 Hello everyone, I'm Russell Wong of Federal Reserve Bank of Richmond. Welcome to our third seminar on Central Banking and Digital Currency. So together with our co-organiser and panelist you see on the screen. I want to thank everyone for joining us again today. Today our host is IMF, so and I will turn over the microphone to our moderator today, Tom Mastow, Machinic Refundi. Thank you. Hi everyone, thank you very much for joining. It's a pleasure to be here and to take part in the seminar. Today we have a paper by Dirk Nepeld, Monetary Policy with Reserves and CBDC, Optimality, Equivalence and Politics. So Dirk will present the paper for 25 minutes without interruptions and David Andolfatto from the Fed system as well will give a discussion for 10 minutes. And then we'll open it up for Q&A. So you're very welcome to post questions in the chat. I'll monitor the chat and ask the questions for you. We have an hour altogether. We may spill over a little bit past 12pm Eastern time, but not so much. So Dirk, the floor is yours for 25 minutes, your presentation. Tom Mastow, thank you very much and thank you very much to all the organizers and to David, my discussant already now for putting that on the program and let me talk a little bit about CBDC from a macroeconomic perspective. So when I say from a macroeconomic perspective what I really mean is that it's not going to be a paper about CBDC properly narrowly right because from a macro perspective, I guess what this is really about is between or the distinction between publicly provided money and privately provided money and that's what this is really going to be about. So a comparison about of two monetary systems on the one hand a two tiered system that we live in. We banked with banks and the banks amongst themselves through a reserve funnel system and on the other hand, the new sort of alternative or you might say the very old alternative that we had in the past, where we all might have an account at the central bank reserves for all. So that's the comparison I'm interested in and again from the macroeconomic perspective I want to talk a bit or understand a bit better the normative consequences, the equivalence consequences or the equivalence properties of these two monetary systems and a little bit political economy implications. I'm kind of asking here or trying to ask is on the one hand, if you have a choice what monetary system would you like to live in. Once you tell me which system I should look at what is the optimum monetary policy within such a system. What are the effects of going from where we are now in a two tiered system to a mixed system what happens if you introduce CBDC into a two tiered system is it a game changer or not that much. My product will also have some give us some information about what the implicit bank subsidies you might call it or the funding cost reductions in the current system for commercial banks are due to their ability to issue deposits. And then I'll have a question about you know what kind of political forces might foster or not the support for CBDC. The framework is going to be a super standard macro framework so I'm going to start from Sidrowski or you might say from the new classical growth model or the RBC model with some role for money which is not going to be micro founded. And I'll introduce into that banks that issue deposits and there's going to be a central bank that issues reserves and possibly also CBDC. There's going to be some market power on the market for deposits and they invest in capital think of that as loans which eventually and funding capital and or into reserves. Why would they invest in reserves because there are some benefit for banks of having reserves. So this is not again not going to be micro founded I will not have a model a lot. I'm not going to issue or follow or another so we thought more carefully about reserves. This is going to be introduced in a very a talk fashion. The central bank here is going to issue reserves and possibly CBDC as I said and it might also subsidize or tax deposits as a second instrument in order to address the competition problem in the market for deposits. There's no payment system to require some resources. Now there's a huge literature obviously about the two tiered system about reserves. More recently in particular there's these papers here, which think carefully about reserves I just mentioned that I'm not going to do that. I've been exploring literature in the recent years about retail CBDC, although, you know, to be an already thought about that but more recently people have thought extensively about that. And there's literature about equivalence and obviously all the organizers and many people might discuss and have all contributed very strongly to that literature. So let me jump to the model. Since time is very limited. Again, as I said this is a basically the neoclassical growth model or the RBC model plus some role for the different types of money in that economy. On the household side, there is a household cares for consumption, cares for leisure, cares for real balances money and utility functions it drowsky. And real balances are a composite of the money that the central bank the government issues I call this M think of that as CBDC, and the money that the commercial banking system issues deposits and that they might not be equally useful in terms of their liquidity properties maybe they are maybe they are not. And this lambda weight might also be endogenous to some extent so it might be a function of how much M you hold relative to the end. For the talk I will have this as an exogenous process to lambda. And basically invest either in capital or in public money or in deposits, depending on which world we live in. And they have some return on their capital all in real terms and return on their M and end holdings they have some labor income. They collect profits because they own the banks in the system and the banks will be profitable. They have consumption outlays and they might pay taxes to the government. So this is super standard, you know it by heart there's a couple of Euler equations or money demand equations that come out of that. And essentially what we need from those Euler equations is that the spread on the different types of assets for example this year would be the spread on CBDC on publicly provided money so the spread on the three illiquid rate and rate on M. This will reflect the liquidity benefits that this particular asset provides to the households. The banks are non competitive, they issue deposits and they invest in capital. Again, think of that as loans which eventually end funding capital and or in central bank reserves. And let me first look at the return on the banks portfolio so these guys issue deposits at time T, which mature at time T plus one and they have to pay some return to the depositors, the bank has to pay some return to the depositors. They invest in reserves part of their assets, which have some return RR, and whatever they don't invest in reserves they invest in capital which carries to return RK. So that's the return on the portfolio. In the first period when they issue deposits they have some costs and operating costs from doing so, because I think of the bank as be as being basically a monopsonist on the island where they serve their particular institutions in the households. And when the households make payments to some other households in the economy the banks have to might have to make transfers to other banks on other islands for other households on other islands. And these transfers basically making payments could potentially be costly for the bank. This cost is new. So that is the unit cost proportional to the amount of deposits that you as an individual bank have has issued. This is the decreasing function of SEDA. SEDA is the ratio of reserves of that bank, relative to the deposits of that bank. Here the idea is something that you know Bianchi Bigi would formalize much more carefully when they solve the problem of an individual bank if you have more reserves that somehow reduces your operating costs there's less risk of a bank run of having to liquidate your assets etc etc fire sales or this kind of stuff. So there's some externalities