 Okay, now we can start. So good morning to all. It's a pleasure to share the first panel that will be about payments credit asset prices. It's a paper by Monica Piazzessi and Martin Schneider. So Monica is a Joan Kenney professor of economics at Stanford. She's a program director of the NBER asset pricing program, a fellow of the Academy of Arts and Sciences and Economic Society and a Guggenheim fellow during 15 and 16. Then we'll be followed by the discussant, Pierre-Caldine Dufresne. The first maybe we can start already with your presentation. You will have half an hour. This looks at my job is mainly to keep the time. So you have half an hour for the presentation and then discussant will have 15 minutes. So thank you. Thank you so much. Thank you very much for inviting me to be part of this conference. This is joint work with Martin Schneider. The motivation for our paper comes from pictures of payments just like this one. This shows payments with inside money in U.S. dollars on the last panel. Non-financial payments are blue and red and brown are payments for securities. And so what you see is that non-financial payments, while they're large, they're about five times GDP, they're dwarfed by payments for securities. These payments with inside money give rise to interbank payments. Banks handle these payments that you see on the left-hand side by transferring reserves to each other. And so the right panel shows you a much smaller amount of reserve payments between banks. The reason why these are smaller is various netting arrangements. These are Fed wire transfers of reserves that are color coded so that they correspond to the payment instructions that you see on the left panel. We also added Fed funds transfers. And so the message that I would like you to take away from this picture is two things. One is payments occurring layers. So there is the layer of bank customers on the left panel that are using inside money to pay for goods and assets. And these payments are handled by banks at a bank layer where reserves are used as a medium of exchange. And second, even if you take into account netting, payments for securities are important. And so these two features are absent from economic models of money as a medium of exchange. And so this is what this paper is about. We want to have a simple model of layer payments and asset prices that speaks to monetary policy issues. In this model, at the layer of bank customers, there are households and institutional investors and they pay for goods and assets with inside money. And think of a broad concept of inside money that includes deposits, money market mutual fund shares that you would use to make payments, and credit lines that one arranges with a bank, like credit cards, for example. And banks handle the payments instructions that they receive from their customers with outside money. And so here outside money is reserves. They help banks to manage their liquidity needs. Banks issue inside money and that involves leverage costs. And these leverage costs depend on the quantity and the quality of the assets of a bank. Then there's the government. The government issues, reserves, and other debt. The government also faces leverage costs. The government sets interest on reserves and trades and assets. And so the questions we want to study with this framework is how does monetary policy affect asset prices and we're also interested in the connection between asset markets and the payment system. How do they interact? Having a model with a layered payment system gives us several interesting implications. The first is that the cost of liquidity for outside money, for using outside money, this is for banks, is the spread between the nominal short rate and the interest on reserves. This spread collapses to zero if reserves are abundant as has been the case in many, recently in many countries. For inside money, the liquidity cost depends on bank balance sheets and that liquidity cost always is positive. It doesn't collapse like the liquidity cost of banks that view bonds and reserves as being perfect substitutes. Inside money always has a positive liquidity cost. The model determines the nominal price level to be higher when banks supply more inside money. And it also says the nominal price level is going to be higher when asset traders demand less inside money. So if less money is going to asset markets there will be more money showing up in goods markets and that pushes up consumer prices. The model features intermediary asset pricing in the sense that assets that are held by banks lower their leverage costs. And so that means that these assets contain a collateral premium. Also asset traders use inside money for their asset purchases and so the liquidity costs of using inside money are priced into the assets that are being traded. In terms of transmission of monetary policy the government here has several tools that work differently. I can use interest on reserves. That's a tax on bank liquidity. It can change the mix of bank collateral by trading assets. And a general property of the model is that interest rates rules are not enough to characterize, to fully characterize the stance of monetary policy. The bank balance sheets will also matter and so determining the collateral mix of banks is going to be important. Also the