 Okay, good morning. I warmly welcome all of you to this year's annual research conference, which is the ECB's flagship research event. The conference offers a wonderful opportunity for our researchers to get insights into the latest trends and research and learn from leading economists in the room and also expand our network in the breaks. In addition, research discussed at this event can improve our policymaking by offering new ideas, by providing new evidence, and by shaping the framing of our policy problems. At the ECB, we believe that good research is a basis for sound policymaking. Now before I kick off the program, I would like to grab the opportunity to advertise some of our ongoing research here. We've done a lot of research on incorporating financial frictions and macro models, and these models are currently being used to inform the ECB's governing council's decisions on a regular basis related to financial considerations for monetary policy. Now, should you have any questions about this line of research, please ask my colleague Marie Orova, who is in the room. Another line of research has been measuring inflation and price stickiness. This work was facilitated by a large-scale effort to collect micro-prices in the euro area, our contact persons for this work, Aluka, Dedala, and Chiara Ospat. Another highlight has been the development of the ECB's consumer expectation survey. This survey of many households in the euro area has been exploited using randomized control methods to study a wide range of consumer behaviors such as those related to inflation expectations. You can reach out to Jeff Kenney or Demetrius Georgarakis during the break for details. We've also invested heavily in research on heterogeneity, the very fashionable topic in macro these days, ranging from developing new macroeconomic theories with heterogeneous agents to exploiting large data sets to identify which factors are operating at the micro level and may have aggregate implications. This work has been led by Orestes Tristani, here in the middle, and Michele Lenza. Our research has also responded to the growing climate crisis out there, with research on implications of climate change for financial stability and monetary policy taking the foreground. Alex Popov is overseeing this research, so please switch out to him during the breaks. And finally, we've just launched a joint research network with researchers across the entire euro system of central banks on the transmission of monetary policy. This research will take advantage of a wide range of data sets available at these national central banks to better understand how monetary transmission works and is transmitted to the real economy. Now, this work is overseen by my colleague Philip Hartman. And I would now like to ask the presenter and the discussant of the first paper to join me on stage so that we can start the conference. So Alp and Lars, where Lars, please join me. And while you take your seats, let me just explain how we will proceed. Following their presentation and discussion, there will be 10 minutes for questions from the floor from you, the audience. And microphones will be available at the time. We ask that you stand up when you ask your question, starting by saying your name. The standing up is needed so that you're visible to the cameras. The entire event also don't get too worried, but it's all live-streamed. And just that's for full disclosure. And with all of that, wish you a very pleasant and above all productive conference. Thank you. Thank you, Luke, for that nice introduction. And thank you for a great program and for including our paper. So this paper is joined with Ricardo Caballero from MIT. And to motivate this paper, let me start with a quote from Feds chairman Jay Powell from last year's FOMC conference about a year, last September's FOMC conference about a year ago. He said, monetary policy famously works with long and variable lags. But then he clarified that their policy decisions affect financial conditions immediately, but then financial conditions take time to transmit to the real economy. So he identified financial conditions as a fast-moving intermediate target that transmits policy to the real economy. And when you look into what central banks like the Fed mean by financial conditions, you realize that they basically have in mind a measure of aggregate asset prices. So for instance, they have in mind things like stock and house valuations, because they can increase spending through wealth effects, through balance sheet effects, as well as through other channels. They of course have in mind bond prices, inversely interest rates, including long-term rates and spreads, because they affect credit and borrowing in the real economy, which then transmits to spending. They also have in mind exchange rates, although I'm not going to talk about that for now. But basically, you should think of financial conditions as a weighted average of different asset classes, each one weighted according to its impact on aggregate spending. And in fact, there are efforts both inside the central banks and in Wall Street to construct financial conditions indices along these lines. Now in this paper, we make the following observation. This perspective that monetary policy works through financial conditions, asset prices naturally imply an asset pricing theory where asset prices are determined according to the macroeconomic needs as perceived by the central bank. So there's going to be at any point in time an asset price level that satisfies the central bank's objectives in the real economy. We call that P star and we normalize that with potential output to make it a little bit more interpretable. We call that P y star. And our contention is that central banks cannot let the asset prices to deviate too much from these levels. It becomes like a pull factor for this aggregate asset price, financial conditions index. And in recent, during the COVID recovery in last years, we've actually seen several episodes in the US where the stock market tried to break away from what we thought was the feds P y star. But then it was brought down toward P y star with a fed speech or policy announcement. You might, some of you might remember chair Powell's Jackson whole speech from last year that kind of was a reversed the market rally that happened during the summer. So that motivates our study. So what determines, we want to understand theoretically what determines this P y star and how it responds to different shocks. And we do that in a relatively standard New Keynesian environment. So we're going to have two less standard features. First, we're going to capture these transmission lags, which are very important in practice, but which are not always explicitly modeled. You know, what Professor Swenson has thought about lags, but most New Keynesian models don't incorporate them. So the way we're going to capture that is by making households respond to financial conditions, but with potential lags and inertia. On the other hand, during the markets are going to be populated by a very different set of agents. These are going to be sophisticated agents fast. They will respond to shocks as well as the policy response to shocks immediately. Think the bond market. And in fact, our second assumption is going to be about the beliefs of these agents. We're going to make them quite opinionated with their own beliefs that might be different than the central bank's beliefs. So that will help us understand also the implications of disagreements between the markets and the central bank, which we see quite commonly in practice. But the central bank is going to be otherwise quite standard here. It's going to, its objective is to ensure macroeconomic balance, to ensure demand lines up with supply. There is no inflation error, disinflation error pressures. In particular, the central bank does not explicit directly care about asset prices. It cares about asset prices only because they might create inflation or disinflation. There is no explicit financial stability objective here. So our goal is to understand if the central bank has this objective, but monetary policy works with asset prices, what asset prices result from this. And I'm going to show you many results, but the overarching theme behind our results is that asset prices in this environment is PY studies aggregate asset valuation ratio is going to be determined by macroeconomic needs as perceived by the central bank. What do I mean by macroeconomic needs? Basically supply demand imbalances. Inflation error, disinflation error pressures in the real economy will matter a great deal for the aggregate price level. And what do I mean by central banks please? Because policy works with lags, central bank needs to anticipate the future. So what the central bank thinks about inflation errors, inflation pressures in the future is going to be the key driver of asset prices in this environment. Now, let me get to the, to the model. And so I'm going to develop this argument in a few steps. The baseline model, in fact, going to be very standard, no lags and no disagreements. And we're going to see that even in this standard environment, aggregate asset prices are determined by macro needs, not necessarily financial forces such as expected cash flows or risk leverage might be the first thing that come to your mind. But then I will bring in our main ingredients and show you how, how that, how they affect asset prices. Now the, the model is standard. There is potential output denoted by Y star and it fluctuates according to these permanent supply shocks denoted by Z. And this is a model with nominal rigidity. It's a Keynesian model. So output is not necessarily equal to Y star is driven by aggregate demand. And for now I'm going to assume, in fact, fully sticky prices, but later I'm going to bring in a Phillips cure and everything I'm going to tell you today applies also when prices are just somewhat with a Phillips cure. And demand will come from two types of agents. There's going to be this group of agents. We call them hand-to-mouth agents. They supply all the labor in the economy. They work and then they spend all of their labor income. And they play more of a technical role in the model. They help endogenize the labor supply and they also generate a multiplier effect. But they don't drive aggregate demand. They're not the main driver of aggregate demand in this environment. It's going to be driven by the second group of agents. These are the asset holding households. They hold all the assets in the economy, the capital. And they make consumption savings decisions, so that therefore they are the ones that respond to monetary policy. And they're going to have relatively standard preferences, time separable, low utility. But we're going to assume they might not necessarily make fully optimal decisions. Instead, we're going to formulate their spending as a rule. And that helps when we bring in our main ingredients, lags and inertia, much easier to bring them in when you think of a consumption function, as opposed to earlier equations and optimization. Although they are not necessarily far from optimizing. In fact, in the baseline model, we're going to assume they mostly follow the optimal rule. So what is the optimal rule with low utility? Actually, optimal consumption is a constant fraction of wealth. And here, these agents, they don't work. And their wealth comes from assets, the market portfolio. So this is the dividend on the assets, the share of capital. And then it's the continuation value. So that's the value of the market portfolio wealth. And they spend a constant MPC out of it. That's quite standard with low utility. And this will be fully optimal, except