 So, good morning, good afternoon, good evening, depending on where you are at this moment. Let me thank the ACV and in particular the organizing team for including our work in this Monetary Policy Conference. As Isabel mentioned, the topic of the paper of my presentation will be Monetary Policy with Opinionated Markets. And it's joint work without. But before getting into that paper, I'd like to describe very briefly our broad agenda. And it's an agenda that we like to describe as a recent macro, or recent macro policy. And the basic idea is very simple. In macroeconomics, we typically, actually in any economy, there is a productive capacity that productive capacity can produce certain amount of goods. That's what we call the supply of goods, a potential supply. And then most macro models and certainly a lot of macroeconomic policy is about an absorption problem, is how to find the right demand for that amount of supply. And now a productive capacity also produces risks, which is embedded in the assets in the economy. And so there is also supply of risk in the economy. And in that sense, it's a second absorption problem, which is to find the right demand for all the risk produced by the productive capacity. So macro is mostly about the top row. Finance, especially asset pricing, is mostly about the bottom row. But it turns out that these boxes are obviously connected. And the linkage between these rows is asset prices. Very broadly understood, asset stock markets, bond prices, the spreads, house prices, and so on. And now I think this distinction is very important for central banks in particular, because most of the objectives of certain banks are in terms defined in terms of the upper row. But it turns out that the place where they operate is really the bottom row. And so this linkage is very important for central bank policy in general. Now, once you start thinking about macro in terms of this bottom row, you have to think about things that are important for financial markets. And one of the key things that is important for financial markets is beliefs. A lot of speculation, trading, and so on is a result of beliefs, difference in beliefs, and so on. A huge role. And so with this perspective, those issues of beliefs and things that are specific, in principle specific to financial markets become issues that are important for macroeconomic policy as well. So in previous papers, what we have done is we have looked at belief heterogeneity within the private sector and have looked at what are the implications for that, for example, for macro-prudential policy, for prudential monetary policy, for large-scale asset purchases, and things of that kind. Now, in the paper that I'm going to present today, though, we don't look at differences of beliefs within the private sector, but a difference of beliefs between the private sector, which we want to call the market, and the central bank. And apologies for calling the central bank the Fed. Maybe I should have called it the ACB for this conference. But as we will see later on, I'm going to be talking about policy mistakes all the time. It may be better that I talk about the Fed. So one very clear source of disagreement is in the forecast of future interest rates. So what you have in this picture here is in the thin line is the federal funds rate, the path of the actual federal funds rate. And what you see in the thicker color lines are forwarders and dots. So the projections by the central banks are summarized by the average dot. So this is right after the FOMC meetings where the dots are released. You can also look at the forward curve and compare these two curves. And you can see that there are very clear differences and at times they are very similar, but at times there are very big differences. Now, you can adjust these pictures in many ways. You can add a reduced premium that actually compresses on average the difference, but it's very small relative to the size of the part that you see there. So there are a lot of dots. I mean, there's a lot of issues of what dots really represent, but you can look at the interest rates implicit in the green book, for example, compared with blue chips, and you see sort of similar big differences. I mean, you can see it also beyond the US and most central banks that we have access to data that do publish this forecast. You do see difference between the corresponding market curve and the forecast. So there is a literature in macro that thinks about information problems between the central bank and the private sector, and it's mostly about asymmetric information and the presumption there is typically that well, the Fed knows more about, obviously, its actions, but it also knows more about the economy. So it's a perspective in which the market is whether it's passive waiting for this great wisdom to come down to them from the central banks. But first of all, that cannot explain the picture that I just described, because those are disagreements just after the FOMC made its announcement. So the great truth has been revealed already to the market, and you still see these big differences. But second and more importantly, perhaps, is that I had a midlife crisis and I spent a couple of years in hedge funds outside of academia and I came back to academia precisely when this literature was developed in macro and it did not sort of match very well with the views I saw traders express. In fact, traders are very opinionated people. They are certainly observing very closely what the Fed and central banks are doing around the world, but mostly to confirm whether the banks have the right view or not in their perspective, the right view. A concrete example beyond my personal experiences December 