 So good morning, everyone. I'd like to welcome you to the second day of this conference. I hope you had a good session yesterday. I was unfortunately not able to participate, but I heard that it was a very interesting day. So this morning, I'm extremely pleased to open the second session and we start with the keynote speech by Heung Son Shin, who doesn't need much of an introduction, but let me give it anyway. So Heung has been economic advisor and head of research at the BIS since 2014. I think he's well known to many of us. Before that, he has been held positions in Princeton, Oxford and at the LSE and I think he has provided a lot of thought leadership on many topics related to monetary policy, banking, finance, financial stability and more recently also to digital innovation and digital currency. So I think we can wrap it up by saying everything that seems to be interesting for central bankers. So we are extremely pleased to have you here and yeah, Heung, you are delivering the keynote speech, so I give you the floor. Thank you, Cornelia. Thank you for the very generous introduction and it's great to be here and also to see so many old friends. What I'm going to do is to go back in history and present something from the 18th century, but something with relevance to I think many of the discussions that we're having now. Okay, so this is some joint work with my BIS colleague, John Frost and also Peter Weirts who recently joined the BIS at the CPMI Secretariat and Wilco Bolt from the Netherlands Bank. And it's about the Bank of Amsterdam, which many of you know as being one of the earliest forms of a central bank, a proto-central bank and historically, we've emphasised the role of the central bank as a way of financing the government. This is the Charles Goodhart approach to the origin of central banking and the origin of the Bank of England. Another tradition and that's something that Ulrich Binseil has really popularised is to focus on the monetary role of the central bank, so the central bank as the issuer of money. And in that role, of course, there is a much longer tradition and perhaps the most famous example is the Bank of Amsterdam which was a public deposit bank. It was chartered by the city of Amsterdam and it served as a payments bank in the sense that merchants would bring coins to the bank. The bank would keep the coins but then issue deposits against those coins and then the deposits were used as a means of payment. So a payment is settled by debiting the account of the payer and crediting the account of the receiver much like what happens today. And it was also used very much as a way of settling financial instruments like bills of exchange in order to facilitate international payments for trade and manufacturing. And of course the Bank of Amsterdam was not the first public deposit bank. There were precursors but it's probably the most famous example because in its heyday, especially in the 1700s, Amsterdam bank money, so deposits at the Bank of Amsterdam had many of the same attributes that we're now familiar with as a global currency. So it was a global currency for trade or financial transactions, not only in the Netherlands and in Europe but really across the world. So it was really in some ways the first global currency. But then as you see there was an end date. The Bank of Amsterdam actually failed and the modern Netherlands bank, the central bank, is a separate entity that rose from the ashes, if you like, of the Bank of Amsterdam. And what this paper is about is to delve a little bit deeper into how it failed and why it failed. And also then to draw some lessons for some of the questions that we face today. One of the reasons why the Bank of Amsterdam is so famous is because there have been many discussions of it. And a very early discussion was actually in Adam Smith's Wealth of Nations. So that he has a very long discussion on the Bank of Amsterdam and the role that it played. And I have this quote from The Wealth of Nations. Adam Smith says, At Amsterdam, however, no point of faith is better established than that for every guilder circulated as bank money. There is a corresponding guilder in gold or silver to be found in the treasure of the bank. The city is guaranteed that it should be so. The bank is under the direction of the four reigning burgamasters who are changed every year. And each new set of burgamasters visits the treasure, compares it with the books, receives it upon oath, and delivers it over with the same awful solemnity to the set which succeeds. And in that sober and religious country, oaths are not yet disregarded. So, you know, he's painting this picture of a payments bank where the deposits are fully backed by metal coins. And there are institutional safeguards that make sure that every guilder of deposits are fully backed by guilders of coins. So Adam Smith was writing in 1776. Well, actually, that was when it was published. But actually, it's worth taking a long sweep and having a sense of how elastic the balance sheet of the Bank of Amsterdam was. So this is going all the way back to its inception in the early 1600s, all the way up to its failure in 1820. And the pink here, so these are the assets of the Bank of Amsterdam. The pink bars correspond to what's called the metal stock. So it's the gold and silver coins. But one thing which really strikes you, and I'll come to the blue and the yellow shortly, one thing that really strikes you, first of all, is how