Hic Sunt Dracones: On the Risks of Comparing the ITCV With Control Variable Correlations

Abstract

To examine the robustness of their results against omitted variable bias, management researchers often compare the Impact Threshold of a Confounding Variable (ITCV) with control variable correlations. This paper describes three issues with this approach. First, the ITCV and control variable correlations are measured on mathematically different scales. As a result, their direct comparison is inappropriate. Second, a fair comparison requires a rescaled version of the ITCV known as “the unconditional ITCV.” Third, even the interpretation of the unconditional ITCV is complicated by the presence of multiple omitted variables, numerous control variables, and correlations between the omitted and control variables. We illustrate these issues with simple computer-generated data, a Monte Carlo simulation, and a practical application based on a published dataset. These results suggest that rules of thumb based on ITCV and control variable correlations are misleading and call for alternative ways of running, interpreting, and reporting the ITCV.