2007, there was a hawkish interest cut by the Fed that led to asset price declines and so on. And you can see in the 100% of the article of the reactions of the market to what the Fed actions as expressed in the World Street Journalist here's a quote, from talking to clients and traders there is in their view no question the Fed has fallen behind the curve. That doesn't sound like it's receiving the great wisdom. They say, look, they're not getting it. Said David Greenlow, Economist at Morgan Stanley, there's a growing sense that the Fed doesn't get it. Okay? And not saying the market is right or wrong, but it's clear that it's not about having received information from the Fed it's about not agreeing So what do we do in this paper? We essentially it's a theory paper. We provide a model of a situation in which the Fed and the markets disagree. So we call this that's the reason we call it an opinionated paper. The paper is opinionated itself, but the markets are opinionated in our model and so is the Fed by the way. So we develop a model of opinionated markets and opinionated Fed. So the key features of this model is that first the Fed and the market are going to disagree about something. They can disagree about many things but the particular thing we would look at is this agreement about future aggregate the market. The second feature the model will have is that they both learn from the data. Okay? Now the players are going to agree to disagree and they know what is a disagreement so they know the beliefs of the player and they also know that each agent will learn as data comes along. So what are the main findings and the ones I'm going to explain mostly in this presentation. The first is that this environment provides a very natural explanation for these agreements about interest rate that I showed you before, the figure. And the second that perhaps more important for this conference is that these agreements matter for optimal monetary policy. Okay? For optimal monetary policy. Certainly it matters for the impact of monetary policy but it also matters for the design of monetary policy. Now the paper has several extensions and I doubt that I will get the time to discuss them in a certain and not in detail but let me tell you what these extensions are. The first one in the basic model prices are going to be completely sticky. But then we're going to add an Eukensian Phillips Curve and the main results of that section is that, yeah, you get more or less the same as the main conclusions survive that environment. But the most interesting aspect is you want to connect for example with Clarida Galli and Gertler, the classic paper on the science or art or science of monetary policy is that now you can think of this agreement as endogenous cost push shocks. Okay? Remember cost push shocks is what in that environment breaks the divine conscience. Well, having these agreements produces something very similar to that in a very formal sense. The second extension is, well, what if we bring into this frame also information as images of the kind that sort of have been developing the macro literature and the main results there is that, well, first the main results of our paper survive but more interesting than that now there's a second dimension of disagreement because the Fed may not know whether the market is willing to agree that that's the signal, the private signal is informative or not. And that can lead to sort of the perception of monetary shocks or information. It may vary depending on the particular market that the Fed faces and that in itself brings reluctance to act from the point of view of the Fed because it doesn't know whether the market will react positively or not to the information is about to be revealed. And the last extension is about heterogeneous data sensitivity. So the Fed and the markets need not be equally data dependent. They're both going to learn from data, but they need not be equally data dependent. Some of the market or the Fed may learn faster than the other. And the interesting implication of that extension is that now every single macro-economic shock has implicitly need a monetary policy shock. So there's a big literature that is intangible looking at the impact of monetary shocks that typically isolates high frequency events around FOMC announcements. Well, once you have this heterogeneous data sensitivity, then it turns out that any macro shock comes with an implicit or the market can focus at that moment that the Fed will react in certain way and the market may not agree with that certain way it expects the market to react. So every single macro shock becomes a compounded macro shock with a monetary policy shock. So that's what the paper does. So let me essentially describe the paper twice. Once, in words and diagrams, and then the second time, it's also going to be in words and diagrams, it's going to be a couple of equations more. But I'm going to sound repetitive, it's deliberate. So let me first tell you what the setup is and what are the main results and what features of the setup give this main result. So the first thing is we're going to have aggregate demand shocks. That's what markets and the Fed are going to disagree about. Now what is an aggregate demand shock for us is something that moves current expenditure given potential out. That's the definition of an aggregate demand shock. And there's many different sources for aggregate demand shock. In fact, the aggregate demand shock that we're going to model, the specific aggregate demand shock is going to be the most aggregate supplied looking aggregate demand model. You can imagine because it's going to be future productivity shocks. So today we're going to learn about