for these delta shocks. And these delta shocks are a modeling device to capture demand shocks. When delta is a little higher, they spend more than usual. When delta is lower, they spend less than usual. But otherwise, they follow the optimal rule. So you could have also captured with MPC shocks, nothing of substance would change. But what I want to point out is that even this fully neoclassical optimal consumption function, P shows up. Asset prices show up. Why? Because there are wealth effects. All our sequel, if stock and house prices are higher, people spend more. In practice, there are many other channels that link P to spending. So you can also view this as an equation as a reduced form for those many other channels. Things like balance sheet effects, things like borrowing effects, borrowing constraints, et cetera. Now, turning to the finance side of the model, there's going to be two assets. There's a market portfolio. That's the claim on capital. And so the claim, the share of capital, alpha y. And its return after Campbell's share approximation is given by that expression you see on the slides. It depends on future output. Why? Because output determines future cash flows. It depends on future asset prices. And it's decreasing in current asset prices. The usual return equation. And there's also a risk free asset. A central bank sets the interest rate on that. And there are portfolio managers. This is what we call the market. And that make this portfolio allocation decision. Think about, these are infinitesimal agents. They don't spend on themselves. So they don't contribute to aggregate demand. But they manage portfolios on behalf of households. Households delegated this decision to these guys. And they're trying to do the right thing. So they maximize expected house or log wealth, which is the optimal thing to do in this environment with low utility under their beliefs. And that leads to a relatively standard financial market equilibrium condition that you see on the slides. The discount rate on the market portfolio, the required return on the market portfolio is driven by two things. The risk free rate plus the risk premium. The risk premium determined by the variance of aggregate wealth. It's very standard, CAPM-like financial equilibrium here. And you can, in fact, turn this into, after combining with the return expression, a present discounted value type equation where this aggregate asset price depends on future output through future cash flows or future asset prices. And it's decreasing in the current risk free rate and the current risk premium. It's a very standard PDV equation. And what does the central bank do? Central bank sets the interest rate. But you see from this PDV equation, central bank actually can also control aggregate asset prices. Because there is the usual inverse relation between interest rate and asset prices. High interest rates, lower asset prices, and vice versa. So central bank can effectively control P. And it's going to be much better in this environment to think of the central bank as controlling P because that's what enters the spending equation. So we think of the central bank adjusting I to control P. But then ultimate objective of the central bank is standard. It's minimizing these quadratic gaps. So far there's no inflation. It's trying to close the output caps. And this baseline model, because there are no lags, in fact the central bank will close these gaps at all times. So output is going to be equal to potential. So let me show you now how this equilibrium of this baseline model works. And then I'm going to introduce our ingredients and these steps will generalize. So I showed you that spending by these households depends on asset prices. And output depends on the spending of these households up to a multiplier. If you combine these two things, you basically get a relationship between output and asset prices. And in fact, in logs, it's a one-to-one relationship. And what is the idea that higher asset prices make households spend more and then it works through a multiplier, eventually you end up with higher output. So that's the wealth effect. But in general, again, many other channels link high asset prices to high spending. Now central bank is trying to set this equal to Y star. And then that means that you can solve from here a unique piece star that will achieve the central bank's objective. That's the piece star in the baseline model. And if you stare at that equation, it's basically an asset pricing equation, but it only features macroeconomic variables. That is the M is like a combination of the MPC and the multiplier, delta is demand shocks. So only macro factors determine asset prices. Why? Because asset prices need to be here just high enough so that they induce households spend enough to clear the goods market, achieve a macroeconomic objective. There is no room for expected cash flows or risk premium to affect asset prices. Where do they go? They're kind of in the background. Well, the central bank adjusts the interest rate to absorb the effects of expected cash flows and risk premium. For instance, if the markets get too pessimistic about cash flows, even though there is no change in macro objectives, asset prices will tend to fall, but then central bank would cut the rate and would stabilize them. That's known as the Fed puts, right? So that's in our model. So asset prices are determined by macroeconomic needs. Central bank adjusts I to achieve that. And the other thing I want to highlight here is you see demand shocks reduce asset prices, positive demand shocks. Why? Because when people spend more than usual, there will be inflationary pressure. Central bank lowers asset prices to give the people spend less signal to reduce the inflationary pressure. Now let me introduce our main ingredient, transmission lags. I don't need to motivate the transmission lags for this audience, but I'm just going to say that they're quite long. Empirical estimates of lags are such that when the central bank does a surprise interest rate change, it can take one to two years to have the maximum impact felt on the economy. So what that means is that central bank in practice has much less control over aggregate demand than in the textbook models that you see. They need, in particular, central bank needs to forecast the future. And the one modeling, simple modeling device to capture lags is to keep our spending equation, but lag the asset prices by one period. So people spend to still financial conditions asset prices, but with a lag of one period, okay? So then output depends on lag asset prices. And you see here, central bank can no longer set output equals to potential at all times, because Pt minus one, which is central bank controlled, is predetermined. But if there is, for instance, a positive demand shock, it will create inflationary pressures, and central bank can do nothing about it. If there's a negative demand shock, it will create a recession, right? Turns out what the central bank does here is it sets output gaps to zero in expectation, right? Because it's setting Pt, influencing yt plus one. It's basically setting the next period's output equal to next period's potential output. And if you solve for the asset price that result here, you see it's very similar to the formula I showed you, except instead of delta, what you now have is central bank's beliefs about delta tilde, net demand. That's net demand. Demand minus supply in the next period, okay? So central bank's beliefs about next period demand minus supply become a key driver of asset prices. For instance, when central bank anticipates high demand in the next period, it's going to now set low prices for the same reason I showed you before, but now it happens to the central bank's anticipation. Conversely, when the central bank sets high supply in the next period, it's going to set now high asset prices because it will try to prepare the demand for the high supply that it anticipates, okay? You see central bank's beliefs about inflationary pressures become the key driver of asset prices. And we think this has many implications. And one implication is macroeconomic news start to matter quite a bit for asset prices, as we see actually in practice. The reason they matter is because macroeconomic news like GDP output, unemployment or inflation leases will affect the perceptions of future demands of life, future imbalances, and that will change the central bank's beliefs and that will change asset prices. To formalize that, let me introduce a belief about future demand. Adding belief about future supply doesn't, news about future supply doesn't change things very much. So here, N is news about future demand. When N is higher, we get a noisy signal that future demand is going to be higher than usual. Think like non-farm payrolls in the US come stronger than expected, okay? And then the central bank's posterior reacts to this N. So as you see, high N now makes the central bank expect higher demand in the future and target lower asset price, okay? But this also affects the output. Because now the central bank anticipates some of the demand charts that would otherwise cause business cycles, actually output becomes more stable. Only the surprise relative to the central bank's anticipation cause now demand driven booms. So the implication of that is that if you make these news more and more precise, maybe might be happening in recent years because we have better data, we have better data analysis techniques, output becomes more stable because central bank does a better job of managing and anticipating demand shocks and keeping output stable. But asset prices don't necessarily become more stable. In fact, they become more volatile and there is more central bank induced volatility in asset prices because asset prices are the central bank's tool to stabilize the economy. So we think this roughly captures the last few years, the recovery from the COVID where we recovered quite quickly from a very big shock. So the output has been relatively stable, but there was a lot of wild swings in central markets and mostly driven by central bank actions. Now let me introduce a very close cousin of the lags, which we call internal inertia. Because if you think about where these lags come from at the micro level, and they emerge because people like you and me have habits or adjustment costs, we go on about our lives and occasionally we react to financial marks. For instance, you might look at mortgages when you buy a home and you might look at if you're managing a firm credit spreads when you do an investment project. If you're going, you might look at stock prices when you go on vacation, but most of the time you wouldn't look at these things. You just go on with your luck. So that's kind of one micro foundation for lags, but that same micro foundation also implies what we call internal inertia. You also respond to your past actions. C is also a function of its past levels and the past asset prices. Then we get this formulation. There is basically inertia in output. All else equal, high output implies high output going forward and vice versa. If you solve the asset price and central bank still does the same thing here, if you solve for the asset price with this additional related friction, you find that it's basically very similar to what I showed you before, except there's one more term and the output gaps show up in the asset price as well. They show up inversely. It's quite interesting, which means that if currently, for instance, the output gap is negative, the economy is going through a demand recession, asset prices are going to be higher than usual. If the output gap is positive, asset prices are demand boom, asset prices