 Okay. So, welcome back for the last session of this amazing conference, which are very well done. But before we end, we have Mark Gertler from NYU who will talk about the macroeconomic model with financial panics. Okay, thanks very much for including me. All right, what we do in this paper is incorporate banks and banking panics in a simple macro model. And this is part of an ongoing research project we have with the goal of developing a framework that can explain the crisis, recent crisis, not only qualitatively but quantitatively as well. Now, the specific goal of this paper is to characterize the sudden and discreet nature of the financial collapse that happened in the fall of 2008. And this is the worst point for the financial sector and the real sector. And it was the case that there was no observable, large, exogenous shock of the kind we typically study in macro. And a number of observers like Gary Gorton and Ben Bernanke argued that what was going on is that there were bank runs at the heart of the collapse, particularly runs in the lightly regulated shadow banking sector. And we're interested not only in characterizing this phenomenon, but also trying to understand what are the circumstances under which it could occur versus current, unlikely to occur. And think of the issue as the following. Think of the banking crisis as the disaster. And what we'd like to do is endogenize the disaster probability. Now, along these lines in the second part of the paper, we model, try to model the credit boom that precedes the crisis. And here the idea is to help account for why the system became vulnerable. And we're going to appeal to optimistic beliefs following Bordello et al. We're going to use a slightly different, we're going to use a different belief mechanism. But we're also going to use survey data as a source of external validation for this approach. Now, you can think of the goal of our paper is to explain the data in the following two pictures. Now on the left side, the blue line is GDP growth. The red line is a measure of financial distress, particularly the spread between the triple A rate and similar maturity government bond rate. And you see leading up to the crisis, beginning at the end of 2007, Q4, when the recession started, you see a gradual slowdown in GDP growth, which continues through the spring and summer. And at that time, people were thinking there was going to be a recession, something like 90, 91, which was also a banking crisis. Then what happens? Well, all hell breaks loose at the end of 2008. You see a very sharp contraction in GDP growth. You see credit spreads skyrocket. And if there's credit spread reflects an increase in credit costs, you have fairly natural explanation for the downturn. Credit costs skyrocketed, durable goods spending, and so on contracted. So the next step is to try and explain why these spreads widened the way they did. So here look at the right panel and what we're showing is the liabilities of the investment banks. And as you all know, the investment banks were funding long-term securities like mortgage-backed securities issuing short-term debt like repos and commercial paper. You see since 2004 there's a growth in liabilities reflecting the growth in assets, mortgage-backed securities. Then around the fourth quarter of 2008, you see a very sharp contraction in these liabilities, which kind of matches the runs that Gorton and Bernanke were talking about. So this is what we want to try and model. So the model. It's a simple New Keynesian model with investment. Now unfortunately, we don't distinguish between non-residential and residential investment. Any kind of complete accounting for the crisis will have to look at residential investment. But for simplicity, we're not going to include it. But hopefully by the end of the talk it'll be obvious how one could fit it into the framework. Okay. Then there are going to be banks that intermediate funds between households and productive capital. And they're going to hold imperfectly liquid long-term assets. I'll be precise later about what I mean by that. And they're going to fund these assets with short-term debt. And this liquidity mismatch is going to make them vulnerable to panic failure of depositors to roll over short-term debt. Now this is going to be in the spirit of Diamond and Digvig, a liquidity panic, but in terms of mechanics, it's going to be closer to the sovereign debt literature, self-fulfilling sovereign debt crises which will roll over crisis. And this is something that we've used in our earlier work. Now the last ingredient is that households may directly finance capital, but it's less efficient at the margin than our banks. And think of households more broadly as non-specialists so they could include life insurance companies, pension funds, small commercial banks, and so on. Think of the banks in the model that are vulnerable to panic. So those are like the shadow banks and large commercial banks that relied heavily on uninsured managed liabilities and thus were vulnerable to runs. Okay, so some key ingredients of the model. So the evolution and financing of capital. So it's useful to distinguish between end of period capital, call it S versus beginning of period. And the former is going to depend upon gross investment, I'm sorry, the gross production of new capital, which is a function of the investment level I, and then also the capital that's less left over after depreciation. Where the gamma function is increasing and concave and here the idea is to capture adjustment costs so we get a variable price of capital. Then we're going to introduce a capital quality shock, which is similar to the one Emanuel discussed yesterday. And this dates back to Merton actually and this is a very convenient way of introducing a source of exogenous variation in the return to capital, which doesn't generate huge variation in output. Okay, so given end of period capital there's a shock that affects the effective amount of capital in the subsequent period. Now this capital can either be intermediate by banks, I'll call the total quantity SB, and SH is going to be the amount which is directly held by households and the mix is going to be determined endogenously. Okay, so if banks intermediate capital, what do they earn? Well the rate of return is the rental plus capital gain, but augmented by this capital quality shock which is going to affect the return. Now as I said, households can directly hold the stuff, but think about them as being less efficient