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Research article

First published February 2007

Interpreting dummy variables and their interaction effects in strategy research

Paul S. L. Yip and Eric W. K. Tsang View all authors and affiliations

Volume 5, Issue 1

https://doi.org/10.1177/1476127006073512

Contents
- Abstract
- References
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Abstract

Dummy variables have been employed frequently in strategy research to capture the influence of categorical variables. However, misinterpretation of results may arise, especially when interaction effects between dummy variables and other explanatory variables are involved in a regression. We discuss two approaches of entering dummy variables into a regression and their associated interpretations. We discuss some common mistakes of interpretation and hypothesis testing found in two recently published strategy papers, and highlight the advantages of our recommended approach over the approach usually adopted by management researchers.

1 It should be noted that dummy variables are usually subject to some kind of constraints that require treatments different from other explanatory variables. For example, if a full set of dummies is mutually exclusive and exhaustive, such as the case of foreign and domestic firm dummies, the sum of the full set of dummies should equal to a vector of one. As we illustrate in the following sections, misinterpretations committed by researchers often originate from the failure to recognize the implicit restriction among the full set of dummies. Owing to this implicit restriction, some of the discussions of multiplicative terms formed by non-dummy independent variables (Aiken and West, 1991; Friedrich, 1982; Irwin and McClelland, 2001; Stone and Hollenbeck, 1989) may not be applicable to the case of multiplicative terms with dummy variables.

2 If the dependent variable is a categorical variable, the regression will be a limited dependent variable estimation (see Maddala, 1983 for more details).

3 Vermeulen and Barkema’s (2001) study is one of the few examples that use the partition approach. Under the column ‘Survival Analysis 2’ in their Table 2, the multiplicative terms between Z_it (i.e. number of preceding greenfields or number of preceding acquisitions) and two dummy variables, namely greenfield and acquisition, together partition the effect of Z_it for greenfield subsidiaries and acquired subsidiaries respectively. Another example is Kim et al.’s (2004) study, which uses two dummy variables to distinguish between keiretsu member firms with strong power and those with weak power.

4 If the regression contains Z_i and Z²_i as explanatory variables, one can also expand them into partition terms of Z_i and partition terms of Z²_i. Nevertheless, researchers should always check whether their polynomial equation is a good approximation of the true relationship.

5 In some other disciplines, the coefficients are sometimes rightly interpreted as the difference of differences in the slopes. Nevertheless, as we show later, the partition specification still has obvious advantages over the base specification in terms of its flexibility in formulating and testing hypotheses among various combinations of coefficients.

6 For simplicity of presentation, we have compressed all the other explanatory variables in X_it θ of equations 3# and 7#. Both equations are in fact well-specified models under the base approach.

7 There seems to be a typo here. It should be hypothesis 4 rather than hypothesis 5.

8 The purpose of our survey was to demonstrate that this problem of misinterpretation of interaction effects is more widespread than many readers might suppose; but this purpose did not include criticizing particular researchers or lines of research. Hence, the specific papers in our survey are not listed here, but they are available upon request.

9 As the PIMS dataset used in the study only has three categories of entrants, we do not have any strong objection to the use of dummy variables. Nevertheless, the use of dummies instead of continuous time entry variables could result in loss of information. Whenever possible, researchers are advised to code their data in continuous measures instead of categories.

10 The two equations in the second panel of their Table 3 (and Table 4) are jointly estimated. Although we only discuss the first equation here for simplicity of presentation, similar comments apply to the second equation.

11 The proof is available from us upon request.

12 With the help of the partition specification and equations 9a–h, the researcher can use the regression result of the base specification in equation 9 to test any combination of coefficients without the need of re-doing the estimation. For example, if he/she wants to test whether c₇ > c₈, he/she can conduct an equivalent test on whether λ₂ + λ₄ + λ₆ + λ₈ > 0.

References

Aiken, L. S. and West, S. G. (1991) Multiple Regression: Testing and Interpreting Interactions. Newbury Park, CA: Sage .

Interpreting dummy variables and their interaction effects in strategy research

Abstract

References

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