are lower than usual. If you think through cash flows, you might reach the opposite conclusion, because recessions are times of firms that have less earnings, less cash flows. You're saying, no, those are times that asset price is actually going to be higher than usual. Why is that? Well, if you look at this equation, it becomes immediately clear because then output is low now, the economy is weak, recession, that tends to persist into the future because of inertia. A central bank doesn't want that to persist that into the future, so it jacks up asset prices to counter the inertial effects of weak output. Asset prices are like the central bank's gas pedal. When your economy is weak, it's precisely when you want to press the gas, so that's when asset prices are higher. When the economy is too strong, you want to press the brakes, and that's why asset prices are too low. Again, if you think about the COVID cycle, we had high asset prices when unemployment was high, the economy was low, and it was mainly driven by low interest rates, but now the economy recovered and we have low asset price, so that's consistent with what's going on in our model. One implication of this is that inflation is bad news for these aggregate asset prices. We introduced inflation via a standard New Keynesian Phillips curve, and it turns out that if there is no disagreement between price setters and central banks, actually expected inflation is zero here, central bank stabilizes both expected output and expected inflation. There is divine coincidence in expectation, if you want, and so expectation, inflation expectations become anchored, so then inflation is driven by the current gaps. So what causes inflation in our model? If demand shock is higher than the central bank anticipated, there's going to be inflation, or if the supply is weaker than the central bank anticipated, there's going to be inflation. So inflation is driven by current gaps, but I just told you that current gaps and asset prices are negatively correlated, so inflation and asset prices are negatively correlated, and that's true regardless of if inflation is driven by demand shocks or supply shocks. So the result about demand shocks, again, here is a little more surprising, because if you have demand driven inflation, like we might have in the U.S., that means the economy is actually doing strong, firms' cash flows are high, but that's still bad news for asset prices because of this overshooting result that I showed you. Supply-driven inflation being bad news for asset prices is relatively more standard. Okay, in the last few minutes, let me show you what happens when we introduce disagreement between the market and the Fed, and we do that for two reasons. First of all, for the model suggests that because I showed you in the model that asset prices are driven by the Fed's beliefs, so you might wonder what happens when the market has a different belief than the Fed, and that turns out to be a very practical, important concern in practice because financial markets criticize the central banks, the Fed, ECB all the time. I'm sure you guys are aware of this, so there's always discussion of central banks making the wrong decision policy mistakes. So how do we capture these disagreements and perceived mistakes? Well, let's go back to the signal that I've introduced about demand, but now I will introduce different interpretations of the signal. So, Laura and I, we both observed the signal, but after we observed the signal, we also draw these muses, which are how we interpret the signal, okay, and then the signal plus mu becomes our centered signal. So if, and it could be that we draw correlated interpretations, if these zero are interpreted, these are always correlated, we never have any disagreements, but if these positive, the occasional will have disagreements. We'll look at the same data and come to different conclusions, which we think, again, happens quite often in practice, because data is often filtered through some model and some interpretation. What happens here, now you see we have belief disagreements, but more interestingly, we think each other's beliefs is noisier than our own belief, right, because I think I'm doing the Bayesian updating correctly, so I think Laura occasionally introduces these additional noise around my beliefs, so her beliefs are noisier, but she thinks exactly the opposite. She thinks my beliefs are noisier than her beliefs. Why does it matter? Because I told you asset prices are determined by the Fed's beliefs, and that's still true here, because the Fed sets the interest, it ultimately hits the asset price at once, but the market thinks the Fed is making a mistake, because the market thinks the Fed should be targeting asset prices under its interpretation, under its belief, so what that means is that the market actually perceives the asset prices to be too volatile here. There's going to be central bank-induced volatility, excess volatility in asset prices, and more so when there's more disagreement between the market and the central bank, and that get priced in equilibrium, so the risk premium in this model is higher, and especially when there is more disagreement between central banks and the market, but ultimately this doesn't affect the asset price, because central bank adjusts the interest rate to keep the aggregate asset price where it wants to be, but it does affect, because it affects risk premium, it does affect relative asset prices, and for instance, it might affect the price of stocks versus bonds, but it's not going to affect this aggregate asset price, so let me stop here. So I showed you, motivated by the observation that monetary policy transmits to economy via asset prices, I showed you a model in which the central bank's objectives determine aggregate asset prices, and this has many implications, and I'm not going to review, but I will look forward to comments by Professor Svensson. Thank you. Thank you very much Alp. The discussion is Lars Svensson, for yours, 50 minutes, thanks. Okay, thank you very much for the invitation to come here, I really appreciate it to get the opportunity to discuss this paper. Let me start with a summary. The authors propose a model where the Fed's expectation of macroeconomic needs, meaning supply and demand shocks, drives aggregate asset prices, and the Fed affects the output with a lag by altering aggregate asset prices. There you see the aggregate demand equation. First order conditions for optimal monetary policy is simply here, zero expected output gap. Y star is the potential output, and then the authors reverse engineer the aggregate asset price P star that achieves the first order condition. They also talk about P y star optimal asset prices to GDP, the expression for which you can see there. The Fed then somehow sets the safe real interest rate i to make asset prices equal to the optimal asset prices. It's as simple as that. The authors derive several implications of their model. Fed believes about future supply and demand shocks drive aggregate asset prices, and then standard financial forces determine relative asset prices. More precise news about future aggregate demand makes output less volatile, but asset prices more volatile. Fed moves asset prices more and stabilize output better. With aggregate demand inertia, the Fed actually overshoots asset prices in response to the current output gaps. Fed moves asset prices more to counter a more persistent output gap response to shocks. Inflation is negatively correlated with asset prices for both supply and demand shocks. There is divine coincidence in this model, which implies that inflation is proportional to the output gap, and the latter is negatively correlated with asset prices. And then the authors also consider belief disagreements between the Fed and the market, and this generates a policy risk premium and potential behind the curve asset price dynamics. So here are my comments. This is a fine paper. It's well written, neat and elegant model, thanks to several clever simplifying assumptions one can add. It's also full of clear arguments and proofs, and it is much thought provoking. In spite of its elegance, I must admit that I'm a bit skeptical. Is the paper convincing? Does it have empirical support? How robust are its results? Does it have any lessons for practical monetary policy? Should central banks, the Fed and the ECB and the Riksbank do anything differently after having read and digested this paper? Well, does the paper have empirical support? Often a paper starts with some empirical correlations and looks for a model that can explain the correlations better than the other existing models. Not here, maybe in the follow up of this paper. I mean, it's easy to check the empirical correlations between asset prices, output, output gaps and inflation for either rejection of the model or some support of the model. So I think that's one thing the authors should do in additional work. Except what asset prices? The S&P 500? A claim to GDP? Bob Schiller has proposed an asset which would work like a claim to GDP, but unfortunately doesn't exist yet. What about housing? The largest asset of most households? Should we construct an aggregate of all these asset prices? In the euro zone, should we have an aggregate of all the assets in all the different countries? And should then ECB try to target that? I mean, well, also one can compare results, the correlation results with those of empirically estimated DSG in other models and see whether there is any discrepancy between their results and these results. Of course, those models, they explicitly aim to explain the moments of the data. And it would, I mean, of course one could try to estimate the model, how does it fit the data? How robust are the results? I mean, it is a very simple model. There are several unrealistic simplifying assumptions. I mean, the transmission channel is pretty simple, just the wealth channel. There is a marginal propensity to consume out the wealth that matters here. In Sweden, we have a strong cash flow channel for monetary policy because we have variable rates and large mortgages which affect the cash flow of households within a few months. Okay. Robustness to empirically supported alternative assumptions. I mean, one example. In the real world, there is no divine coincidence, in particular now. So that is one assumption that one could replace with a more realistic assumption. A small question. There is something I don't quite understand. How can the Fed both set the policy rate and also maintain a zero net supply of reserves and certificates? That seems to be something in the model. There may be an explanation, but I haven't understood it. Usually you fix one of the two, not both. Okay. What are the lessons for practical monetary policy? I have the privilege of having had a six year experience of policymaking at the Riksbank as a member of the executive board. And of course, financial conditions were a pretty big thing in the policymaking process. And I thought of financial condition as essentially a set of yield curves for different assets from safe to increasing risky assets. Essentially, the borrowing costs of various activities and this set of yield curves are affected by news market expectation and by the announced policy rate path. I mean, one of these yield curves is the announced, the bottom yield curve usually is the announced policy rate path for the Riksbank. And these yield curves, these financial conditions, they affect output and inflation with lags. But some transmission channels are fast in Sweden. I mean, the household cash flow channel and exchange rate channel works within a few months. It doesn't take a year or longer. And then forecast