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Central Bank Digital Currency, In ation Tax, and Central Bank Independence Ohik Kwony Seungduck Leez Jaevin Parkx Bank of Korea Sungkyunkwan University University of Mississippi February 13, 2020 Abstract Can introducing Central Bank Digital Currency (CBDC) improve social welfare? We construct a dual currency model to study whether introducing CBDC with a record- keeping technology can reduce tax evasion incentives, and further achieve a better al- location than in a cash-only economy. In our model one type of agents can evade the sales tax by using cash whereas the other type of agents cannot. If the sales tax is perfectly substituted by the in ation tax, then there is no way to evade taxes. How- ever, if the sales tax is required for maintaining the central bank independence, there arises an ine ciency associated with tax evasion in a cash-only economy. Introducing CBDC with a positive interest can correct this distortion by discouraging tax evasion, rewarding tax payment, and raising the sales tax collection. Keywords: cash, central bank digital currency, monetary policy, scal policy, tax evasion JEL classi cation: E31, E42, E58, H21, H26 We are grateful to Jonathan Chiu, Mohammad Davoodalhosseini, and Yu Zhu for their useful comments and suggestions. We would also like to thank the participants at the conference on the Economics of Central Bank Digital Currency by the Bank of Canada and Sveriges Riksbank. The views expressed in this paper are those of the authors and do not necessarily re ect the the o cial views of the Bank of Korea. yEconomic Research Institute, Bank of Korea. Email: okwonbok.or.kr zDepartment of Economics, Sungkyunkwan University. Email: seung.leeskku.edu xDepartment of Economics, University of Mississippi. Email: jpark21olemiss.edu 1 Electronic copy available at: 1 Introduction Recently, Central Bank Digital Currency (henceforth, CBDC) has drawn extensive research among central banks.1 CBDC di ers from cash, issued in physical papers or coins, in a sense that all of transaction information can be recorded in a digital ledger that the central bank keeps. Obviously, this digital ledger of CBDC can be shared with the scal authority for tax collection. Moreover, CBDC can bear an interest because it is possible to verify its ownership in the digital ledger. Due to these features of CBDC, one may argue that the government needs to introduce it in order to reduce tax evasion which can occur in cash transactions, and thus increase the sales tax revenue. On the other hand, one can claim that CBDC is not necessary for reducing tax evasion, because the central bank can levy the in ation tax to cash users instead of the sales tax. Historically, it is true that the central bank seigniorage has been used for government spending when its tax revenue is not enough to nance the expenditure: for example, when tax evasion is severe or war is underway. In this respect the e ects of introducing CBDC could be closely related to the central bank independence (henceforth, CBI) from the scal authority. According to Sargent (1982), a transfer of the seigniorage from the central bank to the scal authority a ects the public expectation about in ation, and thus real allocations at the end.2 However, our understanding of how introducing CBDC contributes to an economy where tax evasion occurs and the CBI matters is still limited. The purpose of our study is to examine how introducing CBDC can a ect the welfare in an economy where cash is used as a medium of exchange (henceforth, MOE) and tax evasion exists in cash transactions. As long as the bene t of tax evasion by using cash is substantial, CBDC might not completely replace cash. However, introducing CBDC with a positive interest can encourage the record-keeping trades and reduce the incentive to evade 1 For example, the Bank of England, the Bank of Canada, the Peoples Bank of China, and the Sveriges Riksbank have been actively exploring the possibility of issuing CBDC. See Barontini and Holden (2019) for survey results of sixty three central banks stance toward CBDC. 2 In this paper, the CBI is referred to as a case where no monetary transfer is allowed from the central bank to the scal authority. We lean toward Sargent (1982) rather than Williamson (2019), which is another aspect of the CBI. Sargent (1982) raises concerns over transferring the seigniorage from the central bank to the scal authority. On the other hand, Williamson (2019) is concerned about the case in which the interest payment on CBDC could threaten the central bank independence since the central banks budget is likely to rely on the support from the government. 