 So this is joint work with Pierre-Paulo Benignio at the University of Bern and Linda Schilling at the Co-Politiknik in Crest. I guess Linda Schilling was originally scheduled to give this talk and then in the last minute or fairly recently, we talked about it and figured that maybe I could give the talk. So here I am. Thanks for having us in the program and having this paper. So this is going to be an entirely theoretical paper and it's about thinking about what the scripted currencies might do to the international monetary arrangement that we've seen, how much they will do to official currencies such as central bank currencies, right? Whether they're digital or not is sort of less of an issue. Okay, so and the motivation for that is that we're seeing these scripted currencies on the rise. I mean, Bitcoin is a granddaddy. Now there are many more, I don't know how many there are maybe a few thousands for sure. And many of them are small. They gather the attention of some regulators but recently there have been some entries that are big and are potential game changers. And so it's as a result, regulators and monetary authorities have really paid attention. One is Facebook's Libra. That's probably the most well-known but it's hard to imagine that that's going to be the last. And as you know, the original concept was that it was backed by pool of low risk asset currencies that it could be circulated by building on Facebook and that it could be used worldwide. Now it's constantly changing. So I don't wanna sort of talk about all the twists in terms of the Libra issue. But it certainly says that Libra is a game changer and central bankers may not like it but have to do something about it and exactly what is a question. So this paper is meant to help understand what that competition does. Now this paper is a theoretical exercise and it thinks about currencies and including digital currencies as money. And if you open a textbook on monetary theory then teach money, then there are always three functions that get emphasized. One is the medium of exchange. One is store value and one is the unit of account. So this paper is really all about the medium of exchange. How much do you use that currency for making payments? The liquidity service that it provides. So that's that center stage here. And what happens if that's taken over by cryptocurrencies to some degree? What we argue is that global currencies change the landscape with the only national currencies. They're not medium of exchange in a foreign country at least not for the well-developed countries and meaning for the extent I mean the dollar is not circulating much in Europe and vice versa. And the exchange rates might fluctuate but with the global currency we get a global medium of exchange. It's the same currency, the same global, the Libra the Bitcoin is Bitcoin whether it's Japan or Europe or the United States. So across these countries exchange is unity at least from a macro perspective I mean they are little wiggles but let's not concern ourselves with that. And so these global currencies compete locally with national currencies and that induces a transnational currency competition through this global currency. And with that, what we are getting is what we call a new impossibility, right? There was this old impossibility due to Mandel and Fleming that with free capital flows you can't both have independent monetary policy and the pex exchange rates. You maintain the free capital flows assumption here but we also introduce above and beyond Mandel, Fleming a global currency circulating alongside national currencies. And if it's used if it's used alongside these national currencies then the monetary policy interest rates are equalizing exchange rates or risk adjusted modern gates. Risk adjusted modern gates means that if there was no uncertainty there would have to be constant. So that's an extreme version of a pex exchange rate if you like. And the monetary policy interest rates are equalized so they're no longer independent. So it's a strengthened version if you like of the impossible trinity because the script enforced monetary policy synchronization or SEMS there are escape options but we are either unpleasant and additional restrictions arise in case of global currencies asset backed as would be the case with Libo. So there's a literature here let me in the interest of time let me skip that and let me head right into the model. So there's this great times to time marches forwards year one, two, there are two countries and there are three currencies. So there's home, there's foreign, there's global people sometimes ask couldn't this be gold? Could you know some other things but you don't see people using gold much for payments. Remember this is all about the medium of exchange here whereas that's the game changer cryptocurrencies really can become the use as a medium of exchange as a means of payment, right? I mean, that's really the issue here. So an example would be think of H as a dollar F as a yen and G as a Libra I chose yen as a foreign country as a foreign currency since I guess most of the participants in this conference can think of yen as a foreign currency. So, but if you're in Europe then maybe H is Europe for you rather than the dollar. So then there's the capital markets that's modeled by nominal stochastic discontact in each country and we have the central bank setting normal interest rates for national currencies and money offer liquidity services. So that's the sense in which we look at the money as a medium of exchange function here. Now the model is very stripped down, right? You could write down the whole protocol of how trades happen and what happens with prices and all the rest of the structure of the economy. But the purpose here of the paper was really to encompass many papers out there in the literature and indeed in the paper go into some of them and show how they all have the key ingredients at mini