Well, many thanks, Fabio, for giving me the floor. And as theme for participants, Fabio, you left a very engaged audience. So I think that we are in for a good session. Privileged to chair the second session of this year's forum, which is titled, Assessing the Costs of Inflation. For a while, high inflation was considered a remnant of the past. Central bankers worry for a long time about inflation that was too low instead of inflation that was too high. How dramatically that picture has changed after the pandemic and the energy crisis, hasn't it? Inflation has been and will continue to be too high for too long, as the president of DCB reminded us last night. Central banks have responded forcefully to the surge in inflation by moving monetary policy from highly accommodated into restricted territory at an unprecedented pace. Central bankers are very much aware of the disastrous consequences of high inflation, especially to those people that have little income or little wealth to guard against it. We need little more to be reminded of the importance of delivering our mandate. That being said, the overall macroeconomic welfare implications of inflation shocks are not easy to assess and depend on many factors, the size and persistence of the shock, the way the economy adjusts, the way the burden of an inflation shock is shared. These are all non-trivial considerations for which we need economic modeling and research. In this session, we have a paper by Francesco Lippi, professor of economics at Lewis University, on exactly this topic. Professor Lippi is currently editor in chief of the economic journal, The Journal of the Royal Economic Society. He received his PhD from Tinberg, an institute, and I'm glad to be able to say that in Dutch, in Rotterdam in 1997. And he worked in the research department of the Bank of Italy until 2006. He's a research fellow at the Center for Economic Policy Research and a senior fellow at the I-now-the Institute for Economics and Finance. His research interests lie in the fields of macroeconomics and monetary economics. He has published many papers on the propagation of monetary shocks, technological innovation, and means of payments choices, and monetary and wage setting institutions. We start this session with Professor Lippi's presentation for about 25 minutes, followed by a 15 minute presentation by our discussant, and I will introduce you in a second chair. Next, we will open the floor for questions and discussion. And at that point in time, online participants wishing to comment or ask questions should be prepared to raise their virtual hands. The online participants were not participating in the discussion in the former session, but please be aware that you are allowed to pitch in as well. But first, let's start without any delay with your presentation. Professor Lippi. All right. Thanks a lot for the invitation.  What I'm going to talk about today is joint work with Alberto Cavallo at Harvard Business School and Ken Miyahara, a very bright student of mine at Louis University. So we're going to do two things in this paper. We analyze with some humility two very difficult questions. The first question is about the propagation of a large-cost shock. So I'm putting myself in the shoes of a firm that in 2020 and 2021 witnesses these very big increases in the energy prices that have been recorded in Europe and has a problem, has to set prices and finds itself with profit margins that are shrunk. So somehow something has to be done. So the paper is going to have two angles. One, a question about the propagation, how those shocks propagate. And the second one, what are the welfare costs that this big shock brings about? Now, this is going to be particularly narrow. I'm going to develop the analysis using what I would say is today's dominant paradigm in monetary policy analysis, the New Keynesian model. Alternatives might have been followed, perhaps. They'll come up in the discussion. But I'm going to do my analysis within the framework of the New Keynesian paradigm, because it is, in my view, by far the dominant paradigm through which monetary policies are studied in central banks. The whole ideas of forward guidance, Phillips curves, they rely on simple models where firms' prices are sticky. They are not where they should be in an ideal frictionless world. And these stickiness create wedges. What in my notation is going to be a PI, the price of firm I, which is not equal to PI star, the ideal price. These wedges, the bigger they are, the more misallocated resources are. Ideally, we'd like to measure them. Problem is, we don't really observe PI star, so we have to come up with some tricks. Second, why do we have sticky prices? Well, the assumptions in this model is that resetting prices takes some resources. Firms have to dedicate resources to the price setting activity. And these resources are a bit of a waste, much like the shoe leather cost we had in the old money demand model. So we're going to measure both distortions using a simple model. And as I said, the third experiment is we'll write down a model for the steady state for the tranquil decade that preceded the big energy shocks and then use the model to answer the question, what happens if we hit this economy with a big energy cost shock? And one challenge for us is going to select a model out of the large classes of models that can be written down that is satisfactory in terms of fitting key patterns of the data. So let me review quickly what are the key patterns. This one, we can go very fast. Everyone knows on the left panel, you see the big increases of energy prices in Europe. Depending on the measure you take, we could say it's something between 100% and 200%, which my rule of thumb is going to be, as I mentioned, I'm going to give a simple model. So I'm putting my reputation at risk here. I'm going to embrace a simple model and take it seriously. And I want to think that firms' marginal costs of which energy is an input shoot up by something like 10%, 20%. Firms had to do something. So what did they do? This is a picture constructed on granular data provided by PriceStats, the billion prices project that Alberto was a pioneer of. So what you see before 2022, this is a picture for the sector of food and beverages. You see that firms in several European countries in the food and beverage were repricing between two to three times a year. There's some noise, but it's roughly stable. Frequency of price changes was stable. We were living in a rather stable environment. Then the big shock comes. And what you see, you see an explosion of repricing activities between two to three times. In France, the average number of price changes goes from 2.4 to five or six. And similarly, many other countries. Now you might think this must be something special with