Testing for complementarity and substitutability in case of multiple practices

A number of recent empirical studies of firm-level productivity (growth) have been concerned with establishing potential complementarity between multiple organizational design practices. These papers have drawn conclusions on basis of the effect of the interaction term between each possible pair of practices. In this paper we show that this approach may lead to misleading results in case more than two practices are considered. We develop a proper testing procedure for complementarity and substitutability in case there are multiple organizational practices that affect output. The testing methodology is illustrated by empirical examples of three and four innovation practices affecting productivity. The testing framework can easily be applied to test for supermodularity.