future productivity. Well, that will have an effect on today's expenditure. And that's usually going to be an aggregate demand shock for today and it's an aggregate supply shock for the future. We're going to look at the current episode. So in the current period, we're going to have an aggregate demand shock. The Fed is going to have to take actions that set the interest rate, give speeches, whatever before it knows the current aggregate demand shock. So it's going to have to make a monetary policy decision. Now the Fed is going to set the interest rate targeting a zero output gap. Now it's a zero output gap under the Fed's beliefs. That's an important distinction now. Now the Fed has beliefs, that's a superscript F, that's what it denotes. And it's going to try to set an interest rate that gives on average, on average across all disaggregated demand shocks a zero output gap. Now after the Fed has set the interest rate for this period and the aggregate demand shock takes place the market sets the output gap. It's a equilibrium. It knows the interest rate and it knows what the aggregate demand shocks. So it determines equilibrium out. Now if the Fed doesn't think that the Fed has the right beliefs that this F is not the right belief, then this equilibrium output here will depend on what the market perceives to be a Fed mistake. So let me explain that and that will take us to the first result and perhaps the most important result for a central bank of this paper. So here is the period I just described, the current period. Remember what I said the Fed will target, will set an interest rate to try to set an average output under its beliefs equal to zero output gap equal to zero. Now the market is going to set output here but when it sets output it not only cares about the current aggregate demand shock, it not only cares about the current interest rate but it also cares about what it expects monetary policy to be in the future. Okay. See in particular suppose that the market believes that the Fed is being too hawkish. That is things of the future is a lot of market things. Then, well that of course is going to affect the current interest rate and that's going to affect the actual output gap but it would also affect the perception that the market has about future output gaps. It understands that the Fed will set the interest rate in the future in order to set an average output gap equal to zero under the Fed's beliefs which the market perceives to be a hawkish belief. So that means that will depress current output. It will depress current output for any given interest rate because now the market expects the future interest rate to be too high for what the market expects to be the actual economic environment, the actual level of aggregate demand. But the Fed understands that the market will believe that the Fed will make a mistake. So when the Fed sets the interest rate here for this period, it also has to internalize that the market will perceive a future mistake from the point of view of the Fed. So the future perception of mistakes by the market of the Fed believes also affect the current interest rate the interest rate that the Fed sets today. So and that's the main result for monetary policy because it says the Fed will have to partially accommodate the market and will have to do so to mitigate the impact that the perceived mistakes by the market, the perceived mistakes of the Fed by the market have on aggregate demand. Now very naturally if this believes are very entrenched and therefore the disagreements are very entrenched and they're likely to affect the future for a long time then the Fed needs to accommodate even more the market. In fact we have an extreme result in the paper in which if the two sides are completely stubborn and they're never willing to learn then the Fed should follow the market and ignore its own beliefs we're not going to look at that extreme in the paper so there's someone in between but you get the effect at least that the more entrenched these beliefs are, the more the Fed needs to accommodate the market. So that's going to be our first main result. The second main result is explaining figure one how can you have, even after the Fed has revealed all its wisdom how can you have different curves, future different forecasts about future interest rates. And that's when the learning block plays a very important role. So let me explain. So this is, remember this is the current period, that's what I just explained in the previous slide and we agreed in you the audience and me the presenter we agreed that the Fed will set an interest rate, take it into account its own beliefs at day one at the first period and also the market's belief. In particular I said, well the market the Fed will set the interest rate trying to set the average output gap to zero in these periods according to some belief but in order to do that successfully it has to take into account and accommodate its interest rate policy to the market's beliefs. Okay, okay. So there's no disagreement today about what the interest rate is today. The market the Fed will set an interest rate the market cannot disagree about the Fed the interest rate that was set by the market there's no disagreement about today's interest rate, it is what it is but there is disagreement about what the future interest rate will be and that's what I show you in the first figure and how does that happen? Well think what happens at day one at day one the Fed says, okay I know that the market has distorted beliefs I think the market is really dovish doesn't understand the market demand is it doesn't understand the market demand will be better on average than what they expect I cannot do much today