food and beverages, which indeed are somewhat special. Now this is a graph I took from a monthly report by the Bank of France where you see this is for old sector, it's not just food and beverages. And the blue line is the industry. The orange line is the services. Now this is also witness to the input-output linkages that have been mentioned before. Things first happen in industry that then transfer to services. What you see once again is that on the vertical axis you have probabilities. So there was an average one price change per year in these industries and following the shock, it jumps up to like two times that or three times that. So we want to have a model that will capture this because it is a big thing in the data that following a big shock, firms are more active. So what I'm going to do, I'm going to write a simple model. This is the only slide that's gonna have something like an equation that is scary looking but it's underlying my sort of reasoning and putting some discipline in what I'm going to do. So what are the essentials ingredients of this New Kenger model we write down? And the details are in the paper that is posted on that. Firms, a firm I is trying to control this variable X. It's a gap between the actual prices they have and the ideal price they would like to have. This ideal price P star is pushed around by idiosyncratic shocks in normal times. If you look at what firms do in normal times, let's say the decade before the shock, sometimes they have big price increases, big price increases. We're gonna think of these idiosyncratic shocks that hit firms, that's a sigma, that's a sigma that you see there. But then in my thought experiment at some point there will be a big, large shock that hits all the firms and everyone's marginal cost will go up. That's the energy shock. That's common to everyone. That's why it's an aggregate shock. Now what do firms do? They solve a complicated problem that I took from Caballero and Engel but in the end it boils down to a very simple idea. Firms have to solve a problem. Prices are sticky, what does it mean? That blue and red object there is the cost for the firm in terms of foregone resources, foregone profits of controlling their prices. They have to hire someone, their marketing guys, their statisticians say okay, tell me what the right price should be, tell me what our competitors are doing. So we're going to parametrize that model in a way that captures aspects from the data. And why are the firms wasting these resources because they want to have a small X. They want to keep X as close as possible to a good value. This boils down to something like this. The model produces this V-shaped blue function. It's a function that has a very intuitive explanation. It's telling us what firms, the probability that we observe a price change. How does it work? Well you see the function has a minimum at zero. At zero, firms are happy with their price. P is close to P star. Now the more P deviates from P star, the more firm is unhappy and it spends more resources such that a price change will occur. Now it might seem totally natural to you. Typically we tend to invest more energies into something that is more important to us. It's basic cost-benefit analysis. Yet I must mention that the textbook version of the sticky price model we use and that I see in several papers is a model that is totally oblivious of this point and assumes that price resetting occurs with some time-dependent probability. Think of tailors, 1980s, you know, you reprise every T-period or maybe the recent Calvo version with which with some probability you do something. Now that seems like a very bad description. You don't tell this to a businessman because that's not what they do. They think about things to do. Anyway, let's keep that in mind because we're going to use it as a benchmark. Now one nice feature of this blue line is that we see it in the data. Several people have tried smart ways to measure P and P star and come up with estimates of probabilities to see a price change. And those V-shaped patterns you see in these three graphs come from different papers and they provide us with strong evidence that behavior is, as we say, state dependent. That the probability to observe a price change depends on where the firm is. Now why does it matter? So ideally what we would like to measure, remember, each firm has an X. So this F of X is the cross-sectional distribution of the X's. Ideally, I, Francesco, want to know how efficient is the economy. I want to go out there and measure all the X's. I want to learn about F of X. F of X is not really directly observable. So we have to come up with some tricks to measure something like the variance of F of X. Jordy has a very nice paper where it shows that the consumer's welfare is approximated up to, first of all, by the variance of those X's. So how do I measure F of X? Well, you know, I have lambda. I have a composition of these two functions gives us something observable, the distribution of the size of the price changes. It's those blue histograms you see there. The red curve you see in the first one on the left is the prediction for the size of price changes in my model and the rest is just data. So some things are intuitive, you know, there's very little tiny price changes. Well, there's no reason to have a price change when your price is close to the good one. There's both very big positive and very big negative price changes that's because of the idiosyncratic shocks. So these are data that we calibrate the model with using three, sorry, these are building blocks of the model that we use to calibrate the model using three different data sets. The first one is this very granular, very high frequency daily, actually. Two of them beverages sector that comes from the billion prices project. And what we're going to measure, we're going to measure standard deviation of the price changes. That's gonna be a proxy for the idiosyncratic shocks, the sigma I mentioned before. If you see an economy where the standard deviation is large, it must be that those firms are hit on average by big idiosyncratic shocks. Big positive, big negative. Now the frequency is a natural measure of how flexible the economy is. If you see an economy where everything happens, reprising is very high. It must mean that maybe the cost of reprising is not so high and firms are happy to do it. Kurtosis is a measure, I should have mentioned it. When we look at these distributions, I want to get some information on how thick are the tails of the distribution. If I have a distribution with thick tails, it means that I have some agents in this economy whose gaps are really big. Big positive and big negative. That's gonna be bad news for efficiency because the costs are non-linear. So having some extreme outliers