中央银行数字货币和非正规经济.pdf

Working Papers in Economics&Finance2020-11Central bank digital currency and in-formal economy Eun Young Oh,University of Portsmouth Shuonan Zhang,University of Portsmouth Portsmouth Business School h 0(13)where is the elasticity of detection probability with respect to CBDC share in money.Equation(13)impliesthat the more CBDC used by households,the more likely their informal income will be detected.The secondcomponent in equation(13)reflects the enhanced monitoring due to CBDC.Household money holding satisfiesMt=Mcbdct+Mct(14)With CBDC,the representative household maximizes(1)subject to(3),(4),(12),(13)and(14).The firstorder conditions for CBDC and cash are:Mt/Pt=t(1 CtMctM2t)+(McbdctMt)MctM2t(witHit+rkitKit)RmtRt(15)Mt/Pt=t(1+CtMcbdctM2t)(McbdctMt)McbdctM2t(witHit+rkitKit)1Rt(16)Combining(15)and(16)and rearranging,we obtain(McbdctMt)(witHit+rkitKit)|zcost due to the detection=Rmt 1RtMt|zbenefit due to interest payment+Ct|zbenefit due to transaction cost deduction(17)Equation(17)suggests that in equilibrium marginal cost of CBDC,namely the detection cost,should beequal to marginal benefits that from interest payment and transaction cost deduction.Define the CBDCshare in money as scbdct=Mcbdct/Mt.We can solve equation(17)to obtainscbdct=Rmt 1RtMt+Ct(witHit+rkitKit)1(18)Equation(18)implies a negative relationship between CBDC money shares and the size of informal economygiven others remain constant;sizeable informal economy could prevent people from using CBDC as thedetection cost is large.113.2FirmThe production sector consists of two sub-sectors,namely formal and informal firms.In each sub-sector,therepresentative firm j use labor and capital to produce output based on the following Cobb-Douglas productionfunctionYojt=Aot(Kojt)(Hojt)1,o=f,i(19)where index f and i denote formal and informal variables respectively.Productivity Aothas two componentscommon to both types of firms,including a deterministic trend(1+gy)tand a common productivity shockatfollowing an AR(1)process.For formal firms,there is a formal-specific productivity shock ftfollowing anAR(1)process.Aft=(1+gy)tatft(20)Ait=(1+gy)tat(21)Profit maximization for each type of firm yields the following first order conditions.wot=(1 )YojtHojt,o=f,i(22)rkot=YojtKojt,o=f,i(23)3.3EquilibriumWith symmetric equilibrium,we obtain the aggregate output,formal output and informal output as follows.Yt=Yft+Yit(24)Yot=Aot(Kot)(Hot)1,o=f,i(25)Combining(7)and(8),we solve for the equilibrium informal laborHit=t(1 Pr)wit(1 )wft/2if(1 Pr)wit(1 )wft0otherwise(26)which suggests a negative relationship between the detection rate and the incentive to engage in informalwork.With CBDC,PR in(26)would be replaced with prtCombining(9)and(10),we obtain the relationship between rkftand rkitas follow.(1 Pr)rkit=(1 )rkft(27)12The labor and capital markets must be clear Ht=Hft+Hit,Kt=Kft+Kit.The resource constraint isYt=Ct+It+Gt(28)Gtis an exogenous spending shock following an AR(1)process.Interest rate is given by a Taylor rule:Rt=(Rt1)rRm(t)(YftYft1)y1rmt(29)where mtis a conventional monetary policy shock.In order to close the model,we need to specify a CBDCinterest rate rule.We assume a Taylor rule for Rmtwhich is likely to be used(Barrdear&Kumhof 2016)after CBDC is issued.Rmt=(Rmt1)rRm(t)(YftYft1)y1rrt(30)where rtis a CBDC monetary policy shock.4CalibrationOur calibration strategy is similar to Restrepo-Echavarria(2014).For parameters well-identified in the litera-ture and less variant across countries,we give them fixed values.For other parameters which show significantcross-country differences or affect the CBDC-informal economy relationship,we consider a benchmark andsome alternative values.In terms of the benchmark values,we mainly focus on Mexico as it is consideredas a representative emerging economy and it has extensively studied(see Aguiar&Gopinath(2007)amongothers).Table 2Calibrated parametersParametersDescriptionValuecapital share0.35discount factor0.992capital depreciation0.05labor elasticity2money preference0.02transaction cost0.01tax rate0.22elasticity of detection rate1Steady-State(ss)1+gyss per capita GDP growth1.006G/Yss exogenous demand share0.15Hss labor hour0.33HI/Hss informal labor share0.32Prno CBDC detection rate0.0213Table 2 shows calibrated parameters.We set capital share and capital depreciation rate as 0.35 and0.05 respectively,in line with Fern andez&Meza(2015).The discount factor is calibrated as 0.99 to matchthe interest rate,1.0145.The inverse labor elasticity is calibrated as 2 which is a standard value used inthe literature.The money preference parameters is calibrated as 0.02 based on money to output ratio(105%)for low and middle income countries.The is calibrated as 0.01 which implies that transaction costsaccount for 0.6%of output.Such a level is found from some Latin American countries such as Uruguay(Griffoli et al.2018),European countries(Hasan et al.2013)and Canada(Kosse et al.2017).FollowingRestrepo-Echavarria(2014),we set the