targeting. I thought of the game as being setting the policy rate path such that forecast of inflation and unemployment conditional on current information, all relevant current information, the policy rate path, financial conditions and judgment, quite a bit of judgment look good. Forecasts looking good. Well, looking good means inflation and unemployment approaching respectively the inflation target and the long run sustainable unemployment rate, approximately minimizing the standard loss function. So that's how I thought of monetary policy and essentially how the Riksbank in practice thought and things of monetary policy regardless of whether they explain it as clearly as I do. And of course, it could be the output cap there instead of the unemployment cap. But the wealth channel and asset prices and housing prices play little or no role, no explicit role in the transmission mechanism that lies behind this. Of course, it's there to some extent, but it's not really exploited. So what are the lessons for practical monetary policy? What is the problem with that kind of forecast targeting? But what I just explained. I mean, this is also what the Fed is actually doing, regardless how explicit they describe it. Should I or us, we, should we instead have tried to infer what aggregate asset prices would be consistent with forecasts looking good? I mean, is there a stable and known relation that can be exploited? And what asset prices as I just mentioned? And should I have tried to infer or we have tried to infer what policy rate would implement those optimal aggregate asset prices? Again, is there really a stable and known relation that can be exploited? I must admit that I would feel quite a bit lost if I was facing such a task to try to implement monetary policy through asset prices. And in the end, I remain unconvinced that targeting asset prices would be better than the kind of forecast targeting I just described. So summing up, it's the most interesting, well written, and in particular, thought-provoking papers. Thought-provoking papers are often the most productive papers and you should look for those that force you to think. However, I think quite a bit of work remains to make this convincing, make the paper convincing, perhaps according to the lines with empirical work that I suggested. Thanks. Well, thank you Lars for this discussion and I'll better understand why you used the Fed as an example in the first comments you had of the Rix bank. Actually, the Fed is called the Fed in the paper. It's not called the central bank. So I just applied the author. Anyway, I thank both of you for not referring to the ECB then. So the floor is open. Questions and mics will be brought to you and we have here on my right, Giorgio Primicieri, please. And again, please stand up, mention your name for the virtual audience benefit. Thanks. Hello, my name is Giorgio Primicieri. Interesting paper up. I want to try to understand at the deep level what is the difference between this model and a more standard model. I'm thinking about a simple New King's model and maybe with capital. Let's put some assets there and with some maybe adjustment cost and make the price of capital change. My understanding is that in that model, some of these mechanisms are present because when monetary policy changes, the interest rate does affect the price of capital, the quantity of capital generates wealth effects. Also, in the standard New King's model, when the Fed changes the short-term interest rates, these affect the long-term interest rate on long-term bonds that affect consumption. So some of these mechanisms are there already. So I correct me if I'm wrong, but my understanding is that this model just focuses, puts at the center of the model, this wealth effect, this connection between the interest rate, the price of assets, and the consumption decision. That is already in the standard model, but maybe it's not powerful enough. Is that a correct interpretation? And if so, I think I agree with Lars that it would be nice to provide empirical supporting evidence that this wealth effect is really at the center of the transmission mechanism. Thank you, Jojo, and thank you, Professor Svensson, for an excellent discussion. So actually, this model is not that far from the standard model. You're right about that. And in that sense, that's one also answer to the comments of Professor Svensson. We are not that far, but we are formulating the model somewhat differently and deriving its implications for asset prices, whereas asset prices in the textbook models are mostly in the background. So something happens to asset prices, but it's never kind of clear what happens. So we are showing you what asset price results when in relatively standard New Keynesian model. And there are some differences from the New Keynesian model, and it's not the wealth effect. The wealth effect is one way of capturing this price output connection, but we could easily put like a Q theory, like you suggested, and then investment would also respond to asset price. We could do borrowing constraints while maintaining the qualitative features of what's going on. But the main difference from the New Keynesian model is that we actually have risk premium, and we don't log linearize the model. So we kind of allow for risk premium or expectations or beliefs drive asset prices, and yet we are showing you that these macro factors dominate. So in that sense, that's close to the part about with lags are slightly more distant from the New Keynesian model, closer to Professor Svensson's work, or some of the New Keynesian literature explores that, explore that, and they tend to be quite important, but in spirit, it's not that far from the New Keynesian model. And I would say this is a highly stylized model, and Professor Svensson, and that's true for the New Keynesian model as well, mentioned. And so we make a lot of simplifying assumptions, and that's by design, because our goal here is like in a textbook model to capture qualitative insights, and we hope will extend to more general and complicated environments at least qualitatively. Obviously, we have our work cut out. We need to demonstrate that claim, but we think the simplicity at this stage is a virtue because it helps make the qualitative mechanisms clear at least to us, helps us think through some of these issues that are present also in the standard model. Thank you. Next question. Laura here. Hi, I'm Laura Gatti at DCB. So I have a quick question about the point on macro needs driving asset prices, because in your model, you have a separation between the households that provide labor and the households that are making these portfolio decisions. And in fact, those consumptions are completely separate, which was a surprise to me, given that you're trying to tie the macro to asset prices. So what would happen if you actually brought those together? So the labor providing households consumption would also be tied into, so if they were allowed to essentially make the portfolio decisions? I mean, the labor providing households making so we make them spend all of their labor income. So they're a bit like these low liquidity, high MPC agents in Hank model. So then that sense is also connect with that literature a bit. If we make them or if you put some labor income to asset holding households, which we can, then again, many of the features here would apply. But then the aggregate asset price that stabilized would also include a human capital component. And depending on what you think about the riskiness of that residual part, which is what you observe, might be not fully stabilized because some of the shocks will be observed by the human capital component. So again, most of what we are saying would apply, it would become qualitatively would be there, but there will be some differences because the asset holding people, there will be also human capital wealth would also be in the aggregate wealth that gets stabilized. Good question. Next question. Michael, how about Chicago, both very nice model. I was actually wondering, I'll give that you mentioned explicitly this role for expectations and risk premia. So following up on last instance comments on like the empirical kind of matchings in the data, the consumption wealth ratio does predict risk premia, for example. And so given that by construction, your model is constantly, if any idea, if you were to allow for this link in the data, kind of how things would look like in the model. Yes, so this goes back to the question of have we tried to calibrate the model to the moments. We have not. Partly we haven't because we needed first think about this, the right asset price, financial conditions index and their efforts out there trying to aggregate different assets and find an FCI. And once we do that, we can take things to data. But to your question, predicting risk premium. So we are actually okay with risk premium moving around for exogenous reasons. We can make it time varying. It's easy to add to the model. And that help that in our model determines the price of stocks versus bonds, but the aggregate asset price and the aggregate consumption become isolated from that. And what drives the aggregate asset price in our model is the Fed induced changes in the discount rate. So for instance, the demand shock is higher. The Fed raises the discount rate. It lowers the aggregate asset price and aggregate consumption. So and in practice, the Fed seems to affect risk premium for reasons that are not in our model. First, the evidence on Hansen and Stein and there is the evidence on Gertler Karate. So somehow we think if you build that into the model, then we can get much closer to what's going on in the real world where the central bank changed interest rates, they changed not only the expected expectations of interest, but also risk premium, but ultimately they affect financial conditions, which is sort of in the spirit of our paper. But we think we are missing something in the connection from central bank decisions to the risk premium. And once we build that in, we think we come much closer to matching the finance evidence on this that you mentioned. Okay. Well, please join me in thanking Alp and Lars for this thought-provoking session. And then I would like to welcome our next lineup of speakers. So we have Hassan, Afrutzi and Klaus Adam. Klaus, we can sit here and floor is yours. Please, Hassan. Well, thank you. I would like to thank the organizers for including our paper on the program. I will be talking about inflation and GDP dynamics and production networks, which is joint work with Seroj Batari. So the motivation for this project is, of course, the rise in inflation that we've seen in recent years around the world. Just to quickly recap the sequence of events that led to this rise in inflation, after the pandemic, we had this increase in energy prices and global supply chain pressures that I'm showing in this figure in these dotted lines. This was then manifested itself in inflation around the world. This is PC inflation in the United States that increased with these after these rise in inflation in energy prices and global supply chain pressures, which was initially accommodated by the Federal Reserve in the U.S. The orange line is showing the federal funds rate that stayed low until the inflation peaked in the U.S. and then started rising afterwards. But what happened with core PC inflation was that it also started increasing. It peaked less than what the peak of inflation was for inflation itself, but it has proved to be more persistent. Recently, core PC is now higher than actual inflation in the U.S. I think the same pattern exists in Europe and around the world as well. Motivated by all of these, we