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

The hypothetical distribution of multiple technology adoptions under the assumption that technologies are mutually independent is compared against the actual observed distribution of technology adoptions on hog farms. Combinations of technologies that occur with greater frequency than would occur under independence are mutually complementary technologies. Combinations that occur with less frequency are substitute technologies. This method is easily applied to simultaneous decisions regarding many technologies. We find that some technologies used in pork production are mutually 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. Our findings suggest that the complementarity among technologies in large bundles is contributing to a form of returns to scale that is leading to increasing growth in average farm size.