 So this is joint work with Moda Yoga and I will start off by first giving a sort of like a broader introduction in terms of like what are our research agenda is about. So as was just mentioned sort of like our approach to sort of thinking about asset pricing is trying to connect portfolio quantities and asset prices to it and it's sort of like broadly motivated by the observation that a lot of the important policy questions that we're thinking about these days regarding financial markets and the real economy that they involve shifts in asset quantities. So you can think obviously about asset purchase programs but also the topic that we talked about yesterday, the growth of like ESG mandates, global savings clubs across countries, across the world, all of those involved changes in asset demand and their impact on and we're trying to understand the impact on financial markets. Now in order to quantify the impact of demand shocks we need a model that's sort of like well described how investors substitute across asset classes and across countries and I'll motivate why the cross-country dimension is important. And so I'm going to refer to this as demand system asset pricing and this is sort of a class of models of asset pricing models, macrofinance models that tries to jointly explain not just prices and fundamentals as we've done historically but also portfolio holdings and sort of like getting that part right is essential to get sort of credible answers to these important. So that is sort of our starting point. Now why is it important to have a global model of demand? Now one way to see that is to go back to the PSPP and look at sort of like who accommodated the asset purchases by the euro system between 2015 and 2017 for which we had data in our earlier project. And so the way to read this graph is that when the euro system purchases one euro of government bonds like who is selling, how are those purchases accommodated? And so what you see on the horizontal axis here are different sectors. So we have banks, we have foreign investors, so those outside of the euro area, households, long-term investors, insurance companies and pension funds, mutual funds and then the leftover category. These bars over here correspond to new issuance, which is of course another way to meet those purchases. And so the lighter gray bars is just the average for balancing. The darker gray bars is a better identified like measure of like who's taking the other side of the trade of the securities purchased by the euro system. And an important observation here is that on the investor side, by large, the most important investor to accommodate these purchases are actually foreign investors, those outside of the euro area. And so what that means is that in understanding the impact of purchase programs, you want to take a global perspective and think about sort of asset demand globally. And so for the big picture, like any asset pricing model, any macrofinance model that thinks about asset prices is a combination of two things. One is a model of portfolio choice combined with market clearing. And so what we want to have is a model that matches cross-country holdings to explain global asset prices. And so what then drives asset price and what drives exchange? So in the setup that we're going to have, and I'm going to sort of like talk about today, is there's going to be like three broad groups that you can think about. The first is demand from global investors. And in this case, a unit of an investor, think of it as a country, think of like external positions of countries. And so these global investors, they are going to invest in assets across asset classes and across countries. And so they're going to have a demand for short-term bonds, for long-term bonds, and for equities, and they're going to invest globally. Now their demand, we're going to model it depending on obviously prices or expected returns. It's going to depend on macro fundamentals, capturing growth expectations, capturing the riskiness of different countries, as well as their sort of like unobserved expectations about those variables, which I'm going to refer to as latent. Okay, so think of that as the first part of the demand side of the model. Then the supply of debt and equity by firms. And then there's the policy variables that sort of complete the model where central banks are going to set short rates. Debt quantities are going to be the outcome of fiscal policy and monetary policy. And then the last important group of policy variables are going to be related to foreign currency reserves. So central banks hold non-trivial amount of foreign assets, and that's going to be an important part of the market clearing inquiry. So think of the model as combining a model of demand with market clearing, and then that demand is coming from various actors, investors, and in part also from the policy side. Okay, and that allows us to start thinking about why do asset prices and exchange rates move, and how important are some of these policy variables. So more concretely, what I'm going to show you today is I'm going to use data from 2002 to 2017. So we're going to have data on the global financial crisis, the European sovereign debt crisis is going to be part of the analysis. We're going to try to understand sort of the joint dynamics of exchange rates asset prices macro variables across 36 countries. It's going to be developed economies and developing economies. In terms of like the holdings data that we're trying to understand, is we're going to look at the cross-country