negatively and its square entering positively though neither of the two coefficients enters significantly at the 5% level. In the panel regressions, on the other hand, we find a concave relationship between GDP per capita and Mortgage Depth. As most of the time-series variation comes from high-income countries, this result suggests that the positive relationship between GDP per capita and Mortgage Depth decreases at higher income levels. None of the other explanatory variables enters significantly in the Housing Loan Penetration regression, with the exception of the transition dummy, which enters negatively and significantly at the 10% level. Overall, the benchmarking model performs quite poorly for Housing Loan Penetration, with an R square of only 42%. The model performs considerably better for Mortgage Depth, especially the panel version. Total population, our gauge of country size enters positively and significantly in the panel regression, providing evidence for scale effects. Higher population density is negatively and significantly associated with Mortgage Depth in the panel regression. A higher share of older dependent population enters positively and significantly in the panel regression, while the share of younger dependents enters negatively and significantly in both the cross-sectional and the panel regression. The offshore dummy enters positively and significantly in both panel and cross-sectional regressions, while the transition dummy enters negatively and significantly. The oil-exporting country dummy, finally, enters negatively in both cross-sectional and panel regressions, but not significantly.

The predicted values of this regression indicate a structural depth or penetration for the mortgage market, i.e. a level of mortgage market development, consistent with socioeconomic and demographic characteristics of the host economy. It is important to note the difference between this structural line and the actual frontier as the constrained optimum as the benchmarking exercise does not take into account long-term institutional factors.<sup>13</sup> Next, we compute the Housing Finance Gap computing the difference between the predicted and the actual value of Housing Finance Depth and Penetration. A positive value therefore indicates that the actual value is below the predicted value or that Mortgage Depth or Penetration is below the structural depth or penetration line, while a negative value indicates that the actual is above the predicted value, which might be a potential warning sign of an unsustainable housing boom. Mortgage Depth and Penetration Gaps based on both the crosssectional and the panel regressions are reported in Appendix Table A3, where for the panel version we use the predicted and actual values for 2006-2010 averages.<sup>14</sup> Figure 10 presents the predicted and actual values of Mortgage Depth across different World Bank regions, while Figure 11 presents them across income groups, using cross-sectional regressions, averaged over 2006 to 2010. As before, we use medians rather than averages to reduce the impact of outliers. We find that Mortgage Depth is above its predicted value in East Asia and Pacific and the Middle East and North Africa region, while it is at the predicted value in Europe and Central Asia, South Asia and Sub-Saharan Africa. On the other hand, it is below its predicted value in Latin America. The variation of the Mortgage Depth Gap

> 13 It is important to note that unlike the structural depth or penetration, the frontier is a concept that varies with the time horizon, i.e. certain institutions and policies are part of a shorter-term frontier but not of a longer-term frontier. See Barajas et al. (2013) for a more detailed discussion on this.

> 14 In a few cases, the predicted value is negative and we therefore censor the values at zero.

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