<!-- Start of picture text --> j = 2 G Decisive<br>Very Strong<br>3 GG 4 GG 34 Strong<br>G 4 Positive<br>5 5<br>GG GG GG GG G G<br>G G G<br>i = 1 GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG 2 GGGGGGGGGGGGGGG G GGGGGGGGGGGGGGGGGGG 3 GGGGGGGGGGGGGGG G GGGGG G GGGGGGGGGGGGG 4 GGGGGGGGGGGGGGGGG GG GGG G GGGGGG 5 G G GGG G GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG ... GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG G GG GG GGGGGGGGGGGGGGGGG G GGG G GGGGGGGGG G G G GGGGGGG G GGGGGGGGGGGGGGGG G G GGG G G GGGG G GG G GGGGGGGGGGGGGGGGG G GG G GGGGGGGGGGGGGGGGGG G GGGGGG G GGG G GGGGGGGGGGG G GGGGGG G GGGGGGGGGGGGGGGGGGGGGGGGGGGG G GGGGGG G GGGGGG G GGGGGGG G GGGGGGGGGGGGGGGGGGGGGGGGGG G GGGG G G G GGGGGGGGGGGGGGGGGG GG G G GGGGGGGGGGGGGGGGG G GGGGG G GGGGGGGGGGGGGGG Decisive GGGGGGGGGGGGGG G G G GGGGGGGGGGGGGG G GGGGGG G GGGG G G G GGGGGGGGGGGGGGGGGGGGGGG GG GGGGGG G GGGGGGGGGGGGGGGG G GGGGGGGGGGGGG G GGGG GG GGGG GG GGGGGGGGGGG GGGGG GG GG GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG G GGGGGGGGG G G Very Strong GGGGGGGGGGGG Positive GGG Strong G GGGGGGGGGGGGGGGGG GG GGGGGGGGGGGGGGGGG<br>0 200 400 600 800<br>Ordered by P(i), then by P(j)<br>4<br>2<br>0<br>−2<br>−4<br>log of Posterior Odds: P(i and j) vs P(i or j but not both)<br>−6<br><!-- End of picture text --> Fig 3. FLS data: Log posterior odds in favor of jointness, log( _Jij_ ).

regions.<sup>6</sup> Only 8 pairs (1% of the total) display some degree of evidence for jointness. These are variables 1 and 2 (GDP in 1960 and Fraction Confucian), which show decisive jointness, the pairs (1 _,_ 3), (1 _,_ 4), (2 _,_ 3), (2 _,_ 4) display strong evidence of jointness, while there is positive evidence for (1 _,_ 5), (2 _,_ 5), and (3 _,_ 4). As was already suggested by Fig. 2, only the regressors with high values for _P_ ( _i ∩ j_ ) and thus, high marginal inclusion probabilities tend to appear jointly in the growth regressions. Both of these probabilities are over 0 _._ 75 for the pairs mentioned above, and over 0 _._ 93 for those pairs with strong or decisive jointness. This means that we do not have, for this data set, any regressor pairs that virtually always appear together, while appearing in less than 75% of the visited models. Fig. 4 summarizes the jointness results graphically. The nodes are proportional to posterior probabilities of inclusion and the thickness of the joining lines is proportional to log( _Jij_ ) for any pair.

Examining sets of more than two regressors, we note that jointness of all four triplets of the first four variables is supported by posterior odds of 7 to one and higher, whereas the jointness of all four of these variables is favorably supported by posterior odds of 7.8. Posterior odds pertaining to jointness for the first five variables, however, are only 2 to one.

Table 1 shows that the visited models typically have 9 or 10 regressors. This means that models tend to have five or six regressors in addition to the four or five that are usually present. Since we

> 6 These cutoff points are easily interpretable— _e.g._ , positive evidence implies the models with both regressors get more than three times as much posterior probability as those with only one of the regressors. The actual values of the cutoff points are inspired by Jeffreys (1961, p. 432).

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