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AN ASYMPTOCALLY UNBIASED TWO‐STAGE LEAST SQUARES ESTIMATOR OF THE STRUCTURAL DISTURBANCE VARIANCES AND THE BIAS
Author(s) -
Kymn Kern O
Publication year - 1974
Publication title -
metroeconomica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.256
H-Index - 29
eISSN - 1467-999X
pISSN - 0026-1386
DOI - 10.1111/j.1467-999x.1974.tb00350.x
Subject(s) - estimator , minimum variance unbiased estimator , bias of an estimator , mathematics , consistent estimator , stein's unbiased risk estimate , efficient estimator , statistics , covariance , stage (stratigraphy) , mean squared error , covariance matrix , econometrics , biology , paleontology
A bstract Let Σ represent the covariance matrix of the structural disturbances of a simultaneous equations model. The conventional consistent estimator of the elements of Σ is usually given as the mean 2SLS residuals. However, neither the bais nor the asymptotic bias of the estimator of Σ by 2SLS have been found. This paper analytically derives an asymptotically unbiased estimator of Σ by 2SLS and determines the bias for finite samples. It is shown that the bias vanishes asymptotically. Then the paper suggests that the derived estimator may be applied in the second stage as well as in the third stage of 3SLS estimation. Other possible applications are indicated.