holdings of the IMF's coordinated portfolio investment survey, the CPIS. And so we're going to set up this model that's going to allow us to understand why prices move, and then we're going to use it to give a decomposition of variation in exchange rates and asset prices. And we're going to zoom in particular on a couple of important events. So first we're going to try to understand the dynamics in European debt markets during the sovereign debt crisis and thereafter. So for instance, we're going to try to understand why did the spread between Greece and Germany sort of like widen as much as it did, what were the spillover effects to other countries like Italy and Portugal, and what role did different investors play, what role did macroeconomic fundamentals play. Similarly, we're going to sort of have a way of thinking about like lower frequency yield differentials between Germany and the US, which was very large before the COVID-19 crisis. As another application of the same framework, we're going to think about estimating the convenience yield on US assets. This was like special demand for US securities. And again, the same framework allows you to estimate the impact on prices, those effects. And then in progress, but I'll sort of like discuss a little bit towards the end of our thinking about this. One thing that we're currently working on is to see what are the demand system approach could be used for real-time policy analysis. And just to give you a hint as to why the demand system may be useful is that it's for two reasons at least. One is that obviously a lot of the interventions involve changes in quantities, and so a demand system is a natural framework to apply. But perhaps more importantly, what is particularly useful we think potentially is that you can consider demand shocks of different players at the same time. So if multiple central banks or across different countries are implementing stimulus programs or purchase programs at the same time, the demand system can account for those for that combined shock as opposed to analyzing each shock in isolation. And so we think that the demand system may be a useful way to analyze the real-time impact of these of these programs. So in terms of the setup, think of it as followed. So there's going to be an investor as a country and so there's 88 of those investors, so there's 88 countries in our example. And then there's foreign currency reserves. Now for each of those 88 countries, we have bilateral positions. So we know what, let's say Germany holds all Dutch equities. And then there's foreign currency reserves. So those are the central bank holdings of foreign assets. For reasons of confidentiality, we don't have the bilateral data. And so we sort of have to aggregate them to one investor unit that manages the foreign currency reserve. And so that makes for 89 investors in total. Now what can those countries invest in? There's 36 issuer countries for which we have complete data on prices and macro fundamental factor. And so those are like the investable securities, if you wish. And for each of those countries, we're going to have three asset classes, short term bonds, long term bonds, and an equity. Of those 36 countries, there's going to be all 22 countries in the MSCI world and next. And then another 14 that are part of the MSCI emerging market. Now, one important aspect is if we're going to think about market clearing is how we define how we define supply. And so in the case of debt securities, both long term debt and short term debt, we're going to think of the total amount that's being held by foreigners. If you think about national accounting, then if the government issues debt and it's purchased by its own residents, then that's going to cancel out in terms of wealth. That's not true for equities. So for equity through what is held internally counts as wealth, but that's not true for debt. So total supply of debt is whatever is held externally. Equity is total market capitalization. So let me first give you a feeling for what the data looks like. So what you see over here are the top 10 investors by asset class. And so the first column is for short term debt, the middle column for long term debt, and the column to the right is for equity. And so there's three important observations about this table. First, you see that short term bond markets are smaller than long term bond markets and they are again smaller than the equity market. The second observation is that if you look at the largest investor in short and long term bond markets, then these are foreign currency reserves. So foreign currency reserves play a non-trivial role, and you'll see that they will come up routinely in the different analyses that we do. The third observation is that again in particular for short and long term debt markets, you see that financial centers are quite important. So you see Ireland, Luxembourg, and Cayman Islands as important to pass through and financial centers that play an important role in the global financial system. Now, in order to start connecting prices to quantities, I want to start emphasizing one idea that runs through our research, which is that financial markets tend to be quite inelastic. So what I mean by that is that relatively small shocks, relatively small shocks to let's say beliefs or flows or anything like that can have non-trivial impacts on prices. In a lot of the standard macrofinance models, demand is very elastic. So a lot of those shocks wouldn't matter. And so the way a lot of the standard macrofinance models work is that