elastic the balance sheet is, how much it fluctuates. In fact, a very important date is 1683, which is that second vertical line you see on the left. So that was the time when the redeemability of deposits into coin was abolished. So from 1683 onwards, the Bank of Amsterdam could issue fiat money. So you don't have to redeem bank money into coins. And you create money in the same way that modern central banks do. So you do asset purchases. So if the Bank of Amsterdam goes into the open market, buys coins. It does so by crediting the account of the seller of the coin. So it's doing QE. You're creating money and buying coins. And similarly, if you want to shrink your balance sheet, you sell coins. And you sell coins to someone in the market, and then you debit the account of that person through shrinking deposits, as well as shrinking the asset side. In fact, the third vertical line is 1763. So that was the time when there was a major crisis, not only in the Netherlands, but actually throughout most of Europe. And I have a paper with Isabel Schnabel on the crisis of 1763. You can read about what actually happened. This was what was happening. That spike you see, that third vertical line, was what was happening to the balance sheet of the Bank of Amsterdam during the crisis. And this was the Bank of Amsterdam doing QE. So there was a great deal of financial stress, the demand for money. There was a huge flight to safety. There was a huge demand for safe assets. And the Bank of Amsterdam created deposits by going in and purchasing coins. There was a huge asset purchase program, if you like, although they didn't call it a program in those days. They just simply went in and bought. And then when the crisis abated, they then shrank the balance sheet. You see the balance sheet going down. Now what are these blue bits? The blue bits are loans. In particular loans to the Dutch East India Company. There was a very close relationship between the East India Company and the Bank of Amsterdam. In a way it was a semi-official institution. And this was when you see the blue coming up. The yellow is loans to the city of Amsterdam. And that's not very usual on a central bank balance sheet. The issues feared money. If I zoom in on that, so I zoom in on the period from the early 1770s onwards. This is what it looks like. So for now, ignore the distinction between the blue and the red. So both are holdings of coins on the Bank of Amsterdam's balance sheet. The difference between encumbered and unencumbered, there was still a kind of repo operation. Then some of it was actually pledged rather than bought outright in the market. So that's the difference here. But the important thing is the yellow. The yellow is the loans on the Bank of Amsterdam's balance sheet. And you see that beginning in about 1780, loans become much more important. And it gets to the point in the middle of the 1780s that the loans become, if you like, the largest share of the balance sheet. So it's acting like a commercial bank, but it's doing it by issuing fiat money. So we call this a proto-central bank because it has elements of what a central bank does today. But it's very different from modern central banks in other respects. So what's similar about this kind of operation with a modern central bank? Well, the Bank of Amsterdam could issue fiat money. So it could issue money in the sense that it's the ultimate liability. It's non-redeemable. It's redeemable in terms of other units of your deposit. There was no right to redemption in terms of coins. It's unlike a modern central bank in that the city of Amsterdam didn't have the deep pockets, didn't have the fiscal powers to fully back the Bank of Amsterdam. In fact, the city of Amsterdam was actually borrowing and it was actually taking the equity. And I don't have the chart here in this pack, but the equity of the Bank of Amsterdam went deeply negative during this period. So what happened in 1780? Well, this is the war with the English. So this was the fourth Anglo-Dutch war. And there were also many sea battles, famous sea battles. In particular, there was many sea battles both in the Pacific, but also around Europe. And many ships were lost from the Dutch East India Company. And some of that yellow was beginning to go bad as well. So there's some bad loans on the balance sheet. For the discussion today, we don't need the credit losses to fully flesh out the story. All the credit losses will certainly strengthen some of the channels that I'll outline in this paper. So here are the questions that I'd like to address today. So the most important one is the title. How can a bank that issues fiat money nevertheless still go bust? When we talk about banks failing, we typically imagine that there's a deposit run, the deposit need to be redeemed, so you have to sell the assets, and then we get into this feedback, this downward spiral. But if you issue fiat money, you can always print more money, and so redemption is not an issue. But the constraint comes from a different direction. It comes from the direction of the holders of money and the portfolio choice that the holders of bank money face means holding bank money and something else. So in this case, we're going to formalize this as a choice between coins and bank money. But we could generalize this in a modern setting by saying, well, it's a choice between your own currency versus an international currency. If you have a choice, how should you form that portfolio? And