want to understand how supply chains and rises in inflation in different sectors affect the transmission of shocks to aggregate inflation. What we're going to do in this paper is to derive analytical solutions and sufficient statistics for inflation and GDP dynamics and production networks with sticky prices. We're going to quantify how these production network economies affect the size and the persistence of the economy's response to monetary and sectoral shocks. We're going to show that these models define a notion of network-adjusted stickiness that is going to characterize the response of these aggregate variables to shocks. In a policy counterfactual at the end, I'm going to show you that how stabilizing inflation driven by these network-adjusted stickiness is going to show itself in GDP and GDP gap. This paper contributes to three literatures, monetary models with multi-sector economies, monetary models in multi-sector economies, with heterogeneity and price-adjusted stickiness and network economies in response to real shocks. But in the interest of time, let me show you the model. We're going to operate in a setting where time is continuous and runs forever. There's going to be end sectors in the economy that are going to consist of a measure of monopolistically competitive intermediate firms. Each of these sectors is going to have a measure of these competitive intermediate firm producers. A final good producer in each sector is going to package the goods of these intermediate good producers and sell it to both households and other sectors in the economy. These sectoral goods are then going to consume it by the household and other sectors' intermediate firms to produce and circulate in the economy. The household is going to maximize the net present value of their utility minus the distributivity of labor, subject to a standard budget constraint where the expenditure of the household on sectoral goods plus the changes in their holding of nominal bonds is going to be less than or equal to their labor income plus interest earned on those bonds plus any kind of profits or taxes that is rebated to them. The aggregate consumption index is going to be defined by an aggregator function that is going to take as input these sectoral consumptions from different sectors in the economy and convert it to a notion of aggregate consumption which we're going to call the GDP of this economy because there's going to be no investment or government spending in this model. This is also going to define a notion of aggregate price index which is going to be the CPI assuming that this aggregator function is homogeneous of degree one then this is going to imply that the price index is just simply a total expenditure of the household divided by this aggregate consumption index. For simplicity in the beginning like in the benchmark model we're going to assume that Machi policy controls the path of nominal GDP so the central bank sets what the nominal demand is going to be in the economy and then the firm side is going to decide how much of this passes to prices versus to consumption. I'm going to show you what this means in terms of the policy rate so this is going to correspond very closely to the notion of an accommodative monetary policy when the monetary policy keeps the path of this nominal GDP fixed and then eventually I'm going to show you what happens when central bank endogenously stabilizes inflation via a Taylor rule for example. Moreover the notion of these preferences that we've considered here which is also used famously by Gallisoff and Lucas is going to imply that nominal wage is also going to be proportional to the nominal GDP in the economy so the central bank by controlling the path of nominal GDP also is controlling the path of wages. Again this is not very restrictive and we consider generalizations at the end of the paper but it sets a very clear benchmark that monetary policy determines nominal GDP and through that determines how much of that passes through to wages and now we want to understand what happens to prices. The final good producer in every sector so we're going to have n of these is just going to be a fictitious aggregator that essentially buys from the intermediate good producers in each sector packages it through a CES aggregator with elasticity of substitution sigma i and then sells it to the household or any other firm in the economy that wants to use the product of this sector as an input and because of the competitiveness the value added of this final good producer is going to be zero but it's going to define there's going to be a well-defined notion of a sectoral good because of this so on the production side every sector is going to have a measure of intermediate good producers by ij i'm going to denote firm j in sector i and j is going to go from zero to one these firms are going to use labor as the factor of production along with other goods from other sectors in the economy to produce using a production function that is going to be specific to their sector so this fi function captures how these different inputs for production is converted to the product of this firm and z it is going to be a sectoral productivity shock or supply shock the key is that we're not going to restrict the shape of this f function which in our linearization is going to denote to like what the expenditure shares of different firms in the economy is on different sectors which is going to allow us to capture a notion of like a general production network on the pricing side these firms are going to have a sticky prices so in sector i opportunities to reset prices for these intermediate good producers is going to arrive as iid Poisson processes at the rate of arrival of theta i that is going to be strictly positive for every sector and then firms knowing that they don't get to set their prices every period or every instant they're going to maximize their profits in expectation taking into account the stickiness of these prices this is a very standard New Keynesian profit maximization problem that i've written here the whole notion is that firms are forward-looking in their price setting and because it's a standard i'll show you what it implies later but it just communicates that the price set by every firm in the sector is going to be affected by these supply shocks prices of other sectors in a forward-looking way and we're going to allow for heterogeneous arrivals for these Poisson price adjustments so that different sectors in the economy have different stickiness in their prices so with the environment at hand let me show you the theoretical results that we derive in this framework so we're going to take that economy that i showed you we're going to log linearize it around an efficient steady state by efficient steady state i mean that we are going to adjust sales taxes on these different sectors so that in the steady state or in the long run of this economy monopoly distortions across different sectors do not distort factor and factor allocation which in this economy is just labor so in this log linearized economy let me denote the vector of these sectoral prices by little pt and little pt is going to be an n by one vector where the ith element is just a deviation of sector i's price from its a steady state level let me also denote by a the input output matrix of this economy in this efficient steady state so we're thinking about element aij of this matrix denoting the expenditure share of sector i on sector j's output now if prices were flexible there is no notion of dynamics in this model so prices would adjust every instant to clear the markets and it would adjust in a way that nominal gdp is the monetary shock or the monetary policy of this economy is going to shift all prices so that's the first element in there mt multiplied by a vector of once so monetary policy should in a flexible world should not have or should not introduce relative price distortions so that's going to be the nominal block of this economy if prices were flexible and then real shocks captured by those omegas or z's omegas are like cost plus shocks and z's are productivity shocks the only reason that i'm distinguishing them is to show them show you that in this economy they both act in a similar way they are going to pass through prices in this flexible counter factual through the inversely on tf matrix which is i minus a inverse it's a very well known result if prices were flexible there's classical dichotomy monetary policy shifts prices and productivity shocks pass through the economy through the inversely on tf but when prices are sticky then this classical dichotomy result breaks down static uh mark clearing break breaks down and what happens is that prices are not going to adjust to slowly and um our first result is to show you that they are going to adjust in a way that eventually closes the gap between prices that are sticky and these prices that would prevail in that counter factual economy ptf so if you look at this equation that i have here which i'm going to spend the next slide on it's just telling us that the rate of change in inflation is going to be equal i'm ignoring the first term because that's not going to really help the intuition so let's assume that that row parameter was zero this equation is just telling us that inflation is going to adjust proportional to a matrix that i'm going to explain what it is like that matrix theta squared times i minus a multiplied by the difference between prices in the sticky economy and the prices that would prevail in the flexible counter factual that i just talked about and it really helps for the next slide to consider the fact that ptf this vector of flexible prices is completely exogenous to the economy it's just a function of uh monetary policy which we're going to fix and shocks either cost push or productivity okay and because i'm going to talk about this matrix theta squared i minus a a lot let me call that the matrix gamma and it's going to have two components in it theta is a diagonal matrix that just stacks the frequencies of price adjustments across different sectors on its diagonal and a is just my uh input output matrix or you can think about i minus a as the leon tf matrix this is going to be an n by n matrix i'm going to call it gamma let me explain a little bit what the significance of this matrix is so first of all we can think about this equation that i'm showing you that i derived in the last proposition as the slope of sectoral philips curves in matrix form what do i mean by sectoral philips curves so we think of philips curves as like equations from supply site that relate inflation to real outcomes um classically like thinking about gdp gap or unemployment gap this is not a one-dimensional economy so there are many different gaps in this economy but we can still like write the equation that i have on top of this slide as a function of inflation on one side and output gap on the other side but because we have so many different sectors and only one output gap some relative prices are going to start showing up in that equation this is something that we know from the work of aoki and benignio but the notion is that um we can write it in terms of output gap and inflation as long as we take into account the effect of relative prices on inflation so that is the component that is missing in the one in the three equation the against in model that comes to be in an economy with production networks and it connects also to work of lauren's own recent work of lauren's only and we're not going to come on conflict inflation um however the reason that i have decided to write the equation not in terms of output gap and relative price distortions but in terms of nominal