there is gonna be costly for our economy. So I take data both from the price stats data, from recent analysis for the Euro area. In particular, the data that appear in the bottom panel are data that I obtained from Erwango Tie who coordinated the Prisma data project at the major project using CPIs. There's a big difference between those data and the one in the first row, the CPI data are obviously more encompassing. Yet, if you eyeball those numbers, they're not incredibly different. The thickness of the tail is roughly close to that of a normal. The frequency for the overall price index is kind of lower. It's one price change per year on average. So what do I do with this data? Well, first, I come up with an idea about, okay, how can I measure, remember, I want to have some information on the variance of X that object you see there. Now, that first equation, there is something that people in my profession consider a synonym of beauty because it's an object that allows you to map something unobservable, the variance of X, into something observable. And what's the idea? The idea in the end is very simple. So the first formula, the eta divided by two times the variance comes from Jordy's approximation of the consumer's representative utility. Now, why is the variance proportional to those red objects on the right? I already mentioned a large variance of price changes means that we are looking at an economy in which when we see an agent taking an action, he does something big. So doing something big on average, that's what the variance is saying, it means that on average, you're far away from where you want to be. So that's bad news for the welfare. It means variance is high. Now, for a given variance, kurtosis means that you have more agents in those stales and that's also gonna compound to the overall welfare cost. Then the model also allow us to quantify how big are the resources that firms employ in this wasteful price management activity. So when we apply this to the data and here for simplicity, I'm just using the Prisma data in the paper we have several countries, what we get is that the misallocation cost, they express in terms of as a fraction of consumption, the misallocation costs are quite sizable. They amount in the steady state. This is before any shock occurs. I haven't yet told you like the interesting part of my story, but it's like 1.5% of GDP. And the price management costs are about 50 basis points. So overall, the simple model, which has many caveats and I'll be happy to discuss them, is suggesting something like the welfare cost because of these sticky prices. This is really what is causing these wedges are not negligible. They're in the order of 2%. So what am I gonna do now?  A shock, what a shock does, you remember this blue distribution this depicts how the price gaps were distributed before the shock. Now the shock shifts the distribution.  In the picture now you see a small shock. Why small? Well, I shifted just by 2%. But the energy shock I claim was big. Big, I mean this, small, big. What happens when the shock is big? Notice the dashed gray line in the background that's reminding us of the state dependent policy, what firms want to do. Now that you have a lot of firms in the red histogram, there are many firms that are sitting on top of a very high reprising probability. That's a V-shaped gray line. So what do you expect? You're going to see a lot of reprising. You can't get that if you're reprising really flat constant, okay? That's obvious. So here's what we get. Large shocks are different. This has been said many times today and I would give you like what I think is strong evidence in favor of that. This is a theory experiment in the model but we saw the data before. So look at the red line. There's like a constant, this is for the, again, the food and beverages. There's a constant reprising at 2.4 price changes per year. Now if we hit the economy with a small shock, you basically don't see much because the shift is small. And so the Kalvo model or this rule of the models, they're good for tranquil times. They work in tranquil times. But when a big shock comes, what the model predicts is that you're going to have an explosion of price changes many more and that cannot be predicted by that model. Now we could say, okay, who cares?  You can fight guys in the back room but I think it has a policy implication and let me get to the policy implication. Let's take an economy where the price is going at 2% per year and then hit it with a shock, the cost shock, that raises by 20% the CPI. You know, 20 is just a random number, that's it. So flexible price is what you would see. You know, it's an immediate jump. Costs go up, market pricing prices go up, that's it. Now what happens if I am an economist and I'm using, I'm predicting what is going to happen using one of those time dependent models that forgets to take into account the fact that, you know, firms respond to the state. I'm going to draw a line like this.  If I'm using a model where half of the firms are just every year, you know, it will take two years until everyone has adjusted. Then that's it. Now, but remember, this is a big shock. So the state dependent model is going to give us a very different behavior. Both models are going to get to P star in the long run. They have to, that's what they're doing. That's not surprising. You know, eventually every model gets to the higher P star. The question is, how long does it take? Now the state dependent model gets there much faster because the shock is big. Everyone is rushing to put the house in order and everything washes out more fast. So why is this interesting? Well, the slopes of the blue and the red line are inflation rates. So if I live in one of these economy and I just look at the inflation rate, remember these inflation rates compound over the two years to the same inflation rate. But in the blue economy, what I will claim is the right one, you will have a lot of front loading inflation, a lot of price changes everywhere. And then calm. If you're using a time dependent model, you're gonna underestimate the inflation increases initially. You end by necessity, you're going to over estimate the speed with which inflation will come down. So I think this has some policy content, you know, in spite of the simplicity of the model. If I was a policy maker, I should keep that in mind because it has a simple implication for the time profile of a big shock. Now, I motivated this paper with the idea that I also wanted to measure what happens to welfare in these models. And as you remember, welfare has two components in this model, one, the sky, the misalocation, how dispersed are the gaps? These are models where essentially you don't like price dispersion. Price dispersion is a symptom of inefficiency as it often