Another line of argument is that excessive or increased emphasis on financial stability may prolong or increase involuntary financial exclusion. An inappropriate calibration of the regulatory framework for basic financial services according to their contribution to risks for the entire financial system can become a cause for exclusion. Financial institutions may limit access to financial services for low-income groups, especially in times of regulatory tightening, in an attempt to boost profits and cut off risky customer segments. This response can negatively affect households’ welfare because financial services ease consumption smoothing, expand investment opportunities, reduce poverty, and reduce income inequality (Claessens, 2006). Nevertheless, Dittus and Klein (2011) point to the need to design regulation of financial innovations in terms of the nature and risks of each different financial service/innovation. Excessive emphasis on financial stability can prolong involuntary financial exclusion by preventing innovation (BIS, 2015). Conversely, financial stability can enhance trust in the financial system, improving financial inclusion (Mehrotra and Yetman, 2014) and the likelihood that households save formally (Beckmann and Mare, 2016). Small denomination instruments allow households to hold diversified portfolios. The pooling of these resources facilitates financing projects on a bigger scale. Moreover, financial inclusion enables more effective adjustment in savings and investment decisions, thereby insulating households’ consumption from output volatility (Mehrotra and Yetman, 2014). Dabla-Norris et al. (2015) use a calibrated theoretical model to illustrate the importance of country-specific characteristics for assessing the implications of financial policies on access to credit, depth of credit markets and intermediation efficiency for GDP and inequality in developing countries.

In a recent contribution to this debate, Sahay et al (2015) use selected cross-country data, relying mostly on the IMF’s Financial Access Survey, to illustrate that financial stability risks increase when access to credit is expanded without proper supervision. Financial buffers tend to decline when access to credit expands; they decline faster in countries with weaker banking supervision. In contrast, countries with strong supervision could see some financial stability gains from higher inclusion. The paper points to large differences in the effectiveness of supervision across countries, signaling the potential risks to financial stability from an unchecked broadening of access to credit. Sahay et al. (2015) also suggest that increasing access to financial services other than credit does not affect financial stability adversely.

Our contribution to the existing literature is three-fold. First, we propose a framework where we identify concepts and measures for financial inclusion and financial stability. Second, we provide empirical evidence on the synergies and trade-offs between financial inclusion and financial stability at different levels of aggregation. Third, we condition the covariance between financial stability and financial inclusion on several country characteristics that are likely to affect the linear relationship between the two outcomes.

# **3 Concepts and Measures**

We define financial inclusion as the use of a range of financial services by individuals and firms (consistent with definitions in Beck et al., 2007; Demirgüç-Kunt and Klapper, 2012; Allen et al., 2012; World Bank, 2014; BIS, 2015; Demirgüç-Kunt et al., 2015; and Sahay et al, 2015). We focus on the use of financial services (account ownership, payments, savings, credit, and insurance) rather than access to those services, because access by itself does not mean that individuals and firms will actually take up financial services, use them responsibly, and benefit from them. For example, individuals may not take up financial services because of their low financial literacy and capability (Cole, Sampson, and Zia, 2011), or because of their preference for informality due to poor quality of public services and general governance problems.

4