transmission of monetary policy is going to depend on the financial structure features such as the extent of netting in financial markets and the share of nominal assets on bank balance sheets. So let me give you a schematic overview of the model. A model where only goods transactions require inside money. I'm going to add asset trading in a second. So there are various assets. There are risky trees that we think of as paying fruits as dividends. There are nominal government liabilities. There's debt and there's reserves that the government issues and households can invest in these assets either directly or indirectly by holding equity or deposits in banks. Only banks hold reserves. You see the blue arrows, these are holdings of assets that provide liquidity benefits. So banks hold reserves that provide to them liquidity benefits and they also borrow and lend reserves to each other in a Fed funds market. So when we add asset trading, households can now invest in these assets indirectly through active traders. So they can buy equity in active traders. These are basically asset management companies that issue equity and use inside money provided by banks to trade assets. And then finally, I'm going to be referring to inside money as deposits, but the paper takes a broader stance and shows you how deposits work just like credit lines. So instead of using deposits, households and active traders can also arrange for credit lines with banks and they work the same way. So let me give you a summary of the model. So there are households that infinitely live. They have linear utility and they're averse to Nigerian uncertainty. This is a tractable way of introducing sensitivity to uncertainty of asset payoffs. These households pay for goods with inside money. Then there are financial institutions, there are banks and active traders that maximize shareholder value. They freely adjust equity and they operate constant returns to scale technologies. They receive idiosyncratic liquidity shocks that require payments. And banks pay for these liquidity shocks with reserves. They can possibly borrow from other banks these reserves and their active traders that pay with inside money. These bank leverage costs are resources when commitments are made. So there's a resource commitment and that's motivated by agency problems or bankruptcy costs. And these leverage costs increase with the amount of inside money that banks provide and the amount of borrowing in the Fed funds market that they do. So these are forms of debt that increase their leverage costs. Leverage costs then decline with how much and the value and the safety of the assets that banks have. The government sets an interest on reserves and sets its path for debts and reserves. And so what we study is competitive equilibria with flexible prices and a constant output. So you see we keep the real side of the economy deliberately simple so that we can focus on the financial side. And so we view the model that you're going to see as a module that you can combine with many other models. So what gets determined here endogenously is inside money, the nominal price level and real asset prices. So the height of the model is bank optimization and so banks maximize shareholder value by picking all the positions on their balance sheets. And so banks pick reserves. Banks pick reserves, they issue deposits, they lend and borrow in the federal funds market, they buy government debt and other trees. And they choose all these positions to equate the marginal cost of issuing equity with the marginal benefit of holding assets and the marginal cost of issuing debt. The structure of the... Yes, it does, but it's almost invisible. Thank you. The structure of the problem is that we determine two key ratios for banks and they're going to be the same for all banks in this model is the liquidity ratio, lambda, which is reserves over deposits, which is inversely related to the money multiplier. And the other ratio is the collateral ratio, Kappa, which is risk weighted assets over debts. So that's one over leverage basically. These two ratios, if you look at the balance sheet, they're related through the balance sheet. For example, if you're a narrow bank and you back deposits only with reserves, your liquidity ratio is equal to your collateral ratio. But more generally, these two ratios summarize the stance of the banking system. Lambda and Kappa, the liquidity ratio and the collateral ratio. So how do banks manage their liquidity? How do they pick their liquidity ratio? Banks enter the period with an amount of reserves, M and some deposits, D. And then they hit by liquidity shocks. These are shocks, lambda, tilde, that determine how many funds they have to send to other banks. Or they can receive funds if this lambda tilde shock is negative, they're receiving funds. The shocks are IID across banks with a mean zero, and this distribution has an upper bound of lambda, upper bar. Banks have a liquidity constraint, which says that they have to send these funds with reserves, M, plus any Fed funds borrowing that they do of reserves if they run out of reserves. So banks choose their liquidity ratio, lambda, the amount of reserves over deposits. And they only borrow if this liquidity ratio that they chose turns out to be too low exposed. So if they receive a liquidity