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Exact Distribution Theory in Structural Estimation with an Identity

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Abstract

Some exact distribution theory is developed for structural equation models with and without identities. The theory includes LIML, IV and OLS. We relate the new results to earlier studies in the literature, including the pioneering work of Bergstrom (1962). General IV exact distribution formulae for a structural equation model without an identity are shown to apply also to models with an identity by specializing along a certain asymptotic parameter sequence. Some of the new exact results are obtained by means of a uniform asymptotic expansion. An interesting consequence of the new theory is that the uniform asymptotic approximation provides the exact distribution of the OLS estimator in the model considered by Bergstrom (1962). This example appears to be the first instance in the statistical literature of a uniform approximation delivering an exact expression for a probability density.

Suggested Citation

  • Peter C.B. Phillips, 2007. "Exact Distribution Theory in Structural Estimation with an Identity," Cowles Foundation Discussion Papers 1613, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1613
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    Cited by:

    1. Jan F. Kiviet, 2013. "Identification and inference in a simultaneous equation under alternative information sets and sampling schemes," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 24-59, February.

    More about this item

    Keywords

    Exact distribution; Identity; IV estimation; LIML; Structural equation; Uniform asymptotic expansion;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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