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New Bayesian Approach to the Estimation in Simultaneous Equations Model

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Abstract

Two stage least squares is an approach to fit a mathematical or statistical model to data where there are simultaneous or bidirectional cause and effect relationship between the independent variables and the dependent variable. Two stage least squares method is frequently implemented in the case that there is no prior information. On the other hand, in the existence of some prior information, Bayesian estimation methods may be preferable to the classical ones in the simultaneous equations model. From this point of view, ridge regression approach is adapted to Bayesian approach in this paper. In mathematical sense, ridge regression can be derived as a solution of Tikhonov regularization which is a method to overcome ill-posed problems. Therefore, the proposed Bayes estimators resulted from the adaptation of ridge regression mitigate the multicollinearity. Theoretical comparisons among the estimators are performed by means of matrix mean square error criterion and determination of the biasing parameter is also examined in this paper. While doing these comparisons we utilize the matrix theory and Euclidian norm. Theoretical results are tested by a real life data analysis and an extensive Monte Carlo experiment. Eventually, the researchers relevant to mathematics and statistics may prefer the proposed Bayes estimators to the two stage least squares estimator in the existence of multicollinearity.

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Funding

This paper is supported by Çukurova University Scientific Research Projects Unit Project no. FBA-2018-9770.

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Authors and Affiliations

  1. Department of Statistics, Faculty of Science and Letters, Çukurova University, 01250, Adana, Turkey

    Selma Toker & Nimet Özbay

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  1. Selma Toker
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  2. Nimet Özbay
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Correspondence to Selma Toker or Nimet Özbay.

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(Submitted by A. I. Volodin)

Selma Toker is a corresponding author

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Toker, S., Özbay, N. New Bayesian Approach to the Estimation in Simultaneous Equations Model. Lobachevskii J Math 44, 3872–3888 (2023). https://doi.org/10.1134/S1995080223090421

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  • DOI: https://doi.org/10.1134/S1995080223090421

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