0.3 for cases of GII‐12, GII‐45, GII‐303, DB‐10, and DB‐41. We choose this number so that a high positive correlation between posterior model probabilities based on empirical frequencies and the exact analytical likelihoods is obtained. We also report estimated total posterior model probabilities visited by the chain using a measure of George and McCulloch (1997).

Note also that in our GII application the number of candidate explanatory variables far exceeds the number of countries when we work with the GII data at the highest level of disaggregation (K=303 but N=70). This means that the space of models to be considered potentially includes very many models that cannot feasibly be estimated since there are more regressors than observations. In this paper we take the shortcut of ignoring this feasibility constraint. We find that, given our choice of prior parameters, the BMA algorithm is able to cover a very high fraction of the posterior probability without ever attempting to visit infeasible models with K>N.<sup>16</sup> This is because our choice of priors ensures that the model size penalty is sufficiently high that such large models have extremely small posterior probabilities.<sup>17</sup> Finally we acknowledge at the outset the important caveat that we are combining inferences from a series of very simple linear OLS regressions. As such, all of our conclusions are subject to the usual limitations of such a model. In particular, a maintained assumption is that the error term is independent of the regressors in all models, an assumption that would clearly be violated if there were reverse causation or omitted variables. We also by assumption rule out any plausible nonlinearities such as interactive effects between variables. As we discuss further below however, addressing these very likely important issues we think would only further reinforce our basic point – that it is extremely difficult to identify a small subset of indicators that are robust determinants of outcomes of interest.

16 More formal approaches to the K>N problem are available. One approach is to formally apply a prior weight of zero to infeasible models. Another example is Eicher, Papageorgiou and Roehn (2007) who propose an iterative BMA procedure applicable when K>N. For a non‐Bayesian approach to this problem, see Candes and Tao (2005) propose an algorithm that can reliably estimate the parameters of a single “true” model with Kj<N variables from a dataset of candidate variables X where K>>N even when the subset of the columns of X included in the “true” model is not known a priori.

17 To see this, note that in the case of GII‐303, the largest model visited by the BMA algorithm has 16 explanatory variables when CPIA is an outcome variable, 25 when DRI is an outcome variable, 19 when EIU is used, and so on. Consider now comparing this with the smallest infeasible model with ki=70. Given K=303 and our choices of =10 and g=0.01 , the model size penalty in the first two terms of Equation (6) would be on the order of 1.7x10<sup>‐99</sup> , suggesting that infeasible models have vanishingly small posterior probabilities and so can safely be ignored. This dimensionality problem also means that we cannot use alternative model selection techniques based on encompassing regressions advocated by Hendry and Krolzig (2004, 2005).

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