shock that they cannot handle with their own reserves, they borrow from other banks. Exempted this means that banks know that by choosing a high liquidity ratio, they get liquidity benefits, especially if this liquidity ratio is smaller than the upper bound, because then that means there's still a positive probability that they may run out of reserves. How does capital structure choice work here? So what is breaking Modigliani-Miller in this model are these leverage costs per dollar of debt that banks issue. These costs, we model them as a smooth function, in C of the collateral ratio, Kappa. So Kappa, again, is the risk-rated assets over debt, and leverage costs, these banks face leverage costs that are decreasing and convex. And this idea, the idea here is that if a bank has a higher value in safety of assets, that lowers their leverage costs. And more and more debt is increasingly costly. So shareholder maximization in this model gives rise to many first order conditions. Let me illustrate how first order conditions work for assets that provide collateral benefits to banks, because that illustrates how these collateral benefits are valued in these assets. So what banks have to do is they have to provide a certain real return on equity that households demand their shareholders. Households are risk-neutral, so they have a discount rate data. So banks know that they have to deliver data. And when they're holding short bonds, they're equating the real return on equity with the nominal interest on these short bonds, net of inflation. But now these short bonds provide them with collateral benefits. And so it's not just the pecuniary return that they're receiving on these bonds, but also the collateral benefit. And the collateral benefit is derived from the last function, C, which we assumed is decreasing, and that means that the marginal benefit of extra collateral is positive. We also assumed that the function is convex so that the marginal benefit of extra collateral is diminishing. So you add more and more collateral, the marginal benefit of adding additional collateral declines. So what do banks do when they face lower interest rates? They look at their first order condition to have a real return on equity. If interest rates on these bonds are lower, they know that they need to increase their marginal benefit of extra collateral, and that means they choose a lower collateral ratio. In other words, if banks are faced with lower interest rates, what they do is they increase leverage to maintain their return on equity. This is a form of intermediary asset pricing because here in this model, the standard Euler equation for short bonds doesn't hold. So households are not pricing short nominal bonds. It's banks that value short bonds for their collateral benefits. Households don't derive collateral benefits, and so they don't price these bonds. And so you get indulgence market segmentation where banks hold these... banks hold the bonds and not the households. Did we...? I think we went. How about assets that provide liquidity benefits? So we just went through the first order condition of a short bond, which only provides it with collateral benefits. Reserves provide collateral benefits, so they also have marginal benefit of collateral priced in, but their first order condition also contains a liquidity benefit, a marginal liquidity benefit, and that's basically the probability that a bank runs out of reserves, the probability that they receive a liquidity short lambda tilde that is larger than their liquidity ratio, times the marginal cost of leverage. So they have to borrow from other banks when they run out of reserves, and so they face a marginal cost of leverage. And so by comparing the first order condition for short bonds with the first order condition of reserves and looking at the difference, you see that the spread between the short rates and the interest on reserve measures the marginal liquidity benefits. That's basically the expected marginal cost of overnight borrowing for banks. An additional collateral lowers these marginal costs of borrowing, and so an increase in Kappa of the collateral ratio lowers these costs. Since there's an upper bound on the liquidity shock distribution, we can think of two regions. One region in which banks choose low liquidity ratios that are lower than the upper bound. In this case, there's still a positive probability of running out of reserves. That's this expression, that's probability is positive, and in that case, banks get a positive liquidity benefit from holding reserves. If they have a liquidity ratio that is above this threshold, this upper bound, that implies that the two assets become perfect substitutes, and short bonds and reserves become perfect substitutes. The interest on these short bonds collapses to the interest on reserves. And so this is what happens in this region. I can show you this graphically. We're going to plot the two key ratios that we want to determine in equilibrium on the horizontal axis is the liquidity ratio, on the vertical axis is the collateral ratio, and there are now two regions that are separated by the upper bound of the liquidity shock distribution for low liquidity ratios. Reserves are scarce. In that case, banks borrow from other banks when they run out of reserves. For very high