Win/loss data, consumer switching costs : measuring diversion ratios and the impact of mergers

The diversion ratio is a key input to many indicators of merger harm. Measuring the diversion ratio, however, is challenging in the presence of state dependence driven by things like consumer switching costs. We propose an identification strategy for diversion based on win/loss data. First, we show that win/loss data from the merging firms and market shares for all firms in two periods are sufficient to identify the diversion ratios between the merging partners. Second, we show that win/loss data from the merging firms alone are sufficient for partial identification, and we construct a lower bound that provides a good approximation to the diversion ratio when switching costs are high. We demonstrate the performance of our method with numerical simulations and with an application to the Anthem/Cigna merger.