2 Electronic copy available at: the sales tax. Exploring how CBDC can improve welfare along with the CBI will provide us more knowledge about the impact of record-keeping MOE on tax evasion. We build up a monetary model, based on Lagos and Wright (2005) and Williamson (2012), in which cash and CBDC can be used as an MOE in pairwise meetings, and MOE choices for transactions are endogenously determined by the relative rate of return on the two monies. A fraction of meetings are monitored by the scal and monetary authority, whereas the rest fraction of meetings are not monitored. In the monitored meetings, the scal authority can levy a proportional sales tax on transactions regardless of MOE types. In the non-monitored meetings, it depends on MOE types. If CBDC is used as an MOE, the scal authority can impose the tax, but if cash is used as an MOE, then the authority cannot impose the tax, so tax evasion can occur. There are two ways that the scal authority nances its expenditure: collecting the sales tax and/or receiving the seigniorage revenue from the central bank. Finally, the central bank can adjust supplies of cash and CBDC and thus the relative rate of return on the two monies. In this environment, we rst study the equilibrium conditions for the coexistence of cash and CBDC, and equilibrium types, depending on the rates of return on cash and CBDC: pooling equilibrium where only one money is used, partially pooling equilibrium where the two monies are used in either non-monitored or monitored meetings, separating equilibrium where cash is used only in non-monitored meetings and CBDC is used only in monitored meetings. For instance, if the rate of return on cash is higher than the rate of return on CBDC allowing for the sales tax, then both monies are used separately: cash, available to evade taxation, will be used in non-monitored meetings and CBDC will be used in monitored meetings. More importantly, we present that whether CBDC is bene cial for welfare depends on the CBI. We compare the welfare of two economies, cash-only economy and coexistence economy of cash and CBDC by addressing the optimal monetary and scal policy mix. First, in an economy without the CBI, introducing CBDC does not improve welfare. When cash is the only MOE within the economy and tax evasion occurs, welfare can be maximized by substituting a sales tax to an in ation tax. Speci cally, the scal authority can lower the sales tax rate to zero and receive the seigniorage revenue from the central bank to nance 3 Electronic copy available at: its expenditure. This policy mix can eliminate the sales tax distortions and achieve the e cient allocation. In this case, even though we introduce CBDC, the zero sales tax rate is still optimal, and both cash and CBDC will be used in a (partially) pooling equilibrium. Introducing CBDC does not change the optimal equilibrium allocation. On the other hand, in an economy with the CBI, introducing CBDC can improve welfare. Since the seigniorage transfer is not available, it is necessary for the scal authority to impose the proportional sales tax, which inevitably causes two types of tax distortions. One is a distortion in the relative marginal utility between the non-monitored and monitored meetings. The other is a loss in the tax revenue, because the sales tax is less e cient than the in ation tax to nance a certain level of government spending. The central bank can correct the former type distortion by implementing a higher growth rate of cash than that of CBDC, and/or paying a strictly positive nominal interest on CBDC. By collecting more in ation tax from cash transactions and less from CBDC transactions, the central bank can make an implicit transfer from those who evade taxes in non-monitored meetings to those who pay taxes in monitored. However, the loss in the tax revenue cannot be perfectly restored although the sales tax rate can go down, because the xed amount of government expenditure must be supported by the sales tax only. In sum, the CBI can rationalize the introduction of CBDC with a positive nominal interest rate, which is bene cial for society. 1.1 Related Literature This paper is closely related to Williamson (2019) and Davoodalhosseini (2018). Williamson (2019) develops a model of multiple means of payment to examine the implications of the introducing CBDC. He incorporates a crime associated with cash such as theft, and shows that introducing CBDC can have the bene ts: CBDC can mitigate the crime associated with cash and also economize on the scarcity of the safe collateral. Furthermore, he raises an issue that paying an interest on CBDC can pose a threat to the CBI. In a similar model with xed acquisition cost of CBDC, Davoodalhosseini (2018) provides a condition under which introducing CBDC can implement the rst-best allocation. We complement their works by introducing a proportional sales tax for tax evasion incentives, and adopting the 4 Electronic copy available at: notion of the CBI explicitly. More speci cally, we consider the proportional sale tax as a cost associated with CBDC explicitly instead of the xed cost of CBDC implicitly as shown in Davoodalhosseini (2018), so in our paper CBDC play a role as an MOE which discourages tax evasion. In addition, we show that the CBI is one of the