in that portfolio choice, if your money loses the trust of the holders of the money, what you will find is that the exchange rate will be the canary in the coal mine. And once your exchange rate then loses its footing, then you can have all kinds of stress dynamics happening. And the actual failure is going to be triggered once your policy framework is then undermined. So in the case of Bank of Amsterdam, what they were trying to do was to keep a stable exchange rate between bank money and coins. So bank money, bank guilders versus guilders in metal coins, and they try to maintain a stable premium or agio relative to coins. And typically that would be between 4% and 5%. Let's say 5%. And it does so by conducting open market operations. So if the price of bank money falls, what you do is you sell coins, you withdraw liquidity, you mop up liquidity, and reduce the supply of money so that the exchange rate goes back up. If the agio is too big, then you go in and buy coins and expand the money supply so that you hit your desired exchange rate. So during the crisis of 1763, that's exactly what the Bank of Amsterdam did. There was a huge demand for bank money. There's a huge flight to liquidity, huge flight to the safe and liquid assets of the Bank of Amsterdam. So you provide that liquidity by going and conducting QE. That's essentially how you would meet that. Similarly, if there's excess liquidity, you go in and mop up the excess liquidity by selling coins and reducing the deposit balances. The crucial constraint is how much can you do that? So how much can you reduce the balance sheet? If all you're holding are liquid assets that can be sold, you can do it until your balance sheet goes very close to zero. And then the money supply will be tiny. A limit to that would come from how much your assets are illiquid and how much negative equity do you have. So if you're holding loans, that's going to be a hard limit to how far you can shrink your balance sheet. If you have negative equity, again, that's going to be a limit to how much you can shrink your balance sheet. And the story that we're going to tell in terms of the model is exactly that once you reach that limit, you have to let go of your policy framework. And in the way that we will formalize it, bank money value collapses to zero, exactly at that point. So as long as you have the confidence of the holders, you can maintain exchange rate, maintain the Agio, maintain the value of money. But if you cross that threshold, then the value of money falls away to zero. Because ultimately, money is only sustained by the trust that the holders of money have. So here are the key ingredients. So we have merchants, which are a bit like modern-day commercial banks. So merchants have accounts at the Bank of Amsterdam. They are the ones that issue bills of exchange that are then settled. They're the ones who conduct these commercial and financial operations. And they are the ones that face a portfolio choice problem between bank money and coins. What we're going to do is to derive a money demand function from that choice. And the Bank of Amsterdam is assumed to have a monetary policy framework where it aims to adjust the money supply so that it hits the target exchange rate. So it's a bit like a modern currency board. You have hard currency backing your local currency, and you buy and sell the hard currency in order to adjust the money stock in order to hit the target exchange rate. And that's the policy framework that we will impose on this model. But then we have this hard constraint that comes from the loans and the negative equity. So that's going to be the story. Let me just give you some ingredients of the model, and then maybe we can come back to some of the broader questions. So it's going to be a global game. There are three dates. And the economic fundamentals here, capital theta, we're assuming is log-normally distributed. It's realized at date one. But at date zero, you know that it's log-normally distributed. And in particular, the log of capital theta, and the small theta is going to be the main variable that we use for the state of the economy, that's going to have an x-ante mean of y and the standard deviation of 1 over root alpha. So alpha is going to be the precision of that realization of theta. Imagine the fundamentals evolving according to a Gaussian random walk. So at date zero, the mean is y, but then we have a realization of the fundamentals according to a normal density with standard deviation 1 over root alpha. And it's a very simple financial system. We just have two assets. We have bank money and coins. So what are the preferences? Well, we have a continuum of merchants, and they're going to be indexed by i. And the merchants value bank money according to that expression, v sub i times f of m. So let me just give you these two components. So v sub i, this is a private value of bank money. That's a private component. We all play slightly different values on the usefulness of deposits. Some merchants may value it slightly higher than others, but it's going to be very similar and it depends on the state of the world. But a crucial component here is the f of m. So f of m is an increasing function of the total money holding in the economy. So m is the total money holding in the economy. So total bank money holding. And it's an increasing function. So we're assuming that f of m is an increasing function and thereby formalizing the idea that the more