A test for complementarities among multiple technologies that avoids the curse of dimensionality

We propose a strategy to identify the complementarity or substitutability among technology bundles. Under the assumption that alternative technologies are independent, we develop a hypothetical distribution of multiple technology adoptions. Differences between the observed distribution of technology choices and the hypothetical distribution can be subjected to statistical tests. Combinations of technologies that occur with greater frequency than would occur under independence are complementary technologies. Combinations that occur with less frequency are substitute technologies. This method is easily applied to simultaneous decisions regarding many technologies. We use the strategy to evaluate multiple technology adoptions on U.S. hog farms. We find that some technologies used in pork production are substitutable for one another while others are complementary. However, as the number of bundled technologies increases, they are increasingly likely to be complementary with one another, even if subsets are substitutes when viewed in isolation. This finding suggests that farmers have an incentive to adopt many technologies at once. Larger farms and farms run by more educated operators are the most likely to adopt multiple technologies. The complementarity among technologies in large bundles is contributing to a form of returns to scale that contributes to growth in average farm size.