about that I have to accommodate a lot but I know that in between this decision and the next decision there will be an aggregate demand shock and I am the Fed I think I'm right, I believe in my beliefs so I think this aggregate demand shock on average is not going to be a surprise to me in terms of realization but it's going to be a positive surprise for the market okay and the market is going to be surprised how good this aggregate demand shock will be and because of that I expect the market to update its beliefs so I expect for the next period so when I have to say I'm the Fed I have to set the interest rate in the next period I expect to have the same beliefs that are more or less the same beliefs I have today but I expect the market to have more optimistic beliefs than it has today because it's going to be surprised by a positive aggregate demand shock and therefore since I'm going to be dealing with a market that is more optimistic than the market I'm dealing with today I expect tomorrow to be able to set a higher interest rate one that is closer to the beliefs I have and that's the reason the top curve is up where it's sloping I have to accommodate a lot today I expect these guys to be positively surprised between today and tomorrow and therefore tomorrow I expect to be able to set a higher interest rate what about the market well the market also thinks the market is right I cannot disagree with the Fed today the interest rate is whatever it is but I know it's going to be an aggregate demand shock here I know the Fed is going to realize that it was way too optimistic when it was setting this interest rate on average I think they're going to get a negative surprise on aggregate demand so I expect to encounter in the next period a Fed that has an F2 lower sorry, than F1 a Fed that is less hawkish than I'm facing today so as a market I expect the interest rate to go down, why is that? again because I expect the Fed to learn that the war is a little worse than the Fed thinks at day one and so that's exactly what is playing so disagreement plus learning if there's no learning there's no way of there's nothing you can do it, we disagree completely we're going to convert to some interest rate but we're not going to disagree about the future either because there's no learning along the way it is the learning aspect that allows us to have this difference between the dot curve, the forward curve or the green spam book forecast and the blue chip forecast and so on so that's what the core of the paper is about now let me go over the paper again trying to tell you a little bit more about those results and a little bit more about the extensions extensions but before doing that the small section, this again is a theory paper but it's a small empirical section moderating our basic ingredients and I'm not going to present that but I'm going to show you one picture that captures what is in that section we there isn't a lot of data on disagreements between the Fed and the market but there's a lot more data about disagreements between different financial institutions big financial institutions there's blue chips data there's a much longer data set so we use this blue chips data to essentially demonstrate two points which are important for our model the first one is that interest rate forecast correlates with aggregate demand perceptions so if we want financial institutions that forecast a higher interest rate we'll also be forecasting higher aggregate demand so we're going to measure as inflation and the second feature we want is that these forecasts are confident in disagreements so even after you include all common information and so on they still disagree and not only they still disagree they continue to disagree over time okay so they're persistent disagreements and those two features you can capture in this picture here what you have is on the top figure you have the federal funds rate so the forecast of the federal funds rate works ahead for different financial institutions the green one is the consensus the blue one is Goldman and the red one is Bear Stearn and you can clearly see that before the global financial crisis Bear Stearns had a higher focus on interest rate and in the lower diamond you see the focus they have on inflation and you can see that Bear Stearns was far more optimistic than Goldman about future aggregate demand and as a result of that they did have a higher focus for interest rate now we all know the reason this line ends here is that clearly Goldman was a lot closer to reality than Bear Stearns but there are consequences of these big disagreements that's what you see here but you also see the second point which is that these disagreements are fairly persistent you can see sort of long periods where you see gaps in both focus of interest rate and disagreements about aggregate demand and then again in the paper there are some progressions and so on that prove this more formally with all sort of individual effects time effects and stuff like that so let me again get into the model and again you're not going to be able to fully understand the model because I'm going to skip almost the model but I want to give you a couple of equations so a few diagrams I'll show you later on make a little more sense the first slide is just to tell you that the basic macro model has nothing new so it's an official new Keynesian model with aggregate demand shocks so standard preferences more ballistic competition in the basic model we're going to assume fully sticky prices and all the firms have exactly the same prices there's no use in static shocks here all the firms have the same productivity AT the aggregate demand shock as I told you before it's going to be