and economic development: St Hill (1992). It argues that banking services play different roles in bringing about economic growth for economies at different stages of development, but it does not study transitions across payment systems. Beck et al. (2018) study the impact of mobile money adoption on entrepreneurship and economic development in a structural dynamic macro model calibrated for the case of M-Pesa in Kenya using firm-level data. Klapper and Singer (2014), relying on data from their Findex data set, advocate for using digital payments to enhance financial inclusion, particularly for women and rural dwellers in developing and emerging economies, thus implicitly arguing that digital payments can be adopted in developing economies as a means for overcoming social exclusion in the access to traditional payments services processed through formal bank accounts.

To clarify key concepts, it is worth recalling the basic definition of a payments system. The Federal Reserve Bank of New York defines a payment system as “the mechanism--the rules, institutions, people, markets, and agreements--that make the exchange of payments possible.” One of the earlier attempts to analyze the digitization of payment systems can be found in Bossone (2001). The author points at the emerging issues of electronic payment systems offered by private actors outside the banking community and national financial regulators. The Bank of England (2014) offers a typology of digital payment systems. _Wrappers_ create a digital interface for traditional payment systems to improve their accessibility; _mobile money_ is a new type of payment system that does not require having a bank account; _credits and local currencies_ are new or alternative currencies, generally making use of existing payment systems; while _digital currencies_ incorporate both a new payment system and a new currency such as cryptocurrencies. Another approach is suggested by Natarajan (2019) who proposes four stages of innovation in payments. The first, second and fourth stages proposed by this author are like the types described by the Bank of England (2014). The third, however, differs by introducing the notion of decoupling payment initiation from the maintenance of an account, a process enabled by real-time and transparent data processing between retailers, customers and payment service providers. In table 1, we follow Natarajan’s framework but add an initial level of traditional banking. Of the five stages listed in table 1, our empirical analysis focuses on stages 1-3, since the last two stages are not yet captured in international data.

# **Table 1: Five stages of innovation in the business of payments**

**Stage 1: Traditional banking** . This is the main means of managing money and payments through the 19<sup>th</sup> century centered around bank accounts and paying through cash or checks.

**Stage 2: Introduction of digital access to bank accounts** . This is the digitization of traditional banking with debit and credit cards, and online banking to process cashless payments.

**Stage 3: Prepaid accounts and mobile money** . This includes prepaid payment cards, apps and mobile money accounts which may not require a bank account.

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