crucial elements to understand the welfare e ect of CBDC. There also has been a growing literature on CBDC.3 Keister and Sanches (2019) construct a model where an interest bearing CBDC plays a role as an e cient medium of exchange and show that the introduction of CBDC can increase welfare despite its negative impact on nancial intermediation. Andolfatto (2018) and Chiu et al. (2019) develop models where an interest bearing CBDC compete with commercial bank deposit and show that the introduc- tion of CBDC increases welfare if the banks market power in the deposit market is limited by CBDC. Meanwhile, Brunnermeier and Niepelt (2019) and Kim and Kwon (2019) con- struct models where commercial banks provide liquidity to examine the impacts of CBDC on nancial stability. They claim that if the introduction of CBDC and the central bank pass- through funding go hand in hand, CBDC needs not result in credit crunch nor undermine nancial stability. This paper also relates to the works on tax evasion and optimal in ation. Gomis- Porqueras et al. (2014) provides a theory to guide the measurement of the underground sector of economy. While Gomis-Porqueras et al. (2014) focus on the measurement of the size of the underground sector, we focus on the optimal tax scheme under tax evasion. In a similar vein, Koreshkova (2006) quantitatively examines the public nance motive for in a- tion to explain the high in ation rates in developing countries. The paper nds a negative relationship between in ation and the size of the underground economy, and shows that the government may optimally choose a high in ation rate when the underground sector exists. Nicolini (1998) also studies how tax evasion a ects the optimal in ation tax and shows that the optimal interest rate is positive when cash is used for transactions in the underground sector. We consider the optimal scal and monetary policy mix, and study it in an economy 3 For discussions on CBDC including its motivations and implications, see for International Settlements (2018), Barrdear and Kumho (2018), Bech and Garratt (2017), Bordo and Levin (2017), Broadbent (2016), Dyson and Hodgson (2017), Engert and Fung (2017), Fung and Halaburda (2017), Raskin and Yermack (2016), and Ricks et al. (2018). 5 Electronic copy available at: with two monies, cash and CBDC. The transfer from the cash users to the CBDC users through the seignoirage revenue can correct distortion caused by the proportional sales tax and tax evasion in an economy when the central bank independence is required. Our model approach is related to the recent papers on the seigniorage with dual cur- rencies. Zhang (2014) studies international currency competition by considering the role of the seigniorage. Hendrickson and Park (2018) show that dual currencies can be useful to improve welfare by making an implicit transfer from one type of MOE user to the other. We extend their model to analyze the e ect of the seigniorage transfer, but focus on the role of a record-keeping money on tax evasion incentives along with the CBI. Finally, our work is related to the literature on the central bank independence.4 There are many papers based on the empirical work to show a negative relationship between the average in ation rate and the measures of central bank independence.5 For example, Alesina and Summers (1993) nd out that advanced countries with high levels of central bank in- dependence had experienced lower levels of in ation during the period from 1955 to 1988. On the other hand, a few papers address the central bank independence in a theoretical way. Rogo (1985) shows that introducing the central bank, who put more weights on in- ation objectives, can improve the outcomes. Instead of dealing with the in ation bias, in this paper we focus more on the transfer between the central bank and the scal authority to capture the central bank independence. In a respect of the scal support, Sargent and Wallace (1981) is the seminal work that studies how a scal authority can force the central bank to generate more seigniorage, when it fails to nance budget de cit. Recently, Martin (2015) shows that the central bank independence can lower the in ation rate temporarily, but not permanently, with a dynamic model where the scal authority chooses taxes and expenditure while the central bank decides monetary policy separately. In this paper, we also consider the optimal scal and monetary policy mix with the scal budget constraints, but we compare the equilibrium outcomes in the long run rather than a trade-o in the dynamics. The remainder of the paper is organized as follows. Section 2 describes the model economy 4 See Walsh (2008, 2011), and Waller (2011) to understand the various concepts on the central bank independence. See de de Haan and Eij nger (2016) for a survey of the literature. 5 See Cukierman (1992) for the survey on the empirical work. 6 Electronic copy available at: and Section 3 analyzes t
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