tiers. So they can all be as for the purposes of this analysis can be all distilled down to these few ingredients. And so it's a minimalistic paper it's a bare-bound striptease paper if you're like maybe only assume what we absolutely need and if you want to build a whole model around it I mean be my guest but it's not necessary. Okay, so we're having these stochastic discount factors here and stochastic discount factors mean that if you have a return, you know that say do you nominate in dollars or you invest a dollar how many dollars do you get tomorrow? So that's terminated in the home currency. I mean you might also have returns that nominate in yen, for example. You know, these returns have to satisfy these as a pricing equations Lukas, Rubens and Breeden as a pricing equation that one has to be the expectation of these returns risk adjusted by these stochastic discount factors. And the same is true, you know if you take a yen return you have to discount it at this yen denominated stochastic discount factor. So as an example, you can think of the normal interest rates and this is all that we have here about central banks really. You know, you can figure out what's the normal interest rate then while if you have a normal interest rate IT that means the normal return is one plus IT. So these equations above immediately give you the equations on the bottom where one plus one over one plus IT is just the expectation of the stochastic discount factor in either country. Now we have to introduce exchange rates, right? And that's always something where my head starts spinning but you know, you just keep track of it and then it's not that hard. So we have ST which is price of one foreign currency in terms of the home currency. So how many dollars do you have to spend per yen? You can talk about the inverse then it's how many yen do you spend per dollars? And they're all to exchange rates of the global currencies in terms of the home and foreign currencies. We call them prices, right? People typically refer to the Bitcoin price but you could also refer to it as Bitcoin exchange rate. So that's what we denote by QT. QT is the price of one global currency in terms of H, how many dollars do you spend per Libre? Or how many yen do you spend per Libre? All right. And here is now our complete markets assumption, right? Remember that we said we have these free capital markets as in Mandel-Fleming. And this is the extent of which we have this. We're saying state by state no matter what state is realized tomorrow, people using the yen stochastic discount factor and the dollar demand is stochastic discount factor agree on how to value that. So these stochastic discount factors agree state by state. The only thing that you have to do is convert it by the appropriate exchange rate. So you have to convert something that's yen tomorrow and yen today into something that's dollar tomorrow and dollar today. But other than that, it's assigned prices to the state. So that's a complete markets assumption here. As a result, one can get these equations that are well-known in the carry trade literature. That is, you can also price the dollar bond, the IT just using the yen denominates stochastic discount factor simply by also including this exchange rate term. There's some economics behind it that is sort of down at the bottom of the slide, but let me not dwell on that. It's all about these carry trades in some sense. All right. And one implication that comes out of this is that exchange rates must be interest, that they interest adjust Martin Gates, if you like. So the expected future exchange rate, the expected future exchange rate is the current exchange rate times the term that denotes differences essentially or here it's a ratio, but first all approximately difference in the interest rates between the United States and in Japan in this case. Now there's a tilde here on this expectation which just means that you have to adjust for the risk. So you have to do this risk adjusting of the expectation, but this risk adjusted expectation with the exchange rate is the current exchange rate times its interest term. Okay. And that's stochastic uncovered interest parity. With that, let me introduce a final element which are the liquidity surfaces because money is a medium of exchange. So imagine that if you use one unit of the home currency, then that it provides L units of liquidity services. If you use G at home, it also provides liquidity services in proportion to its value in terms of dollars. So it's going to provide LT times QT units of liquidity services. Having a dollar in your pocket is nice because you can go and you can shop. You can't do that with a bond and that's exactly what these liquidity service are. Here we're assuming that the home and the global currency are perfect substitutes as far as these transactions are concerned. In the pennies in the paper, we go into questions what happens if that's not exactly the case and that could enrich the model considerably. Here we just wanted to get a very stark, very clean result and that's why we have this perfect substitution. Same thing abroad, right? Now you always see that if is used, right? I mean, you may not use this currency, right? It may be that you don't want to use it, that you just want to hold onto it, right? And when would you do this? Well, look at this equation here, for example, right? What you're getting is always these equations, right? That, I mean, think about this equation maybe first, right? The return on the dollar is just one dollar, right? And so, certainly something that has a positive normal interest rate dominates the dollar and return. So the dollar is a bad store value and the only reason that people hang on to the dollar and have a dollar in their pocket is because they're also getting these liquidity services, LT. Same would have to be true for the cryptocurrencies, right? And here's sort of the same equation. The next equation