a more supply looking aggregate demand shock at any time T there's going to be a level of aggregate productivity AT but we're going to also learn about productivity in the next period so GT is going to be the aggregate demand shock we're going to call it the aggregate demand shock it's really the productivity growth shock but it cannot affect potential output today so we're going to call it the aggregate demand shock so you combine these and you get a pretty standard you log linearized standard new Keynesian model in the version of the paper that you may have seen we don't have linearization and everything is a little bit complicated there's risk premium floating around and so on in the version I'm presenting here and the one we're going to post next we may have just posted yesterday we log linearized so it's much more standard macro stuff in which the current output gap is a decreasing function of the interest rate set by the Fed it's an increasing function of the realization of the aggregate demand shock and it's an increasing function of the expectation of the market about future aggregate demand and in the previous version of the paper here you have a surprises stuff like that there is a one to one relationship between future aggregate demand and a surprises in this paper so that's the standard IS curve and again in which now I need to highlight this M here because it's the market's belief that matters for the actual output gap now monetary policy without commitment is going to be essentially the Fed trying to set this output gap equal to zero under its own beliefs so F okay so F and M will be different and so this interest so where do we see the Fed's beliefs here well in setting this interest when the Fed is going to the tool will have to set this interest at IT so it expects this the expectation of this to be equal to zero okay so what are the main equations we get out of this frame so let me remind you what I just showed you the yes is this so what is the equilibrium interest rate that is the interest rate set by the Fed okay but after it considers all the beliefs of the markets and so on it's own belief remember what it's trying to do is taking the expectation of this expression of the yes under its own beliefs and is setting it equal to zero so from that you solve for the interest rate set this equal to zero that gives you the interest rate then you have to put an expectation here and the Fed's belief and that gives you the interest rate so the equilibrium interest rate the interest rate set by the Fed is obviously going to be an increasing function of the Fed's belief about the aggregate demand shop for this period if the Fed believes the demand shop will be very high it's a very optimistic belief then you're going to set a higher interest rate naturally but and the term that comes from the beliefs of the markets is the second term well the Fed is also going to set a higher interest rate if it expects the market to have a very optimistic belief okay so if the Fed expects the market to expect an output gap given the interest rate policy of the Fed then the Fed is going to have to increase the interest rate to accommodate that conversely if the Fed expects the market to be more pessimistic then it's going to have to lower the interest rate to accommodate the pessimism that the market has okay so that's the optimal policy under the Fed's belief so the Fed is not betraying its belief the Fed is optimizing the Fed is trying to handle its beliefs but it turns out in order to do so it has to deal with the beliefs of the market and that's what we capture in this term here now replace this interest rate up here and you get the equilibrium output gap so the equilibrium output gap is what is a result of a surprise according to the Fed belief so if our demand turns out to be higher than what the Fed expected then the output gap will be positive and this will also be a function of the surprise for the Fed on the degree of optimism of the market so the Fed has an expectation about the degree of optimism or pessimism of the market but it turns out that the market may end up being more optimistic or more pessimistic than the Fed expected and that's also going to affect that really demand okay now in what I'm going to say today I'm not going to talk really very much about this term this is one of the extensions we're going to be mostly in this environment here so but let me move on I have I think six minutes more more or less that or seven minutes more so let me give you the last ingredient and then just pictures from here so the last ingredient is well where does the beliefs come from and what are they about so this is the way we model it so the growth rate and therefore the aggregate demand shocks is going to be is going to be equal to some parameter G plus an unknown component and plus noise so in every period there's going to be shocks IIT shocks and so on the disagreements and the beliefs are about this unknown component how much of the level of aggregate demand we're seeing is permanent or semi-permanent versus how much is noise that's what the market and the Fed are going to disagree about so they're going to have different beliefs different priors and then different posteriors that are going to start to convert over time but different priors about this permanent component of aggregate demand and so this prior again the Fed on the market will have different that J is the Fed on the market and there's also a certain amount of confidence C will capture the amount of confidence that each of these players have on their own beliefs if the players are very I'm not going to look at the heterogeneous and for most of the time so assuming that they have the same