benchmark tax rate as 0.22.The elasticity of detection with respectto CBDC share is calibrated as unity.This implies 1%increase in CBDC share rises 1%detection probability.The lower part of Table 2 shows the calibrated values of steady-state parameters.We set the quarterlyoutput growth rate as 1.006,consistent with Fern andez&Meza(2015).The steady state labor hour iscalibrated as 0.33 as commonly used in the literature.The exogenous demand share is calibrated as 0.15,tobe consistent with data.In terms of informal labor share,we use 0.32 as in Fern andez&Meza(2015)for thebenchmark.This is a moderate level among others.For the detection rate Pr without CBDC,we choose 0.02as the value based on Italy(Orsi et al.2014)in the absence of other references.Finally,we defer calibrationof monetary policy parameters and shock processes to Section 6 as they do not affect the steady-state.5Steady-State AnalysisWe simulate the model to study the relationship between informal economy and CBDC,starting from steady-state analysis.In next section,we consider the relationship in a business cycle framework using impulseresponse functions.5.1The effects of informal economy on CBDCTable 3 shows model predicted CBDC share based on the benchmark calibration and alternative informaleconomy shares as well.We begin our analysis with a non-interest bearing CBDC for ease of comparison.Starting from a moderate informal economy share,such as the Mexican case(0.32),the CBDC share inmoney would be around 8%.This share indicates a low capacity for the economy to accommodate CBDCand the likelihood to replace large amount of cash by CBDC would be low.As the informal economy shareincreases,such as the Brazilian(0.43)and Thailand(0.55)cases,the cost of holding CBDC(or detectioncosts)would become higher relative to the benefits such as convenience and efficiency and hence leading toeven lower CBDC shares.On the contrary,with smaller informal economy shares,such as the US(0.1)andSpain(0.22)cases,the detection costs relative to the benefits would be lower and hence CBDC could be moreacceptable in the economy.To summarize,Table 3 shows a negative relationship between informal economyand CBDC share,consistent with the theory proposed in Section 3.14Table 3Comparison of Steady-State CBDC SharesInformal shareUS(0.1)Spain(0.22)Benchmark(Mexico,0.32)Brazil(0.43)Thailand(0.55)CBDC share0.2500.1120.0770.0590.04600.10.20.30.40.50.60.70.80.91Original informal economy share00.10.20.30.40.50.60.70.80.9CBDC share=0.005=0.01=0.02Figure 4The relationship between CBDC share and original informal economy shareWhile we consider some specific cases in Table 3,Figure 4 plots the relationship between informal economyand CBDC share in a more general way.In addition to the negative relationship as shown in Table 3,Figure 4shows a L-shaped relationship,consistent with Figure 2b.The main mechanism driving the L-shaped patternrelies on disproportional effects of the detection costs and the benefits with regards to the convenience.Inorder to understand the mechanism,we rewrite Equation(18)in steady state and set Rmas unity to satisfya non-interest bearing CBDC condition.(scbdc)=C(wiHi+rkiKi)=CYi=yi(31)scbdcyi=1(1yi)1+1 0detection cost effectyi=?scbdcyi?/yi=1(1+1)(1yi)1+2 0where yi=Yi/C is a measure of informal economy share.The convenience benefit which appears asnominator in Equation(31)has fixed marginal impact on the CBDC share while the detection cost,appearedas the denominator,has negative and diminished marginal effects on the CBDC share.Such a L-shapedpattern is robust to different levels of transaction cost.Furthermore,Figure 4 suggests that the curvesbecome flat when the informal economy share becomes approximately higher than 30%.Considering that15informal economy shares in developed countries are basically below 30%while that in many developingcountries are greater than 30%13,Figure 4 delivers two important implications.Shrinking informal economywould be useful to promote acceptance of CBDC in developed countries.However,implementing the samepolicy might not be effective for developing countries;the presence of sizeable informal economy leads to themarginal effect of detection costs being insensitive to change in the informal economy share.5.2The implications of CBDCTable 4 shows impacts of CBDC on the economy.We focus on three key variables,namely detection prob-ability,formal output share and formalized output share.The formalized output is defined as the sum offormal output and detected informal output yft+prtyit.Table 4Impacts of CBDCOriginal informal share0.10.220.320.430.55Increase in detection prob()3.120%0.630%0.290%0.170%0.100%Increase in formal output share(yft)0.230%0.094%0.062%0.045%0.031%Increase in formalized output share(yft+prtyit)0.510%0.220%0.150%0.110%0.088%Note:The informal economy shares for the US,Spain,Mexico(Benchmark),Brazil,and Thailand are 0.1,0.22,0.32,0.432,and 0.55 respectively.Similar to Table 3,we consider five original informal economy