you have very volatile, let's say demand stocks or belief shocks, that are sort of like hit in fairly elastic market. In a lot of our work, we find that markets are in fact pretty inelastic. And so what it means is that suppose you have fiscal or monetary policy interventions that affect the supply of debt, then if the market is quite inelastic, then let's say that there's a lower supply of long term debt in the euro area as a result of QE relative to the US. Then what's going to happen is that you're going to push up prices and long-term yields are going to fall. Now the impact on exchange rate is going to depend on what happens to the quantity of short term debt. Similarly, if equity markets are inelastic, then if European firms issue more equity, then equity prices will fall for markets to clear. And the exchange rate may depreciate in that case as well. And so the more inelastic markets are, the more quantitatively important these effects are. What I'm going to show you in the next two slides is just some suggestive scatter plots that these effects are at work. So I'm going to show you scatter plots of changes in quantities, relative quantities, and changes in prices. And what you will see is that in all cases, there's suggestive evidence that demand curves are down and sloping. So what you see over here is the relationship between the debt quantity in a given region or country. So top left is the euro area, Japan, Switzerland, and the UK. And it's the debt quantity relative to the debt quantity in the US. And so the way to read this, for instance, if we take the euro area, then the numbers in the boxes, they correspond to years. So if we go to like 2015, 16, 17, then you see that the total amount of debt that's being held by foreigners is going down. That is consistent with the first graph that I showed you. Now, at the same time, you see that prices go up. The price of euro area bonds goes up relative to the price of US Treasury. And so that's phenomenal. And you see sort of show up in all of these figures. The relative change in quantities is associated with the change in prices. And that's sort of suggestive evidence of down and sloping demand curves or inelastic work. Similarly, in global equity markets. And so the horizontal axis here is the change in or the relative amount of book equities outstanding in a given country relative to the US. The vertical axis gives you the relative price in, let's say, the euro area relative to the US. And again, you see this sort of downward slope. So if European firms issue more equity relative to the US firms, see that the relative price of US equities falls relative to the price of the price of euro area equities falls to relative to the price of US. And so that's going to be an important feature of our work. And it's something that that's going to be pretty clear once you start looking at pricing quantities together and you try to estimate slopes of demand curves. A common feature is that demand appears to be inelastic, substantially more inelastic than what's implied by our models. And that's a really important message because if you're going to use pretty off the shelf macrofinance models to assess impact of quantity shifts in demand, you may easily get the wrong answer because you're using a demand curve that's just too elastic. And you may understate the effect as a result. Okay, so this is just suggestive evidence. So what we're going to do now is we're going to have a framework that allows us to formalize things a little bit. So there's a couple of equations I'm going to use just to describe sort of at a high level what we're doing. And sort of like keep in mind the two basic ingredients of the model are the market clearing equation, which is obviously like any model and then it's going to be a model and the model of demand is going to be sort of empirically tractable to get reasonable substitution patterns across countries and asset classes. So let me sort of like first define what we have over here. So the market clearing equation is going to hold for a given country and a given asset. So let's say this is for German equity. Then what we have on the left hand side is total supply. So it is the price per unit of the asset. So in this case for equities, it would be the market to book ratio. Or in the case of a bond, it would be the price per unit of phase value. So this one is unitless in terms of in terms of currency denomination. Then the quantity over here is in case of equities, the total data outstanding or the total phase value in case of sorry, the total book equity in case of equities and the total phase value in case of bonds denominated in local currency. We then multiply it by the exchange rate, which is the number of dollars you pay per unit of foreign currency. And so the left hand side here is the total supply denominated in dollars. Then what you have on the right hand side is total demand. And so it has two components. One is the assets of the different investors. So the subscript I here corresponds to an investor and then WITNL is the fraction that a given country, let's say the Netherlands, is going to invest in a given year into German equities. And so we then add this up across all the investors. So what you have on the right hand side is total demand. And so the way the model is going to work, if you want to think about experiments related to let's say QE or a change in ESG mandates or whatever sort of experiment you're interested in is essentially we're going to change the demand on the right hand side, or you may want to