Jensen, Mark J (1995): A Monte Carlo study on two methods of calculating the MLEs covariance matrix in a seemingly unrelated nonlinear regression. Published in: Econometric Review , Vol. 14, : pp. 315330.

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Abstract
Econometric techniques to estimate output supply systems, factor demand systems and consumer demand systems have often required estimating a nonlinear system of equations that have an additive error structure when written in reduced form. To calculate the ML estimate's covariance matrix of this nonlinear system one can either invert the Hessian of the concentrated log likelihood function, or invert the matrix calculated by premultiplying and postmultiplying the inverted MLE of the disturbance covariance matrix by the Jacobian of the reduced form model. Malinvaud has shown that the latter of these methods is the actual limiting distribution's covariance matrix, while Barnett has shown that the former is only an approximation.
In this paper, we use a Monte Carlo simulation study to determine how these two covariance matrices differ with respect to the nonlinearity of the model, the number observations in the data set, and the residual process. We find that the covariance matrix calculated from the Hessian of the concentrated likelihood function produces Wald statistics that are distributed above those calculated with the other covariance matrix. This difference become insignificant as the sample size increases to onehundred or more observations, suggesting that the asymptotics of the two covariance matrices are quickly reached.
Item Type:  MPRA Paper 

Original Title:  A Monte Carlo study on two methods of calculating the MLEs covariance matrix in a seemingly unrelated nonlinear regression 
Language:  English 
Keywords:  nonlinear SURE models, covariance estimates, hypothesis testing of neoclassical theory 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models; Multiple Variables > C30  General 
Item ID:  39020 
Depositing User:  Mark Jensen 
Date Deposited:  29. May 2012 23:13 
Last Modified:  18. Feb 2013 02:39 
References:  A monte carlo study on two methods of calculating the mle's covariance matrix in a seemingly unrelated nonlinear regression. Mark J. Jensen Econometric Reviews Vol. 14, Iss. 3, 1995 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/39020 