involved. There's also a dependence on this bank's operating costs on the reserves to deposits ratio of all the other banks in the system. So SEDA and SEDA bar. And since this is a monopsonistic bank they realize that if they issue more deposits, the deposit rate in equilibrium will respond. So that's the market power that they take into account. So the multi conditions here are also standard. This is essentially multi client. If you think about issuing a bit more deposits. Well, on the plus side you earn the spread. So the return on capital net of the return on deposits. Then you have to bear those operating. Oh sorry I forgot the theta is the tax or the subsidy that the government might levy or impose on deposits. So this is operating costs on the unit of deposits. By issuing more deposits you drive that up because you implicitly affect the ratio of reserves to deposits, and all of this net benefit of issuing more deposits you have to weigh with the fact that you push up the cost on the marginal units of deposits, which is this year that's the endogeneity of the price that the bank internalizes that depends on the elasticity of of the quantity of deposits in equilibrium how it responds to the interest rate. So that's the decision about the quantity of deposits and the second condition is the one that tells you what is the optimal ratio between reserves and capital on the asset side if you expand reserves you lose the spread on capital because they pay a low interest rate and capital, but what you gain is that you reduced your operating costs and you internalize your internal part of that cost from having more reserves. This is super super standard neoclassical so the firms are just combining cabinet label to produce stuff, the government exposed to capital potentially liabilities are CBDC and reserves, some tax collections, and the resource constraint is also the one that is the neoclassical growth model, except that there so you have output you have capital net of depreciation you have consumption outlays, and then here are the resource costs that are rising because principle I allow for payments to be costly So if the central bank issues public money and there might be resource costs attached to that which is the new. If the deposits have some resource costs new that I just described and you would have those there are a function of the reserve to deposit ratio and reserves issued by the central bank might also come with some resource costs You can solve this you can reduce the system essentially to the three equations of the neoclassical growth model. Plus wedges and eats of the three equations, you can easily figure out how the allocation response to the policy instruments both in the CBDC world and in the banking world. You can analyze how the spreads feed through the system but that's not going to be the focus of today because I want to move to the normative and the equivalence and the political economy implications. So what is what about optimality. How would a social planner behave in that world the social planner maximizes utility subject to the resource constraint spits out the usual first order conditions and when it comes to the means of payment they are obviously versions of the three equations so what is a treatment rule what is a bit different here from Friedman is that Friedman would have told us you should satiate the economy with liquidity. Here that's a little bit different because of these resource costs. So what the optimal thing here is that you should make the margin utility of liquidity proportional to whatever the resource costs in the economy are, and they are a bang bang thing. So if the two tiered system is cheaper than you want to go to tiered only if the CBDC one tiered system is cheaper you want to go one tiered only so if you if the if subject to the optimal reserve to deposit ratio, the operating cost of a bank and what it costs around on the central bank side is cheaper than what it costs to provide liquidity through CBDC then you want to go to banks and otherwise you want to go CBDC. Now this corner solution is bang bang is is an artifact of what I'm assuming here that real balances are a weighted average of M and N, you know if that were a non linear relationship between the two then you would go to some a non linear optimum and you would have a cost minimizing combination of these two means of payment. The second first order condition tells you what the planner would do as far as reserves is concerned. If the planner says I want to live in a CBDC world, sorry, in a world without CBDC with banks with deposits, then the planner also wants to have reserves, and this condition says that the social cost of providing reserves again the resource costs should and that's exactly how much this reduces the operating costs of the banks that provide this means of payment and crucially of course now the planner looks both of the interior cost reduction for individual bank, but also on the externality that comes through the second argument in the cost function. Now, more interestingly, what would the government actually do or a central bank here we don't live in a world of central planners, can the government or a central bank actually implement the first best. And the answer is subject to the assumptions I made yes. If the social planner were to go for CBDC, then that's very easy to implement, you simply issue CBDC as a government, and you charge a spread on your reserves which equals the social costs of providing that with just a resource costs. By doing that you would automatically price banks out of the market they wouldn't have a chance to also offer deposits nobody would be willing to hold them or banks would make them, so the banks are out in that world. If you decide to live in a two tiered system if that is the more efficient thing to do then again, the government can actually implement the first best. And how they would do it is the following they would first say you know, I know what the, what the social planners preferred reserves to deposits ratio say the star is. And the banks are sort of not internalizing the externality. So I know that their first order condition is this one, which means that I shouldn't charge for my reserves the social costs, the social resource costs of providing reserves, but I should actually subsidize reserves I should pay a higher interest rate on reserves in order to make it attractive for banks to hold more reserves and thereby implicitly internalizing this externality. So that pins down the the optimal spread on reserves that the central bank should implement. And then we have one more distortion the system because banks are non competitive. So now you might think well, probably you want to subsidize deposits in that case, because you want to make banks to to to issue more deposits and the answer is can be but need because by implicitly subsidizing reserves by paying this high interest on reserves, you already give also an incentive for the bank to lengthen the balance sheet to issue more deposits and that alone can already correct for the market for the market power friction in the system. So it really depends on the one hand on the on the market power let me call it the market power friction, which is reflected in the elasticity here on the one hand. And on the other hand, on the externality that reserves provide in the banking sector depends on the size of these two distortions if you want whether the optimal theta is going to be a tax or a subsidy on deposits in under the optimal policy. Let me move on to equivalence. The question here is, suppose we start in the two tiered system today, and we introduce a bit of M a bit of CBDC is this a game changer, or can we expect nothing much to change on the macro economic and the argument is going to be that under one condition, which I'm talking about in a second. The central bank can always make sure in that in that economy here that nothing changes, nothing meaning the allocation is unaffected as well as the price system. What is the condition. The condition is very, very basic. It simply says that whatever equilibrium you start out with in the two tiered system. This is the cost that it that it requires to provide a unit of liquidity to the