is the same equation for the QT now. But you might not want to spend it, right? The right-hand side is what you get if you actually go ahead and spend the cryptocurrency. You get the liquidity services, LT, and you then also get the discounted future value of the cryptocurrency. But there may not be, you know, that may be less than what you paid for it, right? And so maybe you really want to use them in a foreign country for some other purposes and you're not ready to spend it. So that's why the inequalities go this way. This took us a lot of thought that the inequalities really have to go this way rather than the other way around. And that's sort of, you know, good talk at length about that. But that's sort of the key part of this paper. Now, if you get equality, interpret this as saying that you may use it at home. I mean, there could be the knife edge case where it's not used nonetheless equal, but you're slightly sloppy in the language. You say equality means it's used at home. Bigger than means it's not used. So that's what we mean by used and not used. If it's used, it definitely has to be equal. If it's equal, you know, you might be in the borderline case where actually, you know, very small quantities are only used. So that's a possibility for me. All right, so lots of examples. Here's now our main result. Suppose the national currencies are used in their countries. You know, that seems natural, right? So the dollar is used for transactions in the United States. The yen is used for transaction in Japan. Suppose the global currency is valued. They're always equilibrium, often in these, you know, tons of models where, you know, particular currencies that are worth no intrinsic value are valued at zero. You know, they're always there. That's not, you know, the true, but, you know, they're not of, you know, those are not particularly interesting for our analysis here. We don't want to move them out, but that's why we make this assumption, suppose it's valued. And suppose now that the global currency is used in both countries. Now remember, we don't have a full blown model here. So we can't, I can't tell you the circumstances under which it might be used or not be used, right? That's outside, you know, the model is so minimalistic or the framework is so minimalistic that, you know, these questions could only be answered in a larger model, presumably, where we go into the details of all that, right? And here we just sort of, you know, take elements of this model and sort of have to take something from that equilibrium in order to get the result. But that seems reasonable. So suppose the global currency is circulating alongside the national currencies in both countries, right, that may be a future that you envision. If that's the case, if you see that, then it must be the case that the normal interest rates on the bonds are equal, that the liquidity of services in home and foreign are equal, and that the normal exchange rates become risk-adjusted martingales. Now, remember I told you this uncovered interest parity, the uncovered interest parity results, right? And so, if the interest rates are equal, right, then this result, you know, follows right away because this risk, this interest rate adjustment term that was there before, now, you know, it's just equal to one. And so maybe that's, you know, that's an immediate consequence of the first bullet point. But the first bullet point, the second bullet point, maybe a little bit, you know, surprising that indeed you have to have that the normal interest rates are equal. And another consequence is you don't only have that for the exchange rates, you know, between dollar and yen, you also have that for the exchange rates between global and home or global and foreign. So you're also getting these risk-adjusted martingale pricing results, right? So I was thinking of Amin's talk, right? I mean, what can we say in general, you know, if a currency is adopted, if it's used as a medium of exchange, right? If a cryptocurrency is adopted as a medium of exchange, you always get these kind of martingale looking results, right? There's notice that there's no return term in here because again, these cryptocurrencies would offer liquidity services. So that's, you know, we had, Linda and me had this in a different paper and it's just always worth emphasizing. Okay, so what's the logic here? Well, the logic is that the introduction of global currency creates global competition between national currencies. So you're getting this currency competition at home between home and global, also between foreign and global, and that induces transnational currency competition between home and foreign. So that way they have to have the same liquidity services and ultimately people in essence don't care which bond they hold, right? And you get this competition between global and between home bonds and foreign bonds and that induces the normal interest rate equalization. And that's like super, you know, the proof you have to, you have to string together all these, you know, few elements that you have and just the right sequence to get the results. And so it takes, you know, you have to be, you can't trip yourself up by having the assumption that's actually not in the paper. So that's the tricky part, but that's essentially the logic. Okay, are there escape options? What if the home central bank says, no, we don't wanna play this game, we wanna lower our interest rate below that of the foreign country. Now after all, with the central bank, we are free to set the interest rate anyway we please. That's true. And if they do that, they make the global currency too expensive to be used at home. Liquidity services, you know, become very cheap in that country. And therefore you wouldn't want to use the global currency at home. And so that will be one way of getting rid of the global currency at home by just having a very low interest rate. But then if the other foreign