A weighted average limited information maximum likelihood estimator

Muhammad Qasim ()
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Muhammad Qasim: Jönköping University

Statistical Papers, 2024, vol. 65, issue 5, No 1, 2666 pages

Abstract: 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.

Keywords: Endogeneity; Instrumental variables; LIML; 2SLS; Shrinkage estimator; Stein estimation; Many weak instruments (search for similar items in EconPapers)
JEL-codes: C13 C26 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01485-2

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