employed by Beck et al. 2005 for their survey, though data for China has not been included in that survey.<sup>38</sup> Given these numerous difficulties it is heartening to discover that data on bank account numbers and on average bank account size (as a proportion of GDP) are quite closely correlated with household survey-based data on access percentages (Table A1, regressions A and B; and Figure 6). The log-linear relationship is close enough to suggest using extrapolating fitted values for countries in which there is no household survey data available. Using the bank account database, this allows synthetic access percentages to be derived for about 45 countries. Even more encouraging, for countries where both exist, the bank account numbers are quite highly correlated with – though not equal to – the WSBI numbers (Table A1, regression L). Thus, where the number of bank accounts is not known but the WSBI numbers are, we can use the fitted relationship to compute a substitute regressor. Using this substitute, we obtain G, which shows that the relation between accounts numbers and household survey data holds up well on a much wider sample. The coefficient values from G can then be used to approximate access percentages for all 138 countries in the WSBI database. As a further refinement, noting also the correlation between the deposit size data and GDP per capita (regression M) one can proceed in an analogous way using the fitted values from M as regressors in J, whose coefficient values in turn generates an alternative approximation to the access percentages. We call this alternative the **_synthetic_** access percentage.

In notation, let _mi_ is the ratio of MF accounts and _bi_ the ratio of bank accounts to adult population in country _i_ ; let _hi_ be the household survey-based percentage access, _zi_ the average deposit size and _yi_ per capita GDP.

ˆ Let α _k_ be the fitted values in a log-linear regression of _b_ on a constant term and _m_ , and β<sup>ˆ</sup> _k_ the fitted values in a regression of _zi_ on a constant and _y_ .

ˆ ˆ ˆ ˆ Then, let _bi_ = _bi_ for countries where data on _bi_ is available, _bi_ = α 0 + α 1 log( _mi_ ) otherwise; ˆ ˆ ˆ ˆ _zi_ = _zi_ for countries where data on _zi_ is available, and _zi_ = β 0 + β 1 _yi_ otherwise.

Let γ ˆ _k_ be the fitted coefficient values from a log-linear regression of _h_ on a constant, _b_<sup>ˆ</sup> and _z_ ˆ . The **_synthetic_** access percentages are then obtained by computing γ ˆ0 +γ ˆ1 log _b_ ˆ +γ ˆ2 log _z_ ˆ .

A final adjustment is to replace this last mentioned synthetic access data with surveybased data where available. The result<sup>39</sup> is the **_composite_** indicator tabulated in Table 1, and on which Figures 5, 7 and 8 are based.

> 38 The household survey percentages used here are drawn from the compilation in Claessens (2005), the original surveys were conducted with various methodologies and at various dates between 1988 and 2004. Including the date of the survey in the various regressions changes little.

> 39 In addition, a final adjustment was made to prefer the predictions from B to those from J, where the former was larger.  I.e. the WSBI data was not allowed to result in a lower composite estimate than would

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