Jointness of growth determinants

Abstract

SUMMARYThis paper introduces a new measure of dependence or jointness among explanatory variables. Jointness is based on the joint posterior distribution of variables over the model space, thereby taking model uncertainty into account. By looking beyond marginal measures of variable importance, jointness reveals generally unknown forms of dependence. Positive jointness implies that regressors are complements, representing distinct but mutually reinforcing effects. Negative jointness implies that explanatory variables are substitutes and capture similar underlying effects. In a cross-country dataset we show that jointness among 67 determinants of growth is important, affecting inference and informing economic policy.

Unveiling covariate inclusion structures in economic growth regressions using latent class analysis

“…In this group of models, two of the most relevant variables in terms of (unclustered) PIP, EAST and TROPICAR, lose their importance and their information is captured by a different set of geographical and religious variables (CONFUC, LAAM and SAFRICA). The results in Doppelhofer and Weeks (2009a) concerning the complementarity of EAST and TROPICAR and the substitutability of EAST with respect to CONFUC, LAAM and SAFRICA are perfectly in line with these results. In addition, Doppelhofer and Weeks (2009a) find the latter to be complements, which is also supported by the comparison of the PIPs in our third cluster with those in the other two.…”

“…The difference in average model size across these two important clusters in the space of posterior inclusion probability structures is in line with the strong impact of different parameter shrinkage approaches on the relative importance of the variables which is highlighted in previous literature. In addition, in their study of pairwise jointness measures, Doppelhofer and Weeks (2009a) report that P60, IPRICE1, DENS65C and TROPICAR exhibit significant negative bivariate jointness with MALFAL66, a result that can be easily reconciled with the output of our analysis. While Ley and Steel (2007) find very limited evidence for jointness structures in the SDM dataset, the only triplets of important variables for which disjointness is reported also involve TROPICAR and MALFAL66.…”

“…Such a concept has been quantified in the form of bivariate jointness measures in the context of BMA, put forward first by G. Doppelhofer and M. Weeks in a working paper of 2005 (Doppelhofer et al, 2005), which got published in a slightly different version as Doppelhofer and Weeks (2009a). Ley and Steel (2007), Strachan (2009) and Ley and Steel (2009a) offer alternative measures of jointness.…”

“…Additionally, they propose two other indices which satisfy all of their suggested properties. Strachan (2009) shows that the interpretability of the jointness measure of Doppelhofer and Weeks (2009a) may be limited in contexts where one or both of the analyzed variables have a negligible PIP and offers yet another measure in order to tackle this shortcoming. Doppelhofer and Weeks (2009b), on the other hand, argue that another desirable property of jointness measures happens to be fulfilled by their indicator but not accounted for in the indices of Ley and Steel (2007) or Strachan (2009).…”

“…The statistic of Doppelhofer et al (2005) is known as log-ratio, the measures of Ley and Steel (2007) are related to the Jaccard index. The index of Doppelhofer and Weeks (2009a) is known as odds-ratio and Strachan (2009)'s measure is closely related to the so-called two-way support (see Tan et al, 2004;Glass, 2013).…”