On the basis of 50 subsamples of 1012 observations, we get the results for _g_ , numbers of models visited and model size presented in Figure 10. Results are now a bit different from those in the growth applications, as a result of the much larger value of _n_ . In particular, the Maruyama-George, Forte _et al._ and Zellner-Siow priors as well as the case with fixed _g_ = _n_ lead to much higher posterior medians of _g_ , a smaller number of models visited in the chain and smaller mean model size than in the previous applications. Of course, all of these priors depend on _n_ , but it is interesting that the F-Z prior with _a_ = 2 + 2 _/n_ and the hyper- _g/n_ and horseshoe _/n_ priors are less affected. Of course, the benchmark priors and the Bottolo-Richardson prior depend on _n_ through max _{n, k_<sup>2</sup> _}_ , which is here of the same order of magnitude as for the FLS data.

<!-- Start of picture text --> log ( g ) : Random θ , m = 7 Number of Models: Random θ , m = 7 Model Size: Random θ , m = 7<br>G<br>G G<br>G<br>G G G G<br>G G<br>G G G G G G<br>G G<br>1 2 3 4 5 6 7 8 9 11 13 15 1 2 3 4 5 6 7 8 9 11 13 15 1 2 3 4 5 6 7 8 9 11 13 15<br>7<br>4e+05<br>6 3e+05 14<br>5 12<br>2e+05<br>4 10<br>3 1e+05 8<br>0e+00<br><!-- End of picture text -->

**Fig. 10.** Tobias-Li data: log posterior medians of _g_ , number of models visited and posterior mean model size.

Prediction based on prediction subsamples of 178 observations each is summarized in the lower panel of Figure 7. Even though there is some variability in the posterior inclusion probabilities of the regressors over the different priors, we observe virtually identical predictive performance. This is related to the fact that the full model here predicts very similarly to using BMA. This is not surprising as the number of observations _n_ is much larger than the number of potential regressors, so we can hardly overfit and for prediction not much is lost by including all _k_ regressors. In the full model, the only effect that the prior for _g_ has on prediction is the different shrinkage of the coefficients, but as the shrinkage coefficient is very close to one anyway, that will make very little difference. Of course, BMA still has an important role in identifying the important determinants of wages, but is not that critical for prediction. In line with this, the null model does very badly here and never beats BMA or the full model. BMA predicts best in 20% to 46% of the subsamples, with the lowest percentages occurring for the benchmark Beta priors with _c_ = 1 and the fixed- _g_ cases. BMA is beaten by the full model in 42% to 48% of the cases with random _g_ . For the two specifications with fixed _g_ , the full model beats BMA in 52% of the subsamples, while the best model also beats BMA there in over a third of the cases.

Figure 8 tells us that the likelihood marginalized with the prior of everything but _g_ is rather similar to that of the growth datasets. This is perhaps surprising, given that the number of observations _n_ is quite a lot larger in this case. This leads to somewhat similar behaviour of the Bayes factors as for the two growth datasets, with the exception of the 28