A Monte Carlo Study of the Necessary and Sufficient Conditions for Weak Separability

Weak separability is an important concept in many fields of economic theory. This paper uses Monte Carlo experiments to investigate the performance of newly developed nonparametric revealed preference tests for weak separability. A main finding is that the bias of the sequentially implemented test for weak separability proposed by Fleissig and Whitney (A New PC-Based Test for Varian’s Weak Separability Conditions, Journal of Business and Economic Statistics 21, 133-143, 2003) is low. The theoretically unbiased Swofford and Whitney test (A revealed preference test for weakly separable utility maximization with incomplete adjustment, Journal of Econometrics 60, 235-249, 1994) is found to perform better than all sequentially implemented test procedures, but is found to suffer from an empirical bias, most likely because of the complexity in executing the test procedure. As a further source of information, we also perform sensitivity analyses on the nonparametric revealed preference tests. It is found that the Fleissig and Whitney test seems to be sensitive to measurement.