Academic journal article Electronic Journal of Business Research Methods

Negative Denominators in Index Variables: The Vulnerability of Return on Equity, Debt to Equity, and Other Ratios

Academic journal article Electronic Journal of Business Research Methods

Negative Denominators in Index Variables: The Vulnerability of Return on Equity, Debt to Equity, and Other Ratios

Article excerpt


For decades, management scholars have criticized their own field for not placing the same importance on the measurement of variables representing constructs as is placed on the theory connecting those constructs (Venkatraman and Grant, 1986, Lubatkin et al., 1993, Hoskisson et al., 1993, Boyd et al., 2005b, Boyd et al., 2005a, Boyd et al., 2013, Ketchen et al., 2013). A lack of confidence that our measures reflect the constructs we intend them to, forces us to question the validity and reliability of our field's findings (Wiseman and Choi, 2011). One place where this occurs is when scholars use index variables (in which one number is divided by another) to operationalize a construct. It is important to ensure that the denominator of the index cannot become negative. If the denominator of an index can become negative, the data requires careful examination because the validity of any statistical analysis is jeopardized if the data includes indexes with negative denominators. The concern here is twofold. First, these indexes will not possess ordinal properties throughout the full range of observations. This limits our ability to compare different values for such indexes. As is shown in this paper, negative denominators can cause two indexes representing the same theoretical construct to have no statistical relationship to one another. Second, it may be difficult, if not impossible, to interpret the meaning of such indexes when the denominator of the index includes negative values. The inclusion of such cases distorts any analyses based on the related index measures. Evidence from contemporary research suggests that management scholars may not be aware of these issues or address them properly, which may have led to the publication of erroneous or misleading results. Further, when the weaknesses of common negative denominator ratios, such as return on equity and debt to equity, are discussed in publications, the issues outlined in this paper are not highlighted (Gallo, 2016, Gallo, 2015).

The purpose of this research paper is fivefold. First, we explain and illustrate why organization scholars should exhibit caution when using indexes in which the denominator can be negative, which we title negative denominator indexes. Second, using variables from strategic management as exemplars, we highlight the prevalent use of negative denominator indexes which suggests that scholars are unaware of this problem because most research papers do not mention transformations to negative denominator indexes. Therefore, we review negative denominator indexes used in strategic management, and show the frequency in which these measures are used in major publications. Third, to illustrate the effects on analyses, we replicate relative aspects of a published study and show substantial changes in results when accounting for our concerns. Fourth, we critically review potential remedies of the problems described and find that transformations of negative denominator ratios have potential flaws. Finally, we offer recommendations that improve the interpretability of findings.

2.Literature Review

Before we begin, it is important to define and clarify our terminology. Following established terminology (Stevens, 1951), we refer to single variables such as net income, total assets, total liabilities and total equity as scales. Scales can either be nominal, ordinal, interval, or ratio in nature. When one scale is divided by another scale, such as net income divided by total assets to create the measure return on assets, we refer to the quotient as an index (following Cohen et al., 2003). Analog to scales, indexes can have nominal, ordinal, interval, or ratio properties.

The appropriate use of indexes has gained more scrutiny in the business literature recently (Faello, 2015). Additionally, indexes are prominently being used in contemporary research in the areas of firm performance (Mubashar and Tariq, 2017), operations (Färe and Karagiannis, 2017), real estate (Mills, 2016) as well as accounting and finance (Kristanti and Herwany, 2017). …

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