is in our model. So what happens to price dispersion? Well, following the big shock, with the small shocks, those are the red lines, not much. You can forget about thinking of small shocks and asking questions about welfare. They're not important. There's some technical reasons why, but I'll skip them. Essentially, they have to do with the fact that these are even moments and even moments don't respond to small shocks. But the blue lines are depicting a large shock. So what happens with a large shock? Well, right after the large shock, all firms are just shifted down. Many of them reprise and they have right now a very high price. So think about the cross-section in this economy. It's an economy where the price distribution fans out and that's not efficient. And until time goes by and everyone has reprised, you have this pattern for the blue line that misalocation first increases and it's gradual because it takes time for, as some prices change, some prices are high, some prices are low, that's inefficient. And the right panel is showing you the price management cost. These exceptional reprising activity by our assumption is costly to the firms. So firms have to dedicate resources to fixing this problem. So if we want to come up with a number and I compute the present value of this cost, this cost is at every point in time. So if I compute the present value relative to consumption, I come out with pretty big numbers. The estimate for the Prisma data, so CPI-wide of the misalocation cost, this is like present value, are in the order of staggering 1.5%. This is an additional cost on top of whatever was the inefficence in the steady state. And likewise, a similar magnitude is attributed to the cost of the price management activity. These reprising activities by firms are very costly. Now these numbers, of course, I take them with two grains of salt. They depend on my assumptions about elasticities. I'm using demand elasticity of six.  You may notice that the bottom line for the food and beverages data has much smaller costs. And that's because that sector is a much more flexible price sector. It's a sector where reprising occurs more frequently. So the model is telling us, for these agents, the price management costs are not so big on average. So everything can occur through more smoothly. Okay, so I guess I can sum up my job. So I focus on two questions in this paper. The first one concerns the dynamics, the propagation of the shock. So last night, Gita mentioned Godot. We're all waiting to decide whether or not we'll come back. I think we sort of go one layer down and try to understand how Godot moves about. What transportation he uses and information on the means of transportation may tell us something about the likelihood that he will come back. And I think our guess is that he will arrive, unlike in the play, because we do see, with our real-time data, we do see that the frequencies are coming down. So the storm seems to be passed. I agree with what Daniel said in the previous presentation. In fact, you know, in my stylized presentation, I am not sure if I'm going to be able to do that, I am standing at once and for all shock where the price of energy goes up and stays there. But of course in reality, it has come down. And one can easily use the model to do that. It's a bit more complicated and I do think the model has a mechanism for generating asymmetries. In particular, the distribution of the price changes that firms face when the negative shock arrives. It's very different from the statistic one. So that might give you, I don't know where Daniel is, that might give you some mileage to answer that question. But so what we are trying to do is there is a policy insight that the data show very clearly and that simple theory suggests large shock travel fast. I think it's wrong to use old Phillips curves, either you know, call them linear or call them calvo in those situations, because in those situations, the economy behaves very differently from what it does in normal times. Now the second point of the analysis was an attempt to quantify the welfare cost within the New Keynesian framework. It was surprising to me that the number that came out were kind of big. To me these are big numbers. I used to work on the old money demand estimates and there you have to really struggle to get welfare costs of a 10% inflation, of reducing a 10% inflation to zero in the order of 1%. You really have to push it to think that money is a very broad aggregate. And there are some beautiful papers by Bob Lucas and Stan Secher trying to take seriously some simple public finance model to answer these questions. Well somehow it turns out that in this New Keynesian framework, the costs are bigger. I don't know if this speaks about, maybe the framework, we don't believe it, or really these costs are very big. There are many extensions that one could do to improve the analysis. First one of course to consider more realistic path for the shocks, adding sources of stickiness and other sources of heterogeneity that may matter like financial constraint, et cetera. But let me say once more, to me, I'm all for adding financial frictions, heterogeneity, stickiness here and there, but to me what a monetary model cannot miss is a firm deciding about what to do with its own prices. I just cannot use a monetary model in important times that assumes that firms are waiting for a lottery or a ferry. To me that's really, when I was a kid I used to say I wanted a compass on my board and you know, it was expensive, I put a fake compass and the fake compass worked in the port but it doesn't work if you're sailing so we shouldn't use a fake compass, thank you. Thank you, thank you very much Francesco. I was going to compliment you with your wonderful time management but then I saw that you were one minute over time so I'm not gonna do that now. So thanks a lot. And before opening the floor for general comments and questions I will now move to our discussion. Let me introduce Sharon Kozicki who will deliver the discussion. Sharon is the deputy governor of the Bank of Canada since 2021. She shares a responsibility for setting monetary policy and overseeing the bank's activities in the financial system. In an earlier capacity she led the review of the monetary policy framework for the 2016 renewal of the bank's inflation targeting agreement with the government of Canada. Sharon, we look forward to your discussion and you have a full 15 minutes. Well good morning. I'm pleased to be here with you today and very thankful for the opportunity to discuss this important research by Alberto Cavallo, Francesco Lippi, and Ken Miahara. Their paper, inflation and misallocation in New Keynesian models makes two distinct contributions. First, they argue that understanding inflation dynamics