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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

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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.

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  • Hirschberg, Joe & Lye, Jenny, 2017. "Inverting the indirect—The ellipse and the boomerang: Visualizing the confidence intervals of the structural coefficient from two-stage least squares," Journal of Econometrics, Elsevier, vol. 199(2), pages 173-183.
    • Handle: RePEc:eee:econom:v:199:y:2017:i:2:p:173-183
    DOI: 10.1016/j.jeconom.2017.05.008
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    Cited by:

    1. Jenny Lye & Joe Hirschberg, 2018. "Ratios of Parameters: Some Econometric Examples," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 51(4), pages 578-602, December.

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    More about this item

    Keywords

    Indirect least squares; Inverse test; Fieller method; Anderson and Rubin test; Delta method;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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