bank also thinks about this, you might get to raise to the bottom and to the zero lower bound, you know, where both central bank tried to get rid of it and then they both stuck at the zero lower bound. And now they both have a normal interest rate of zero. And now again, you know, the global currency might as well, you know, be circulating both countries. So that will be a further victory if that happens, right? I mean, if you try to stick it to the other country, I mean, maybe that could happen, but that's not, you know, that's maybe not be good for global diplomacy, I guess. The other possibility is, well, wait a second, why can't we just raise the interest rate above that of the foreign central bank? Well, in that case, the home currency becomes too expensive as a medium of exchange. And it's rendered obsolete as a medium of exchange, may still be used as a unit of account, but now only the global currency would be in circulation. And that's surely for central bank, you know, should be thought of as being very unattractive. So this goes in the details. We also have this result about asset-black global currency. We were thinking of Libra. So there's a consortium that fixes essentially the price of this global currency. And how do they do this? They're accepting assets and they hope onto these assets until you cash in your global currency again. Now, while they're holding on these assets, they earn interest rate IT. We assume that this consortium also charges a fee, fee T for their services. And so that means that, you know, they didn't order for this to be no Ponzi scheme that the accounts would be happy with this result. The currency price of this global currency would have to develop at this rate, right? One plus IT minus five T should be the growth in value on the QT. But remember, we had this exchange rate that the exchange rate should be martingale. So in particular, in the non-risk case, right? The QT should be constant if both the home currency and the global currency are in circulation. And so what you see from this equation here right away is what we have as the next result, which says that only if fee T and I is equal to IT, so that this term that I had here, if this term is equal to one, only then both can exist at home. But if the fee is smaller than the normal interest rate, then the home currency is crowded out and only global currency is used at home. So what this really says is that the fee structure for this consortium puts an upper bound on the normal interest rate that the central bank can charge and therefore really effectively constrain the monetary policy. So just to put it in words of the global currencies asset-backed as described, then the home central bank cannot raise its interest rate beyond the management fee without abandoning its own currency as a minimum of exchange might still be used as a unit of account. The low management fees imply low interest rates if the home currency remains in use and that means central banks are forced to stick to narrow range just above the zero lower bound. All right, so with that, let me conclude. The question was, and it's a deja vu slide, but why not just repeat the key lessons here. What are the monetary policy implications from reducing global currencies? The old answer is we would get this impossible trinity with free clappable flows when kind of both have an independent monetary policy and the pegged exchange rates. New here is if you introduce a global currency circulating alongside the national currency and all three currencies are used in particularly the global currencies used at home as well as as abroad, then the monetary policy interest rates are equalized and exchange rates are risk adjusted, Martin Gates. So that's a strengthening of this impossible trinity that's in Mandel Fleming because of the script and force monetary policy and institutional sense. There are these escape options, right? You could try to lower the normal interest rate at home in order to get rid of the global currency as a medium of exchange, but then maybe that invites the other country to do the same and then all of them just heading heading towards a zero lower bound, you're stuck there or you can raise the normal interest rate, but then you give up the national currency as a medium of exchange. So you can, so now additional restrictions to rise of the global currencies asset backed would be the case in the liberal, right? It sort of gives us this very narrow range for the normal interest rate that central banks can be and if the fee is small and it all means that impossible trinity becomes even less reconcilable. And it means that these global currencies if they are circulating widely might have quite an impact on international monetary system international central banks. So it's no surprise, right? That central banks might start to worry how the future looks like here and want to think about it, right? And so that's what this paper's meant to say. I should also say just maybe as a last remark here this isn't the paper that says this is a bad thing or a good thing. As a matter of fact, there's a substantial literature monetary economics that argues that the Friedman rule is optimal that it's a normal interest rate at zero is pretty much as good as it can do. So if these global currencies, if the effect is giving national currencies competition and a run for their money as a pun here, right? It might be that what we end up doing is making national monetary policies more efficient that could actually be beneficial for the consumers, right? We're taking away the monopoly of the national central banks and monopolies can be bad, right? But monopolies can also be good if they are national monopolies. And so our paper has nothing to say on welfare. I just don't want to go away saying, oh, these global currencies are dangerous. I mean, you could read it either way. They might have to be very positive, yeah. Thanks, so that's about it.