})^2 }{ ∑_i b_{i,g1}^2 }} < \code{tol}
(b_{i,g} is the ith coefficient of the gth iteration step).
The method for calculating the estimated covariance matrix of the residuals
(\hat{Σ}) can be one of the following
(see Judge et al., 1985, p. 469):
if methodResidCov='noDfCor':
\hat{σ}_{ij} = \frac{\hat{e}_i' \hat{e}_j}{T}
if methodResidCov='geomean':
\hat{σ}_{ij} = \frac{\hat{e}_i' \hat{e}_j} {√{(T  k_i)*(T  k_j)}}
if methodResidCov='Theil':
\hat{σ}_{ij} = \frac{\hat{e}_i' \hat{e}_j}{T  k_i  k_j + tr[X_i(X_i'X_i)^{1}X_i'X_j(X_j'X_j)^{1}X_j']}
if methodResidCov='max':
\hat{σ}_{ij} = \frac{\hat{e}_i' \hat{e}_j} {T  \max( k_i, k_j)}
If i = j, the formulas 'geomean', 'Theil', and 'max' are equal. All these three formulas yield unbiased estimators for the diagonal elements of the residual covariance matrix. If i \neq j, only formula 'Theil' yields an unbiased estimator for the residual covariance matrix, but it is not neccessarily positive semidefinit. Thus, it is doubtful whether formula 'Theil' is really superior to formula 'noDfCor' (Theil, 1971, p. 322).
The methods for calculating the 3SLS estimator lead to identical results if the same instruments are used in all equations. If different instruments are used in the different equations, only the GMM3SLS estimator ("GMM") and the 3SLS estimator proposed by Schmidt (1990) ("Schmidt") are consistent, whereas "GMM" is efficient relative to "Schmidt" (see Schmidt, 1990).
If residCovWeighted
is TRUE
,
systemfit
does a OLS or 2SLS estimation in a first step.
It uses the residuals from the firststep estimation
to calculate the residual covariance matrix
that is used in a secondstep WLS or W2SLS estimation.
Then, it uses the residuals from the secondstep estimation
to calculate the residual covariance matrix
that is used in a final SUR or 3SLS estimation.
This threestep method is the default method of command "TSCS"
in the software LIMDEP that carries out "SUR" estimations
in which all coefficient vectors are constrained to be equal
(personal information from W.H. Greene, 2006/02/16).
If no crossequation restrictions are imposed,
residCovWeighted
has no effect on the estimation results.
A list of the above components.
Arne Henningsen arne.henningsen@googlemail.com
Judge, George G.; W. E. Griffiths; R. Carter Hill; Helmut Luetkepohl and TsoungChao Lee (1985) The Theory and Practice of Econometrics, Second Edition, Wiley.
Schmidt, P. (1990) ThreeStage Least Squares with different Instruments for different equations, Journal of Econometrics 43, p. 389394.
Theil, H. (1971) Principles of Econometrics, Wiley, New York.
1 2 3 4 5 6 7 8 9 10  data( "Kmenta" )
eqDemand < consump ~ price + income
eqSupply < consump ~ price + farmPrice + trend
eqSystem < list( demand = eqDemand, supply = eqSupply )
## SUR estimation: calculation of residual covariance
## matrix without correction for degrees of freedom
fitsur < systemfit( eqSystem, "SUR", data = Kmenta,
control = systemfit.control( methodResidCov = "noDfCor" ) )
print( fitsur )

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