in managing and evaluating capital. So there's this holding cost which is quadratic in the share of capital that households hold so long as the share exceeds gamma. So up to a certain point they can costlessly hold capital, they go above the share, there's a quadratic cost. So what does that mean? That means the return to households from holding capital is going to be lower than the return that banks receive, and how much would depend upon this marginal holding cost, and this marginal holding cost is going to be linear in the share of capital they hold. So the more that households have to absorb the greater this marginal holding cost and the greater the discount on the return is that they would get. And why do we have this in here? Well again, if you have a banking crisis, banks are going to shed assets, households are going to be the marginal buyers, and we'd like to have a fire sale, we'd like for them to buy them at a discount, and you see the more that households have to absorb, the greater the discount and price they're going to demand. All right, so we can characterize the key aspects of the model with this simple diagram. And in the normal case, the case of no bank run equilibrium, you have households which are saved in the form of deposits, they can also directly hold capital. They're going to be the owners, although not managers of these banks, so they're going to receive the dividend payout. Okay, so what happens? Banks are going to fund assets by issuing deposits and their own equity, and they can't issue new equity, they have to, they only accumulate by returning earnings. So if banks take a loss on their assets, oh I should say the other thing is the banks are going to be constrained in the amount of deposits they can raise, it's going to depend upon the amount of equity they have. So banks take a loss on their assets, that's going to cause their equity base to shrink, that's going to reduce their ability to attract deposits, they're going to have to shed assets, households absorb them, but households are less efficient at holding them, so they buy them at a discount, asset prices are going to fall, excess returns are going to go up, and this is going to lead to a contraction of the economy, and this is a kind of standard financial accelerator mechanism. Now it's going to turn out that in certain circumstances, there could be a run equilibrium, and in a run equilibrium, the households are not going to roll over the debt, that's going to force the banks to liquidate, they sell to the market, and they're going to have to sell at fire sale prices to these households that have difficulty absorbing the assets, and the big drop in prices and high increase in excess returns, or you can think this is a high increase in spreads, that's going to cause a sharp contraction in real activity. That's what we want to try and model. All right, so I need to go a little bit deeper into the bank's problem, so what the banks are going to do is maximize the discounted payout of dividends to shareholders. Now the banks are going to be subject to financial frictions, so what this means is they have an incentive to accumulate equity to kind of save their way out of the financial constraints, so we're going to have to reduce the incentive for them to do this, so we assume that there's an exogenous exit probability one minus sigma, so they effectively have a finite expected horizon, and so what happens, and then what's going to happen is when they exit, new banks are going to start up and take over. So what happens is with probability one minus sigma, they exit, and then any retained earnings they have, they're going to pay out to households. If they don't have to exit, they survive for another period and they continue. So the objective essentially is the expected discounted payout of earnings to shareholders, okay? Net worth is going to be accumulated by retained earnings, no new equity issues, so how does that net worth go up? It's going to be the difference between earnings on assets, net deposit costs, so this is what happens if there's runs, if there's a run, the bank has to sell off its assets and it's left with zero net worth. Okay, so how does the bank fund assets? As I said earlier, assets are funded by net worth, which the bank takes as given at the beginning of the period and just accumulates over time, so the marginal form of finance is going to be deposits, so financing more assets for a given level of network means the bank has to leverage itself. Okay, deposits, so let's let RT plus 1 be the return on deposits. If there's no bank run and the probability of a bank run is P, which is going to turn out to be, or which we're going to make endogenous, they receive the promised return R bar. If there's a run, what they get is the recovery rate X per unit of deposits times the promised deposit rate. And what's the recovery rate? The recovery rate is the numerator is the liquidation value of assets, so Q star is the fire sale price, so in the event of a run, the bank has to sell off its assets and this is the liquidation value. The denominator is the deposit obligation, okay? So each depositor is going to get this ratio per deposit times the promised deposit rate, and this is going to turn out to be important. Okay, now if there were perfect markets, banks would issue deposits until excess returns are zero. Okay, lambda is the household stochastic discount factor, banks would just keep issuing to drive excess returns to zero. Here there would be no leverage constraints for the bank, and also you can't have financial panics because if they're withdrawals for some reason, the bank can just go out and issue new deposits. So to have a banking panic, you need to introduce some kind of limits to arbitrage, so you get an occasionally binding leverage constraint where excess returns are positive. So the bank isn't levering as much as it would like to. And what's a bank run in this case? A bank run is going to be an extreme increase in excess returns, kind of like what I showed you on the first picture. So excess returns go way up. That means the cost of capital goes up, and that feeds over and affects real activity. All right, now I want to be explicit here because I'm ultimately interested in endogenizing the disaster probability. And so I need to have a very explicit motivation for the banks, the constraints that banks face, so I can endogenize that probability. So what I'm going to assume is that after the banker borrows funds at time T, it may decide