price gaps is that um if we write it that way we can see that this equation now fully characterizes the dynamics of uh of prices given a path for uh ptf which is an exogenous disturbance at this point we have solved for pdf if you really like want to like uh uh think about the details of this this is a second order differential equation so combined with a set of boundary conditions this gives us what's going to happen to prices what that tells us is that we have arrived to a sufficient statistic uh for the solution of the model because the only thing that matters for the evolution of prices is this matrix gamma and the parameter row row is just a discount factor of the household so the only thing that is going to affect how prices will adjust in this economy independent of the shape of the network or the distribution of prices to Guinness across sectors is the matrix gamma um more over we can think about how shocks are going to affect the evolution of prices and that's just going to be captured by the term ptf so gamma is a matrix of parameters ptf is like consolidating how different shocks are going to affect the transmission uh uh to inflation so all shocks are going to affect price dynamics through ptf this also tells us that we arrived to a sufficient statistic in terms of independent of the nature of the shock how prices will evolve is can be decomposed into understand how shocks affect ptf in that counterfactual economy how prices will adjust to a shock and then given that pass through understand what's going to happen to prices through the philips curve that we're presenting here so what is the bottom line let me show you some uh impulse responses in terms of like solving that system and showing you what's happening to prices so consider i'm going to also like in the slides just set row equal to zero because it gives more tractability uh and more intuitive uh expressions so imagine that in this world normal gdp increases by one percent in an unanticipated way so if we were in a steady state before and now not nominal prices are higher by one percent i know by long run non neutrality that eventually prices will adjust and go up by one percent because nothing real has changed in its economy the significance of a sticky economy is that that doesn't happen immediately okay so what i have here is that the impulse response of the vector of prices in the economy that pt is the vector of prices is going to be a matrix multiplied by one that one at the end of that expression captures the pass through of the monetary shock to flexible prices that's just saying that flexible prices should go up by one percent in the long run the matrix captures how slowly we're going to go to that which is like the core question of what is the persistence of response of prices uh to monetary or sectoral shocks and it's just going to be captured or is just going to be a function of the principal square root of the gamma matrix that i showed you in the previous slide now i'm packing a lot of different things i put all parameters in a gamma matrix now i'm telling you that there's going to be a principal square root of this matrix that matters for the transmission of prices i'm going to spend some time in unpacking this but i want to first show you that what i'm going to unpack is actually worth something and here it's worth in the following sense the response of prices in the economy to a monetary shock and in the next slide i'm going to show you to any sectoral shock is just going to depend on the square root of this matrix so forget about networks forget about like stickiness forget about heterogeneity and stickiness all of them are going to matter only through this matrix um i also have to mention that like matrices don't have necessarily unique square roots or sometimes they don't have a square roots but the assumptions the economic assumptions that we've made here also makes this a unique matrix so we're talking about a unique equilibrium here once i have the response of prices of course i can take the time derivative and get the response of sectoral inflation rates once i have the response of sectoral inflation rates i can create any weighted average that i want including the not the cpi inflation by multiplying by a vector of expenditure shares and i can calculate the output gap by just going back to how it was defined in the beginning so that was for a monetary shock the same intuition holds for a sectoral or a tfb shock imagine there's a one percent increase in the sectoral supply shock of sector i the only thing that's going to change from the previous slide to this one is that sectoral shocks have a different pass through to flexible prices than monetary shocks monetary shocks shifted it sectoral prices passed through uh to flexible prices through the inversely on tf if you replace that vector of ones that i had at the end of my impulse responses by the pass through of sectoral shocks which is the inversely on tf multiplied by the shock the same intuition goes through the dynamics are just going to be governed by the same matrix or the operator that we discussed before and i'm going to talk about the notion of cir in my next few slides and that's just defined as the integral of output gap from zero to infinity so to unpack this matrix gamma notice that like i can take any of my impulse responses and just plug in the eigenvalue decomposition of my matrix and just write it as a function of sum of exponentials and then i can say that every impulse response in this economy is just going to be a weighted average of different exponentials with different decay rates the problem is that there's not a really intuitive way of mapping these weights or these eigenvalues to the underlying parameters so what we do in the paper is we come up with an approximation to a network that allows us to do this mapping in the interest of time i'm going to pass through this but the idea would be to start from an economy that doesn't have any input output linkages across the sectors and start adding those links by a small weight epsilon and the small weight epsilon is going to allow me to derive approximations in terms of the parameters and how they affect the response of aggregate variables to these shocks the only thing that i want to mention is that we show later in the paper that this approximation is very accurate at least for the input output structure of the u.s economy so we're not losing a lot of information by doing this so i told you when i was presenting the idea of the sectoral philip's curves that we have arrived into sufficient statistic argument that i only need to know matrix gamma to understand what happens to prices in the economy the flip side of that is that i can go to the data and calculate it and actually show you what those impulse responses look like we do that using the input output tables for the u.s economy and data from pastin schole and weber michael is here who kindly shared their paper data with us first we derive some aggregate effects of monetary shock in the paper and quantify how much networks amplify monitoring on neutrality this is well known we just put numbers on it so i just want to pass but i want to show you what happens to the distribution of sectoral prices or sectoral responses of prices in the economy to a monetary shock so intuition was that when a monetary shock happens all prices eventually have to go to the same place they have to increase by one percent right the problem is that in a network economy some prices will adjust fast so they're going to have a very high response on impact and some prices will adjust very slowly so on an impact they're going to have a very low response but the because they're all going to the same place if you have a fast response like if you're the oil sector and you have like a very flexible price and your response to a monetary shock is really high then that effect has to be by definition very transient because all the other sectors have to like catch up with you so that's one intuition that comes up out of this model and the question is that what is the persistence of these responses and that's where we define this notion of network adjusted the stickiness that what derives the persistence of these responses is just going to be the frequency of the sector multiplied by an adjustment that comes from the network of the economy so that's number one then we can also ask what happens if we what happens to monitoring on neutrality as a consequence of input output linkages instead of like spending too much time on this on this formula let me just tell you that if we think about the area under the impulse response of GDP gap in response to a monetary shock there's going to be a direct effect that comes from like work of Carvalho for example but the indirect effect of like these different sectors is just going to be captured by this notion of network adjusted the stickiness and to showcase what I mean by that let me take the US economy identify the three sectors with the highest network stickiness and just say what would happen to monitoring on neutrality for example if I excluded these three sectors from my analysis and we show that that would reduce the GDP response by 16 percent even though that these economies even though that these three sectors don't have any direct expenditure share by households so these like indirect effects of networks are really important for the transmission of shocks to monetary policy we have similar results for persistence and response to sectoral shocks with a similar intuition that this network adjusted the stickiness really matters and is very important here I'm showing you for example the correlation between aggregate response of GDP and the half life of the aggregate inflation which are both driven by this notion let me skip my endogenous monetary response slide and just jump into my conclusion in this paper we derive sufficient statistics for dynamics of sticky prices on production networks and we show how the structure of the network and the structure of price of stickiness across the economy matters for the transmission of shocks to inflation and GDP thank you so much and I apologize for going over time a little bit thank you thank you as some close floor is yours so yeah thank you for having me here to discuss this paper it's great pleasure you know to go through this work by Hassan and Sarash um so I think you know what this paper really does it provides you with closed form elegant solutions for an economy with two features number one input output linkages between production sectors and number two sector specific price rigidity and in this sense it makes important progress over existing work which until this point hasn't been able to characterize in closed form the dynamic impulse response of such an economy to economic disturbances and they look at the number of disturbances they look at the monetary shock they look at the markup shock a monopoly power shock and they look at productivity shocks which are perhaps the three important shocks center banks are also interested in in current times okay so this is very welcome work and then they show that these impulse responses are given by two sufficient statistics these are in fact matrices okay so two matrices characterized the dynamic impulse response one is very familiar because it's known from network economies with flexible prices it's called the Leontief matrix the inverse of the Leontief matrix and the other one is a new matrix and that's what this paper shows it's this square root of a stickiness adjusted Leontief matrix so it's again Leontief matrix but adjusted for some price stickiness and then you also have to take a square root out of it out of a matrix okay so then that's it