households. Both from banks and from the central bank in the background. If it happens to be the case that the cost of providing liquidity through the central bank is the same, then you can get equivalence if the central bank behaves in the right way. And the argument to get that here, the logic of that is much, much broader than that particular model so you need obviously some assumptions and we can I'm very happy to talk about them later on, but the result extends by far above the balance of that particular model. So what is the argument really the substitution of M of CBDC for deposits effects balance sheets in equilibrium and in rather complicated ways, some of them, but not the allocation and the price system. When the central bank simply refinances the banks. That's basically what has to happen. So, if there is, if they're a Citibank and they're losing one deposit to the Fed, then Citibank might also shed part of its reserve holdings because it doesn't need as many reserves anymore. That means it's it's net, it's net funding is reduced by that one unit of deposits times one minus data, the reserves to deposits ratio, and the central bank simply needs to refinance that amount to city. Now the Fed itself has exactly gained that amount of net funding they have lost say that times one unit in reserves funding, but they have gained one unit in CBDC funding. So exactly the net funding that the Fed gains they can re channel into the banking sector. The big question though is, of course, what interest rate to charge on that. And the next generation tells you what interest rate the Fed would have to charge city in order to make the choice set of Citibank being unchanged relative to the situation before. That's that's very intuitive. If you think about how much did it cost city before to fund its investment in capital. Well, it issued one unit of deposit that was the cost on that it also had this resource cost to bear. The data set of that it invested in reserves so the one minus data units left from here, the Citibank could invest in capital and now in the new world with this one unit change in funding. The central bank should basically charge this interest rate are L on this one minus data units of loan that the central bank extends to the bank sector, and then the choice set for the bank would be the same under some additional the central bank would essentially have to provide that funding, not totally inelastically sorry not totally elastically but it would basically have to replicate the schedule with which the household sector was funding the book commercial banking sector before note that in that economy there's no socialism in the sense that now the Fed is extending credit to the real sector. The Fed is refinancing the bank, but all the real capital is still on the balance sheet of the commercial bank so there's no loans extended to the real economy by the Fed but it's still being done by city. This implies for funding costs of banks, you will be what we see here if you buy into that is that the status quo, the two tiered system is essentially equivalent to a world in which we replace deposits by CBDC and the Fed refinancing bank refinances banks at that particular interest rate RL that I showed you on the previous slide. Now you might say why should the Fed in that case refinance the banks at RL at that particular interest rate I mean, why not simply refinance them at the illiquid risk free interest rate right after all these loan this loan funding of the bank is no longer in any sense liquidity being used by the household sector. So if you compute essentially what the funding cost reduction of city in that example is, or how much would the funding cost for city increase if it had to pay RF, the risk interest rate, rather than the load this equivalent loan rate is this hypothetical synthesized equivalent loan rate I showed you on the previous slide. You can see this spread your multiplied by the effective funding that commercial banks in the present system collect by issuing deposits. You divided by GDP and that's what I call funding cost reduction, and I compute this for the US. So these are the interest rates I'm using all in real terms and all gross the road from 99 to today. And this is the risk free interest rates my measure of illiquid rate from public or not the green one is the deposit rate, and the blue one is the interest rate on reserves. And this is the reserves to deposits ratio basically up to the financial crisis the banks hold essentially no reserves and then they increase them to something between 20 and 40% of their deposit. Now this is what comes out if you use this formula for the equivalent central bank gross loan interest rate basically something that goes from one and a half percent to today minus 1% here it follows basically the deposit rate. And it increases at a time when banks started to hold more reserves, because at that time the interest rate on reserves was lower than the interest rate on deposits that made it more expensive in some sense to get funding for the banks. Recently, this trend has fallen again. And this is what comes out for the funding cost reduction as a share of GDP, which is something between in the beginning half a percent of GDP then goes up to say between half and point 8% after the financial crisis turns out to be negative because here we have this strong interest rate compression, basically funding for banks is not cheaper than if they had simply gotten alone at the risk free interest rate. But on top of that they had this operating costs for running the deposit business so basically it was a negative or a loss making business for banks to have this deposit business on their on their neck. And during COVID basically the story is repeating as it looks like here. There's different ways in the paper that I discuss different you have three minutes. Thank you to my three minutes different different ways of computing that I showed you one there's another one in the paper where I rely a bit more on the models equation. So if you sort of look at these different different computations is that basically you have this funding cost reduction between say half a percent of GDP prior to the financial crisis. Then this disappears and even turns negative. And right now the pattern is sort of repeating itself if you look at NEPA data. The contribution of financial sector profits is, of course, a bit larger, well substantially larger, but you see that there's a significant component could be related to things going on like yeah. Finally politics. So here the question really is that I'm asking, you know, how should I think about how the monetary system either of those two different polar system shapes central bank profits and what does this imply for the political support and note, I don't have crisis yet there's no bank runs or anything of that sort in the model there's no real bank crisis. So if you are in the CBDC world, and you follow the Friedman rule then we saw before that the optimal policy says you should set the spread equal to the resource costs of having CBDC circulating that means the central bank basically make zero profits. And if you're in the two tiered system, and you have deposits and reserves and again you follow the optimal policy rule, then it turns out that you will always have negative profits from doing so because you have to correct these two distortions the externality that you want to address by raising rates and reserves, and this theta instrument to correct for the market power, and the two together will always give rise to negative profits, whatever the theta is but that's positive for negative. And what I'm speculating that it's really speculation debate but there's no political economy aspects in the model is that if you're sort of indifferent between CBDC and the two tiered system that might give rise to political support for CBDC simply because you need less taxpayer support less taxpayer money in the system. So if you have some distortions that would reduce tax distortions in the system, you have less of redistribution to bankers which looks a bit like redistribution to bankers if you do the optimal policy, and you might also argue that this sort of strengthens central bank independence