Tricks with metrics: combining statistics for improved inference in regression analysis

Pierre Nguimkeu

Econometric Reviews, 2024, vol. 43, issue 8, 581-594

Abstract: In maximum likelihood methods, the three classical tests statistics are often unreliable for inference in small samples, even under the correct model specification. In this article, I discuss how likelihood ratio and Wald test statistics can be combined to obtain highly improved parameter inference in regression models with small samples. I consider modifications obtained from both the Barndorff-Nielsen and the Lugannani and Rice likelihood approximations, and I show how they can produce highly accurate parameter inference in a general (possibly non linear) regression model with possibly non spherical disturbances. I discuss the underlying theory and provide Monte Carlo simulations demonstrating the superior accuracy of the proposed procedures over the first-order classical likelihood methods (i.e., the signed log-likelihood ratio test and the Wald test). An empirical application to a regression model of mobile money (“M-pesa”) adoption in Kenya is provided as an illustration of the usefulness of these methods in practice.

Date: 2024
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DOI: 10.1080/07474938.2024.2351819

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