requires a model of the price setting decisions of a large number of firms. The model they build is very successful at capturing the state dependence of the distribution and frequency of price changes. Second, they provide estimates of the welfare costs of inflation and their contributions give us a deeper understanding of the cost of price setting and how these costs may depend on the level of inflation. However, there's more to welfare costs than the model can explain. And in my comments I'll talk about some additional factors that are important to understanding the costs and welfare costs of inflation. But first, I'm gonna offer some views on the costs to firms of price setting. So observation one, price management activities are always part of doing business. Price management always incurs costs and these costs are higher when inflation is higher. New Keynesian models have tended to assume that prices are fixed at a fixed frequency or with a fixed probability and with fixed costs of changing prices. And these fixed costs of course only incurred when the prices are actually changed. But ultimately, activities related to price setting will always incur costs even if the prices themselves are not actually being changed. So a 2004 study by Zbaraki, Ritzen, Levy, Dutta and Bergen looked at a large US industrial manufacturer and its customers. It found that businesses face a variety of costs when they set prices, their physical or menu costs, managerial costs such as information gathering, decision making and communication and customer costs such as communicating and negotiating prices. Now, while menu costs are most directly tied to price adjustment, these are not the most significant costs. Managerial costs are more than six times as much and customer costs are more than 20. In total, the price adjustment cost comprised 1.22% of a company's revenue, a little more than a fifth of its net margin. Now, that study was looking at an intermediate goods producer, but it does provide concrete evidence that price management activities are part of the ongoing costs of doing business. Macroeconomists should have taken note long ago and I applaud Cavallo, Lippi and Miahara for having done so. I very much liked their model and their use of micro data. By allowing firms to choose how much to spend on price management as a model, on price management as part of their profit maximization problem, their model can evaluate how these costs and the price setting behavior firms may change with the state of the economy. This also helps us develop a fuller understanding of the mechanism behind the propagation of economic shocks and their analysis shows considerable state dependence and price setting decision with higher inflation accompanied by higher costs. Importantly, these higher costs can be thought of as implying lower productivity, which means they will weigh on consumer welfare. And they've illustrated why large shocks are passed through to prices more quickly than smaller ones and this result is clearly important for monetary policy. Now, before moving it to a discussion of additional factors that are likely relevant in assessing welfare costs of inflation, I would like to make one additional point. Now, in a flexible price environment, the efficient or desired price is actually an artificial construction. Don't get me wrong, it's very meaningful in models. Just maybe a little less so in the real world. In New Keynesian models, efficient or fully flexible prices play an important role in how we evaluate the welfare costs of inflation. The efficient price is the optimal price that a firm would choose if there was no price stickiness. But prices can never be totally flexible and as I've discussed, setting them always incurs costs. As I've been discussing, in the real world, businesses need to allocate resources to optimizing prices and there are inevitably costs associated with doing this. In a recent Liberty Street Economics article, Bruin de Bruin, Dougra, Heiss, Notek, Meyer, Rich, Shondli, Topa, and Vendorclaw reported survey results about the factors that influenced firm's price setting. Firm's reported that the strength of demand was the most important factor and while labor costs and steady profit margins were also very important. The overall rate of inflation also made the list. Many of my view, many of these factors could be seen as relevant for determining the efficient or desired price in a flex price environment. Not only for determining where to set a price relative to that efficient price. Thus, rather than using so-called efficient prices as the basis for cost analysis and welfare calculations, my recommendation is to compare costs across states. And my interpretation, this is exactly one of the things this paper did. It provided model-based evidence that both the costs of price management activities, sorry, model-based evidence that the cost of price management activities are higher when inflation is higher. But there are additional costs to inflation besides those related to price management. So, observation number two. Households always spend time or money to plan, budget, and shop. And these costs are also higher when inflation is higher. Businesses' costs of price adjustment are certainly not the only factors to consider when examining welfare costs associated with inflation. In economic models, consumer welfare is a function of the present value of current and future utility of consumption and leisure. And it captures the tendency of consumers to prefer to smooth their consumption over time. So in examining the welfare costs of inflation, what happens to wages and leisure matters as well. So I'm gonna talk a little bit about these. So, this is a rather busy chart, but all it's trying to show is different trends in price setting. Why? Because in most cases, consumers are taking prices a given and they're allocating their income to consumption and savings. Their consumption of specific goods and services is gonna depend on their own preferences and relative prices. And in general, these relative prices are different than those in New Canesian models. Over the long term, prices of individual goods and services follow very different trends. And these trends are dictated largely by the underlying productivity trends. Over the short term, some prices can be quite volatile, especially prices of food, fresh food and gasoline. Now, consumers might not like having to deal with these types of price movements, but they do adjust to them by allocating time to budgeting, planning and shopping. They look for good deals and change their consumption patterns depending on how the prices of various goods are shifting relative to each other. So let me move on. Recognizing that consumers make spending decisions all the time in the face of prices that move