change the quantity of that outstanding in the case of QE and you're going to resolve for the system. And then if these parameters are stable, then we can use this sort of setup to forecast how prices would change if parts of the demand system would be modified. So that is sort of the market clearing equation. What we're then going to do is we're going to model the total demand. Now in terms of total sort of number of equations that we have, we're going to have three asset classes. So the short and dead, long term debt and equities. For short term debt we're going to assume that within the euro area there's one price and that there's no differences across countries. But in total gives us 26 countries plus the euro area for short term debt market. So those are the equations we need to clear there. Then we're going to have long term debt in 36 countries and equity in 36 countries. Now the assumption that we're going to make that's going to be important in interpreting some of the results from also from a policy perspective is that we're going to assume that the central bank is going to choose the short rate. So we're going to take that one as given. But if you're going to take the short rate as given, then you don't sort of naturally clear the market clearing equations anymore for short term debt. And so for short term debt markets to clear something else has to adjust. And what we're going to assume is that it's the exchange rate that is adjusting. So we're going to have three sets of market clearing equations and the endogenous prices that we sold for are exchange rates, long term yields and equities. What the model is going to do, it's going to match cross country portfolio holdings. We now want to have an easy to estimate model of demand and demand elasticities that allow for flexible substitution within and across assets. And so what the next slides will do is to give you a model for demand over here for this component. Okay, so our demand is going to have two components. One is an allocation across asset class. So an allocation across let's say equity markets and bond markets. And then the second part is within a given asset class, your allocation across countries, so between let's say the UK and Germany. We allow for this separate structure to give us more flexibility and to not assume that markets are perfectly integrated. If markets are perfectly integrated, it would be a special case and we would be able to estimate that. So how are we going to model the demand in a given asset class across countries? So the demand over here, let's say for the UK in equities, is going to depend on these deltas relative to capital D. Capital D is nothing else than one plus a sum of the deltas. Think of that as the relative attractiveness of a given asset class. Now, these deltas over here give you the demand that you want to have for a given country in that asset class. And it's going to depend on three components. One is expected returns. Beta L is going to control how sensitive you are to expected return. Then it's going to be other observable characteristics. So here you're going to have let's say inflation, GDP, GDP per capita, risk variables, ratings, things like that. Also trade relationships, other variables that you can observe that you think drive demand. And then there's going to be unobserved demand shocks. So those could be expectations about those macroverbals in the future that we don't observe as econometric. Okay, so that's the demand model within an asset class. Then across asset classes, we're going to have a model where you're going to have this capital D, which measures the relative attractiveness of a given asset class. Let's say short and bonds, long bonds, or equity. The key parameter to look for is this lambda over here. If lambda over here would be zero, what that means is that in my allocation across asset classes, I do not pay attention to the prices of let's say equities relative to bonds. So there will be a very extreme sort of like form of segmentation. If lambda over here is one, then you would have perfect substitution, similarly as the within asset class substitution. So what that would mean is that if lambda is one, then I consider the substitution between UK equities and German equities to be the same as between UK equities and German bonds. Now that also may be sort of too sort of strong of you. And so what we're going to find empirically is that the estimates of lambda are somewhere between 0.2 and 0.5. So markets are integrated and it's important to think of these markets jointly, but they're not perfectly integrated to the extent that stocks between two countries are equally close substitutes as equities in one country and bonds in another country. And so it's important to have this slightly more flexible structure to understand the global impact of dementia. Okay, so now bringing the model to the data. So what are the observed characteristics we're using? So we're going to have macro variables, GDP, GDP per capita, inflation, equity volatility, and sovereign debt rate. In thinking about these variables, there's a micro-founded model that we have in our earlier work where you want to choose those characteristics to capture measures of risk and expected return. And so these are sort of the natural variables that we thought one would include. Now there's also a large literature showing that import, export share, and distance matter for cross-country allocations. And so we account for that as well, as well as home buys. So on average firms hold way more of their own equity