okay and then this is actually a very very useful result for empirical work because it allows for a number of applications it tells you what you should look for in the data to understand whether inflation is going to be persistent or not and I think that should be of high interest to center banks and in my discussion I'm going to focus on this disturbance in which sectors are going to be persistent and what drives that okay so I'm going to do two things I'm going to go through the main analytic result and provide some perspective so there's a bit of a recap here it's a very beautiful result and then I'm going to look at sectoral origins of inflation persistence okay so they're really in terms of the setup it's very simple there are only four model objects and two prices okay and so the first model object is an input output matrix A of steady state input shares that tells you how much each sector is using as an input from another sector okay that's a very simple thing we can measure this in the data and this is effectively also defining the labor input shares because there's a constant return to scale assumption in the background so we have everything defined in terms of the steady state input shares so that's the first object and then the second object is a measure of price thickness okay that's a diagonal matrix theta okay which and the diagonal has just the rates of price adjustments in each sector okay that's the second object we need to understand we can also measure that in the data you can measure the price adjustment frequencies in the data and then we have the vector of household expenditure weights which is a bit of a side show okay because we're going to all we're going to all solve for the sectoral price dynamics and then we can use these expenditures what share of expenditures goes to which sector now from the household side to construct aggregate inflation and aggregate measures once we have solved all for the others but it really doesn't matter it plays no role in the solution okay that's great okay and then we have various shocks and that's the last ingredients these inflationary shocks be they a monetary shock a negative productivity shock or a markup shock of course they can also do the reverse but these are perhaps a shock set of interests at the moment okay that's it and now with this we can define the sufficient statistics okay the sufficient statistics are number one this Leontief inverse it's one minus the sectoral input share matrix inverse why inverse well because you know in these models it's a bit odd because you take something from another sector but that sector takes something from you and then it take it back and it all goes all all all roundabout roundabout to the infinity and then you sum it up and then you get to the inverse okay of one minus a to this Leontief inverse okay that's just you know what the network is going to do and what is this Leontief inverse relevant for well it gives you something like the impact effect of shocks in the flex price case okay it's well known okay and that's what this determines and then there's the second matrix and that's the new one it's again the Leontief matrix now not inverse multiplied by this squared price thickness matrix and then take the principle first principle root of this so it's a stickiness adjusted the root of a stickiness adjusted Leontief matrix and this is what's going to be exclusively determining the dynamics then okay given the price dynamics okay these are the two sufficient statistics to look at in the data okay according to this model and then there are two prices one is you know the vector pt of sectoral prices so that's an n by one vector that tells you at every point in time what is the price level in that sector and then there is this thing that drives everything which is a counterfactual price in a completely different world in which all prices are sticky and that world is hit by the same monetary policy and the same structural shock okay so it's a bit of a mystery how this other you know object is in this other world is going to drive dynamics in this world where prices are sticky and we're going to come to that okay so then we're going to look you know the main result is that most transparent actually if you look at two things namely a permanent shock okay so then the sticky price dynamics are very similar you move up or down prices in the various sectors by a certain amount and then they stay there okay if you have that permanent shock everything gets very transparent if you're then also look at the limit where you have no discounting okay where the discount rate is very small okay so that you don't get effects from pricing that just come because you value profits across different periods differently okay so in a sense the adjustment is fast relative to the discount rate okay that's fine and then you can look at the sectoral price dynamics and they become very simple okay so the we know what will happen uh under flexible prices under flexible prices prior to the shock prices are stable then they jump to a new level okay and stay there okay so we're going to have never inflation except in this one instance when the shock hits okay but that's not going to be true in the in the sticky price account because price is now going to adjust slowly and then there's going to be inflation and inflation is going to move over time and it's going to move according to this you know the level of the stickiness adjusted price matrix theta squared is the the you know diagonal matrix of price taken is squared times one minus a the leon tiff matrix and then what is driving it well it's the gap between the price level in the sticky price economy and the price that would emerge in this counterfactual economy okay which has reached already this new level okay and that's great it's a second order the differential equation you have the level of the price on the right hand side and then you have the second derivative of the price the first is the inflation the second is the change in inflation on the left hand side okay and this permits closed form solutions okay and now suppose we start in t minus one at the situation where the price in the sticky price economy is equal to the one in the flexible price okay and then in t equals zero we have this permanent shock that moves the flexible price up say okay so the delta zero is by how much you move the flexible price up what exactly is going to happen depends on the shock you're going to look at if if there's a monetary shock all prices will jump up by the same amount if there is a monopoly shock in certain sectors or productivity shock in certain sectors this is going to look very different across different sectors okay and then we can have the sectoral price response okay and the sectoral price response is going to be pt in the sticky price in economy relative to the initial level is going to be one minus e to the minus t to some uh-huh now this new matrix this new sufficient statistic matrix times the flex of the price response okay so what this going to tell you now is as you let t go to infinity this second matrix is going to be going to the unity matrix okay because of the roots all being positive there okay and therefore we're going to over time converge to the flex price okay that's what this says because the flex price you know is the flex price changes this delta zero and the speed is going to be determined by this matrix okay okay that's very nice initially of course if t is zero then you know we're going to not move on impact prices don't move in the sticky price economy it's going to take a little bit of time for them to move okay so now let's talk a little bit about the speed of convergence okay and and this is of course going to be determined by the eigen value eigen vector decomposition of this matrix okay so the speed of convergence depends on that in particular if you have shocks delta zero in the flex price world that generate deviations in directions where the eigen values of this matrix are very close to zero okay then it takes a large t to sort of get convergence okay so really shocks that move you know the flex price in the direction where you get very slow adjustment according to that eigen vector at that eigen value associated with that eigen value is going to generate persistent inflation okay and now different shocks going to have you know going to push the economy or the flex price response in different direction okay monetary shocks are going to move all prices okay and that's going to be a linear combination of these eigen values and then other shocks going to move them in different direction and in which direction they're going to move well it depends now on the leon tiff inverse okay that is going to be giving you the direction where this shock is going to be so here the leon tiff inverse is going to depend determine the impact effect of non monetary shocks and the root of the stickiness adjust the leon tiff matrix determines the dynamics in terms of the persistence okay speed of adjustment okay this philips curve is a little unusual okay because it has well it you know it has the change of inflation that's like the standard new gains in philips curve okay but then as forcing variables it has this price gap the price relative to the flexible price so let's try understand a little bit you know why it doesn't have the output gap there okay okay in particular it has these gaps relative to this counterfactual world where the why where the where the price is flexible okay so the reason is actually underlying this is that um we have um local linear consumption preferences which means that the wage has alluded to it is equal to nominal demand in terms of consumption units now and that nominal monetary policy determines this nominal demand okay so in the flex price world and in the sticky price world nominal demand is the same we keep the in both worlds the you know the counterfactual world we implement the same policy and therefore the nominal wage is the same so in both the nominal wage is the same so now think about when would you ever want to adjust or charge a different price in the flexible price in the sticky price economy than in the flexible price economy both have the same wage the only reason to charge a different price is because the other firms prices are different okay so you have basically a statistic that says the only way why inflation should move differently you know than there is because they charge other firms charge a different price so in this sense the flexible price and the other firms price in the sticky price economy are sufficient statistic to understand where inflation is going to move okay and of course this is going to be you know depending on that if you had different preferences then an output gap will show up and actually they show that and how that is then going to generalize okay okay so that is the reason why we have that now it also needs to be said that if you take a linear combination of these objects that show up here on the right hand side you know to take the household expenditure weight times the sector price level and the household expenditure shine away times the flex price level you're going to get the output gap there on the right hand side so in some sense you know there's something very similar to the output gap showing up plus a relative price term of course okay okay so now let's have a look at inflation persistence this is the formula I told you the eigenvalue eigenvector decomposition determines to and then the speed of convergence and then they show that the first approximation you can look at a diagonal economy where there are no eigen no cross-sector linkages and then introduce them via perturbation approach okay and