around and with diverging trends. Ultimately, it seems that to them, it doesn't matter so much whether the prices are high or low relative to the efficient price. It matters whether they can afford what they're used to buying. Thus, where there may be some misallocation associated with price stickiness, it's also likely that wage stickiness is gonna be a big issue for consumers. And especially if wages are stickier than prices. Now, Druant, Fabiani, Kezdi, Lama, Martens and Sabatini examine a cross-country survey, this is over Europe, and found that firms tend to adjust wages less frequently in prices. So if we think about firms changing prices every year or less, about 50% of firms, 75% of firms, it's going to be less frequent than a year in terms of changing their wages. So this matters because when we're talking about those implications for welfare, when wages are not rising at the same rate as prices, then you're likely to start seeing more people hitting up against some of their budget constraints. Real wages in the euro area have been declining year over year since 2021. So more people are likely to be finding themselves to be liquidity constrained. I mean they're spending all of their money right now on their goods and services. In other words, when an increase in inflation leads to real wage declines, fewer households will have the flexibility to smooth their consumption, and this reduces consumer welfare. Inflation imposes additional costs on consumers. So the costs I'm gonna discuss now are, again, on top of the costs that firms are already incurring to set prices. And I'm gonna give you a few examples just to try and build some intuition. Doesn't matter so much if you can see the charts in the table, I realize they may be small. So the chart does show survey results for consumers in Germany from earlier this year. Now across income levels and household sizes, consumers reported they were changing their purchasing behavior due to higher inflation. This includes actions like buying cheaper products, which are often lower quality or embed fewer services. They're using vouchers or coupons which require time to research and organize. And they're cutting spending on some services such as subscriptions. So again, people are accustomed to seeing price changes from day to day, week to week, and month to month. And they know they need to spend time looking for the best prices across different retail outlets. But with higher inflation, they face more dispersion across inflation rates of goods and services. And they also increased price volatility and greater uncertainty. So consumers need to spend more time to do this. This comes at their expense of their leisure. Or you can think of this as, if consumers have a productivity function over leisure, it's a negative productivity hit on the production of leisure from hours not in work, right? So if consumers are allocating more time and they have less time for everything else, again, their utility goes down. If they buy fewer goods, their utility goes down. If they work more so they can pay higher prices, their current leisure and utility goes down. And if they save less or borrow more, their future utility could go down. All of these are welfare costs. So now perhaps another way of thinking of these costs is as cognitive costs, as in the recent article by Agarwal and Kimball. They used consumer confidence to measure such cognitive costs as they called them and found that between 1980 and 2021, higher inflation is associated with lower consumer confidence. The bottom line is this, just as firms need to allocate time to price management and consumers need to allocate time, effort and funds to planning, budgeting and shopping. Sorry, just as one, the other. These factors are generally not modeled. So they're not usually considered when we're looking at model-based evaluations of the welfare costs of inflation. Finally, observation three. Financial system participants always have to manage risks. With greater uncertainty when inflation is higher, costs of managing risks are also higher. So same sort of logic here. We need to be thinking of the cost to inflation to individuals and businesses. We need to consider the financial sector. Now this is an inflation chart. It's actually inflation rates across CPI components in the Euro area. The point of this is to show that from 2019 to 2022, this distribution of inflation rates across components shifted to the right and got wider. So not just higher inflation, but more differences across the inflation rates of the components. And really, I'm just using this chart to show an indication of greater uncertainty that has come with the higher inflation. But frankly, we can look to the session that we just had on the services costs to understand how there has been greater uncertainty in the current period with these larger shocks. So again, more generally, more uncertainty, increased uncertainty impacts the economy. It could be a single household considering a major purchase. It could be a business contemplating a new investment project or a financial institution that's considering whether it should lend to them. So again, I don't wanna spend a lot of time. The logic's similar. Greater uncertainty forces all economic agents to put more resources into risk management. And in addition to risk managing risks, the possibility of tail events increases. And these issues are particularly relevant for financial institutions. You know, to make this concrete, higher inflation can lead to higher inflation risk premiums and bond yields resulting in hiring borrowing costs for governments, businesses, and households. So let me just conclude. Inflation is costly, but not just because price dispersion may increase. Higher inflation tends to raise price management costs for businesses and reduce productivity and consumer welfare. Higher inflation tends to raise planning, budgeting, and shopping costs for consumers and reduces consumer welfare. And higher inflation tends to increase uncertainty, raising costs of risk management. So price stability is important because it really is a key ingredient to a prosperous economy. Low and stable inflation strengthens competitiveness forces in an economy and allows households and businesses to plan and invest with confidence that their money will hold its value. Thank you, Sharon. So before I open the floor, and there is an urge to intervene, I've already noticed, so some people have already asked for the floor, so I'm building on a little list here. And I am also, again, welcoming any questions from those who could not join us here physically. But before I do that, Francesco, maybe you want to take the opportunity to respond to Sharon. It's almost a court case here, and a reply and a... Thank you, it's my pleasure. First of