other people hold bank money, the more I value holding bank money. And the idea is that holding bank money is subject to network effects where the more that it's used in the wholesale payment system, the more useful it is to me. And so the higher the value that I put to it. So this is just a formalization of the idea that money is a coordination device and it sets off positive network effects. The private value vi has a common component, which is theta, which is the underlying fundamentals that we just saw, plus some idiosyncratic component epsilon i, which is also normally distributed. But we think of epsilon i as being very small relative to theta. So it's very, very small deviations around the common value that we all have. But the idiosyncratic component is also normally distributed, but with standard deviation one over root beta. So when beta, so just keep that in mind. When beta goes becomes very large, it means that the differences in valuation shrink to zero. So we all end up having the same value. We're going to be taking limits when beta becomes very large. The catch is that merchants know their own valuation, but they don't know the two components separately. So they have to infer what the valuations of the others are and they have to form their portfolio based on that inference problem. What about the monetary operation of the Bank of Amsterdam? So we've simplified this by simply having on the asset side coins and loans. So coins are the liquid assets you can buy and sell in the open market. Loans are illiquid and some of it may go bad, but we don't need credit losses itself to tell the story, although we can come back to how credit losses may actually strengthen the argument. On the liability side, we have money and equity. And we're not going to make a distinction between the money that's issued against the repo coins or money issued against simply the purchase coins. It's simply going to be money. So money is created and reduced by market operations. Just like today, if you go in and buy coins, you do it by crediting the account of the seller. So that's QE. You reduce your money balance by selling coins and debiting the account of the sellers. So in that respect, the merchants are like modern-day commercial banks. So they have accounts at the Bank of Amsterdam and they're the ones that actually hold money and it's their portfolio decision, which is going to be absolutely crucial for the value of Amsterdam bank money. And the sequence is going to be such that at date zero, the merchants form their portfolios subject to this exchange rate that the Bank of Amsterdam sets the price of bank money at date zero at one plus gamma bar. So gamma bar is the agio. It's a target agio. There's a premium to holding bank money. And if you want to create a deposit, you have to pay a slight premium to do so. If you read Adam Smith, he has a long discussion of why bank money earns a premium. Well, because of its convenience and of its useful function in the wholesale financial system. So gamma bar is a fixed target agio. And you can always exchange coins and bank money at that exchange rate. So this is the way that we're going to solve this game. It's a very familiar way of solving these global games. Firstly, we're going to confine our attention to just switching strategies, where we say there is a marginal type of merchant called it V-Star. And that merchant is indifferent between holding bank money and coins. But anyone with a valuation higher than that is going to be holding bank money. And anyone with a valuation lower than that is going to be holding coins. And once we have V-Star, we can see what are the conditions that would indeed make the V-Star type indifferent between holding bank money and coins. So we will have an indifference condition. That's going to be one equation that's going to be important. And then there's going to be another equation that's going to show us, well, if that threshold V-Star is the marginal merchant that will switch between bank money and coins, what is the true state of the world, theta, whereby the supply of money is too big and you have to let go of the exchange rate. And that's going to give rise to what we call a breakpoint, theta-Star. And if you're like in jointly solving the theta-Star and the V-Star, it's going to be the way that we solve for the unique equilibrium. And then we have to come back and complete the argument by showing that the switching strategy, which we assume to begin with, actually turns out to be dominant solvable. So the only equilibrium that survives the iterative deletion of dominated strategies is the one in switching strategies. And so there cannot be any other equilibrium, whether in switching strategies or in any other strategy. That's going to be the structure of the argument. So let's just derive the money-demand function. So at a particular state, theta, we have a well-defined density of valuations around theta because, you know, remember valuations are theta plus some idiosyncratic term. So the total demand is going to be how much of those valuations are above the threshold V-Star and how much of it is below that threshold V-Star. Essentially, because it's all iid, all we need to do is to look at the probability that any particular valuation is above V-Star, conditional on the true state being theta, and that's the right-hand expression. And the switching point is going to be satisfying. So let's go back to the preference. So this is the