# systemfit.control: Create list of control parameters for systemfit In systemfit: Estimating Systems of Simultaneous Equations

## Description

Create a list of control pararameters for function systemfit. All control parameters that are not passed to this function are set to default values.

## Usage

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 systemfit.control( maxiter = 1, tol = 1e-5, methodResidCov = "geomean", centerResiduals = FALSE, residCovRestricted = TRUE, residCovWeighted = FALSE, method3sls = "GLS", singleEqSigma = NULL, useMatrix = TRUE, solvetol = .Machine\$double.eps, model = TRUE, x = FALSE, y = FALSE, z = FALSE ) 

## Arguments

 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 first-step 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 singleEqSigma is NULL, it is automatically determined: It is set to TRUE, if restrictions on the coefficients are imposed, and it is set to FALSE otherwise. useMatrix logical. Use package Matrix for matrix calculations? solvetol tolerance level for detecting linear dependencies when inverting a matrix or calculating a determinant (see solve and det). 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.

## Details

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,g-1})^2 }{ ∑_i b_{i,g-1}^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 GMM-3SLS 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 first-step estimation to calculate the residual covariance matrix that is used in a second-step WLS or W2SLS estimation. Then, it uses the residuals from the second-step estimation to calculate the residual covariance matrix that is used in a final SUR or 3SLS estimation. This three-step 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 cross-equation restrictions are imposed, residCovWeighted has no effect on the estimation results.

## Value

A list of the above components.

## References

Judge, George G.; W. E. Griffiths; R. Carter Hill; Helmut Luetkepohl and Tsoung-Chao Lee (1985) The Theory and Practice of Econometrics, Second Edition, Wiley.

Schmidt, P. (1990) Three-Stage Least Squares with different Instruments for different equations, Journal of Econometrics 43, p. 389-394.

Theil, H. (1971) Principles of Econometrics, Wiley, New York.

systemfit
  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 )