Modeling and Interpreting Interactions in Tradeoff Research

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We examine the use of regression interaction terms in accounting research, focusing on studies of tax and financial reporting tradeoffs. We attempt to correct misunderstandings about interaction terms found in studies published in top accounting journals, reconcile disagreement about using interactions to test tradeoffs, and examine related statistical issues and techniques. Interaction terms allow for tests of whether the rate at which firms trade competing incentives is dependent on the magnitude of the incentives. We begin by defining the term tradeoff and distinguish a linear model, with no interactions, from an interaction model. We then discuss statistical issues that affect the interpretation and design of interaction models. Although we advocate the use of interaction models in tradeoff research, we show via simulation that noise levels common in tradeoff research greatly reduce the ability to statistically detect interaction effects. We discuss potential solutions and the need to provide a balanced discussion of unconditional and conditional effects so readers appreciate that Type II error may be hiding systematic differences in an effect across firms.