than equities in other countries. So it's important to account for that. There's going to be year fix effects. And then to capture the specialness of U.S. assets, we're going to have a U.S. fixed effect interacted with year. Now, in terms of estimating the model, one has to be careful because prices are endogenous too late in demand. If there's a lot of demand that's unobserved to us for a given country, it's going to drive up its price. And so demand shocks and prices will naturally be correlated. And so we develop an IV strategy, instrumental variable strategy, to estimate the demand elasticity. Okay, so let's look at the, at what demand looks like across these asset classes. And so the way to read this table is that the first line over here tells you the sensitivity to expected returns in three asset classes. First column, short-term debt, then long-term debt, and then equity. If you want to translate this to elasticity, then the demand elasticity for short-term debt is around 40. It's around four for long-term debt and around two for equity. All of those suggest, and in particular for long-term debt markets and equity, that demand is fairly inelastic. For long-term debt, the estimate of around four is quite consistent with the event study estimates that we have about the price impact that QA has had on government bonds. Then if you look at the, if you go down the different roads, then you see there's about unit elasticity with respect to GDP. So larger countries are going to allocate more capital to it. Inflation has a negative impact on demand across all asset classes, but particularly for short-term bond markets and long-term bond markets. The risk variables work in the direction that you would imagine. So higher risk is the lower allocation. So that's the standard risk return trade-off that is observable in these holdings. Import and export shares. So there's some notion of either familiarity or other forms of connections between countries that drive the drive demand, similarly for distance. So countries that are closer together, you see a larger allocation. Lastly, for equities, there's a strong home-buys effect. So on average, you allocate seven times more to your own country compared to other countries. So that sort of like gives you a flavor of like what estimated demand looks like. And what we're going to do now is to use the demand system to try to understand like fluctuations in prices and how important different types of variables are to explain exchange rates, long-term bond prices and equity prices. And so what we're going to do is we're going to take one year and go from one year to the next, and we're going to move the variables one step at a time. So let's say we first move the macro variables, including equity quantities from 2015 to 2016. Then we solve for all the new prices in equilibrium, and that's sort of step one. Then we think of like, think of conventional monetary policy. So we move short rates and short and debt quantities. Again, we solve for prices. Then we do monetary fiscal policy, we move long-term debt quantities, so for prices and so on and so forth. By the time we move all five of those variables, those groups of variables, we get to the next year's prices. And so then we do a variance decomposition, ask how important are these different variables in explaining exchange rates, long-term yields and equity prices. Okay, so if we summarize those that variance decomposition, then what you get is the following. First column is exchange rates, second column is long-term debt, third column is equities. So the first observation is that these three bars are reserves, debt quantities, and short rates. In all three asset classes, and in particular for long-term debt, policy variables are important, and so they have a large impact on fluctuations in financial markets. The macro variables explain 25% in exchange rates, and another 30% is explained by policy variables. The remainder that we cannot explain is coming from these unobserved demand shocks. Now what is interesting though is that we can decompose these unobserved demand shocks by country and by asset class, and I'm going to use some of that later on. For long-term debt, again, policy variables are important, and in particular debt quantities. So fiscal and monetary policy plays a particularly important role in this case. If you go to equities, macro variables are explaining 60% of the variation, which is to a large extent driven by the risk variables. Okay, so let me now zoom in on two particular questions that perhaps are particularly relevant here. One is understanding the yield spread between Germany and the US, which was very large before the COVID crisis. So US long-term yields were somewhere around 2%, and German yields were negative. And so the question is like, why do you get this large, large yield spread between the two sort of safe countries? A second sort of application of this is to look at what happened during the European sovereign debt crisis to the southern European countries like Greece, Portugal, and Italy, and Germany, and how do we understand the dynamics of the yield spreads during those episodes? So we're going to do exactly the same decomposition. So we're going to move one of these variables at a time, and we're going to ask what can explain these yield dynamics. So let's first look at the difference between German yields and US yields. And the thing that jumps out on you is that the policy variables are incredibly important. So 88% of the variation is driven by these policy variables. So 