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Least Orthogonal Distance Estimator and Total Least Square

Naccarato, Alessia and Zurlo, Davide and Pieraccini, Luciano (2012): Least Orthogonal Distance Estimator and Total Least Square.

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Abstract

Least Orthogonal Distance Estimator (LODE) of Simultaneous Equation Models’ structural parameters is based on minimizing the orthogonal distance between Reduced Form (RF) and the Structural Form (SF) parameters. In this work we propose a new version – with respect to Pieraccini and Naccarato (2008) – of Full Information (FI) LODE based on decomposition of a new structure of the variance-covariance matrix using Singular Value Decomposition (SVD) instead of Spectral Decomposition (SD). In this context Total Least Square is applied. A simulation experiment to compare the performances of the new version of FI LODE with respect to Three Stage Least Square (3SLS) and Full Information Maximum Likelihood (FIML) is presented. Finally a comparison between the FI LODE new and old version together with few words of conclusion conclude the paper.

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