liquidity ratios beyond the upper bound of liquidity shocks, reserves are abundant. In that case, banks never borrow reserves from other banks. So we want to determine the equilibrium in our model, and we are going to do that with two curves. The first curve is the liquidity management curve. It describes how banks manage liquidity. This curve answers the question, how much collateral is optimal at some liquidity ratio lambda? And the liquidity management curve is derived from the first order condition of reserves that I already showed you. And so if you look at this last term here, this liquidity benefit, you can see that the liquidity management curve is going to slope down. Why? Because when banks have a high liquidity ratio, they have to borrow overnight less often from other banks. And that means that it is okay to have high borrowing costs. So it's fine for them to have a low collateral ratio. And so that's why this curve slopes down, and if they have abundant reserves, if the liquidity ratio is very high, there's no further reduction in this collateral ratio. Equivalently, if you don't want to think about the first order condition of reserves, you can equivalently think of this function as a money demand curve for banks. A high collateral ratio corresponds to high interest rates, and high interest rates mean that there's a high cost of liquidity for banks. And so when that happens, when interest rates are high, they choose a low liquidity ratio. If they have high enough reserves, banks are in a liquidity trap, their money demand is no longer sensitive to interest rates. The second curve, we need an equilibrium, we need two curves to intersect, and so the second curve is the capital structure curve. We've already seen that the balance sheet of banks connects liquidity ratios, the liquidity ratio and the collateral ratio. And so the capital structure curve answers the question, given the other collateral available to banks, what liquidity ratio is needed to achieve a certain collateral ratio? This curve slopes up just mechanically because to get more collateral, banks have to add reserves. The equilibrium is the intersection of these two curves. The equilibrium can be either in the region where reserves are scarce or in the region where reserves are abundant, and these curves will shift around with policy and asset market shocks. But before I show you examples of shifting these curves, let me talk more about how the model determines the other variables in the model, once you know what banks' liquidity ratio and collateral ratio is. If these two ratios are higher, that means that it's cheaper for banks to provide deposits, so deposits are cheaper, and it means that active traders will hold more of these deposits. They have a higher demand for inside money when deposits are cheaper. This cheapness of using inside money gets priced into the trees that are being traded, so they will go up these prices. The nominal price level will then be determined by quantity equations. The nominal output, remember, output is fixed in this model. Nominal output equals the amount of reserves M times the money multiplier, and so that's the amount of inside money deposits, times velocity in the model, and here velocity is 1 minus the share of deposits that active traders hold in asset markets. So it's the amount of money that goes into the good market. It's 1 minus the deposit share of asset traders, and so only money circulating in the good market is going to matter for determining the price level, and velocity is low if deposits are cheap, because more if deposits are cheap again, asset traders will demand more deposits for asset trading. Their demand is interest rate sensitive, so they will demand more inside money, and more money will go to asset markets, and that is going to lower the price level. Here in this model, velocity is also low if asset markets boom, because if asset tree prices are high, if, for example, active traders perceive lower uncertainty about tree payoffs, they are valuing the trees more, and so they need more inside money to buy and sell these trees. And so if you see an asset price boom, that is going to suck money inside money out of the goods market and brings it to the asset market, and that's going to lower the price level. That's going to be deflationary. So let me talk about two types of policy that the central bank can do to tighten money. So here it's all about how can central banks tighten money. They can either do an asset sale, they can sell bonds to banks in exchange for reserves, so they withdrawing reserves and give bonds to banks. That means that more collateral other than reserves is available to banks, these bonds. That means that a lower liquidity ratio is needed to achieve any collateral ratio copper, because there's all these other collateral around, banks can reduce their reserve holdings. And so that means that the capital structure curve shifts left. So now we're walking along the money demand curve for banks to the new equilibrium, and you see that the banks are going to pick lower reserve holdings, the liquidity ratio is going down, and lower reserve holdings along the money demand curve means higher interest rates. Higher interest rates correspond to higher collateral ratios. This policy is deflationary because there's fewer reserves