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Estimation with Pairwise Observations

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  • Felix Chan
  • Laszlo Matyas

Abstract

The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The paper shows that such estimator is consistent for carefully selected weights. Other properties, such as asymptotic distributions, have also been derived to facilitate valid statistical inference. Unlike traditional methods, such as Least Squares and Maximum Likelihood, among others, the estimated residual of this estimator is not by construction orthogonal to the explanatory variables of the model. This property allows a wide range of practical applications, such as the testing of endogeneity, i.e., the correlation between the explanatory variables and the disturbance terms.

Suggested Citation

  • Felix Chan & Laszlo Matyas, 2024. "Estimation with Pairwise Observations," Papers 2401.11229, arXiv.org, revised Feb 2024.
    • Handle: RePEc:arx:papers:2401.11229
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    References listed on IDEAS

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    1. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, Decembrie.
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