to divert a fraction theta of its assets for its personal use. And if it does so, if the bank does not honor its debt, the creditors can recover the residual funds and then shut down the bank. And so the creditors realize this. So what's going to restrict the lending relationship? Well, what the bank would gain from seizing assets has to be less than the continuation value of the bank. And what this is going to do is this is going to involve restricting leverage because the more the bank levers itself, the greater, you know, you're using other people's money, the greater the incentive to divert funds. OK, now what's the solution? The solution, you can show that the continuation value is a multiple of equity. Where psi t, think of this as the Tobens Q value of a unit of equity for the bank. And why is this Q value possibly greater than one? Because the bank can use the equity to lever itself and it can earn excess returns by levering itself, OK? And this Q value is going to be increasing in the excess return. So if a bank is facing all of these opportunities, but it's constrained, the shadow value of another unit of equity is going to be really high. So if we combine this expression for V with the incentive constraint, we get the following endogenous leverage constraint, which says assets have to be less than or equal to some multiple of equity. And I call fee bar the maximum possible leverage multiple. And that's going to be increasing in the Q value of the bank and decreasing in the bank's ability to seize assets. And so in the end, what's going to happen is this leverage multiple, maximum leverage multiple, is going to be increasing in excess returns. And the idea is that the creditors see the bank can earn high excess returns. The bank has less incentive to cheat. So the lenders are going to be more forgiving and let the lender borrow more. So what's the point of all of this? That, well, excess returns are going to be counter cyclical because in bad times, these constraints really bind and excess returns are high. So what's going to be true in this situation is the maximum leverage multiple is going to be counter cyclical, okay? So leverage relative to market value of equity is going to be high in bad times, which is consistent with the evidence. And what's the significance here? Well, it's going to turn out that runs are more likely if leverage is high. And I'll get to that later. But here I have in my back pocket that leverage is counter cyclical. The other thing that's going to be key is note if the bank has no equity, there's no way to satisfy this incentive constraint so the bank can't operate without any equity. And that's also going to be important for the existence of the run equilibrium, okay? Now, the maximum leverage multiple fee bar is going to be independent of bank specific factors so we can aggregate across banks so we have assets held by the banking system is going to be a multiple of bank equity. And so what this is going to imply is that excess returns are going to be positive. It's clear if the constraints binding, that's going to be the case. Even if the constraints binding but the banks know there's some chance it could bind, there's going to be precautionary behavior because the bank is going to be worried about getting caught short so it'll be conservative and excess returns will still be positive. Then we get net worth evolving as follows. It's going to depend upon the accumulated equity of the surviving banks and the fraction sigma survive and how much they earn is going to depend upon the excess return on assets weighted by leverage, okay? And so variation in excess returns is going to cause variation in N and that's going to be magnified the more levered the bank is. And the last term is the injections of new equity from entering banks. So absent runs, there's a conventional financial accelerator with non-linearity because this constraint's not always binding. Okay, where do runs come in? Well, a self-fulfilling run equilibrium that is a rollover crisis that's possible if a depositor believes that if all other households do not roll over their deposits, the deposits with her will lose money by rolling over. And this condition is met is banks net worth goes to zero in the liquidation because if Nt is zero, the bank can't operate because a depositor gives money to a bank with no equity, the bank is just going to run off with it, okay? So this means that the run equilibrium is going to exist if the recovery rate X satisfies this condition if it's less than one. If the liquidation value of bank assets in the event of a run is less than the deposit obligation, bank equity would go to zero in the liquidation and then a run equilibrium is feasible, okay? This is going to be a sunspot so the normal equilibrium exists as well but there's also a run equilibrium, okay? All right, so what's the probability of a run? That's what we want to endogenize. So the run equilibrium is going to occur if the equilibrium exists and it doesn't always exist and if a sunspot is observed. So we're going to assume that if a run equilibrium exists, we're just going to fix the probability that the sunspot will be observed because we don't want to rig the counter cyclicality of the disaster risk okay, so we'll keep this as a cyclical, the probability you get a sunspot when the equilibrium exists. Okay, on the other hand, the other component, whether or not the run equilibrium exists, that's going to depend upon fundamentals, okay? And we know that because leverage is counter cyclical, okay? Because leverage is counter cyclical and because liquidation prices are pro cyclical, the run equilibrium is going to be, the probability of the run equilibrium existing is going to be counter cyclical, more likely in bad times than in good times, okay? All right, where does the liquidation price come from? Well, this is the price of the asset if households were forced to hold everything and you can read that off of the first order condition for households asset demand assuming households hold everything. So what this is assuming is that these marginal holding costs are at a maximum which is going to push liquidation prices to a minimum, okay? And then what happens after you liquidate, new banks enter, assets are going to slowly build up and you get a return, get a return to new, okay? The rest of the model is very standard. It's New Keynesian nominal rigidities where asset prices feed in as there's a Q relationship for investment and then also monetary policy