all, thanks, Sharon, for the kind words about the paper. It's a simple model, and I agree with you there are more wedges that one can think of. Certainly, I hope it's not the way that the paper comes through that we do an estimate of the overall cost of inflation. It's just a niche attempt to zoom in one particular, but very prominent view of prices and money and interest rates that we have out there. I agree with you about these other wedges. There are important consumer expenses, these additional searches for bar gains and the changes in behavior that we have actually, we know a lot about. There's a lot of documentation about how in recessions or after big shocks, less well-off consumers spend time looking for bar gains, et cetera. They also have associated welfare costs that would be great to understand. And likewise, I think in financial services, I think of an old paper by Ayagari Brown and Svixtin, probably in JPE, where they studied the cost of inflation as inflation creates a needs for some social insurance. Everyone is trying to pass the hot potato to another guy, and this is great for financial intermediaries that thrive on providing not such a great service. I mean, society would be better off without this intermediation. In the end, someone has to bear the grant of the inflation tax. And that's, I'm all for these models. It's just that for today, I had something else on the menu, but thank you very much. Thank you. Thanks again. So I'll first give the floor to Governor Francois Villoreal de Gallo. And no need to remind anyone that the questions should not exceed one-and-a-half minute. No, thank you very much to Professor Lippie for putting such slides on the relation between firms' behavior and macroinflation. And thank you, by the way, for quoting Bank de France data and Bank de France work. And one of the lessons of the Bank de France graph you showed is that the frequency of price adjustment has decreased very significantly in the latest month, which is encouraging. But this brings me to my question about the symmetry of adjustments. Apparently, in your model, be it the blue or the red curve, price adjustments are symmetric. And we could think that when price go up, it's easier for firms. When prices have to go down, they are a bit slower. This is all the debate about margins. So could you test in your model an asymmetric stickiness of prices? And this is a key question for us forecasting inflation in the present situation. And very probably, if we introduce asymmetric stickiness, welfare costs are significantly higher. Thank you very much, Francois. Maybe we take two questions. So I'll go to Ignacio Fisco, the Governor of Bank of Italy, and then to Oscar Arte, but maybe after Ignacio we answer and then we go on. And maybe a microphone. Well, thank you very much. Thank you. Well, I'm not going to say anything about the MISA location because we have really to study whether the quantification makes sense. But since that from what you have shown us, we may have some conclusions on the statement that inflation is being too high for too long. I'd like to understand what you think about. Basically, you seem to say that the size of the shock implies a higher frequency of responses and a quicker adjustment of prices to the increase in marginal costs, total costs. This produces higher inflation than in normal times, the ones before 2022. That is in our language. The pass through of the increase in energy costs is much faster now. The implication may be that had we not taken this into account, we would have been under predicting the actual increase or stickiness if you want in core prices. And secondly, I think Francois hinted to that, what would be the implication for the downwards. Daniel Gross showed us that terms of trade have moved dramatically upwards and now downwards. So the symmetry of the adjustment might imply that we risk to overpredict the inflation level, core inflation in the future months if we don't allow for the nonlinearity you were mentioning. Final point has to do exactly with this nonlinearity. We have been talking very much about profits. Now my understanding is that profit margins in this case more or less over a time period are constant except now increase more and they will be reduced later. This implies that there is now sufficient profits to absorb the increase in wages that are currently predicted. Thank you. Thanks a lot. Why don't we take the two questions, so the questions from the two governors and then we continue, please. Very challenging. So let me take them in order. To the Banque de France governor, yes, first I agree we see in the more recent data that those frequencies are coming down quite fast. We also see it in our own data, in the price stats data that the frequency of repricing is going down very fast which to me is a very positive signal in terms of inflation expectations. I expect inflation expectation and here I connect with the other to go down much faster than we think. Just like this model is suggesting it went up faster than a simple rule of thumb would have told me. And look, I'm not trying to teach anyone's job. I mean, I want to be very modest. I know these are super difficult things. It's easy to do it within a simple model where everything is understood and make this statement. But my view is that there is an element of reality in noticing that when these large shocks occur everything happens faster and this seems to be a natural consequence. So as Iñatsu said, the faster is gonna be faster so there is a risk to under predict initially and then to miss the slowdown that's going to come. That's what the model would suggest. Now, I think both of you also hinted at one question about yeah, but what happens if then prices go down, the asymmetry for instance. Now again, I haven't done the exercise. This was already quite a challenge for us doing all these things, but certainly the model can give us some guidance. So my guess is the following. First of all, a little more realistic model would have firms worrying not just about their marginal cost but also about the price of the competitors. So right now you have a situation where a lot of firms have high prices, some still have to reprice. Firms don't like to have prices too different from their competitors. So that's an element of slowing down. My guess is that eventually, if you remember my picture with the line of P growing, then jumping up, then the ideal price jumps down. I think the actual prices will land on that curve. I think it's unlikely that we see a quick and deconstruction of the price increases that we've seen because price changes are costly. But the model will predict that in the medium run, the prices will return to the regional baseline. And I think I agree with Ignacio. Also profits in these models where stickiness gives