confidence if the players are very confident then the the priors are going to account therefore the difference are going to account for a very long time because they're not going to learn a lot of data if they're not very confident about their priors then they're going to learn fairly quickly and therefore the disagreements are also going to convert fairly quickly let me skip a few things so news are going to be here expectations about aggregate demand so this picture is important and then I'm going to get back to the results I already explained but using a different data so suppose that we start Fed that is more optimistic than the market so this is the expected aggregate demand by the Fed for this period and this is for the market so the Fed is more optimistic so what this figure shows is well what does the Fed expect to expect in the future about aggregate demand well the Fed expects to expect the same about aggregate demand in the future because the Fed thinks it has the right beliefs so today's expectation by the Fed of its own future expectations is a flat line, it expects to expect the same what about the market well the market expects to expect exactly the same aggregate demand in the future ok so the expectation for its own expectation of the market is also flat but the expectation of the market for the Fed is downward sloping because it expects the Fed to learn that the conditions are worse in the space over time so the expectations of the market for the Fed is downward sloping conversely the expectation of the Fed for the market expectations is upward sloping because it expects the market to figure out over time as it learns that it got the expectations wrong here. They had their own beliefs. So it expects the market to come to the Fed's beliefs. So here is disagreement. So imagine a situation where let me look at the left diagram here. So what I'm showing here is what happens when there is a shock to beliefs. So suppose that both the market and the Fed have these levels of belief. Let me give you first a benchmark. Suppose that both become more optimistic. And now both believes that the aggregate demand conditions is better, so that this permanent component of aggregate demand is better. Then what will happen is that the interest rate, the doctor and the Fed and the fore-workers are going to coincide at a much higher level. Both are going to go up. Suppose instead that all that happens is that the Fed becomes more optimistic. So suddenly the Fed sees the future better than the market sees it. Well, then what happens is, well, the Fed, we want to raise interest rates because it expects our aggregate amount of prices to be positive in the future. But it knows it cannot raise interest rate too much because if it does so, that's going to depress a lot the market. Because the market hasn't updated its belief. It does still remain pessimistic. So that will lead to a big crash in asset markets, collapse in aggregate demand, and so on. So the Fed cannot afford really to increase interest rate a lot, is in this sense that the Fed needs to accommodate the market's beliefs. The Fed became optimistic. It believes that we're on a full road to recovery. But it cannot fully increase interest rate because the market is still stuck there. And the Fed wants to prevent the effect of the market's perception of the Fed's mistakes on aggregate demand. Now, why is though the curve upward sloping and this one downward sloping? Well, because of what it just explained, the Fed says, OK, I cannot increase the interest rate a lot today because the market is very pessimistic. But I expect the market to become increasingly optimistic over time because they're going to learn from the depreciation of aggregate demand that the aggregate demand is better than what they expect. So that's the reason the Fed cannot have a upward sloping thought curve here. The market thinks the opposite. It says, no, no, no, this guy's made a mistake. They're going to realize after they see recessions and recessions that they made a mistake, they're going to have to retrace their steps. And therefore, we expect a lower interest rate. Now, the diagram on the right is essentially the same as the diagram on the left. The only big difference is that here the players have not very confidence on their beliefs. So they weigh the data a lot. Well, here they're very confident. So if you see the main difference, what I want to highlight of this picture is the main difference. The main difference is that here when the players are very confident, the Fed has to accommodate the markets a lot more than here. And why is that? It's because the Fed thinks, OK, I believe that the conditions are great, but I believe and I believe that the data will prove to be right. But the market will be very slow in learning. Worse than that, the market will think that I'm going to be very slow in learning. So the market expects me to make lots of mistakes in the future. And so it's going to be very depressed by an increasing interest rate, OK? Because, again, my problem as a Fed is that the market is going to be very stubborn. So it's going to continue to believe despite the data proving me right, it's going to continue to believe that I'm going to continue to make mistakes. And since the market believes I'm going to make mistakes for a long time, then that's going to depress us as prices a lot. It's going to depress our rate of demand a lot. And therefore, I cannot increase interest rate a lot. What happens here is the opposite. What happens here is, OK, I raise the interest rate. And I'm going to raise it more than I would have done here. Why is that? It's because I know that the market thinks I'm a fool, that I'm raising