led to very similar findings. For completeness, Table 1 also displays the estimated total posterior model probability visited by the chain, computed as suggested in George and McCulloch (1997).

For the random _θ_ cases, the specification and the posterior probability of the best model is not much affected by the choice of _m_ . However, changing from _g_ = 1 _/n_ to _g_ = 1 _/k_<sup>2</sup> has a dramatic effect on both.

Finally, the size of the best model varies in between 5 and 20, and is not much affected by _m_ for random _θ_ .

Of course, one of the main reasons for using BMA in the first place is to assess which of the regressors are important for modelling growth. Table 2 presents the marginal posterior inclusion probabilities of all regressors that receive an inclusion probability of over 10% under any of the prior settings. It is clear that there is a large amount of variation in which regressors are identified as important, depending on the prior assumptions.

Whereas three variables (past GDP, fraction Confucian and Equipment investment) receive more than 0.75 inclusion probability and a further two (Life expectancy and the Sub-Saharan dummy) are included with at least probability 0.50 in all cases, there are many differences. If we compare cases that only differ in _m_ , the choice of _g_ = 1 _/n_ with fixed _θ_ leads to dramatic differences in inclusion probabilities: Fraction Hindu, the Labour force size, and Higher education enrollment go from virtually always included with _m_ = 20 _._ 5 to virtually never included with _m_ = 7; the Number of years open economy has the seventh largest inclusion probability for _m_ = 7 and drops to the bottom of the 32 variables shown in the table for _m_ = 20 _._ 5. In sharp contrast, the case with _g_ = 1 _/k_<sup>2</sup> and random _θ_ leads to very similar inclusion probabilities for both values of _m_ .

Finally, note that results for model size, chain behavior and inclusion probabilities are quite similar for the cases where _g_ = 1 _/n_ with fixed _θ_ = 7 _/_ 41 (the preferred implied prior in SDM) and where _g_ = 1 _/k_<sup>2</sup> with _θ_ = 0 _._ 5 (the prior used in FLS). This is in line with the negative trade-off between _g_ and _m_ illustrated in Figure 4, which explains the similarity between empirical results using BACE and the FLS prior on the same data. The same behavior is observed for the other datasets presented in the next subsections.

# _4.2. The Data Set of MP_

MP investigate the role of initial conditions at independence from colonial rule on the economic growth of African countries. They focus on the average growth rate in GDP from 1960 to 1992 and construct a dataset for _n_ = 93 countries with _k_ = 54 covariates, obtained by combining 32 original regressors and 22 interaction dummies.

Table 3 records the main characteristics of model size and the MCMC chain, and illustrates that results are quite close to those with the FLS data, leading to the same conclusions. Probably due to the somewhat larger model space, convergence is now even more problematic for the fixed _θ_ case the chains. Longer chains will typically capture marginally more of the posterior probability, but they will only add models with very small posterior probabilities and this will not affect any of the conclusions.

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