preference function, V times F. So that's what you're trying to maximize when you're... So, you know, that's your utility of holding bank money. The only problem is that you don't know what M is because M is a total money stock out there. And that depends on what every other merchant chooses. And so when you enter the reasoning as to whether you should be holding bank money or whether you should be holding coins, you have to form a view as to what the other merchants are doing because that's going to give you an answer to what M is and that's going to then give you an answer to whether you should be holding coins or holding bank money. And this is why you're very interested in the F of M. So the expectation of F. So here the variable is M. That's the money stock that you care about. That's a random variable. And V times the expected value of F is what's going to really determine your value of holding bank money. And so the indifference condition is going to be that second line where the left hand side is the value of holding one unit of bank money. The right hand side is just the normalized value of one unit of coins. So we just normalize that to one. That's going to give us a solution for V star. So calculating this is the important step. And if you look at the paper, it so happens that you have to go through this reasoning, of course. You have to think, well, I'm exactly... So if you find yourself exactly at that valuation, you're asking what is the total stock of money at that point? And that's like saying, what is the proportion of merchants that have a valuation higher than me? Because that is going to determine the proportion of merchants who hold money and therefore the money stock. So a way to calculate the expected value of F is to ask, what is the density of the possible money stock that's going to be held? And it turns out that the cumulative distribution function that corresponds to that is that second expression. It depends on... Yes. So in fact, of course, because of this network effect, if this were a complete information game, you would have multiple equilibria because of the network effect. So one equilibrium is where everyone holds bank money. The other equilibrium is where no one holds bank money. By solving it as a global game, we can always solve for the unique equilibrium. And indeed, let's go straight there. And then come back to the breakpoint. So we can always solve for the unique equilibrium provided that beta is sufficiently large. So remember beta was the precision of the private values component. And so when the variation in valuations goes to zero, what happens in a global game is that the strategic uncertainty becomes very, very large. So when you have your particular realization of your valuation, the calculation as to whether the money stock is very large or very small, it tends towards a uniform density. So this is one of the results. And so we have a unique equilibrium provided that beta is sufficiently large. But let's go back to how the money stock is going to affect the equilibrium. What the Bank of Amsterdam is doing is to adjust the money stock so that the price of bank money exactly hits the target agile. And so M of theta is the money supply at the state theta. D of theta is the money demand at theta. And what we have is that condition which depends on, among other things, the true state theta itself. In particular, if you go back to the balance sheet, when the state of the world is very low, demand for money falls, other things being equal, you need to reduce the money supply in order that you can set supply equal to demand. But you cannot go negative in your coin holdings. And so there's going to be excess money supply whenever the money stock is larger than the total stock of loans, minus equity, because you can finance the assets with equity as well. But if equity is negative, what this does is to raise this lower bound. So whenever the money stock goes below L minus E and when E is negative, that's a big number, then you cannot meet the agile. You cannot meet the exchange rate target. You have to let go of the exchange rate target. And that's what we call the breakpoint. So here are the results. So the first is that in that case where beta is large, we do have a unique equilibrium and we can define exactly that marginal point. I think a more interesting result is the second one, which is that if we take the limit in such a way that we let both alpha and beta become large, but then they become large such that the density is well defined even in that limit, then in fact the equilibrium theta is going to depend on the y itself. So the way to think about this, it's decreasing in the y. So when the fundamentals deteriorate, the bar for maintaining the peg is going to be higher as well. So this is like saying if the merchants find themselves when the economy is in the doldrums, then actually the bar for keeping the value of money intact is going to be that much higher. So even for the same fundamentals that would have been consistent with the peg remaining, we have the peg failing. And so this gives the power of public information. It's the power of what's commonly known and what's commonly assumed by the merchant. And in that limit of course, all the noise goes to zero, all the id is in credit noise goes to zero, and then the demand function for money goes to a step function. So when the demand trips over that threshold, it goes to zero. The demand for money evaporates. And