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A weighted average limited information maximum likelihood estimator

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  • Muhammad Qasim

    (Jönköping University)

Abstract

In this article, a Stein-type weighted limited information maximum likelihood (LIML) estimator is proposed. It is based on a weighted average of the ordinary least squares (OLS) and LIML estimators, with weights inversely proportional to the Hausman test statistic. The asymptotic distribution of the proposed estimator is derived by means of local-to-exogenous asymptotic theory. In addition, the asymptotic risk of the Stein-type LIML estimator is calculated, and it is shown that the risk is strictly smaller than the risk of the LIML under certain conditions. A Monte Carlo simulation and an empirical application of a green patent dataset from Nordic countries are used to demonstrate the superiority of the Stein-type LIML estimator to the OLS, two-stage least squares, LIML and combined estimators when the number of instruments is large.

Suggested Citation

  • Muhammad Qasim, 2024. "A weighted average limited information maximum likelihood estimator," Statistical Papers, Springer, vol. 65(5), pages 2641-2666, July.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:5:d:10.1007_s00362-023-01485-2
    DOI: 10.1007/s00362-023-01485-2
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    More about this item

    Keywords

    Endogeneity; Instrumental variables; LIML; 2SLS; Shrinkage estimator; Stein estimation; Many weak instruments;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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