interest rate before I should have done that. But I know that I expect the data on average to come my way. Therefore, the market is going to learn very quickly that it's making a mistake. The market thinks the opposite. And that's the most important result for this. The market says, OK, the Fed made a mistake. The market raises interest rate. But I know these guys are not a great data dependent. They're going to get very unpleasant surprises in the next period. And therefore, they're going to retrace their steps very quickly. So you see, the forward curve here is very downward sloping, expecting a bigger version by the market. So there, again, that's really the summary of the core of the paper. And I think I'm beyond my time. And let me just tell you again what we do in the next part. The first station is to introduce a New York Ainsley and Phillips curve. And I think the most interesting result you get here, you get more or less the same result. But the most interesting result is that you can, this is like introducing in the basic benchmark model in the Claria Galli-Gertlum model, cost push shocks. And believe this agreement, act exactly as cost push shocks. And so that's interesting because it breaks the, then it introduce a trade-off between stabilization of inflation and output. The second extension, as I said before, is introduce signal. Suppose the Fed also gets applied a signal. Suppose first of the market agrees that the Fed has some private signal in addition to this agreement. And then when you get a weighted average of the result that you have in the standard signal in literature and our results, the more interesting result is that if the Fed doesn't know whether the market agrees or not on whether the Fed has a more informed signal, then it will tend to underweights its own signal because it's very scared of another reaction by the market to the perception to what the market will perceive as a mistake from the point of view of the Fed of assuming that it had better information than the market. And the last extension is assuming is what happens if you have different degrees of data accumulation, if what happens, for example, if the data is more responsive to data than the Fed, then the most interesting insight from that section is really that every single macro shocks, as I said before, has an optimism or pessimism in shock. If the Fed in particular is more data dependent than the market, then every time the market sees a positive shock in aggregate demands is, oh, well, the Fed is gonna get away with this and gonna hike interest rate faster than it should. And so you start getting sort of high volatility in interest rate as a result. Now that may be good or bad, that's a definition. Okay, good. So let me stop here. I just want to leave you with what we do in the paper. Sorry, I've rushed a few things, but there's an optimal amount of rush so you get to read the paper. Thank you very much, Ricardo, for this very clear presentation. We started already getting some questions on the paper and I'm encouraging the people in the session who are listening to, of course, submit more questions. The first question I have is from Anton Nakov and he's asking, why doesn't the Fed update its own beliefs eventually, rather than only updating its beliefs about the market's view? He's questioning if this learning only about other agents' learning is rational. No, no, that's not, sorry, I misspoke then. No, the Fed learns about updates. Both agents update their beliefs and they both converge to the truth eventually, okay? What I was showing there was not the update of beliefs. I mean, they're both patient, so they do standard patient updating. So they're both rational given the priors, okay? They disagree on priors, but they're both rational. The figure I show you there, and I was a little rushed, is what the Fed expects today about its expectations or beliefs being in the future. So it's purely rational not to expect to update your beliefs in any way. You expect to believe the same. You understand that you're not gonna believe the same because you're gonna get data along the way, but you should expect to be unbiased with respect to your beliefs. And so in that sense, it's rational condition on the prior. Thanks for the clarification. Second question that we came in is one titled More to Concrete Policy. What are really the policy implications from your paper? This is a question by Diego Rodriguez Palenzuela. He's asking, should we expect more transparency from the Fed or should the Fed be using the belief asymmetry? What is your view there? Well, this is not a communications paper, and it's a very interesting paper one could write about communication. But you already have a policy conclusion in the paper, which is look, the Fed needs to accumulate the beliefs of the market. And it needs to accommodate the beliefs of the market. Of course, it may try to influence the beliefs as well. And that's what the information part has. You may try to influence the beliefs and you can give speeches and so on to try to influence the beliefs. But at any point in time, you are gonna have some disagreements in belief. And this paper tells you you should give weight to those beliefs. And especially if you think that those are very entrenched beliefs. So that's what the paper tells you. And especially if you think that the market thinks that your beliefs are very entrenched. And so in that sense, for example, sometimes saying, look, I'm gonna be very data dependent. It's a way of communicating to the market. Look, my beliefs are not that entrenched. I'm gonna be very flexible. Well, that will help you here in the sense it will give you more space to move interest rate because you're