that means that the price of bank money collapses at that point. So above that threshold, money has a trust of all the merchants and the Bank of Amsterdam can keep the target agile. It has a stable exchange rate. Below that, the exchange rate collapses and then we have the collapse of the currency. And that's how a bank that issues fiat money can go bust when its money collapses and value to zero. Sorry, Livio, the audience online cannot hear you, so we're almost done anyway. Yeah, yeah. Actually, Livio, why don't we come back to your question? Because I think your question, I can guess what your question is, but there's a microphone that's being prepared just for you. Okay. But let's come back. Let's come back to this. And let me finish with some further questions. So what is the relevance of this kind of model for today? Well, merchants are like modern-day commercial banks. They actually have accounts at the Bank of Amsterdam, just as modern-day commercial banks have accounts at the central bank. And the key here is the portfolio decision that the commercial banks have. And this is where the exchange rate is going to be a really key variable. So for a small open economy that has its own currency, the exchange rate turns out to be a very, very important variable. And it's a barometer for the value of money issued by the central bank. And balance sheet operations of the central bank will have a bearing on that portfolio choice. So if you are a small open economy and you're conducting QE, of course you pay a lot of attention to your exchange rate. And that's true whether you're an emerging market central bank or an advanced economy central bank. What are the breakpoints? Well, I think here that depends very much on how negative your equity is and what are the illiquid assets that you cannot sell. And in particular, what is the scope for fiscal recapitalization? If, for example, you had fiscal backing and the government simply issues government bonds and then just gives it to you, you have replenished your liquid assets and then you can reduce your balance sheet thereafter. Bank of Amsterdam didn't have that and in fact the city of Amsterdam was in fact actually taking the equity away from the Bank of Amsterdam. And so what this gives us is a very important focus on the exchange rate. It's a barometer for the value of money and it's worth thinking about the way that exchange rates enter into macro financial considerations. So typically we think of the exchange rate through the trade channel. So a devaluation, a depreciation is going to boost exports you think and it's going to be stimulative. Well, when you see a country that's in the throes of a currency crisis, you have both a very rapidly depreciating exchange rate. It's in fact a collapsing currency together with very deeply depressed economic activity. And then you have inflation. And inflation is not simply a question of aggregate demand. You can have inflation when your money loses trust even when the economy is depressed. I think a very important question with regard to financial innovation is what is the equivalent of the outside option for the commercial bank? Well, for a small opening economy it will be between your domestic currency and an international currency. That will be the relevant choice. I think to some extent, if you had, let's say, stablecoins also entering the picture, the technology could also be a way to make that choice much more, you know, much sharper. If you have a wider choice in the portfolio that you can form. So this is sometimes known as cryptoization at the IMF, so Ellen is here, you can tell us more about that. And cryptoization could be, if you like, the modern day prevalent of dollarization. But I think a relevant question here is what is the outside option? So I think there are some interesting and relevant questions for us to consider, even though this is a very, you know, very long time ago when this happened. And it does raise some, you know, very interesting questions, even for us today. So, let me finish there. Thank you very much. And that was a fascinating story. And I think I really liked it the way that you drew managed to draw a simple picture of what central banks do. Yeah. And I think you can interpret it both in looking at small economies that are targeting exchange rates, but also lessons for the larger economies that do QE or QT. And so that was really interesting. So the floor is open now for questions and would also like to encourage those online listeners to put their questions into the chat. And maybe, Livio, we can start with your question and then I have Alistair and Erland. Thank you. And I also agree that it was a great talk. So, you know, but my question was whether there are these discontinuities, a function of the illiquidity in the asset side and, you know, spur to you from, you know, by your remark on crypto. I was also thinking of think of the central bank like DCB. You know, if we had a run on, say, suppose that now we have a dollar stable coin, you know, how will you translate your setting in our framework? So how would the run on the euro look like? You know, where it is continuing. Thank you. And let's collect three questions also. So Alistair is next. Yeah, thank you. Such an interesting presentation. But you're giving that at the ECB now and a number of the banks in the euro system, central banks are actually talking about this negative equity issue, which is curious, right? I mean, as a