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On the joint and marginal densities of instrumental variable estimators in a general structural equation

On the joint and marginal densities of instrumental variable estimators in a general structural equation
On the joint and marginal densities of instrumental variable estimators in a general structural equation


Starting from the conditional density of the instrumental variable (IV) estimator given the right-hand-side endogenous variables, we provide an alternative derivation of Phillips' result on the joint density of the IV estimator for the endogenous coefficients, and derive an expression for the marginal density of a linear combination of these coefficients. In addition, we extend Phillips' approximation to the joint density to 0(T−2,) and show how this result can be used to improve the approximation to the marginal density. Explicit formulae are given for the special case of no simultaneity, and the case of an equation with just three endogenous variables. The classical assumptions of independent normal reduced-form errors are employed throughout.
0266-4666
53-72
Hillier, Grant H.
3423bd61-c35f-497e-87a3-6a5fca73a2a1
Hillier, Grant H.
3423bd61-c35f-497e-87a3-6a5fca73a2a1

Hillier, Grant H. (1985) On the joint and marginal densities of instrumental variable estimators in a general structural equation. Econometric Theory, 1 (1), 53-72. (doi:10.1017/S0266466600010999).

Record type: Article

Abstract



Starting from the conditional density of the instrumental variable (IV) estimator given the right-hand-side endogenous variables, we provide an alternative derivation of Phillips' result on the joint density of the IV estimator for the endogenous coefficients, and derive an expression for the marginal density of a linear combination of these coefficients. In addition, we extend Phillips' approximation to the joint density to 0(T−2,) and show how this result can be used to improve the approximation to the marginal density. Explicit formulae are given for the special case of no simultaneity, and the case of an equation with just three endogenous variables. The classical assumptions of independent normal reduced-form errors are employed throughout.

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Published date: April 1985

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Local EPrints ID: 417377
URI: https://eprints.soton.ac.uk/id/eprint/417377
ISSN: 0266-4666
PURE UUID: 8c15d018-7615-4aca-a83e-dc62522ee011

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Date deposited: 30 Jan 2018 17:30
Last modified: 13 Mar 2019 18:58

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