The Explanatory Power of Explanatory Variables

45 Pages Posted: 1 Jul 2020 Last revised: 29 Oct 2020

See all articles by Erik Johannesson

Erik Johannesson

City University of NY, Baruch College, Zicklin School of Business

James A. Ohlson

Hong Kong Polytechnic University - School of Accounting and Finance

Sophia Weihuan Zhai

Hong Kong Polytechnic University - School of Accounting and Finance

Date Written: September 28, 2020

Abstract

This paper concerns potential disparities between narratives and statistical evidence in empirical accounting research. We focus on the extent to which a regression model’s main variable of interest contributes incrementally to the explanation of the dependent variable. We replicate ten recently published accounting studies, all of which base their conclusions on t-statistics and statistical significance. In eight of the replicated studies, we find that the incremental explanatory power contributed by the main variable of interest is effectively zero. For the remaining two, the incremental contribution is at best marginal. These findings highlight the apparent overreliance on t-statistics as the primary evaluation metric. T-statistics tend to reject the null hypothesis primarily due to a large numbers of observations (N), a point we examine in detail. As a potential remedy, we evaluate the use of Standardized Regressions (SR). The magnitudes of estimated SR coefficients indicate variables’ relevance directly. Empirical analyses establish a strong correlation between a variable’s estimated SR coefficient magnitude and its incremental explanatory power, without reference to N or t-statistics.

Keywords: explanatory power, classical statistics, large N, standardized regressions

JEL Classification: M40, M41

Suggested Citation

Johannesson, Erik and Ohlson, James A. and Zhai, Sophia Weihuan, The Explanatory Power of Explanatory Variables (September 28, 2020). Available at SSRN: https://ssrn.com/abstract=3622743 or http://dx.doi.org/10.2139/ssrn.3622743

Erik Johannesson

City University of NY, Baruch College, Zicklin School of Business ( email )

One Bernard Baruch Way
New York, NY 10010
United States

James A. Ohlson (Contact Author)

Hong Kong Polytechnic University - School of Accounting and Finance ( email )

M715, Li Ka Shing Tower
Hung Hom, Kowloon
China

Sophia Weihuan Zhai

Hong Kong Polytechnic University - School of Accounting and Finance ( email )

Hung Hom
Kowloon
Hong Kong

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