The relative performance of bivariate causality tests in small samples

Abstract

Causality tests have been applied to establish directional effects and to reduce the set of potential predictors. For the latter type of application only bivariate tests can be used. In this study we compare bivariate causality tests. Although the problem addressed in general and could benefit researchers from different fields, most attention is given to marketing applications. Even though there are many alternative tests, applications in marketing have almost exclusively been based on the Haugh—Pierce test. We compare five bivariate tests in a specific marketing application. The empirical results indicate that conclusions about causality may depend strongly on the test used. To provide generalizable insights about the relative performances of alternative tests we conduct a simulation study with data characteristics that cover the range of conditions encountered by researchers who have applied causality tests in marketing. We find that the Granger—Wald test has the highest power but also the greatest upward bias in alpha (the probability of a type-I error). If causality testing is done for the purpose of selecting a good subset of the available predictors, this combination of high power and high alpha may be attractive. For researchers desiring a simple test with a substantial amount of power and little upward bias in alpha we recommend the Granger—Sargent test. Interestingly, neither of these Granger tests has been used in marketing.