Exact Distribution Theory in Structural Estimation with an Identity

Peter C. B. Phillips ()

No 1613, Cowles Foundation Discussion Papers from Cowles Foundation, Yale University

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.

Keywords: Exact distribution; Identity; IV estimation; LIML; Structural equation; Uniform asymptotic expansion (search for similar items in EconPapers)
JEL-codes: C30 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: Written

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Journal Article: EXACT DISTRIBUTION THEORY IN STRUCTURAL ESTIMATION WITH AN IDENTITY (2009)
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