is given by a simple Taylor rule. All right, I'm not going to go into detail into the calibration. There's a number of standard parameters and there's a number of parameters that are specific to the banking sector and we use targets like leverage ratio, the share of bank credit and total credit, run probabilities, you know, given the frequency of runs, spreads and so on to pin down these parameters. Also, we assume this capital quality shock is first order serially correlated and we pick the standard deviation and the serial correlation parameter to match the standard deviation of output and the standard deviation of investment. Okay, all right, now to understand, before turning to runs, let's try to understand how the model works and look at a simple shock to the return to capital and we're going to look at a one standard deviation shock, which is a 50 basis point shock. Now, we rigged the model so that in the steady state, the bank run equilibrium doesn't exist, so this shock is not going to trigger a run. And in fact, the dotted line in that same panel is the shock you would need in the following period for the run equilibrium exists. And what this says is in the next period, you'd need a 100 basis point negative shock, which is a two standard deviation shock to move into the run equilibrium. Okay, all right, so what happens? Well, the dashed line is the model without financial friction, so a shock in the return to capital, a serial correlated, it reduces investment, it reduces output because they're nominal rigidities, you get this output contraction. But notice there's something in the model with financial frictions, asset prices go down, bank net worth falls, excess returns go up, so you get an extra kick in the drop in investment and an extra kick in the drop in output. Now, this is a standard financial accelerator. Now, something else goes on, note that leverage goes up, leverage is counter cyclical. Well, leverage going up moves you closer to the run equilibrium, so you actually see the run probability goes up, okay, as the contraction happens. All right, now let's look at the same kind of experiment, but now let's say there's enough shocks to push you into the run region and then look at the effect of a collapse. So what we do now is hit the economy with three small shocks. So the first two get you within a one standard deviation shock of the run equilibrium, so that's what we're starting. There's been two shocks and now you only need another one standard deviation shock to get in the run equilibrium. So we hit the economy with that size shock. Now, after this small shock, because you were at the edge of the run threshold, you're pushed into the crisis zone where equilibrium is possible. Now the dashed line is the case with no run equilibrium. The blue line is where the run occurs and you can tell the run's occurring because net worth goes to zero, the banking sector has collapsed. Households are absorbing all of the assets now, so excess returns jump like crazy and now you get a huge contraction investment and a huge contraction in output. So the run causes a sharp contraction and it persists for a bit as well. So it makes a significant difference to real activity. Okay, now we can do this kind of real time attempt to capture the crisis. So we do the following experiment. We start in 2007 Q4 and we hit the economy with a sequence of capital quality shocks so that the model matches the actual investment data. Okay, then we check and see how the model does for the other data from 2004 to 2008 Q3 and the model does a pretty good job of matching most of the other data over that period. Then what we do by 2008 Q4, the economy has moved into the crisis zone so a run equilibrium is now possible. In fact, the bottom row here threshold, that's the size shock you would need to get to the run equilibrium. So in 2008 Q4 we give this just a large enough shock to get into the run equilibrium. Then the dashed line is giving you the actual collapse. The dotted line is what happens if there's no run. And you can see that we match the actual contraction in economic activity. The timing's a little bit off because we don't have any of the adjustment costs that are usually put in these models to match the data. And also we don't really match the persistence of the recession. Now there's several factors here. One is after the run occurs we don't feed any more shocks into the model and we know there was a fiscal contraction. We know there was a sovereign debt crisis. And then we don't have other factors which could add to persistence like household debt and so on. But in terms of capturing the collapse I think we do a pretty reasonable job of capturing the features of the data, the collapse in bank equity, the rise in spreads, contraction in GDP and investment and so on. Okay. All right. Now I want to end up with, so that's modeling the contraction. Now I'd like to talk briefly about the credit boom. So here we start things off back in 2004. And we introduce a shock to news, a new shock. Now the standard new shock is you learn at some time in the future there's going to be some kind of disturbance and you learn that with certainty. Now we want to relax that. You get some news but it's not going to be certain that the shock occurs and it's not going to be certain when the shock occurs. Okay. And so you're going to start out with a prior probability on whether the shock is going to occur at all and then you're going to start out with a prior distribution over the time periods in which the shock could occur. That's what we're going to do. And we're going to kind of rig things so that what you're going to get is consistent with survey evidence. The analogy Moat Noble gives is through his research with John Moore, they get an idea, they think they're going to be able to complete it, finish it three months from now, they start working, they get some positive results, they get all excited, then the time gets near, they're not that far along, then at three months they still haven't solved it, time passes and then they panic and their optimism has shaken and beliefs become negative. Okay. So here what we do, so on the upper left-hand panel, that's the prior distribution of when you think this positive shock, the capital quality is going to occur. And we rig it so it's most likely to occur at the peak of the housing crisis in 2007 Q2. So we're starting in 2005 Q1. So this is the prior distribution conditional on the shock happening and the prior probability in the