central bank, I don't know why you would, but the Austrians and the Bundesbank is keen not only to talk about it, but they're suggesting that the ECB sets policy on the basis of this accumulated loss. Which is whether you only comment on the relevance, the direct relevance of your analysis to that particular sort of curious approach. Thank you. Yeah, thanks. A fascinating talk here. Coming from the IMF, we are thinking quite a bit nowadays on why it is that emerging market economies conduct foreign exchange interventions. And I was kind of thinking that your theory is, in a way, a theory of foreign exchange intervention of an emerging market economy, where the currency loses value and we're trying to, in a situation where output is weak, and we're trying to lean against that by selling foreign exchange. So I was just wondering whether you could connect that a little bit to other theories of foreign exchange intervention. So why don't we take those three? So let me start with Erlen first. I think, and the IMF is doing great work on the integrated policy framework, which really has, I think, a very rounded picture of the macro financial implications, both of FX intervention, but also of domestic macro potential frameworks as well. And at the BIS, we've also done some similar work, as you know, on what we call the macro financial stability framework. I mean, this picture of FX intervention is, in a way, a little bit too rarified to address some of the issues that come up in the IPF, because there is no domestic credit market here. And we're not looking at, in particular, how do global conditions affect domestic credit conditions. And so we will need to bring those aspects in. And both in the IPF and also in the BIS's work on the macro financial stability framework, there is a lot of accumulated evidence that global credit conditions, global financial conditions, do have an impact on domestic credit conditions, domestic financial conditions as well. And it turns out that exchange rates play a very important role in that kind of framework. And it goes through various channels. So if we had a banking sector, well, I guess what we would need to do in this model is to really model more fully what the merchants are doing on their asset side. But in that IPF type of approach, what you have is the banking sector that would have lending to the domestic corporates, if you like. Some of those corporates may have currency mismatches. The banks may not have currency mismatches, but it's intermediating dollars. And as you know, the corporate sector globally typically, you know, the large corporates borrow in dollars. And so dollar credit conditions also feed into this partly because of what we call the risk taking channel, where if you are lending to corporates that have dollar liabilities, then the exchange rate movements have an impact on the individual credit risk of all of your borrowers. And then in any kind of credit risk model, even if you're well diversified, that's going to have an effect on the tail risk in that portfolio. And that's going to determine how much you lend in any kind of credit risk framework. And so the exchange rate has a direct impact on credit conditions through the risk taking channel. And in that respect, FX Intervention would be a complementary tool to domestic macroprudential tools like, you know, LTVs, debt serviced income ratios and so on. So I think, you know, we would need to bring that in here. This is a much simpler framework where you're simply targeting an exchange rate, but there's a limit to how far you can do that. And this goes to Livia's question, which is it's because of the illiquid assets on your balance sheet, and it's because that you have limited fiscal backing. If you had the full fiscal backing, you can always, you know, recapitalize a bank like this. And if you recapitalize it by just granting it, you know, newly issued government bonds, then you can sell those government bonds in the market and then reduce the money supply, you know, that way. So you can always do that. But when you hit that constraint and you're out there by yourself, it's not part of the consolidated public sector. Then you're in trouble. And this is exactly why the Bank of Amsterdam failed. And it goes to Alistair's question, which is on losses. Now, I would point you, Alistair, to a bulletin that we published, exactly on this question, on central bank losses. And in fact, historically, central banks have many central banks have operated with negative equity, perfectly fine. It doesn't mean that losses don't matter. Of course, losses do matter. But for the losses do matter in the sense of the accounting and eventually the central bank, you know, will need to replenish its equity. But there are two issues that make this kind of example unsuitable as a way of talking about what's happening today. So first is that today, central banks are part of the consolidated public sector. So there is fiscal backing. And so, you know, we shouldn't take the central banks balance sheet purely in isolation. And the second is that, you know, these losses that we're talking about are really quite small compared to the types of thresholds that might lead to something like this. So if you read the bulletin, what we go through are actually very, there are a number of historical episodes where central banks have gone through this, you know, through this period of negative equity, especially after major financial crises. And they