shares.Table 4 shows negative relationshipsbetween original informal economy shares and its impacts on the three variables.With the original informaleconomy share increases,the increase in detection probability become smaller and thereby leading to lessincrease in formal and formalized outputs.As suggested by our previous analysis in Section 5.1,high sharesof original informal economy decrease households acceptance of CBDC and through the spillover of CBDCon detection,the increases in formal and formalized outputs become smaller.Among the five original informal economy shares considered in Table 4,we find the most significantimpacts when the original informal economy share is 10%.In this case,the issuance of CBDC stimulates adetection rate from 2%to 5%,increase formal and formalized output shares by 0.2%and 0.5%respectively.The increase in formalized output is larger than that of formal output because not only some informalemployees shift to formal production but also the detection of informal output is more effective.5.3Roles of tax rate and CBDC interest rateIn this section,we consider alternative values of tax rate and CBDC interest rate Rmto study the implicationof them to further understand the relationship between informal economy and CBDC.As suggested byEquation(18),tax rate and CBDC interest rate are important determinators of the CBDC share.13In 2016,US,Japan,and United Kingdom show low levels of informal economic activities at 8%,8.1%and 9.5%respectively.In contrast,Nigeria,Ukraine,and Sri Lanka show have high informal economies,at 53.4%,43.9%,and 36.4%respectively.16(a)CBDC share and tax rate0.050.10.150.20.250.30.350.40.450.5 tax rate00.10.20.30.40.50.60.70.80.91CBDC shareHiH=0.15HiH=0.32HiH=0.45(b)CBDC share and CBDC interest rate1.0011.0021.0031.0041.0051.0061.0071.0081.0091.01Rm CBDC interest rate00.10.20.30.40.50.60.7CBDC shareHiH=0.15HiH=0.32HiH=0.45Figure 5The relationship between CBDC share and tax rate or CBDC interest rateFigure 5a suggests a negative relationship between tax rate and CBDC share.As the tax rate increases,incentives to engage in the informal activities would be larger and the potential detection loss could bemore significant.With such a concern,household would avoid detection due to using CBDC,which resultsin a lower CBDC share.This mechanism has important implication for issuance of CBDC as tax cut haspotential to encourage people to use CBDC.Comparing with the benchmark result as in Table 3(7.7%ofCBDC share),cutting tax rate from 22%to 10%alongside with CBDC issuance leads to much larger CBDCshare(17%).However,it should be noted that tax rate in developing countries are not high on average,implying limited policy space of tax reduction to promote the acceptance of CBDC.Shifting our attention to another policy tool,namely CBDC interest rate,Figure 5b suggests a positiverelationship between CBDC interest rate and CBDC share.Higher CBDC interest rate adds one morebenefit to hold CBDC in addition to the convenience gain,making CBDC more attractive for households.This mechanism implies that a positive CBDC interest rate enhances acceptance of CBDC,which complementthe effect of tax reduction.For instance,setting CBDC interest rate as 70%of deposit rate could double theCBDC share compared with the benchmark result.Table 5Impacts of CBDC on formalized output share(a)with lower tax rateOriginal informal share0.150.320.45=0.059.120%2.990%2.060%=0.101.650%0.720%0.510%=0.150.710%0.320%0.230%(b)with CBDC interest rateOriginal informal share0.150.320.45rm=0.3r0.930%0.400%0.280%rm=0.5r1.780%0.670%0.450%rm=0.7r4.780%1.080%0.700%Note:is tax rate.rmis CBDC interest rate,shown as percentage of conventional interest rate.Next we investigate how the tax reduction and positive CBDC interest rate affect the role of CBDC informalizing output.We consider three alternative tax rates in Table 5a,all of which are lower than thebenchmark value(0.22).Unlike Table 4 where issuance of CBDC only has minor impacts on formalizedoutput share,Table 5a suggests more significant effects when tax rate is lower.For example,when tax rate17is 10%and original informal economy share is 32%,the issuance of CBDC could stimulate about 0.7%offormalized output share rather than 0.15%as in Table 4.If we further cut offthe tax rate to 5%,the effectcan rise to 3%.Moreover,a more formalized economy provides a larger tax base which partially offsets thefiscal burden results from the tax reduction.Turning to the CBDC interest rate,Table 5b suggests that a positive CBDC interest rate can also boostformalized output share.For instance,when the CBDC interest rate reach 70%of the deposit rate andoriginal informal economy share is 32%,the issuance of CBDC could stimulate about 1.08%of formalizedoutput share.This effect is much larger than the case(0.15%)with a zero CBDC rate(see the last entry offourth column in Table 4).The presence of CBDC interest rate increases CBDC share and strengthens itsspillover effect on detection,through which