shock happening is some number less than unity. So the middle panel tells you how beliefs evolve. So what's happening is as you go through time and there's no shock, well in the beginning you're kind of confident the shock will happen because it still hasn't happened, you still haven't reached the peak of when it's most likely to happen. But then you get past the peak and your faith gets shaken because it becomes less likely to happen. So the probability that the shock has happened starts to shrink. The red dash line is the probability it's going to happen in the next period conditional on it having to happen sometime and as you go through the end of time this has got to converge to one, okay? So the probability the shock is going to happen is the probability of these two lines, the blue line, the probability it'll happen at all and the red line, the conditional probability. So what you get here is just to illustrate how you get a wave of optimism, this is the year ahead forecast of the capital quality shock, okay? The blue line is the actual shock, there's no shock but you get optimistic before the peak and so optimism rises but then it keeps passing without any action and beliefs start to shrink. So what happens in the real economy in the model is because as you're believing that these are bankers' beliefs, you believe asset prices are going up, so I'm sorry, you have positive beliefs about the quality of capital, asset prices go up, investment goes up and you get a modest output boom. What's happening is to finance this, these bankers are levering themselves, okay? There's been no fundamental change but just because they believe there's going to be a change they lever themself. So then what happens is, well, because they're increasing their leverage the probability of being in the crisis zone increases as well. Okay, so we can do the same kind of exercise and since I'm probably over time, just let me briefly summarize, you get very similar results but now we're starting the crisis off in 2005 with these optimistic beliefs and the other thing that's relevant is it's easy, you're closer or more likely to be in the crisis zone. Now during the whole experiment, the economy's actually in the crisis zone and in 2008 Q4, you don't need an additional shock, it's just without additional shock, you're still vulnerable to a banking panic, the panic appears, the panic happens and it plays out very similarly to the way it did in the earlier example, okay? Oh, last thing, the check on the model. So we modeled these optimistic beliefs and this is going to lead to serially correlated forecast errors because this shock is really never realized or just you believe something positive is going to happen. So the blue line is the median forecast, I think this is from the survey of professional forecasters of what the credit spreads are and you see that they're too optimistic, this is the forecast error so the actual spreads were higher than forecasted, meaning that leading into the crisis, the forecasters were too optimistic. The dash red line is what the model gives you and the light blue line, these are the distribution, this tells you the distributions of errors of the different forecasters, that is, there are a bunch of forecasters and this is the distribution of forecasts and these are 95% confidence intervals and what this says is for the most part, the forecast errors that the model generates are pretty close at least within the confidence bounds of what you see in the data. Okay, let me just, okay, so let me just say what are the next steps, well we didn't think about policy, here there's a natural role for macro potential policy in addition to the usual externalities, there's also a run externality, that is the probability of a run, it's going to depend upon aggregate leverage but individual investors are going to take that as given, individual banks are going to take that as given in their leverage decision and then also there's a roll for lender of last resort policies and here one of the problems is that liquidation prices are going to be low and if liquidation prices are low that's going to make the panic or the being in the crisis zone more likely, well if you had a lender of last resort who kind of committed to stabilize secondary prices that could reduce the likelihood of a run equilibrium, okay, thank you. Thank you very much, Mark. Discussing is Veronica Guilier from University of Chicago. So hello, thanks a lot for giving me a chance to discuss this interesting paper. So after the recent recession and financial crisis there has been a new wave of papers trying to incorporate financial frictions and financial markets into macro models and the authors in particular Mark and Nobu have been working on that way before the recent financial crisis but now of course the attempt is to see if these type of models can account both qualitatively and quantitatively for the recent episode. So recently some of you were at the Brookings conference there has been a lot of discussion spurred by Ben Dornanke on what is really behind the recent recession and the way I see it is there are like two main potential source of the recent recession which can be of course part of the story in combination but different people have highlighted the role of one versus the other. Bernanke in the new paper at Brookings has highlighted how financial panics, so he says I also provide new evidence to suggest that the severity of the great recession reflected in large part the adverse effect of the financial panic on the supply of credit. Other people have been emphasizing more the boom and bust in the housing sector and Krugman for example has argued that that was probably the more relevant side of the story. So probably both are important and in this paper Mark and his co-authors incorporate banking panics into a standard New Keynesian model. In particular they use their previous work published on the AR to think about banking panics and then they use these in the New Keynesian model to look at how can they replicate what happened in the recent episode with the recent financial crisis and their propagation to the real economy as Mark has shown. In the main results are that quantitatively on top of qualitatively they seem to do a decent job in explaining main macro aggregates. Other two interesting results are one that Mark showed with his first two figures that the financial in his models there are both banking panics and occasionally binding constraints that are part of many macro