if you have less dependence or interaction with the Treasury, or with tax collections from the outside. Okay, so this is a model of on the one hand a two tiered system on the other on on the one tiered system or the combination of the two. The optimal system is really determined by the resource costs and the implementation relies heavily on Friedman rules or modified Friedman rules. You might tax deposits or not under the optimal policy it really depends on the size of these two distortions. And on the one condition about resource costs, there is a macro equivalence result. And from a political economy perspective, you might expect some support for a CBDC system. Thanks very much. Thank you very much, Derek that was a great presentation of a very nice paper. To put down you've quantified what some of us have been speaking about in a in a way that adds a lot of depth to the discussion. You've also managed to end exactly on time. What else would you expect from somebody speaking from the heart of Switzerland. I won't say anything about Swiss versus Italian habits in keeping to time because we do have David speaking from the US, although, although with background from Italy. So thanks to David 10 minutes. Yeah, and then we'll open it up for questions. If you're on the panel which means if you have your video on just raise your hand and I'll turn to you to ask the question directly. And I'll also take questions from the Q&A and chat apparently the Q&A is not working very well so I can also take questions from the chat directly. So feel free to add your questions there. So it was yours for 10 minutes. Thanks very much. All right, see this. Yeah, and I'll probably go over in keeping with my heritage. Let's see. First of all, can everybody see this is this okay control. I guess. There you go. So is that okay. Okay, thank you. Thank you to the organizers for giving me the opportunity to discuss this paper by Dirk. It was a lot of fun to read. I learned a few things from it. Dirk's broadly interested in, in, I would say, the optimal monetary policy optimal monetary systems he does so as he explained in the context of a neoclassical growth model. It's kind of been appended to permit kind of liquidity demands, say emanating from the household sector households value liquidity both in the form of deposits and currency so both private and public forms of currency. The firms sector where banks value reserves, potentially to produce the deposits. The firms in the in the model do not value liquidity kind of interestingly although I asked myself why not and indeed dirt does mention this in a footnote it might be interesting to extend the model in that direction given the assumed liquidity demand coming from other sectors of the economy. Why not also the firm sector, and importantly, banks are modeled as a local monopolist, which I like so in terms of the structure of liquidity supply demand I mean as Dirk mentioned, demand is generated really kind of in a reduced form a manner it's money in the utility function for households reserves kind of modeled as an input in the production of deposits for banks. These cost functions for for producing liquidity. There's a unit cost of issuing deposits for banks that's assumed to be decreasing in the banks own reserve to deposit ratio but not only that potentially also unit costs of producing deposits are assumed to be potentially a function of the aggregate reserve to deposit ratio so this implies the existence of an externality. The banks in the model may not want to hold the socially desirable level of reserves. And it's for the government, the government also faces unit costs of issuing its liquidity both in the form of currency, and also reserves these are parameters. These unit costs are potentially stochastic. Although I don't, I don't think it's a terribly important for the analysis but as much model it in a general form like that. Now, some people ask the question what's the difference. I noticed that the Q&A people asking what's the difference between CBDC and physical currency in the model and the answer is as Dirk actually alluded to you there really is no difference. There's a policy can be used to support a real rate of return on currency. And the same is true if we reinterpreted this to be CBDC. Okay. So we can we can take a look at the optimal allocation here to serve as a benchmark the planner in this setup needs to respect the demand for liquidity. And the resource cost of creating liquidity. Now, you know, kind of as a person who's going to work for many years and kind of micro foundations, you know, I kind of ask, you know, should a planning solution involve money in it, especially since money is, you know, the way we typically view money as an exchange medium, it's not something that we think of people valuing intrinsically. And the answer is well probably not. But I don't want to be dogmatic about it. I mean, because whether whether the micro foundations of money demand matter here likely depends on the set of questions being addressing. I think that maybe some of the basic results that Dirk has derived are probably not sensitive to the specific micro foundations although ultimately one would have to check of course. But in the model, it's generally going to be optimal for reserves currency deposits to coexist, you know, in a most general specification at the optimal. And the planner is just going to adjust the quantities to equate the marginal social costs and benefits of all these objects just as treating money just in the same ways it would treat any normal good. I'm going to focus on just a section of Dirk's paper because it's the part that interested me the most as a policy advisor, I'm going to focus on the Ramsey planner. And because that's just only have time really to focus on this part. So Dirk considers a few scenarios one scenario is in a region of the parameters space where say currency dominates deposit so suppose banking is just very expensive deposit issuance is very expensive. And so you basically have this physical currency or the central bank digital currency that's the source of liquidity. And what you get here is kind of just a standard kind of like Friedman rule results. So that's kind of comforting, I think it's kind of like a generalized Friedman rule because Dirk explicitly assumes that there's a cost to issuing or maintaining this currency system. And to the extent that there is a cost you may not, you're not going to be able to kind of get the full Friedman rule but it's basically the same idea. You want to kind of subsidize the real rate of return on currency and satiate the economy's liquidity as much as it's possible up to the costs of actually managing this monetary system. And another region in the parameters space. See when currency issuance is assumed to be very difficult it's very cumbersome for some reason it's it's just not just costly. And in the banking system is the relatively more efficient way to provide a society with the liquidity needs in that region of the parameter space becomes a little more interesting because the banks here are modeled kind of in an interesting way, right? We have two types of distortions coming from the banking sector to contend with your first is the monopoly distortion because these banks, they all are viewed as local monopolies. And then there's this externality issue, right, that the costs of the unit costs that for the bank for producing reserves is assumed potentially to depend on the aggregate reserve to deposit ratio. And the Ramsey planner had a single instrument say interest on reserves, you know, the planner would try to adjust that instrument as best as he or she could, but you're not going to go all the way given you have multiple distortions. It's kind of interesting that in this environment as describes it would be introducing the currency at this point as a second instrument would be interesting, even if currency issuance is relatively inefficient. It would not potentially be used to improve the allocation because by issuing a competing currency, you can kind of whittle away at the monopoly power that the banks have. Of course, this comes out as a social cost because by assumption currency issuance is a relatively expensive