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

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  • Joe Hirschberg

    (Department of Economics, University of Melbourne)

  • Jenny Lye

    (Department of Economics, 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.

Suggested Citation

  • Joe Hirschberg & Jenny Lye, 2017. "Alternative Graphical Representations of the Confidence Intervals for the Structural Coefficient from Exactly Identified Two-Stage Least Squares," Department of Economics - Working Papers Series 2026, The University of Melbourne.
    • Handle: RePEc:mlb:wpaper:2026
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    References listed on IDEAS

    as
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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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