Alternative Graphical Representations of the Confidence Intervals for the Structural Coefficient from Exactly Identified Two-Stage Least Squares

Joseph Hirschberg and Jeanette Lye

Department of Economics - Working Papers Series from The University of Melbourne

Abstract: In the case of 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. Robert Basmann (1960, 1961, 1974) used Fieller’s 1932 result to derive the density function of the estimator. In this paper we employ a novel graphical exposition of Fieller’s subsequent 1954 technique to approximate the confidence interval for the ratio. This approach involves the construction of a constraint shape that provides an insight as to how the characteristics of the reduced form estimates influences the comparison of the Delta and the Fieller confidence intervals. In particular, the degree of endogeneity and the relevance of the instrument can be shown to have a direct influence on these shapes. An example application of this approach is then applied to consider two specifications of an exactly identified model.

Keywords: Indirect Least Squares; Inverse Test; Fieller Method; Anderson and Rubin Test; Delta Method (search for similar items in EconPapers)
JEL-codes: C12 C18 C26 C36 (search for similar items in EconPapers)
Pages: 61 pages
Date: 2017-01
New Economics Papers: this item is included in nep-ecm
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