that the restrictions that are the use of the credit-to-GDP ratio are implied by supported by our cross-country panel data. Our view thus is that the use of the credit-to-GDP ratio to determine equilibrium credit, and therefore also to determine excessive credit provision, appears to be inappropriate.

# **4.3. Linking the cross country variation to country-specific characteristics**

As outlined in Section 3.1.3, we use the BMA framework to reduce the large set of 42 potential development indicators to a smaller subset of around 15 _−_ 20 variables. The criterion for inclusion of a given variable in the subset is its posterior inclusion probability (PIP). We use a PIP threshold value of 25% for a variable to be included in the subset. This value may seem low, nonetheless, the purpose here is to perform a first round of _”pruning”_ rather than finding the final model.<sup>30</sup> Our objective is to reduce the set of all potential regressors to a smaller set of highly relevant determinants of the cross-country variation in _β_<sup>_gdp_</sup> and _β_<sup>_de f_</sup> . The Lasso is thus used as a variable selection tool.<sup>31</sup> Note that we follow the same variable selection or reduction procedure to model the cross-country variation in the _β_<sup>ˆ</sup><sup>_gdp_</sup> as well as in the _β_<sup>ˆ</sup><sup>_de f_</sup> and _α_ ˆ coefficients. To avoid unnecessary repetition and to keep the section as short and informative as possible, we only present the BMA and Lasso regression results for the _β_<sup>ˆ</sup><sup>_gdp_</sup> coefficient in this section and provide equivalent results for the _β_<sup>ˆ</sup><sup>_de f_</sup> and _α_ ˆ coefficients in the Appendix. Also, we will initially refer to the regressors in the preliminary discussions of the BMA and Lasso estimations in Section 4.3.1 and Section 4.3.2 by their short names listed in the first column of Table 3 and Table 4. Although the short names are not very informative, these are only preliminary discussions to highlight some initial variable exclusion results.<sup>32</sup> We discuss the economic meaning of the regressors and their significance in the context of the final selected models in detail in Section 4.3.3.

> 30Eicher _et al._ (2011) have recently used a PIP value of 50% as the variable inclusion threshold in a growth regression context to determine the _”Number of Effective Regressors”_ (see Figure 1 on page 38). One could thus naturally adopt that value here as well or even set the cut-off mark higher. Nonetheless, we do not follow such an approach here and use the Lasso penalized regression estimator instead in a second step to further ” _shrink_

> 31It should be clear that the posterior mean of the BMA procedure under the given priors that we use is analogous to a Ridge regression estimator, which is also a penalised regression estimator like the Lasso, with the penalty function being the sum of squared coefficients rather than the sum of absolute coefficients (see (17) for the objective function of the Lasso). One important difference between the Lasso and the Ridge regression estimator is that the Ridge estimator cannot shrink coefficients to zero, but only to small values to reduce the importance of these variables. This means that all variables are included in the regression, which we want to avoid, given the large number of potential regressors. The advantage of the Lasso is that it shrinks unimportant variables to zero, thereby acting as a variable selector. We should also point out here that the reason why we use the BMA in the first step rather than using the Lasso on the full set of 42 potential regressors is that we ran into numerical problems when implementing the penalised regression procedure using the Matlab lasso function. We therefore found it sensible to reduce the number of potential regressors to a smaller subset first and then proceed with the Lasso.

32A more detailed description of these variables is provided in the second column of these tables.

24