Testing for Complementarity and Substitutability among Multiple Technologies: The Case of U.S. HogFarms

We propose a strategy to identify the complementarity or substitutability amongtechnology bundles. Under the assumption that alternative technologies are independent,we develop a hypothetical distribution of multiple technology adoptions. Differencesbetween the observed distribution of technology choices and the hypothetical distributioncan be subjected to statistical tests. Combinations of technologies that occur with greaterfrequency than would occur under independence are complementary technologies.Combinations that occur with less frequency are substitute technologies. Unlike pastanalyses of technology adoption, this method is easily applied to simultaneous decisionsregarding many technologies. We use the strategy to evaluate multiple technologyadoptions on U.S. hog farms. We find that some technologies used in pork production aresubstitutable for one another while others are complementary. However, as the number ofbundled technologies increases, they are increasingly likely to be complementary withone another, even if subsets are substitutes when viewed in isolation. The resultingincentive to adopt many technologies at once leads to economies of scale, contributing togrowth in average farm size over the past 20 years.[...]