Following the theoretical innovations of complementarity theory, management control studies have investigated interdependencies between different management control practices. In this paper, we compare the two dominant statistical specifications to test for the presence of an interdependency. We show theoretically how the power of the demand and the performance specification varies with the level of optimality in the sample and how those specifications are vulnerable to correlated omitted variable bias. Our simulation results reveal that the demand specification is more robust to variations in optimality and correlated omitted variables than the performance specification. We use these results to formulate recommendations for future research into management control interdependencies.