models that incorporate financial frictions including their previous work, work by Brunner, Meyer and Sannikov, work by Krishnamurti and Hei. In this model in particular they show that the panic seems to play a much bigger role quantitatively than occasionally binding constraints. So if this point into the direction of incorporating really panics if you wanna think seriously about the role of financial markets into the macro economy. And then another part of the paper that Mark showed at the end that I find particularly interesting is showing how credit boom can probably driven even only by expectations can generate can actually make the economy more sensitive to financial instability and so possibly subject to runs. So in a nutshell what are the ingredients of the model? There are two goods, non-durable and capital and capital can be held by households and by bankers but of course households have some efficiency cost in holding capital and so this is the main friction that when banks run and they sell the capital they need to, the price of the capital drops so there is kind of a fire sales because households are gonna pay a cost to hold that capital so they're not gonna be willing to demand capital for a high cost. So bankers use deposits and network to invest in capital and there are two main banking frictions into the model. First of all bankers cannot issue new equity and second there is this limit to leverage that they model with this moralizer story that is important to give the possibility of runs into the model. What is the main mechanism? Well negative capital quality shocks are gonna reduce the value of bankers' capital and so what happens banks may default and there are two possibilities that they highlight in the paper unless in the presentation there can be a pure insolvency problem or there can be a bank run. So what does it mean insolvency? Insolvency issues when the bank's value of the assets is below the value of the debt repayment but the bank runs arise when even if the current prices the banks are not insolvent if banks expect the run to happen then they know that they will be insolvent at the liquidation price and this is the scenario where they focus in the paper. So what's gonna happen is that the capital price is gonna collapse and then with a new Keynesian aspect of the model this is gonna induce a drop in investment and the financial and the nominal rigidities are gonna amplify the drop in output and employment that is gonna come as a result of that. So what I'm gonna do first of all I'm gonna give you a strip down very stripped down version of the model to try to explain the idea of the run and what can generate what can make the economy more fragile and subject to run and then I'm gonna talk a little bit more about this lack of propagation that we saw are in the results of the paper. So let's think about a model where the supply of capital S is given and so as we saw there are bankers and households that demand capital so SB is the demand from bankers and SH is demand from households. Banks invest in capital using net worth and deposits. So what is the return on deposits? It's just X times R, X being smaller than one if there is default. So in that case the banks are gonna repay everything that they can to their depositors in a random way and X represent that ratio between the value of the asset that they have the total amount of debt but if there is no default X is gonna be equal to one and R is simply the deposit return. So the bank's net worth is gonna be equal to the value of the capital that they hold minus the value of their debt. XI, this doesn't work. So XI is the capital quality shock. Q is the price of capital. Delta is depreciation rate. S minus B is the initial level of capital of the banks. XI as we saw is the return on deposit and D minus is the initial level of deposits that the banks have. So when is that the bank is gonna default? Well the bank is gonna default even if the value of their assets is gonna be smaller than the value of the debt. So there is gonna be a cut off price Q star. Sorry for the change of notation Q star is different from the Q star in the paper actually in the paper is the liquidation price. Here is really the cut off. So Q star represent the price below which banks are gonna become insolvent and so they're gonna default. And interesting thing is that even in this simple model you can see that Q star depends negatively on the capital quality. So if there is a change of shock to the capital quality so if the capital quality decreases Q star is gonna increase so the cut off for the run is gonna increase so there is gonna be more run or more default in the economy potentially. So in a sense we can think about a good equilibrium and a bad equilibrium. A good equilibrium is an equilibrium where there is no default and a bad equilibrium is an equilibrium where there is default. Notice that in this model there is only room for systemic default so all banks are homogeneous and if there is default of one bank so all banks are gonna default. This is different from the diamond deep big story of a possible run for a single individual bank. So there are three scenarios possible in this simple version of the model. In one scenario there is only the good equilibrium. In one there is only the bad equilibrium and in the other there is a multiple equilibria story which is where run can arise. Let me show you with a graph. So here the red line represent the demand for capital by the bankers and the blue line represent demand for capital by the households. So the way to read this graph is that there are like two symmetric quadrant here. On the y-axis there is the price of the capital. On the x-axis there is the amount of capital and so you're gonna read the downward sloping demand curve for the bankers looking at the origins on the left side and the demand for the households looking at the quadrant, the symmetric quadrant with the origins on the right side and the sum of the two has to be equal to big s which is the length of the x-axis in between the y's. So q lower bar is the price at which households are gonna be willing to hold the whole capital, the whole amount of capital. Q star is our cut off price for default and Qe is a potential price at which there is an equilibrium with an interior equilibrium where some capital is gonna be held by the bankers and some capital is gonna be held by the households. So in this scenario for how I draw the Qs there is only one equilibrium and this equilibrium