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Grant and Lebo (2016) and Keele et al. (2016) clarify the conditions under which the popular general error correction model (GECM) can be used and interpreted easily: In a bivariate GECM the data must be integrated in order to rely on the error correction coefficient, $\alpha _1^\ast$, to test cointegration and measure the rate of error correction between a single exogenous x and a dependent variable, y. Here we demonstrate that even if the data are all integrated, the test on $\alpha _1^\ast$ is misunderstood when there is more than a single independent variable. The null hypothesis is that there is no cointegration between y and any x but the correct alternative hypothesis is that y is cointegrated with at least one—but not necessarily more than one—of the x's. A significant $\alpha _1^\ast$ can occur when some I(1) regressors are not cointegrated and the equation is not balanced. Thus, the correct limiting distributions of the right-hand-side long-run coefficients may be unknown. We use simulations to demonstrate the problem and then discuss implications for applied examples.

We investigate the effect of personality on prosocial behavior in a Bayesian multilevel meta-analysis (MLMA) of 15 published, interdisciplinary experimental studies. With data from the 15 studies constituting nearly 2500 individual observations, we find that the Big Five traits of Agreeableness and Openness are significantly and positively associated with prosocial behavior, while none of the other three traits are. These results are robust to a number of different model specifications and operationalizations of prosociality, and they greatly clarify the contradictory findings in the literature on the relationship between personality and prosocial behavior. Though previous research has indicated that incentivized experiments result in reduced prosocial behavior, we find no evidence that monetary incentivization of participants affects prosocial tendencies. By leveraging individual observations from multiple studies and explicitly modeling the multilevel structure of the data, MLMA permits the simultaneous estimation of study- and individual-level effects. The Bayesian approach allows us to estimate study-level effects in an unbiased and efficient manner, even with a relatively small number of studies. We conclude by discussing the limitations of our study and the advantages and disadvantages of the MLMA method.