We estimate the relationship between the concepts of financial inclusion and stability by using the best available cross-country data. For the inclusion measures, ��<sup>�</sup> , we assume that they comprise of four orthogonal components: ��<sup>�</sup> , the aggregate component ; ��<sup>�</sup> , the component specific to economic agent (firms or individuals) ; ��<sup>�</sup> , the component specific to the type of financial service (payments, savings, credit, insurance),,; and ��<sup>��</sup> , the measurement error that comes with any empirical data.

On aggregate, the ��<sup>�</sup> component will prevail and capture the systematic variation across all financial inclusion indicators. When dissecting the empirical measures by type of economic agent, ��<sup>�</sup> ���<sup>�</sup> will prevail with the possibility that ��<sup>�</sup> dominates. Recall that ��<sup>�</sup> and ��<sup>�</sup> are orthogonal so that ��<sup>�</sup> disappears in aggregation across economic agents. Similarly, when dissecting the empirical measures by type of financial service, the ��<sup>�</sup> ���<sup>�</sup> components will prevail with the possibility that ��<sup>�</sup> could dominate ��<sup>�</sup> . In the latter case, the service-specific results (the covariance between inclusion in savings and stability) will be different from the aggregate results. In all cases, there is the possibility that the measurement errors (a white-noise process) associated with the empirical measures could be so large that they will prevent identification of any relationship whether it exists or not.

For the stability measures, ��<sup>�</sup> , we assume that they comprise of three orthogonal components: ��<sup>�</sup> , the aggregate component ; ��<sup>�</sup> , the component specific to each dimension of financial stability considered, ; and ��<sup>��</sup> , a white-noise measurement error.

Again on aggregate, ��<sup>�</sup> will dominate the data. But when dissecting the stability measures by the considered dimensions of financial stability (resilience, volatility, and crises), ��<sup>�</sup> ���<sup>�</sup> will prevail in the data with the possibility that ��<sup>�</sup> dominates ��<sup>�</sup> in which case the results by dimension of financial stability will be different from the aggregate results. The measurement error could be again so large that it will prevent drawing any inference on the underlying relationship be it zero or otherwise.

Using these component assumptions, we study the linear interdependence between stability and inclusion at different levels of aggregation, following equations (2) and (3), to gain deeper insights into the microstructure of the relationship between financial inclusion and stability. To avoid issues of possible endogeneity, we use a non-parametric approach, emphasizing that our estimates are indicative of an association, which does not necessarily imply causality between inclusion and stability.

The analysis is conducted at four levels. First, we compute the Spearman’s rank correlation between individual measures of inclusion organized by type of product/service and agent (individuals and firms), and stability dimensions. Using these results, we explore the distribution of the pairwise correlation coefficients for all considered measures of financial stability and inclusion, to broadly characterize the shape of their association. We examine the modes, central tendency, dispersion, as well as skewness of this distribution. Moreover, to gain a better understanding of this association by type of economic agent, we examine separately the distributions for the inclusion of individuals and firms.

Second, we examine how the correlations between inclusion and stability vary across types of economic agent (individuals and firms), financial services (account, e-payments, deposits, credit, and 9