The Explanatory Power of Explanatory Variables

48 Pages Posted: 1 Jul 2020 Last revised: 11 May 2022

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 examines empirical accounting research. We ask: in general, do the results related to the estimated regressions support the promoted storylines? We focus on a regression model’s main variable of interest and consider the extent to which it contributes to the explanation of the dependent variable. We replicate ten recently published accounting studies, all of which rely on significant t-statistics, per conventional levels, to claim null-rejection. Our examination shows that in eight studies 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. A close look at the data shows that the t-statistics produced reject the null hypothesis primarily due to a large number of observations (N). Studies often require N>10,000 for null-rejection. To avoid this drawback of t-statistics with large N, we consider the implications of using Standardized Regressions (SR). SR coefficients, as estimated, 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, t-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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