within the banking system, and so there's overall less inside money provided that through the quantity equation is deflationary. This policy has a stronger effect if the sale, this asset sale is large enough to bring you all the way from abundant reserves to the scarce reserve regime. As I'm showing you this in this graph, I'm pushing the capital structure curve all the way to scarce reserves, and so that's a strong effect because now we're changing interest rates, because the collateral ratio changes. It also has a stronger effect if there's less inter-bank netting, because now the lower reserves in the bank system really have a maximum effect on interest rates, if there's less netting, if banks really need these reserves. An alternative is to increase the interest on reserves. So what does it mean for the central bank to increase interest on reserves? Well, that's a higher return on assets for banks. To maintain a given return on equity, they can now lower their leverage, and so banks will choose a higher collateral ratio at any given liquidity ratio, and that means their money demand shifts up. Here I drew this picture so that a higher interest on reserves leads you to the same interest rate as the asset sale that I was considering in the previous slide. You see that the dots end up on the same collateral ratio, and so what happens with higher interest on reserves is we get a higher collateral ratio. Also banks, and a higher interest rates, that means banks will hold a higher liquidity ratio, and that is going to be deflationary because a higher liquidity ratio means a lower money multiplier. Also, because these two ratios went up, it's now cheaper for asset traders to hold inside money, and so they will demand more money, and that's going to be additionally deflationary because now more money is going to asset markets. This effect is stronger if there's more active traders who can absorb the money into asset markets, and if banks have less nominal collateral because this deflationary policy creates a higher value of nominal assets and that will counter effect this increase in interest rates. Let me summarize the type of result that you get from a model with layered payments. One key result is that policy transmission now depends on the financial structure. If you change interest on reserves, that changes the profitability of bank assets and the optimal leverage decision of banks, and so then to which extent this policy is going to generate inflation, that depends on exactly how exposed bank assets are to inflation. The government can also trade assets. It can change the collateral amount that are available to banks to back inside money, and here the effect is going to depend on how much inter-bank netting there is to which extent asset trading changes reserves and that really matters for banks if there's very little netting. One key result is that thinking just about setting a short nominal interest rate, that's not enough to think about monetary policy in this world because you also have to think about bank balance sheets. The payment system and the security markets interacted in this model because asset market shocks affect the nominal price level. First because when asset values are less valuable, when asset values decline on bank balance sheets, that lowers the money multiplier and that's deflationary. That's the Friedman and Schwartz effect. That's a traditional effect. The new effect here is that lower... It also affects money demand from asset markets because if you have lower asset values, asset traders demand less inside money and that is inflationary because more money will show up in goods markets. Monetary policy affects real asset prices. Both through a supply effect and a demand effect, asset purchases make bank assets more scarce that increases their real value and also asset purchases increase the cost of liquidity for asset traders and that lowers asset values. Thank you. Thanks very much. I was going to provide some easing, but I think the policy transmission was optimal. So now Pierre-Claude Dufresne with a professor at the Swiss Finance Institute of the Ecole Polytechnique Fédérale de Lausanne. So you now have 15 minutes for your... Sorry. Maybe look, I think your IT skills are needed. Never saw such a difficult laptop. Is it a research laptop? So Pierre, you have now 15 minutes. Okay, thanks a lot. I'll collect questions. Okay, great. Thank you very much. So this was a fun paper to read. I thank the organizers for asking me to discuss the paper way outside my comfort zone. I don't usually do monetary economics. So many things have changed with this great recession and monetary policy, as you know, there are nominal interest rates and certainly even negative rates. A lot of central bank asset purchases, a very large amount in reserves held by banks even increases in interest rates on reserves and persistent low inflation. So we have few models to think about a lot of these implications and what these guys do is develop a new equilibrium model for monetary economy with two payment layers. One is the consumption good layer where agents trade using deposits inside money and then there's this interbank settlement of all the transactions using cash reserves outside money. And in the model, monetary policy has two distinct layers, one which is changing