Joint Modeling of Individual Differences Across Predictions Mitigates the 'Paradox' of Converging Evidence: Comment on Davis-Stober and Regenwetter (2019)

Davis-Stober and Regenwetter (2019; D&R) showed that even if all predictions of a theory hold in separate studies, not even a single individual may be described by all predictions jointly. To illustrate this 'paradox' of converging evidence, D&R derived upper and lower bounds on the proportion of individuals for whom all predictions of a theory hold. These bounds reflect extreme positive and negative stochastic dependence of individual differences across predictions. However, psychological theories often make more specific and plausible assumptions, such as that true individual differences are independent or show a certain degree of consistency (e.g., due to a common underlying trait). Based on this psychometric perspective, I extend D&R's conceptual framework by developing a multivariate normal model of individual effects. Assuming perfect consistency (i.e., a correlation of one) of individual effects across predictions, the proportion of individuals described by all predictions of a theory is identical to D&R's upper bound. The proportion drops substantially when assuming independence of individual effects. However, irrespective of the assumed correlation, the multivariate normal model implies a lower bound that is strictly above D&R's lower bound if a theory makes at least three predictions. The multivariate model thus mitigates the 'paradox' of converging evidence even though it does not resolve it. Overall, scholars can improve the scope of their theories by assuming that individual effects are highly correlated across predictions.

New Evidence of Asymmetric Dependence Structures in International Equity Markets

A number of recent studies finds two asymmetries in dependence structures in international equity markets; specifically, dependence tends to be high in both highly volatile markets and in bear markets. In this paper, a further investigation of asymmetric dependence structures in international equity markets is performed by using the Markov switching model and copula theory. Combining these two theories enables me to model dependence structures with sufficient flexibility. Using this flexible framework, I indeed find that there are two distinct regimes in the U. S.-U. K. market. I also show that for the U. S.-U. K. market the bear regime is better described by an asymmetric copula with lower tail dependence with clear rejection of the Markov switching multivariate normal model. In addition, I show that ignorance of this further asymmetry in bear markets is very costly for risk management. Lastly, I conduct a similar analysis for other G7 countries, where I find other cases in which the use of a Markov switching multivariate normal model would be inappropriate.