way of providing liquidity. So there's a bit of a trade off that is kind of interesting to examine. But what what what Dirk does is introduce another instrument that's assumed to be costless to operate, which is the deposit subsidy so the interest on reserves and the deposit subsidy if calibrated correctly can restore efficiency. Now in the very general kind of environment, kind of with the non linearities that Dirk explained in the in the production of liquidity services. Generally you're going to have currency and deposits coexisting at the optimum. And in this case, the analysis shows how you can use all the available interest instruments interest on reserves interest on currency the deposit subsidy. Of course, you have this lump sum tax floating around at the background. It could these can all be used to implement the optimal allocation. Kind of he alludes to an interesting result that it's generally not going to be optimal to equate interest on reserves and interest on currency in this setup. And I didn't have time actually to dig deeply to see what the was driving this result. I think it's because the potentially these two liquidity forms have different costs of production. But I'll let I'll let Dirk kind of elaborate on that point in his comments reply. And then the result is of course that the optimum policy, you know the interest on reserves the interest on currency the subsidy they all should react to the state of the economy. All the in the model these are modeled as shocks to the money cost production function. These are the shocks that are modeled explicitly. The cost of producing deposits a cost of issuing currency, all of these things are potentially fluctuating stochastically and optimal policy should react to these. Now, I like the section on policy rules and this is the part I'm going to focus on, again, because policy advisor I like this part. Unfortunately, he considers only the deposit only case, at least in the body of the paper. What you get in the in this case as he demonstrates is an optimal deposit subsidy and an interest rate rule that kind of depends on on the deposit cost reserve cost parameters so for example as I've written there. The interest on reserves is going to be some function of what you might call the natural rate of interest or the RF and is in this notation, multiplied by the expression in square brackets which which consist of parameters, potentially time varying potentially stochastic that reflect the cost of supplying reserves that's row, and the cost of producing deposits that's a fight one and fight to so fight one represents kind of the sensitivity of unit cost to the bank's own reserve to deposit ratio, fight to represents the sensitivity of the unit cost to the aggregate reserve to deposit ratio so fight to is a parameter that indexes the degree of the externality in the production of deposits. I take a look at this expression, you know and I think okay. Fair enough. I wonder how big row the cost of producing reserves is in reality. I'm not to question the empirical relevance of the size of the externality, the fight to there. And kind of what I have in mind here is that, unless I'm thinking about things different in the wrong way I mean, if I think about the an optimal central bank policy I mean to me and not in an optimal central bank. So managing the payment system would include a system where the central bank was still ready to provide intraday credit to banks kind of the way the Fed did pre 2008 right. There were tremendous volumes of interest intraday credit being extended to banks to help facilitate payments to the banks and potentially banks don't have to carry very many reserves overnight at all kind of as was the case in Canada for example, just recently. Now if that's the case. So, I, you know, I don't know what role is this fight to plane is this, I don't really that the externality in the production of deposits kind of doesn't really resonate with me. And so maybe dirt might like one, like, want to rebut that part. You can try to wrap up in the next minute or so that would be great. Thanks. I told you I was going to go over. This should have been a rational expectation, but I will wrap up it. So, I would have liked to see the, the case with coexistence and with specific application to see BC. And, because I think it's, this is a setup that I think and deliver a very interesting answer to the pertinent policy question which is if we do introduce a CBDC kind of what should it be its rate of return not necessarily how should it vary over time in response to what are the principles that would govern whether or not a CBDC should earn a higher rate of return, say that interest on reserves, I think Dirks provides a very nice framework to kind of provide a way to for us to kind of think about that question. And I'd like to see the answer that question both with and without an optimal deposit subsidy because it's not immediately clear that an optimal deposit some subsidy something say a central bank and count on say if it depends on legislation. So let me wrap up. I think that, you know, modeling bent mark bank power I think is important, I think it's really interesting in general to see how the principles of optimal interest rate policy kind of might change in the context of an environment where banks have market power I think this is kind of very relevant. The question kind of the resource cost of issuing deposit liability say as opposed to non deposit liabilities are the significant are the resource cost of using reserve significant and this this positive externality have alluded to some, some empirical justification here I think would be welcome. I think that the to the extent that much of the analysis, especially early on on the policy rules is qualitative. I think the analysis could have been much made much simpler and without loss of generality just by by simplifying assuming linear utility and consumption for example, fixing the labor input and doing away with the aggregate shocks I mean at the end of the day, the principles of interest rate or policy setting is going to be driven by the technology money in the utility function the cost of producing money. And maybe bring back the more general framework for a quantitative exercise, I don't know. But overall, really, really a nice contribution I think I enjoyed reading it and I look forward to the finished product. Thank you. Thank you very much, David. That was a very nice very useful and constructive discussion. Derek why don't we hear from you if you want to take three minutes or so to respond to David and then we'll open it up for questions. So while you speak, hopefully others will think about the questions they want to pose to you. Well, David, thanks so much. Thanks very much a great discussion and I hope I get I can ask for your slides. I knew I was safe on the market power assumption given that you have made the same assumption before. I was, I'm actually pleasantly surprised of how easy you let me get off the hook so to speak given my money and utility function, given your background I expected much more pain in that respect but you but you seem to be fine with that one so I basically agree on whatever you said firms could have liquidity demand I don't think it would change much again given that I have this black box that generates money demand it would be just more money demand and not much difference from there. I think the thing that I definitely should do, and which I have been thinking about but I have sort of deferred it for now is, let's forget about the theta instrument and let's see how good you can, you know, respond to developments with just the rate of loss and still introducing cash although cash is maybe not a very efficient means of payment. So how far in terms of second best analysis how far can you go so that's something I should definitely look more closely into it. Let's talk about the difference between the first best rate on return on public money versus reserves, you're absolutely right your interpretation is the correct one that hinges on the on the resource costs in the background so I think that is my interpretation as well. So, how important are, you know, these costs in reality. Now, if you say they are