the interest on reserves and two is how much the government chooses to borrow. And so these two mixes of monetary policy in the model will affect banks' decisions to hold bond and risky assets and to issue deposits. And the way the bank's decisions will be affected by the monetary policy decisions comes through essentially two things, two types of constraints. One is bank balance sheet leverage constraints and the other one is deposit withdrawal, liquidity shock that banks have to insure against. So essentially it's these two mechanisms. And the model has the potential to explain how monetary policy choices with respect to outside money and with respect to the mix between government borrowing and reserves can affect the deposit creation. So really it could potentially explain how monetary policy changing these two levers will affect inflation and then also how monetary policy interacts with asset prices. So it's a really complicated model with many, many equations and you saw only a few of them. So I'm going to show you a few more just so it really looks like a research conference. So this is the setup. So you have a bunch of risk neutral consumers and they have a discount rate delta and they face a cash in advance constraint so whatever they consume consumption times price has to be less than deposits and they receive an exogenous endowment and they own the banks. Because everybody's risk neutral and consumers essentially only get liquidity benefits from deposits. In equilibrium they'll only hold deposits. They'll hold nothing else. And essentially the rate on deposits, the real rate the normal rate minus inflation will essentially be their time preference parameter. That would be it if there was no cash in advance constraint but because there's a cash in advance constraint they'll accept sometimes a lower and in fact in equilibrium in steady state this is going to be a constant and they'll accept a real rate on deposits lower than the time preference parameter by essentially the value of the constraint the cash in advance constraint. The other assets in the economy reserves, borrowing and risky trees are all held by banks. Banks are maximizing the NPV of their value for investors, for consumers since consumers hold the banks. And so what banks will do essentially is finance by either issuing deposits or by interbank borrowing and equity their purchases of trees of lending to other banks and of holding reserves. And when they do so they incur two types of costs. First they incur real leverage costs so if they issue more deposits or if they fund themselves by borrowing from other banks that's the amount that they borrow then I will decide they'll incur C of Kappa where Kappa is essentially the collateral ratio. Kappa is this risk weighted asset reserves plus trees. Notice that the trees are multiplied by a row here. Row is kind of an exogenous factor by which you want to weight your risky trees when you compute your risk weighted assets. It could also be thought as another policy actually tool in this model. And then plus bank, plus lending so this is essentially all their risk weighted assets and then this is reliably side deposits plus short-term borrowing from other banks. So they face this risk with real leverage costs and they have a cash in advance constraint they need to finance these leverage costs with actually deposits they place at other banks. That's the leverage cost side and then banks are also hit by random deposit redemption shocks these land are tilde. So there's a whole continuum of banks where banks will be hit by some land at tilde. Land at tilde could be large, it could be small. There's an upper bound which is lambda bar. Banks come into the period with some amount of reserves and so they have an liquidity ratio M divided by D. If that ratio is insufficient so if lambda is less than one if this ratio is insufficient so that they can't face their liquidity shocks then they have to fund themselves in the interbank market. So you can see the decisions of banks is one on the asset side choosing the mix of risky assets to hold and then on the liquidity side choosing this liquidity ratio which is related to the inverse of the money multiplier to essentially cover the hedge themselves against those random liquidity shocks. So we're going to have two essentially decision variables for the banks. They have to pick Kappa collateral ratio they have to pick lambda to essentially insure against liquidity shocks Kappa to insure to try to minimize real leverage costs. There's also a government. The government borrows overnight in the interbank market and so it can fix, it can choose B of J here and it can also choose the interest on reserves. And it turns out the government also faces it's very important this model a real leverage cost. The government faces a real leverage cost depending on essentially you can see it's also there's a risk-vated average collateral of the government but viewed as essentially related to the endowment of agents. I guess this is sort of a present value of taxes and then divided by how much the government, the liability side of the government which is reserves plus government borrowing. And then they study a steady-state equilibrium where essentially output is fixed and where the government holds the reserves on a constant growth