Econometric Theory and Practice: Edgeworth Expansions for the Wald and GMM Statistics for Nonlinear Restrictions

@inproceedings{Hansen2006EconometricTA,
  title={Econometric Theory and Practice: Edgeworth Expansions for the Wald and GMM Statistics for Nonlinear Restrictions},
  author={Bruce E. Hansen},
  year={2006}
}
  • B. Hansen
  • Published 2006
  • Mathematics, Economics
An Edgeworth expansion is derived for the GMM distance statistic for a real-valued nonlinear restriction on a normal linear regression. The Edgeworth expansion takes the form F (x − n −1 α1x)+o(n −1 ), where F is the χ 2 distribution. We also provide a reÞnement of the Edgeworth expansion for the Wald statistic derived by Park and Phillips (1988), which takes the form F (x − n −1 (α1x + α2x 2 + α3x 3 )) +o(n −1 ). Our calculations show that the leading coefficient α1 is the same in these two… 

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