basically zero at the margin. That will be fine given the policy rule that you showed essentially you would, you would say that interest rate on reserves should basically be the benchmark interest rate in that case. Fine. Basically I'm not married to any particular assumption I think it's important to have that in mind that payment systems and monetary systems create some resource costs, and that the equivalence result depends on that I mean if you, if you don't meet that particular assumption that I showed, then the equivalence is impossible to generate for obvious reasons right I mean if it's more, more requires more resources to generate liquidity in world a than in world b then you can never hope to get equivalence that's that's sort of obvious. And that's why I want to have it there. But yeah, other than that I fully agree with whatever you said and I hope that I can get access to your slides thank you very much David. Thank you very much. Thank you very much American thanks again David for the discussion. When we open it up for questions. Let's see if there are any questions among the panelists so those of you who have their video on you can raise your hand and unmute yourselves to ask the question directly. So, Catherine. Thank you for the presentation. And I was struggling a little bit with your argument that there would be political support for introducing CDC, because while following the discussion. I don't see a lot of this support. And I think it hinges on your assumption that there is a subsidy that is paid to banks. What are you thinking of in terms of this subsidy and practice so I see it from your model, and I can see how you come to the conclusion that there is political support for stopping the subsidy. But in practice, do you think that's kind of that. Politics allow banks to have this market power or so so there are at least not physical transfers to banks in practice so so I was wondering what you have in mind with the subsidy. I mean we don't we don't observe exactly that instrument you're perfectly right Catherine right I mean you might argue that there's sort of more hidden implicit things going on. I think that the general feature here is the way I want to think about this is that if you believe that there are some distortions in the banking sector. If you believe that you use some instruments and these are typically physical instruments to correct them, then in the end this will have physical implications, negative physical implications. Now, I think it's natural to believe at least if you have this Ramsey perspective on the economy that if the central bank provides means of payment. In a natural way, it's not it's less natural for me to think that there should be these kind of distortions so there's no need to use these kind of instruments to correct any decisions, because the central bank directly takes the decision itself right. So in that sense I think beyond these particular distortions I look at here. I would think it's natural to assume that there are some distortions in the banking sector but fewer or maybe none in the central bank providing means of payment and if there are some distortions in the private sector that you want to correct. There will be some fiscal costs attached to them. Now will it be exactly those instruments that you use to address those frictions, or some other ones. I don't think it really matters in the end it will generate some fiscal costs. That's the that's the picture I think. Are you thinking of financial inclusion issues in that respect. Is that something that could be at the heart of that. No, I was I was thinking, I mean, I'm not sure about what you have in mind financial inclusion if it's just about, you know, I was thinking about the subsidy that maybe maybe paid to banks to offer services also to people they wouldn't probably want to offer simply. But then the first best way in that world it would be to make payments to the financial excluded directly in the first place right and let banks set their prices as it's optimal to do I guess. I don't know whatever distortion you have in mind I haven't thought about financial inclusion really carefully there I would think you just give money to the poor people and then they should buy the bank services that they need. Okay thanks let's go to Cyril. You have your hand up. Thanks. Thanks to my son. So this is more like a comment than a question and it's about the fact that when we think about CBDC we think that CBDC has to be provided by the government of the central bank. And as we know from Tomaso's work, you know you could have the same result by providing a synthetic CBDC where, you know that is very close to a narrow bank. Now a narrow bank is a market provision of CBDC it's a market driven it's a market initiative. CBDC, and these initiatives. They don't exist so we know TNB in the US the narrow bank TNB has been on the on the map by people we know, you know people from previous central bankers. But there's been a lot of hurdles that has been put to this operation to this market initiative, which goes into the politics of it right so because the hurdle. So basically I don't understand why the government would put breaks to a market. I understand why the market would break to a government driven initiative. So I wanted to hear the views of Dave and maybe Tomaso as well. I'm sorry Cyril, you were breaking up I couldn't hear what you couldn't hear everything in the end. Did you understand everything Tomaso didn't catch everything. But I think Dirk was asking about the different models of providing CBDC including the model by which the narrow bank or synthetic CBDC model and how that compared to your paper you seem to make a distinction is either or. I think Cyril was saying well but can't it be done. Isn't there a third way to do this. Well, I mean you can think of the narrow bank here as a bank that is fully invested in reserves right. Now, and there with this assumption about resource costs. You as a specialist in the topic of the synthetic CBDC would have to help me because I mean, one way would be to say well in that world. There's a bank issuing reserves and there's some costs attached to that. And then the commercial bank is basically transforming that one to one into this means of payment is the synthetic CBDC. And again there's probably some balance sheet cost or whatever associated with that one. If this is the way to think about synthetic CBDC, then synthetic CBDC would be different from the real thing right because there you have just one balance sheet and if the cost is sort of related to balance sheet positions then you don't want to, you want to have a short was balance sheet positions as possible. Maybe another perspective would be, you know, I mean the central bank in that case doesn't have any costs right it's really just the, the guy that interacts with the household in the end that bears some resource costs and operating that system. And then in the end it wouldn't make much of a difference whether you have this intermediate layer or not so. Yeah, I guess I don't know enough about banks and the real world to give an answer about this cost it comes back to David's question I guess you know what are these costs really I mean do we have a sense of how big they are. Are they existent at all, and it really depends on that in the model it's just a parameter and with the parameter it would make a difference, but I don't know about the real world really. Since we don't observe the synthetic CBDC is really as at this point. Thanks very much, Dirk for those thoughts I think it's about cost it's about about benefits as well the idea when you have these liquidity benefits and, you know, potentially, having more variety, and having types of money that are more targeted towards specific use cases may bring welfare to the system. So let's go to Umberto. So, Dirk, I was interested in part of your presentation you talked about the CBDC replacing deposits. And then the bank, the central bank kind of funding banks. And I'm a little concerned about, you know, it's like banks don't just get that are funded not just with deposits and in general it just feels to me like somebody is going to still need to do a lot of what you know we call