that actually works very well numerically for the input output linkages in the in the US economy okay if you look here at the table you see on the right hand side the eigenvector that would come out of the eigenvalue that would come out of the full matrix if you look at the sectoral input output linkages in the United States and then what would happen if you do this approximation where you only looked at the diagonal entry of the input output matrix and at price thickness okay and these two things align very well okay so basically if you want to understand the persistence of the response in a certain sector what you should look at is the stickiness in the sector times the square root of one minus what this sector sources from its own sector okay that is a sufficient statistic for all practical purposes that's even simpler than the other statistic that is generating you know that's going to tell you is this going to be a fast or slow adjusting sector okay if you have a shock in that sector okay and it's you know this is a surprising result because you could think of many reasons why this may go wrong the eigenvectors look different the shocks you know all of these things you know could not work out it just miraculously does a very good job you can just look at the stickiness in this sector and how much of this sector sources from its own and that's going to work in a quantitative term okay now if you look at this previous thing if you look at this table and you look now at the leftmost column it actually turns out you know that because what a sector sources from its own isn't varying all too much in the end you know an even simpler approximation to whether a sector just fast or small is the price adjustment rate okay we knew that already okay but it generalizes here in quantitative terms to a sector to an economy with the full input output linkages so in some sense you know if you want to understand is a sector generating a persistent or a short-lived inflation response to a shock just look at the degree of price adjusting okay now the reason inflationary episode of course you know price stickiness appears to have shifted quite a bit in response to the shocks we have seen and the question then is of course to what extent this is really offering a reliable prediction as to whether this sector is going to display fast or you know long-lived price adjustment dynamics in response to the shock so I want to you know caution here a little bit this is a bit outside the framework if you want to apply this understand do we get persistent inflation response it probably want to also take into account that this inflation price adjustment frequencies could be shock dependent in particular in the response to very large shocks these approximations which are to first order may not work very well okay that's it I think it's a really insightful paper I enjoyed really reading it it makes significant progress in characterizing the dynamics in a network economy with price stickiness it's you know has great close form results and that guide empirical work on the one hand and going to be very useful for phd teaching going forward thank you thank you very much Klaus so the floor is open for questions was first Bartosz again please stand up Bartosz Machkovac ECB so in discussions of monetary policy there is often a tendency to focus on the slope of the aggregate Phillips curve and this is justified in simple sticky price models where monetary policy affects aggregate expenditure and then the elasticity of inflation with respect to aggregate expenditure is given by the slope of the aggregate Phillips curve so I was wondering if you could summarize what the kind of model that you work with applies or implies about this kind of approach to thinking about monetary policy um thank you and thank you Klaus for the great discussion so regarding the question I think one main insight that we can take from economies like this to the extent that we think heterogeneity in the production sector matters for the transmission of monetary policy this model is telling us that single dimensional variable like the slope of the Phillips curve can be a very misleading indicator of the transmission of shocks to aggregate inflation in the paper actually we discussed this I didn't present today but we have a contra example we construct two economies one of them has a steeper Phillips curve on the aggregate classically defined but the transmission goes exactly the other way that the steeper Phillips curve economy has higher monitoring and neutrality and more persistent inflation and the reason for this is those relative price gaps that I was mentioning that show up in a model with heterogeneity in production sector those relative price gaps play a very critical role in transmission of shocks to aggregate inflation that is ignored in the simple model with one sector okay next question no Georgia Prime Minister from North Wesson so you motivated the talk by showing the graph of the recent experience of inflation core there's also super core that gives information about what the elements really are fluctuating there and which ones are sticky but then maybe I got lost in the math but can we connect some of these results with that motivation is that what what we really learned about the last two years of inflation based on this model can you make that connection so what I wanted to motivate with that figure I wish I could answer like what like caused inflation and what we learned about inflation but we were very humbled by how much we didn't know as the authors of this paper so I'm gonna like tell you what I hopes to take away from that figure in the beginning how the theory connects to it and then how maybe we can move forward in understanding this so my core observation from those figures was that we had a setting in the last few years where monetary policy was dealing with the pandemic and later with this inflation so it wasn't a monetary policy that was following a single rule necessarily we were stuck in the zero lower bound for a while of it so like you know the monetary policy was accommodative where interest rates were fixed and then like we had a response that was based on the rise in inflation so we wanted to have a framework that like you know how different monetary policies affect the transmission the only the other core observation that I wanted to have from that figure in the beginning was that a core inflation um rose less and were much more persistent whereas headline inflation rose a lot and came down faster well generally our intuition supports that that notion that qualitatively this should be the case that headline should be more volatile than core but what really derives the distance between the persistence and the size of these responses and how it is affected by the network economy was the main question that we were going after and the way that theory connects to that is that eventually you can come up with this notion of network adjusted the stickiness that clause really summarized much better than I did that really governs that that difference so across these different sectors you can construct these different indices and that is going to according to theory determine exactly the difference between the persistence of core headline or any other inflation index that you want to create what's next maybe I can follow up on George's question which is um I mean we went through very large shocks and um so I was wondering what your view is on the importance of of these network effects when you experience actually very large shocks so just to give an example I mean you mentioned yourself watchmaking is a sector with a lot of price stickiness but as estimated over a period where on average there were small shocks I think you can make up many stories where on the large shocks even the watchmakers become more flexible and would that that imply that the importance of the networks actually would be reduced is that the right way to think of it I want to start with a disclaimer that I'm going to speculate because we were very much interested in understanding how big shocks affect the transmission and we were very humbled by how much we couldn't do in that area but I think based on some empirical work that we have done I think your intuition is absolutely right that let me recast your intuition in terms of services versus goods services generally has much higher stickiness in their prices than goods at least historically and what we have studied in the data and kind of seen based on some preliminary analysis for a follow-up paper is that if you basically use shocks to the oil industry as an instrument for movement and prices of different sectors before the pandemic or like in low inflation environments services good prices respond to inflation to oil shocks a lot which is driven by their like more flexibility in their prices but services don't really respond whereas in high inflationary periods where we think like these shocks are bigger or like you know prices are more flexible we see that even services start picking up so the gap between the response of sectors with higher and lower stickiness in normal times seem to like shrink in high inflationary periods and at least we know what happens in the limits right if the shock is really big everyone is flexible and then like everyone's prices go up by one by exactly the size of the shock now whether that is monotonic or not I don't necessarily know at this at this time Michael Michael Weber Chicago I was actually intrigued by your figure showing the negative correlation between the impact and the persistence and so like I want you to help me understand a little bit I guess it's the way the model is set up so you could also think you know that maybe kind of where you are in the production chain matters further upstream you tend to see like prices being more flexible versus further to end consumers you are more sticky and so like you know you could then think that indeed like you know it might take a little bit of time until you go further down and it then shows up and through like kind of the accumulation of price stickiness along the production chain in fact you actually inherently also bake in like I think what kind of uh uh frank smats calls like pipeline pressure along the production chain but given that the clouds nicely kind of illustrated this i minus a inverse given that it all happens automatically at the same time I think because of that partially and there's no no lacks in kind of that mechanism you don't get that but I was curious to see whether I get that right so so uh the figure that I showed you about the straight up was for a monetary shock so um we can see like that mechanism that you just described I didn't show today but it exists for the case of a sectoral shock so what what you have in mind is that a shock happens to an upstream sector that doesn't directly affect anybody else then of course even like even this theory like in spite of its simplicity would predict that you're not going to move your price until it moves along the chain and gets to you and that's like you can even get like if you look at the distribution of impulse responses of different sectors to and a sectoral shock to oil for example you will get these hump shaped responses downstream that are far away from oil the reason that the figure that I showed had that feature is because monetary policy this is like monetary policy is a hammer argument because like it affects the desired prices of everyone so you are directly affected by it equally like everybody else but if you're downstream you're also like you know waiting for the propagation to come down to you correct well thanks Hassan and Klaus please join me I'm thanking them