By L. G. Godfrey
By way of bringing jointly effects from the transforming into literature in econometrics on misspecification checking out, this examine offers theoretical analyses and handy equipment for the implementation of checks in utilized paintings. even though the most emphasis is at the Lagrange multiplier precept, a number of different techniques are mentioned and the relationships between assorted equipment are tested. the writer reports basic tests of version adequacy that don't contain the formula of another speculation. normal and particular assessments are mentioned within the context of a number of regression types, platforms of simultaneous equations, and types with qualitative or restricted established variables. This wide-ranging yet built-in booklet could be important to a large viewers of utilized and theoretical researchers, graduate scholars, economists.
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Additional info for Misspecification Tests in Econometrics: The Lagrange Multiplier Principle and Other Approaches
The test of the significance of n*c(6) is implemented as a test of the hypothesis that the intercept coefficients of y0 are all equal to zero. As noted by Tauchen (1985, p. 24) will never be smaller than Newey's OPG variant. Consequently the arguments against the general use of Newey's algorithm apply a fortiori to Tauchen's procedure. Details of the application of these algorithms will,therefore, not be provided below. 7 Summary and qualifications We have discussed some of the advantages and disadvantages of both pure significance tests and tests based upon investigating the consistency of a set of parametric restrictions with the data.
Engle (1982a) h a s considered the asymptotic distribution of quasi L M tests for models with n o n - n o r m a l errors which are correct to first order a n d have been estimated using a weighted least-squares approximation to quasi M L E . 2 4 H e provides a set of regularity conditions in the spirit of D o m o w i t z a n d White (1982) which a r e sufficient t o ensure that the quasiL M statistics will converge in distribution t o y 2 under the null, the degrees of freedom parameter being equal t o the number of restrictions being tested.
Assuming that root-n norming is appropriate, we have under H o . 1) will, using an obvious notation, be partitioned as so that the efficiency of 61 relative to 0X implies that (Z — E A A) is a positive semi-definite matrix. The vector difference n^(^ — 6J will converge in distribution to multivariate normality with a zero mean vector under H o , so the large sample theory required to derive an appropriate x2 criterion reduces to the task of finding its covariance matrix. Hausman (1978) establishes that this matrix is simply the difference between the asymptotic covariance matrices of n*(0!