The unconditional distributions of the OLS, TSLS and LIML estimators in a simple structural equations model. (7th February 2019)

• Record Type: Journal Article
• Authors: Forchini, Giovanni; Jiang, Bin
• Is Part Of: Econometric reviews. Volume 38:Number 2(2019)
• Page Start: 208
• Page End: 247
• Publication Date: 2019-02-07
• Subjects: Exact distribution -- limited information maximum likelihood -- linear structural equations -- ordinary least squares -- two-stage least squares; C13 -- C36; Econometrics -- Periodicals; 330.015195
• DOI: 10.1080/07474938.2016.1261072
• Languages: English
• ISSNs: 0747-4938

Abstract

ABSTRACT: The exact distributions of the standard estimators of the structural coefficients in a linear structural equations model conditional on the exogenous variables have been shown to have some unexpected and quirky features. Since the argument for conditioning on exogenous (ancillary) variables has been weakened over the past 20 years by the discovery of an "ancillarity paradox, " it is natural to wonder whether such finite sample properties are in fact due to conditioning on the exogenous variables. This article studies the exact distributions of the ordinary least squares (OLS), two-stage least squares (TSLS), and limited information maximum likelihood (LIML) estimators of the structural coefficients in a linear structural equation without conditioning on the exogenous variables.