Quantifying the robustness of empirical inferences in strategic management: The impact threshold of a confounding variable and robustness of inference to replacement

In this chapter, we explicate two related techniques that help quantify the sensitivity of a given causal inference to potential omitted variables and/or other sources of unexplained heterogeneity. In particular, we describe the Impact Threshold of a Confounding Variable (ITCV) and the Robustness of Inference to Replacement (RIR). The ITCV describes the minimum correlation necessary between an omitted variable and the focal parameters of a study to have created a spurious or invalid statistical inference. The RIR is a technique that quantifies the percentage of observations with nonzero effects in a sample that would need to be replaced with zero effects in order to overturn a given causal inference at any desired threshold. The RIR also measures the percentage of a given parameter estimate that would need to be biased in order to overturn an inference. Each of these procedures is critical to help establish causal inference, perhaps especially for research urgently studying the COVID-19 pandemic when scholars are not afforded the luxury of extended time periods to determine precise magnitudes of relationships between variables. Over the course of this chapter, we define each technique, illustrate how they are applied in the context of seminal strategic management research, offer guidelines for interpreting corresponding results, and delineate further considerations.