is a good equilibrium where some capital is hold by the bankers, some capital is by the households. But what happens if there is a negative capital quality shock and Q star rises? If it rises above Q lower bar but still below Qe what's gonna happen is that now two equilibria appears. So once Q star is above Q lower bar what happens? Well the demand of the bankers for capital is gonna be downward sloping and the same as before up to Q star but below Q star there is gonna be default so the demand is gonna be zero. So one equilibrium is the standard good equilibrium. The bad equilibrium is equilibrium where Q lower bar is gonna be the price arising in equilibrium so the liquidation price as Mark referred to it which is the price, the collapse price at which households are willing to hold all the value of capital that is liquidated by the banks who are gonna default in equilibrium. Now in this case you can see that if the price was Qe the banks would be solvent. So it is not a problem of solvency here is really a run is a sun spot. If the banks think that other banks are gonna run well then there is gonna be a run to the other banks well then if all banks default the price is gonna be so low that they actually in expectation becoming solvent and so they prefer to default and so this is how banks make a ordinate on a bad equilibrium. Now there is a third possibility is that the Q star is so high that actually the good equilibrium does not exist anymore and so there is only a bad equilibrium I would call this the case of insolvency. So the shock can be so bad that really banks becomes insolvent effectively and so this is really the worst scenario because. Okay so let me say one thing I'm not a particular fan of these negative quality capital shocks so if anything I think this is the biggest weakness of the model because I understand that are very tractable and many people now use those but it's really not clear what they stand for especially if you wanna go quantitative and understand what really is the mechanism thinking about the financial friction and where the financial markets and the interaction between financial markets and real economy. So I like much more the part of the paper where the run actually comes from this increase in leverage coming from expectations at least I understand where this is coming from and you can see from the Q star expression that I wrote down that clearly Q star is positively affected by D minus from the level of deposits in the model and so the level of deposits represent basically is one to one with the leverage of the bank so if in the particular case that the authors presented it when people get positive optimistic expectation they can increase the leverage and this can make actually the run happens just because they leverage so much that in the end the economy becomes more fragile. There may be other possibility of thinking of different shocks for example it would be nice to explore the possibility of a risk premium shock probably would be less tractable so I understand where the authors are coming from but for future research I think it would be interesting to explore other possible shocks. So let me go on the crisis experiment so the authors use this model embed this panic model into the New Keynesian model and then they hit the economy with these capital quality shocks and in particular they do it so that they obtain the investment between the fourth quarter of 2000 they drop in investment between the fourth quarter of 2007 and the third quarter of 2008 and then they add a shock to obtain the run to have the economy going into the possibility of the run to arise in the fourth quarter of 2008 when the lima collapse happened. So as like Mark showed you the picture I knew that so I didn't show them again but so you could see that the model does pretty well in obtaining the magnet and as Mark recognized if anything where he's missing something is the lack of persistency of the recession. So where this comes from, Mark talked briefly about some possibilities I would say I would like to classify these two possibilities in two categories. One maybe there is something missing on the way they model the financial sector in embedded in a macro model. So for example I mean one could think about the banks changing behavior after a crisis, a rare event happening and there is for example a recent paper by Koslowski and quarters where they argue that after observing a rare event the probability assigned to the tail risk may increase and this may change the risk taking behavior of the banks and so also the strategy of the banks in investment strategies and so on and this may feed back into the real economy. Another possibility is that instead I mean this going back to the original initial discussion about what are the sources of the crisis so here we kind of focused on the panic and how the panic generated the crisis but there is all the other real side of the boom and bust in the housing sector. They may probably play a role more for the persistency of the recession because as actually Thomas showed us yesterday clearly the deleveraging of households in response to the collapse in housing prices may create a slow recovery and these may play an important role in the story. So I'm sympathetic to the view that financial panics are an important part of the story but I think that we don't want to forget the real side of the economy and the big deleveraging of the households because this was where the underlying economy was when the financial panic succeed and this makes an important role for the real consequences of the financial panic. Thank you very much, Veronica. So we have eight minutes for questions and then I'll... Here you go. So my question is about the structure of financial intermediation at the time of the crisis. Any story about the crisis needs some mispricing happening at some point and in Marx model the mispricing is happening through this optimism wave. There's another narrative which is a story of mispricing due to asymmetric information across financial intermediaries. Those who originated the mortgages, those who warehouse them, financial intermediaries who create the past flow securities, the one who created the structure securities and the eventual banks or financial institutions that held these securities. So my question is about whether this is an issue which is completely or relatively orthogonal to the fragility that it's represented, how it's represented in this model. And one issue that it could be