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Inverting the indirect—The ellipse and the boomerang: Visualizing the confidence intervals of the structural coefficient from two-stage least squares

Joseph Hirschberg () and Jeanette Lye ()

Journal of Econometrics, 2017, vol. 199, issue 2, 173-183

Abstract: In the just-identified model,the exact distribution of the two-stage least squares (2SLS) estimator of the coefficient of the endogenous regressor is a ratio of two normally distributed random variables. Basmann (1960, 1974) used Fieller’s 1932 result to derive the density function of the estimator. In this paper, we present a novel graphical exposition of Fieller’s 1954 technique to approximate the confidence interval for the 2SLS estimator. We use this approach to examine how the degree of endogeneity and instrument relevance influences the correspondence between the Fieller and traditional asymptotic confidence intervals for the estimator.

Keywords: Indirect least squares; Inverse test; Fieller method; Anderson and Rubin test; Delta method (search for similar items in EconPapers)
JEL-codes: C12 C26 C36 C18 (search for similar items in EconPapers)
Date: 2017
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