monitoring. It's sort of like, it feels like it's too much trust on our ability or the ability of the government to properly monitor. You know, so I don't know but it's sort of like I think in some sense, because we're not money, we're not modeling monitoring we get the stark, stark results and then yeah anyway just a call. Yeah, I mean you're absolutely right. I mean, I'm, this is an equivalence result like any equivalence result it's supposed to give a benchmark to think what matters but it's clearly not the real world right I mean banks, banks balance sheets are are complicated that's not the issue the issue is that in the real world there are connections between the liabilities and the assets on the banks balance sheet at least that's what many people would argue and what a big literature would argue. If you talk about monitoring as the monitoring that banks do relative to the loans that they extend that would not be an issue in the model right because the banks still invest in capital as they did before that's not I get that but the issue is the monitoring of the central after commercial bank funding. Yeah, right, I mean you're replacing all of the yes, you know and it's sort of like we do a lot of you know monitoring of banks, but yes, yeah. But if you say we then I have a bit of I mean, if you talk about we being the depositors and I have my doubt. No, no, I mean, I mean the central bank that's a lot of monitoring of banks, and it will still do it right. Yeah, yeah, but I mean I think that doesn't mean you know that it would sort of be equally effective than if it shares that monitoring with the private sector or, or if, or how costly that would be and how, and you know how much can the government mess up the things you know, if, if we just leave it to the government to monitor bank activity. Well if it's just about the monitoring and I would argue the central bank and the financial market authorities these days they do most of that, and they could still do exactly the same amount in this new world right. And if you take the equivalence as the benchmark you could actually argue that in this new world, the central bank would be doing better right because in the current world in spite of all these monitoring there is the there's there's externalities there's run externalities among all these small depositors which is not modeled in the paper at all. But in the new world you would have this large creditor this guy who could in principle replicate what all these small depositors do, but presumably this large guy could actually do much better right because this is a large guy that internalizes these kind of run externalities. So you might think the central bank would actually be able to do better than just generating the equivalent result. Maybe. But what I wanted to say before, there's many reasons to argue that the equivalence does not go through in the banking sector because a large literature argues that the bank liabilities are tied to the bank assets there's some, there's some synergies between the cashier and Stein and Roger and cashier Stein would argue that deposits are useful that it's not just the funding that matters but there are synergies in some sense between the liability side and the asset side. And here those synergies could potentially break down or could disappear because now it's a completely different type of liability which is in the balance sheet of the of the commercial bank. And you would also question whether the quote whether the central bank would extend the loan against no collateral right that's another reason why you might say central banks would never do that. Derek thanks very much. Why don't we take a similar question from the Q&A from Oscar soons, who asks, does the central bank take on credit risk by compensating the banks for deposit outflows. In the equivalent arrangement, the loan is extended against no collateral. So, every central banker I ever talked to in my life just laughed at me when I told them about this thing right because he said it's completely unrealistic. But then, I guess you have to ask you in what world are we currently living in the current world. We depositors, we fund the banks against no deposits against no collateral right when we when we hold deposits at the commercial bank and we do this because we trust that in the end there's this big land of last resort in the background that will make sure that in the future we essentially hold real dollars and not just city bank dollars right on our account. So if that is the world, if the real world is really one of a big land of last resort that is committed, at least in most of states of the world to to provide this assistance. The equivalent arrangement really would not call for collateral on the cb on the on the refunding by of city by the fed system. Otherwise, and we live in a schizophrenic world right now I don't I'm not sure in which world we live, but if you live in a world in which the land of last resort is there, and is actually committed to interact, then the equivalent arrangement should not ask for collateral. I had a question or comment on, related to this as well. I was surprised that you didn't push back against what David said a little bit more. When he was questioning the size of those of those costs, because it seems to me that the, although we can question the size of the cost directly the extraordinary cost has to be significant to this story the work, you don't you don't model it of course but the notion that my ability and the dangers of the needs for reserves are going to be greatly dependent upon how much the rest of the economy, what the rest of the banking system is doing seems like it ought to be a fundamental part of the story and so through the face sheet that ought to be an important, an important cost to think about. Well, thanks a lot. I mean you know much better about this than I do. And if you have a reference that I could even use to sort of, you know, strengthen that case I would be very, very glad. My point though Chakas I mean that would surely depend on how the central bank is set up to deal as a lender of last resort I mean, or to facilitate interday credit. And we've, if the central bank stands ready to facilitate the interbank credit why should me as an individual bank care about what the aggregate reserves are out there that's kind of my point so. If anybody else wants to come in. Feel free to unmute yourselves and ask the question. I don't see any hands up. Cyril came back with a clarification, or I guess an open question. So speaking, he directed the question also today, I don't know if you want to take the state is why do regulators, not like the notion of a narrow bank, holding reserves as assets and issuing payment liabilities. What's, what's wrong with that asks Cyril. Do you want to go. David will first. I don't know if that's even true. I mean I guess I'm I'd have to speak to the regulators I don't know what the issues there. Regulators I guess just naturally very conservative and cautious and I don't have any details as to what the attitudes were in terms of the narrow bank specifically, maybe and one, I'm going to nominate and one who was much closer to the action. Take it away. I think the only thing I can say is that there has been no decision made on on whether to grant an account at TNB. And I believe a lawsuit that TNB brought was dismissed on the grounds that no decision had been made. My reading from the outside, not being part of the fat system whatsoever was that I think there's this usual sort of fear that, you know, whatever might lead to deposit outflows is something which is dangerous right and of course, typically central banks don't view that there might be an alternative way of funding banks that certainly don't like that idea. So, to me it sounds very natural that you want to avoid everything that could lead to an outflow of deposits from the bank. Well then what explains the existence of government money funds and I mean, well that's the case. Yeah. And as you said there's other ways for banks to actually they could, as I said in my paper I mean the response would be for banks to compete more vigorously for the deposits to retain them. I mean, that's also an option so. But that's a