path and where the government essentially borrowing to reserves is constant. Now we have market clearing market clearing in the goods market that's imposed by the cash and advance constraint. Overnight borrowing market clearing which is essentially how much do banks need to borrow? Well it's going to depend on the distribution of the liquidity shocks and they only need to borrow if the liquidity shocks are higher than what they came into the period with the liquidity ratio. So we integrate essentially for every bank the fraction of banks that have liquidity shocks larger than the decision they made to hold reserves in the first place. And then there's market clearing in the bank borrowing, banks borrow and government borrowers has to be equal to how much is lent. Now if we look at this and we look at a steady-state equilibrium we immediately see that if lambda, this liquidity ratio has to be constant in steady-state then both reserves and deposits have to grow at the same rate. That means everything grows at the same rate that means from this equation we immediately that inflation is fixed at the exogenous growth rate. So inflation is going to be fixed at a constant growth rate in steady-state. We have a bunch of first-order condition that Monique already discussed. It's always of the same order which is first-order condition for bank borrowing. The real rate that banks are willing to take on borrowing has to be equal to the time preference parameter. That would be it if there were no constraints but there's collateral constraints so we're sometimes willing to take in fact in equilibrium always willing to take a lower rate than the discount factor if the collateral brings benefits. Same thing for trees. The trees have exactly the same equation as bonds. They're essentially isomorphic except for this row. Remember the risk-weighted assets have this exogenous row so if row is really really small then you know the benefit that holding trees will give you from a collateral perspective is lower than bonds. So essentially this mechanical or you could think of this as a policy lever to essentially manipulate the relative return on risky assets and on bonds. And then you have this difference between bond normal rates and rates on reserves which here is one of the very interesting part of this model which is related to essentially has essentially the same flavor as bonds because reserves also help you with your collateral constraint but then on the other hand reserves also bring liquidity benefits so that's why you have this difference in the marginal cost minus marginal benefits of bonds versus reserves and multiplied by this factor here which essentially depends on the probability of needing to actually borrow. So when lambda is sufficiently large at g of lambda which is the probability of having liquidity shocks larger smaller than lambda so essentially the one minus g is the probability of having liquidity shocks larger than lambda and needing to borrow then you have a wedge between the rate of reserves and the rates on bonds. Of course nobody ever needs to borrow because reserves are sufficiently plentiful then you can see that these two are equal. Now how do we extract the two equilibrium curves from here? Well one is you combine this equation here with this equation there so you plug in ib in here and you can see that you have only exogenous coefficients here on this left hand side and essentially an equation that depends only on lambda and kappa this is the liquidity management curve the first equation and the second equation just takes the actual definition of collateral remember collateral is risk weighted assets divided by liability divide the numerator and the denominator by d and you get an expression that's also only a function of kappa and lambda so you get two equations two unknowns and that's how you solve for the equilibrium now what's interesting is you immediately see from this equation that the liquidity management curve does not depend on b only depends on ir one of the policy tools and the capital structure curve on the other hand is the opposite only depends on b remember b is the ratio of government borrowing to outstanding deposits so it's you can see that this is going to be effected by how much the government chooses to borrow this is going to be interest rate on reserve that the government chooses to set and so we study essentially how in equilibrium the solution to this system of two equations to announce depends on changes in policy variables such as ir ir and b okay and so that's the whole the whole idea of looking at these graphs and then thinking about changes in parameters and how they would affect the equilibrium you can immediately see from the graph right that you have these essentially two regions to the right of this region this is essentially in this equation where g of lambda is equal to one when g of lambda is equal to one right you can see that this equation essentially pins down kappa so for the whole region where lambda is greater than lambda bar the liquidity management curve picks down kappa equal to a constant so this is this component here and then you know so we have the liquidity trap region if you so wish and then the more standard region on the left and we can see now that if we sort of shift for example the interest rate