important to give in mind is that one enduring legacy of the crisis is that it completely wiped out a market which is private label segregation for separate mortgages. So is that something that just happened or is that something that's actually making the financial system more resilient? Thank you, Alberto. Well, thank you. Thank you, Mark, for the presentation. So I just have one comment and two questions. The first comment is I like the model and I especially appreciate this attempt to try to, how can I say, focus on the possibility of multiple equilibria. So, you know, also Veronica mentioned and you mentioned yourself this other story for housing. You know, some people have tried to model the crisis as the bursting of a housing bubble. And in many regards at a very abstract level, these two stories are somewhat similar conceptually in the sense that, you know, the economy is prone to coordination failures. There are some fundamental situations that make them more prone to such coordination failures. And so, you know, micro-economies typically like to ignore a multiplicity of equilibria, but I think this path of research of trying to, you know, see whether we can discipline it somehow or understand the role that they play, I think it's very important. Now, having said that, I have two questions about the modeling per se. The first one is, you know, you mentioned the coal and key home model and will you build their runs? In that model, agents don't like to put themselves in this run situation. And in fact, you know, the model starts there and countries start trying to build down the debt because there's a huge premium from exiting this crisis zone in terms of the interest rate that you pay and so on. So I guess I was wondering whether banks in your model are constantly trying to get out of it or how do they get into it in the first place and whether these distorted beliefs are somehow important for that. And the second question is, it's in terms of policy. I guess many of these runs you could eliminate if you had, you know, liquidity facilities exposed or depositing sure and some of which we have in place. But I guess in real time for the policymaker it's important to understand, okay, is this a run I'm seeing or is it a fundamental shock? And the response to these two situations may be very different. So does your model, can it help you understand whether, you know, I see a deep crisis is it driven by fundamental shocks or is it a run? Are there observable differences between these two? Seb now? Very nice presentation and discussion. So I just want to ask a clarifying question. This leverage plays a big role, right? Both for your contraction and also the boom. Now, are you thinking, again, this is just a clarifying question because I was a little bit puzzled. Are you thinking two different concepts of leverage? So Tobias Adrien and Huyun Shin, they show that there is this, you know, book leverage for banks where you look at like asset and liabilities and that's pro-cyclical and that's important for the lending which I guess relates to your boom. And the other one, the market one, is actually counter-cyclical and that's based on the bank's network. So let me answer this quickly before I forget. Clarifying. What's relevant is market leverage and that is counter-cyclical. There's all sorts of confusion because every time we present it say isn't it pro-cyclical? No, that's book leverage is pro-cyclical. So market leverage, so that's the one that is really working in the contraction. And then during the credit boom so that's, you know, it also works through the way that, because they're also lending, right? So, but then you still use the same concept because they argue that during the boom for the lending, the assets are more relevant than the bank's network which goes down during, of course, the bus. So just ask one question. Yeah, the bankers are more optimistic about the process, yeah. Okay, Mark. Okay, I'll try to be quick. First of all, let me thank Veronica. First of all, we're presenting the model more clearly than I did. And secondly, I agree with everything she says. And last, I want to emphasize that I think that both the household balance sheet and the banking panics were important. In fact, Simon Gilchrist and I have a paper in the Summer Journal of Economic Perspectives that we argue that you have to take into account both phenomenon, to have a full accounting for the crisis. And I think of them as interdependent phenomenon. The losses on mortgages of what got the banks into trouble in the first place. Then the financial collapse helped push down housing prices. In fact, half of the decline in housing prices happened after the layman collapsed. So that helped weaken household balance sheets and I think that's probably the leading explanation now for what the slowness of the recovery is. So I think any explanation has to factor in both. Federico, just to be clear, the actual mechanism doesn't require distorted beliefs. What it does require is the segmented markets where the banks are the experts funding these assets. And when they lose equity, the assets get shifted to the non-experts. But beliefs can come in and play, do play a role in kind of amplifying things. And the kind of mechanism that you're talking about could be relevant as well. It'd be interesting to think about that. On Alberto, the two things. They said, do bankers take into account the fact that they're in the crisis zone? And here, there's an externality because they take the probability of a disaster or a panic as exogenous. That probability depends upon the leverage of the whole system. So they kind of get into that danger because of the externality. They don't perfectly internalize it. The last thing is if there's a panic, how can central bankers tell if it's fundamental or a panic? My view is that's why we pay central bankers. I guess right now I'll say it's in the kind of you know it when you see it. Within the day, if there's a massive exit as you know, that kind of looks like panic. OK, I think we basically ran out of time. Let me thank both Mark and Veronica for an excellent concluding session. And I would also like to take this opportunity to thank Luke and the organizing team, Bartosz, Marie, Alex, Sabine, for putting this together. I think it did serve some of the purpose that you mentioned at the beginning. Got lots of new ideas and lots of things to work with. So thanks a lot for coming and have a good trip back home. Luke, is there anything else? OK, so.