have managed to conduct monetary policy, their monetary policy framework was intact all the way through. I think what this kind of model is useful for is if you like to find the outer boundaries. So just to clarify our thinking on what are the relevant institutional details that we have now that actually make this kind of example unrealistic. And therefore, you know, for us to value those features more than ever. And so it's something that, of course, you know, we are facing, and central bank losses are a topic that has really come to the fore because of the rising interest rates and the large balance sheets of central banks. But we're talking about quantities here, which are very, very small relative to the total balance sheet. And in any case, there is the full fiscal backing of the fiscal authorities. We can take maybe one more question over here. And before I give the floor to you, we have one in the chat by Victor Perez, who has a question on how the bank can actually do QE. How is it possible that the bank enlarges the money supply by undertaking open market operations if the total money supply does not change? So coins and bank money deposits, is that exclusively via increasing fired money by giving unbacked loans? Is one question, do you want to go directly? Yeah, I think that can be easily tackled. So when I talk about the money supply, I mean Amsterdam bank money supply. So I'm excluding the coins. So think of coins as a liquid asset, a liquid financial asset in this context. And so in the sense of QE, what I have in mind is increasing the balance sheet of the Bank of Amsterdam or shrinking the balance sheet. And it does so by buying and selling coins. Thank you. So I think Katja, did you raise your hand? Thank you very much. Thank you for this time travel. It was fascinating to listen and a very neat model. I have a question, which is a bit more mainly misinterpreting your model. Do I understand it correctly? Because you emphasized very strongly this trade off, which appears depending on economic conditions. So if I summarize in short, central bank with fired money will be good enough as long as the economic conditions don't break down. Because then we can, fired money can lose value. But there's one parameter in your model, which I think is like a can soften this trade off. And this is beta. So the distribution of preferences or distribution of valuations across merchants. And is it my interpretation of a model correct that if we have a credible central bank, meaning beta, which is such that the variance of valuations is low. So this is how I would interpret credibility in your model. Then this trade off shifts favorably for the central bank. So I think it's like this is a positive takeaway from your model that I don't know how strong it would be for different parameterization. But to a degree we do support fired money by credible policies. Or do I read too much? Yeah, I think the beta parameter, I mean, for those of you who are not aficionados of global games, I mean the beta is just a modeling device. And the interesting results come when we take the limit when beta become very large. So beta going very large means that distribution of values shrinks to zero. But in a global game there is a huge discontinuity between the limit when beta goes to infinity and when everyone has the same value. Because if everyone has the same value we have multiple equilibria. In that limit in a global game we have still a great deal of strategic uncertainty in that limit. So it's like saying what's crucial is where I am in the distribution of the values. It doesn't matter whether beta is large or small, I'm still very uncertain as to whether I'm in the top of the distribution or at the bottom of the distribution. And by shrinking that density what we do is we maximize that strategic uncertainty. But you raise, your first question is a really interesting one which is the difference between shrinking and expanding. There's an asymmetry here in the model. The Bank of Amsterdam has no constraints in expanding the balance sheet. Because all it needs to do is just to go in and buy coins and print money to pay for that. But if it wants to shrink it has a limit. So this asymmetry is what really gets the Bank of Amsterdam into trouble. Because when there's a huge flight to safety and the demand for money is sky high you can always satisfy that demand by going in and purchasing assets and creating money to satisfy that demand. The only limit is the availability of coins. You can buy all the coins in the market if you wish. But if your monetary policy imperative is to shrink your balance sheet and you want to defend your currency, that's the constraint. And you cannot defend your currency by printing money. You've got to shrink liquidity in order to defend your currency. And if you have illiquid assets or if you have negative equity that's when you really hit the hard constraint and your currency collapses. And so that's the lesson I think here. And so when we think about central bank operations we have to think about it in this two-way approach. Expanding is easy, contracting is difficult. And I guess we're now in the contraction phase around the world. Thanks very much, Jens. But I also understood that even though now we are in the more dangerous phase that we are still far from those thresholds that you outlined in your model. So I hope that can be one conclusion. So let me thank Jens very much for your very insightful keynote.