and Spanish colony dummies. They find pairwise disjointness between the Fraction tropical area and Malaria prevalence and between the Sub-Saharan dummy and Malaria prevalence (whereas we found this disjointness to exist only through the triplet). In addition, none of the jointness relations we find are identified by the DW criterion. Of course, finding conclusive evidence of jointness in the sense of DW in cases where the inclusion probability of one of the variables exceeds 0 _._ 37 is precluded by the very definition of _Jij_<sup>_DW_</sup> , as explained in Section 2. The criterion in DWa identified jointness in four of the seven pairs in which we encountered at least weak jointness. However, two of the three remaining pairs (East Asian dummy with the investment price and with primary school enrollment) are labelled significantly disjoint according to _Jij_<sup>_DW a_</sup> . As the three variables involved are the ones with highest posterior inclusion probabilities, this may be related to the potentially erratic behaviour of _Jij_<sup>_DW a_</sup> for important regressors, as discussed in Section 2. Both the measures of DW and especially that of DWa indicate many bivariate jointness links beyond those found through _Jij_ . All this clearly shows that the DW and DWa jointness measures provide very different summaries of the posterior distribution than the measure introduced here.

# **4. Concluding Remarks**

Growth regressions are affected by uncertainty regarding which regressors to include from a set of _k_ potential covariates, where _k_ could be quite large ( _k_ = 41 and _k_ = 67 in our applications). Bayesian Model Averaging is an effective and intuitive way of dealing with this problem and leads to a _k_ -dimensional posterior distribution for the vector of regression coefficients _β_ , which consists of a mixture of continuous distributions and point masses in each dimension. Summarizing such a posterior distribution beyond the information contained in these marginals is quite challenging and requires well-honed tools for extracting relevant pieces of information. It is important that these tools provide us additional insight into properties of the posterior that are particularly interesting for both researchers and policymakers, and that they are easy to interpret. We argue that our jointness measure proposed in (8) satisfies both criteria: it addresses relevant questions and is directly interpretable as the posterior odds ratio between models that include a set of variables and models that include only proper subsets. In addition, it is naturally defined for any set of regressors and is not restricted to bivariate jointness evaluations (between variables or sets of variables).

We applied this jointness measure to two data sets used for growth regressions in the recent literature. In both data sets we encounter jointness only between important determinants of growth. The regressors involved are complements in that each of them has a separate role to play in explaining growth. Much more frequently, we encounter situations of disjointness, where regressors are substitutes and really should not appear together in interesting growth models. However, the regressors displaying disjointness relationships tend to be fairly unimportant drivers of growth. When we consider triplets rather than pairs of variables, these conclusion are strengthened in that we find even less jointness and more disjointness. However, even then decisive disjointness is mostly confined to variables with relatively small posterior inclusion probabilities.

Thus, the data sets analysed here seem to contain a few key growth determinants that have a clearly defined and separated role to play, and should, thus, occur jointly in growth regressions, while a substantial fraction of the regressors is of relatively small importance and captures effects that can also be accounted for by other regressors. In between we have a number of variables with typically moderate explanatory power and no clear jointness or disjointness relationships. It 14