saying, look, I'm gonna react to data very quickly. So don't be afraid that I may be making a mistake, but I'm not gonna make mistakes for a very long period of time. That's so this has obviously lots of implications for communication. This paper in particular is not about communication, but it has. And then in the final section, which I was in one of the sections, extension section, a point I made, obviously way to rush is one about what happens when you don't know how disagreeable the market is. So if you don't know, if you have a view on the market, but you don't have a very clear sense on whether the market is likely to believe your view or not, then that would naturally lead to underweighting your beliefs, for example. That's one conclusion. Now, the other conclusions that are not in this part of the paper, that you can begin to see, especially when I add sort of the Phillips curve there, is that you start getting some certain role for commitments and so on. Part of it is for the same reasons as you get it in Claria at all, because now you have a certain, it's a sort of cost push. And so you may want to, having believed this agreement is like introducing a cost, it's an endogenous cost push. And you may want to alter the variance of that endogenous cost push. And so that's another policy implication. We don't develop that in this paper, but you could imagine that. So I think it's just lots of policy implications and I'm sure that you're gonna get even more implications than I do. A lot of thought for follow-up work. Another question that we have received is from Carlo Altavilla, where he's asking, is there in your model a risk that the central bank ends up accommodating, let's say, market beliefs? And do you see that risk in actual policymaking? No, well, one of the main messages was that the Fed should accommodate the market's beliefs. And the question, something that the paper does, it tells you where you should accommodate more or less. And that's a bit what I was saying in the previous answer, which is look, if the market thinks that you're very stable and the market is in itself very stable, then you better accommodate a lot otherwise you're gonna leave a big mess. Now, there's this extra layer, which is the communication part. And remember, it's a weighted average. So if the market, for example, if the, I have two terms, I have a term that says, look, at the end of the day, the Fed or the ECB has to accommodate, it's used to interest rate together, zero would grab on average under its own beliefs. So it's not that it's giving up its beliefs, it's taking, but as parts of its beliefs, is it the beliefs about, it has about the beliefs of the market and about the stubbornness of the market with respect to those beliefs and about the beliefs of the markets, about the stubbornness of the Fed, about its own beliefs. But it's not that the Fed is giving up its beliefs, it's optimizing under its own beliefs, but it's acknowledging that there's a disagreement of beliefs. So it's not giving up beliefs. If the Fed gave up on its beliefs, then essentially what would happen is that it would set exactly what the market wants. And there is a particular case where that happens, which is if the two agents are infinitely stable, then the Fed accumulates the market, sets the interest rate with the market. Why is that? Because by doing so, it still hits the output gap at once on average. Why is that? Because what happens in that case is the following, is the market is very pessimistic. It gets surprised by a positive aggregate in the mind shot, but it's upset because the market said, oh, the Fed is gonna raise interest rate again tomorrow. This was an accident. Tomorrow is gonna be terrible and the Fed is gonna give us, we give this very high interest rate. And so, I'm gonna have a recession and that term completely overwhelms the other term. So the Fed does the right thing by setting the interest rate the market has, but it does the right thing under its own beliefs. And so that's the nice thing. It doesn't give up its beliefs, but it never know its things under its own beliefs. The question is, what does it have to do in order to get the right result under its own beliefs? I wanna stop here because I don't want to crowd out Giovanni, I think. Well, I won't find a question. You just saw that, but I can see Giovanni in the background, so it's a, I think about it. We have one final question also from Anton Nacov. If you have a question that you went, it's a super interesting discussion. I had one follow-up question, Anton, because it goes a bit in the other direction now. Could the Fed actually be trying to influence the market beliefs? So one question was, of course, to what extent the market should influence the Fed. The other question is whether the Fed should be influencing the market beliefs? For sure. As I said, this is not, well, both things are true, by the way. Again, this is not a communications paper, although it has some information in symmetry section at the end in which the Fed, in which everyone knows that the Fed knows a little bit more. So when the Fed starts something, it does affect the market's beliefs, okay? So we do have that. That's one in which, but it's obvious that it's an enormous play for communication here. And how do we inform beliefs? The novelty of the paper is the disagreement component. But obviously there is value in having converges in beliefs. And if there are other tools to do so, then of course you should use them. And in practice, they do use them. I mean, that's the reason Fed members give speeches and so on. And it's also, there is a two-way communication. There is no doubt that the market's also telling things to the Fed.