pretty sophisticated argument. No, I think competition. In addition to keep your deposits and service your clients, you know, make them happier. I don't, I don't think that's that's that's sophisticated, but, and then of course the central banks going to stand ready to to manage any disruptions and payments flows, again, as long as the Fed stands ready to, to provide liquidity on demand. I don't I these these these stories of financial instability and deposit flows, leaving the banking sector I think are greatly exaggerated. And honestly, I think it's because banks just don't want to face the competition. I understand that part. I tend to agree with you David we have one last quote. I think that just came in from Scott is that right. Yes. Thank you. I don't see it. Can you hear me. Yes, okay. I'd like to ask both Dirk and David to kind of weigh in on this and I apologize it's the, it's a question about the black box that you didn't really want to talk much about but I spent much of the second half of my career trying to figure out consumer payment choices and use of different assets for for for medium of exchange. So I'm wondering, I still don't understand as I think through this how, how the central bank digital currency is going to provide a superior product in terms of deposit services to the deposits that private banks currently, currently provide I've heard a lot of bankers say, you know, with regard to we need faster payments or we need digital payments. They always say we have that it's a it's called the debit card. And I see that your analysis of the household side relies heavily on potential differences in the rates of return to CBDC versus a deposit account but there's a whole another side of that which is the payment networks and payment services currently have increasing returns to them. And I'm just wondering if you, if either of you think much about like how, how practically would the CBDC provide payment services they, they have to get terminals and every store do they, do they join a, you know, a debit card network, and how would they be able to do that better. And this isn't that duplicating services that are already provided by a single network already. Well, I mean, I'll take that. I mean, in principle, I mean, I'm not in the weeds, you know, in the kind of how these things actually worked it down in nitty gritty but conceptually the way I think about it is, if we could design a payment system from scratch. And indeed in a model like how would you design it. I know how I decided I'd have a central ledger, where everybody had an account and could just directly debit and credit accounts on the central ledger directly without any, any middleman. That's like a CBDC universally accessible by by all you just have a card and and everybody just pays with money and their central bank account. And this system of courses has evolved over time as technologies institutional arrangements is this interconnected network you have, you know, the middlemen are there. What role are they playing. Obviously they played an important role in history. Do they still play an important role, given the technologies that we have available. I just think it's probably intrinsically more complicated to make a payment if you have to go through several banks you know correspondent banking issues and stuff like that, the conceptually just have one single central ledger to handle basic payments just at least at a conceptual level seems to make sense to me. That's how I think about it Scott. So I sort of agree with what David said here on the on the other hand when I when I talked to people in Zurich bankers. Nobody of them would answer you know that they would ask for or would hope for higher efficiency on the on the on the retail level for payments from CBDC than what they currently have. What they are emphasizing is that some of their customers would like to have that store value right available to have a bit more safety maybe for some of their assets and investments. But I think from the macro point really where I'm coming from from the macro perspective there. I see a big plus in CBDC that it would help reduce some too big to fail problems, and thereby lower the need for regulation, because there's a huge time inconsistency issue that could potentially be moderated or resolved by having to reduce public money rather than private money. And I see the competition argument that David has emphasized right I mean, there's reasons to expect that could help. I don't think talking to people who are really into payments and in the nitty gritty of that they tell me that this cross border transactions in efficiency that many people emphasize I don't think that's a big deal in terms of technology to improve their it's rather again competition and regulation that seems to be the main, the main problem to be solved and then CBDC per se is probably not that the root of the problem or the absence of CBDC it's competition and regulation that is that is potentially prohibiting better solutions. My understanding but yeah, second hand information. Just one quick follow up it if the CBDC payment provision is dominant. Would it not in the long run is eventually push out the private deposits of banks and if so then where did they get funds loanable funds. If you come to the model, they would be I mean, if you want the banks to stay in place then the central bank would refinance them that's what the model says so you could keep the banks in existence by simply refunding them through the central bank system. Maybe you don't even want that right who knows. And another and maybe more in my view more dangerous question or issue would be, if you have this cool CBDC around what would happen to the demand for cash actually, would people lose interest in cash and there are some interesting papers on that right where people try to model that once the CBDC is available why should I still demand cash. I think it's quite use I mean but that's a that's a personal opinion it's quite useful to have cash as a, as an insurance device and also to keep some government interventions in check but if the political support for cash would weaken as a consequence of CBDC I would consider that as a potential disadvantage of CBDC. Thanks very very much for that discussion, perhaps one last thought is, you know, Dirk you're talking about a very cool CBDC and, and it may be very cool but it may not also I mean there is a risk in in David's world where you have this one one payment system the CBDC one that in a world where technology is evolving very rapidly. There is a risk that the central bank or whatever institution is putting out that currency is not going to keep up with the evolution of technology and may not offer a product that fits everyone's needs there is a lot of variety there's a heterogeneity of users, and that at some point maybe you'll start to have private payment companies that will take your CBDC from you that you no longer want to use so much, and will issue a better in some way or another a better payment liability. And in a way in a sense by having introduced the CBDC which you make available to all you've allowed the possibility of having the private sector hold the CBDC and issue a payment liability. Without necessarily giving the private sector access to central bank accounts at the central bank right without giving the private sector access to reserves you give them access to CBDC, like everybody else and they can then turn around and issue another type of payment liability. Just an interesting thought to keep in mind. I thought this was a really interesting paper very thought provoking very deep, very nice discussion. Wonderful to see all these familiar faces around the room congratulations to the organizers put this together, and I'll turn it back to Russell for some closing words. Thank you, everyone. Thank you. Thank you, David. Thank you. So I, we hope to see you again next month on June 25, which usually the last Friday of the month where the New York Fed will host the next session. So we'll be moderate by Anton Martin, Michael Lee will present a paper monetizing privacy and being no Bria's as we will discuss this. So have a good weekend. Thank you. Thanks very much. Thank you very much.