on reserves if we shift the interest rate sorry if we shift the interest rate on reserves only this equation is affected it shifts up this one doesn't change so shifting for the interest rate on the reverse up means that the blue curve is shifting up and the green curve is unchanged you can see that this should always change both the collateral ratio and lambda and you can work out how this affects the equilibrium outcomes and Monika already explained that so essentially the mechanisms of the model they extend this in many many different ways so it's very very rich model is hundreds of equations you know so you can think about adding nominal collateral assets credit lines carry trades active freight is netting uncertainty premium and so on and see how this affects these two equations let me give you my comments so you know first as you can see from the description of the model this is crucially dependent on these leverage cost functions I mean we need I would like to hear more about the micro foundation for these functions and especially the one of the government because already in this model if you think about the optimum it's discussed in the paper so it's not an insight of mine they know that it's optimal to set B to zero because bonds and reserves essentially offer the same collateral advantage but only reserves offer liquidity benefits so you would have to find a story for why B should be not zero in the model but furthermore from my perspective if there's almost no cost reserves why not have always live in the plentiful reserve regime where we pay no real leverage cost remember there's really these are real costs what about the role between the link between bank leverage and aggregate consumption so in this model you have this since it's an exogenous aggregate output world you really have that when banks leverage up real costs increase so really the consumption of households decreases so it's you get this idea that if we should we try to minimize bank leverage but if we think that bank leverage serves a purpose of financing say new products and maybe new development, higher productivity then in a production model you might expect a positive relationship between bank leverage and output and that might move a little bit in a different direction bank leverage and there's no bank solvency issue in this model at all so in the model abundant reserves lead to interbank lending freeze right if you have more reserves well you don't have any interbank borrowing anymore but I would argue that as an explanation of the crisis maybe this is putting things upside down during the crisis really what is the sense we get at least looking at exposed at it is that interbank froze because there was a solvency concern and then as a response the government had to come in at the center and provide more outside liquidity whereas in the model the way we stop interbank borrowing is by starting by issuing more reserves and then lastly when you look at this model you ask why do we need actually banks right in the model banks really only serve as a costly technology to transform outside money reserves into inside money deposits that's all they but then maybe let's get rid of it let's go to the Chicago plan or you know we Swiss are always ahead of this you know we're trying to vote on this it's going to be a it's actually going to be a referendum on whether or not we want to go there in Switzerland which is another scary thing to think about such a referendum now we barely understand as economists so let's try to explain that to the public but you know or we could move to electronic digital currency and then we would get rid of that so I think I'm almost out of time in fact I can't move forward or backward anymore so that probably is a sign is that what it is you can't either see that's not just me okay I managed to manage okay great yeah I mean so I don't think I think I'm pretty much out of yeah the last point I wanted to make is in steady state inflation is equal to the exogenous growth rate of reserves in this model so when we really think about the impact of say open market operations on inflation it's really only when thinking about the transition across as we get interesting action in this model and in transitions as they are smart to to prove they can achieve but one period is one day so that kind of limits the insight I think we can get from that and I think also this one for one relationship in steady state between the growth rate of reserves and inflation doesn't really fit well the empirics and there was this nice consistent with our keynote speech in the morning I just put this picture out of the FT which pointed out this incredible cross-sectional variation in inflation when you look across different goods you probably all read the article but it sort of points towards perhaps the fact that we also need some technological explanation to the persistent inflation and not just the think of inflation in the recent period as a purely monetary phenomenon okay I have one big comment for the authors is before I recommend that you read the paper I think they have to rewrite and make the equations even easier to read for the mere mortals because we spend a lot of time on those thank you thanks very much so now we have 10 minutes more or less for questions so I will collect a few questions