Consistent Testing for an Implication of Supermodular Dominance

Supermodularity, or complementarity, is a popular concept in economics which can characterize many objective functions, including utility, social welfare, and production functions. Further, supermodular dominance captures a preference for greater interdependence among inputs of those functions, and it can be applied to examine which input set would produce higher expected utility, social welfare, or production. However, contrary to the profuse literature on supermodularity, to the best of our knowledge, there is no existing work on either testing or empirical analysis for supermodular dominance. In this paper, we propose a consistent test for a useful implication of supermodular dominance and suggest a correlation dominance testing for Gaussian random variables as a special case. The test is based on a novel bootstrap critical value, which has potentially enhanced power performance by exploiting the information on the contact set on which the null hypothesis is binding. We also conduct Monte Carlo simulations to explore the finite sample performance of our tests. We then apply our test to analyze two economic questions. We first investigate whether the interdependence of stock returns among major firms has increased after the COVID-19, and find evidence supporting this conjecture. We also compare the interdependence of patent citations depending on distance, where greater interdependence can imply greater expected social welfare effect. The results suggest that, in most cases, between-state citations seem to have greater interdependence than within-state citations, implying that lively interaction between firms across states might engender greater expected social welfare than knowledge spillover within a geographically confined area.