53% by short rates, 15% in terms of debt quantities. Now, given that it's sort of like so strong, you can actually see it in very simple scatter plots. So these are similar style plots that I showed you in the beginning, but now the horizontal axis is relative short rates in Germany and the US, and relative quantities in Germany versus the US. What you see on the vertical axis is the German yield minus the US yield. And you see this very strong relationship between changes in short rates and changes in long-term yields, changes in debt quantities, and changes in long-term yields. So as for instance over here at the bottom left, as that quantity outstanding held by foreign investors goes down, you see that the German yield falls a lot relative to the yield in the US. And that is sort of an important driver of the yield spread between the two countries. And so this is really identified and sort of like pretty salient in scatter plots because the times of monetary easing was quite different across the two geographies. Now, if we look at the yield spread and the dynamics of yields during the European sovereign debt crisis, like we think a really interesting picture emerges. So what you see over here, top left is Greece, then it's Italy, and then here you have Portugal. The solid line, that's the change in the yield spread. So the yield spread jumps up by something around 15% and then comes back down and then there's no further, not much of a change thereafter. Now, how does the model interpret this sort of change in the yield spread? In the model, we can explain this almost entirely by the dashed line, the smaller dashed line, which are macroverbals. And so to understand the spread between Greek yields and German yields, we don't need to rely on demand shocks, we can explain it with macrofundamentals. Interestingly, at the same time as we all know, like the yield in Italy and the yield in Portugal also jumped up and came back down at the same time as the Greek yield that came back down. Now, here the model can't explain it with macroverbals. And so what the model is doing is that it's attributing old variation in those yields to latent demand. And so there's sort of a spillover effect from what happens in Greece, where the macroverbals are shifting to the demand shocks for Italy and Portugal. But what it's sort of like we think is useful about the demand system is that you can take it one step further and you can now ask, well, whose demand shocks gave rise to the jump in Italian spreads and Portuguese spreads. And so if we go back to the table that I just showed you, here you see a decomposition of latent demand. And so the most important component of latent demand are in fact other European countries. And so the narrative that emerges from this analysis is that the spread between Greece and Germany is within the model well explained by just changes in observable characteristics. That's not the case for Italy and Portugal. So those are demand shocks. Think of that as sort of like contagion under the microscope. But then you can take it one level further and you can see whose demand shocks it are. And it's in fact other European countries who rebalance away from Italy and Portugal. And that's why their yields then spike up. And so that gives you a better understanding as to where the price dynamics comes from. Instead of just seeing all the yield spreads spike up and come down at the same time. So we can truly attribute sort of every variation in the yield or in equity prices to any given investor. Okay, so as a last application, what we do is we look at sort of the convenience yield on US assets. And so there's been a lot of discussion of the special status of the dollar as a reserve currency. And so the way we're capturing this in the demand system is as fixed effects for US issuances interacted with the year. So the convenience yield or the specialness of US assets or dollar assets can change over time. Now what is sort of different from what we do compared to some of the earlier literature is that we estimate this in all asset classes. So there could be special demand for US equities for reasons we can think about or long-term bonds or short-term. And so what you see over here is that there's very strong additional demand for US assets. And if you sort of like would take that out, there would be a very large effect on long-term yields in the US. And so this is a different approach than the typical approach which is using sort of like an arbitrage argument where two near perfect substitute assets trade at trade at different prices. So like the work of like Annette and Arvin has been sort of like seminal in this context. And what this is doing is essentially saying that well all of the US assets could be in special demand and how strong is that demand and what would be the price. So that's essentially what this calculation tells us. Okay, so what we're currently doing is to see whether the demand system is useful in real time to evaluate monetary policy. And so why do we think that this could be helpful beyond sort of like using estimates of event studies and extrapolating those. And we think there's two main reasons. One is that current fundamentals and current ownership looks quite different from let's say 2008-2009 where some of the other estimates are coming from. And secondly, sort of by the nature of an event study what you're doing is you're looking at sort of like one central bank's action at a time. But really what you're interested in at a somewhat lower frequency is the fact that the ECB