TY  - BOOK
AU  - Phillips,Peter C.B.
TI  - Exact distribution theory in structural estimation with an identity
AV  - HB139.T52 ECO 
PY  - 2009///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Exact distribution
KW  - Identity
N2  - 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 formulas 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
UR  - 10.1017/S0266466608090361
ER  -