undertook like several steps the same as true for the Fed, for the bank of Japan and so on. And so you really want to understand sort of like the role of the combined shock and the marginal impact of your own shock on that. And so the demand system potentially allows one to do that. And so what we showed in our earlier work is that so if you can forecast demand then you can forecast you can forecast right. And so the way sort of the setup would work is you would calibrate prices, holdings and fundamentals to the pre COVID pre sort of announcement values. You feed in the monetary policy shocks kind of all across the world and you compute counterfactual prices. The better predictions that you have for characteristics, let's say volatility or economic growth or asset quantities coming from fiscal policy all of those would be would be useful. Of course you'd be worried about like issues related to Lucas critique and what have you. But the whole goal here would be to say like what are the best estimates that we have to forecast the impact of purchase programs which would we think come from event studies. And to see like how far can we come with the demand system approach in predicting those effects and then compare out of sample which method works better and where the successes and failures are. So that's where we're going. So let me let me wrap up. So the main idea behind the demand system approach is to use prices and quantities portfolio holdings together. And we think it provides a new way to interpret sort of the dynamics of asset market. So I give you the example of the German US yield spread European sovereign debt crisis. Now one of the things that is quite salient in the data is that there's a solution across asset classes and across countries. And so what it means is that to understand these effects of let's say QE it is important to understand the impact on exchange rate long-term yields and equity prices jointly and to think about it in a global framework. Our estimates suggest that policy plays an important role for exchange rates and asset prices. And so what you see over here by asset class or by endogenous price how important different policies are short rates that quantity and reserves and she in all cases that it accounts for a non-trivial price variation. And so in ongoing work as I mentioned with sort of thinking about potentially ways in which this framework could be useful for real time real time policy analysis and hopefully that could be could be a new tool for for central thank you all for very very interesting paper. I have two questions. So we receive two questions. So let me read them one after the other one is from Wolfgang Lemke by the way it's a question I would have asked if it had not been asked already it's on negative interest rates and negative yields. So Wolfgang asks bond yields are negative in some countries some claim that portfolio rebalancing works differently under negative rates. Can your model explore that more generally can you check whether supply demand interacts differently with negative bond yields and maybe you answer that and then I'll come in again with another one. No I think it's a terrific question and in fact you can. So one thing that you can do is currently the coefficients are stable over time and do not depend on state variables. But what you could do is to say well maybe the level of interest rates matters for demand elasticity or for your attitude towards like risk or generally like some notion of like reaching for yield. And so the way to think about it is that if I go back to the model to make it concrete these coefficients over here the betas and gammas they may depend on the level of interest rates. So if you think that demand is more elastic when interest rates are negative or that investors are more willing to take risk if interest rates are negative then essentially what you can do is you can model these coefficients as a function of interest rates or allow for a non-linearity around zero and those coefficients would then change. And so what that would mean is that sort of substitution effects would change and the impact of QE would change if you operate in this negative interest rate environment. Similarly if there's like investors let's say insurance companies that or pension funds that have promises to guarantee a certain rate of return and they want to have higher yielding assets as a result you can build in similar effects as well. And so anything that depends on other variables you could in principle sort of incorporate it and test whether those effects are sufficiently strong. Thank you there is another question now just coming Elena Febrell asks are variable variations exogenous or endogenous in your model? Okay so it's a great question. So everything is in principle everything is endogenous if you think about sort of the bigger picture macro model. So the way I view the current estimates is really as a variance decomposition. So we're just sort of like we're decomposing demand and we're trying to understand which of the variables explain demand. Now where we want to go in terms of like the longer term like research program is to endogenize those characteristics as well. And so what you can think about is and we're trying to do some of that for the real-time policy analysis sort of like framework. What we're trying to do or what you would like to do is to endogenize the macro variables. So firms investment decisions and decisions and so on but do that in the presence of a realistic demand system. And so one way to think about sort of the framework that we have here is kind of an endowment economy. So taking the correct risks as given you could do that some prices. But then sort of the next step that you that you that you want to do is to go to a production economy and endogenize endogenize those as well. Now sort of like the macro models we currently have are not sort of like sufficiently sort of like advanced that we can deal with like like very high-dimensional I don't like 36 countries like we have and do dynamics. And so there's a trade-off here in terms of like what you can and cannot endogenize. But for now think of it as like a variance decomposition that you can run both in any model you're going to write down and we can compute it empirically. And empirically it's telling us sort of like gives us a narrative as to why and why markets move. You can use it for forecasting we showed that in our earlier work. So demand is sufficiently stable that you can use it for auto sample forecasting all if you can forecast demand you forecast prices. And so we're sort of like hoping that if demand is sufficiently stable or we can capture the key dimensions in which the demand shifts that once you use it for forecasting let's say QE or something like that it would still provide useful predictions for how prices and exchange rates would move. But that's really sort of like it's such a great question and ultimately we would like to endogenize characteristics. There is one last maybe question from Tillman Bletsinger. To what extent are asset prices in your model not explained by fundamental policy and demand factors? Is there scope for irrational price developments or dynamics? Yeah so okay that's a very good question so it's the model is it doesn't sort of take a stand on whether it's rational or not. Now what you can do is you can microphone the model using sort of like me let's say standards of like mean varying style preferences and have a rational model of like risk and expected return. Now where does irrationality come in? Is that suppose that there's a certain characteristic let's say inflation or or a country's rating that forecasts future future growth. I suppose that there's a certain relationship between that characteristic now and future growth. If investors have like way too high or too low price assign way too high or low weights to that particular characteristic it's going to look like I know like investors are like overreacting to certain pieces of information that's going to lead to sort of like prices are too high or too low and expected returns that are fluctuating over time. And so we know that we need some sort of notion of access volatility somewhere in the system and but to what extent that that's rational or irrational that's not something that we that we can that we can tell. So in the model like everywhere sort of like whenever you just use quantity data what you're effectively estimating is something like a risk adjusted assessment of that characteristic. And so what it means is that that if I really like a particular characteristic even though it doesn't forecast future future growth maybe the case that characteristic is particularly useful to assessing the risk according to that according to that investor. And so but it may also be the case that the investor simply is simply overreacting. And so it's not that we are ruling out that there's irrationality or that we're sort of or that we can easily we can easily test for it. The one thing that you can do and which we have done in other work is we can directly compare those coefficients to how those characteristics forecast future let's say earnings in the case of equities. And you can see which investors have very different beliefs from from what you would expect purely from that forecasting exercise. And so in that sense if you think if you want to take that as a measure of like irrationality then that would be like one way to use these estimates at least to go down that path. But in principle we can sort of like say that that the model is that the market is like rational or irrational. I think there's one aspect where the irrationality debate is like potentially like like as a starting point most important which is in all of our models in fact rational and behavioral models are like markets are very elastic. And I think that's a really important point to to appreciate if we want to think about sort of like like policy interventions. In all of our models sort of like like you have very volatile quantity shocks leaves and or preferences and very elastic markets. And what we're suggesting is markets are in fact inelastic. And now the question is like why are markets so inelastic. And there I think you very quickly get into much more behavioral arguments as to like why if equity prices move around like they fall let's say 25 percent in March and they bounce back as much as they did. Like why do investors not respond more more aggressively to those to those price movements to sort of make to make prices more stable. And so I think the key fact if you want to go down into like where the main challenge is perhaps for standard macrofinance models which has I think the closest connection to rational behavioral discussions. It is the observation that that demand estimates suggest demands inelastic. And so the question is like why is why is demand inelastic. And that's a very sort of like like big discrepancy between standard models. And I think most of the theories we have for that suggest that it's much more related to kind of irrationality than than than something.