an element of investment to prices. They are high initially, but then you know that eventually they will be low, so your profits margin are going down. So the right measure of profits is not profits now, but it's kind of some average measure. And so I guess that on average, these things will balance out. Do you think you would ask the chair? Quickly, I think in terms of thinking of whether there's gonna be a symmetry going down, we need to not think about the symmetry in inflation or in price space, but the symmetry of what could have been driving the inflation. So that if there's a symmetry on the downside to what we saw on the upside, then we're more likely to see the symmetry in the inflation outcome. And I raise that because on the upside, we had very strong demand simultaneous with cost shocks and supply disruptions. And in some countries that means estimates of the Phillips curve have steepened. Well, on the downside, what if we don't get all three of those reversing? What if we only get a fraction of them? Then we're less likely to see the symmetry on the down that we saw on the up. And that's in addition to all of the potential pass-through discussions that we had in the first session. Thanks a lot. I'm aware of the time. But we started a little bit later. I don't know why. So I think that I can allow for three more questions because I have three more people on my list. So Oscar Arce is one. The gentleman sitting behind the governor of Austria, Holtzmann, but I couldn't see you well. And then we will end with Silvana, who also has for the floor. So maybe all three questions at the same time and then we wrap up. Oscar. Thank you very much, Oscar Arce, from the ECB. Thanks for the presentation. I mean, I fully agree with the idea that the state continues in pricing. It's absolutely critical at the current juncture. Let me share with you a very recent result produced by the ECB staff. I mean, my colleagues find that, for instance, following a large shock to gas prices, the pass-through on core inflation is significantly faster and larger than if the stock were to be smaller. So this matters a lot in the current juncture. But of course, the other important element as emphasized by Governor Viscou and Viderois is asymmetric behavior. Now, here my specific question is whether you think that this time may be different in the following sense. I mean, all this evidence that you saw us before, 22 before the COVID, corresponds to an economic environment in the Euro area in which wages did not react almost at all to any kind of shocks. I mean, wages were completely flat over the last decade before the COVID or so. This time, we know it's different. They are, wages are reacting quite strongly and they are expected to grow persistently at relatively high rates for the coming years, as emphasized this morning by President Lagarde. So intuitively, one would tend to think that this strong growth of wages will limit the space of firms to moderate the path of inflation. Even if they are going to absorb part of these increases in wages through lower profit margins. So my specific question, I guess fits very well with the previous two questions, is whether you think that this time, given this reaction of wages, this symmetric behavior that was detected in previous data is going to hold or not. Or we face the risk of finding a more persistent disinflation process than if we were to estimate it just based on past regularities. Thank you. Yeah, so Harold Ullich from the University of Chicago. Thank you, Francesco, for the beautiful analysis. Emphasizing state dependence makes a lot of sense. Now, to put it more simply, consider a state dependent model where firms adjust for sure if the deviation from its ideal price is large enough. And indeed, as you argued, why would they not? In such a world, all firms would adjust after large shocks. The welfare cost of price dispersion then goes to zero rather than shoots up. So it seems the welfare analysis itself is very dependent on the specific nature of the state dependence. Moreover, in that world, you would get a one-time adjustment to prices and inflation goes back to normal instantly afterwards to a degree that's true in your analysis as well. The results here are firmly in team transitory, but team transitory lost by a mile to team persistent, it wasn't even close. So clearly you must look elsewhere to understand inflation persistence. I believe your analysis actually enhances the point raised by a folk of even before that it can't have been these temporary shocks to prices because otherwise your analysis would have led to temporary inflation. It must have been expansive fiscal monetary policy. It must be that the ECB is still keeping its force on the accelerator. It's not getting to the brakes just yet. Do you agree? And I'm gonna be super generous because Isabel has also asked for the floor and I know she is particularly fast in her question. And then we take them all together and we wrap up. So long. Very nice and elegant woman, Francesca. I agree with her and that state contingency makes a lot of sense. One implicit assumption in your welfare calculation is that the shock affects all firms and sectors in the same way, but we've been exposed to very asymmetric shocks since COVID. So, you know, and that deviates from the victim of any prices version is costly. Have you tried to calculate the effect when the shocks affects the cost of different firms differentially? Thanks. Isabel. Just very briefly, I mean, you showed these charts showing that the repricing frequency is actually coming down. But now we are entering a phase where input costs are actually going down. So if the repricing frequency goes down, that may actually mean that lower prices are not passed through, I mean to the consumers. So it could have the opposite effect from the way up. Thank you, Isabel. I trust my two panelists here to be able to somehow address all these questions in a succinct and intelligent manner. Who? I can jump in. You want to go first? Please. Sure. There's a lot again on, you know, thinking about persistence to think about transitory and to think about what the ultimate drivers are. And I think we all know that this has been a challenging period and I don't want to say that there's one set of drivers that have been mentioned that were correct in another set that were incorrect. I think, you know, broadly, we know this has been a very historic period with a lot of different shocks. But in terms of the question on, you know, wouldn't everything adjust immediately? And if it didn't, doesn't that suggest there's something else at play? I think in that world, the thing to think about is when the shocks hit, the persistence is unknown. And the size of the shocks wasn't even necessarily known.  All of that means that you're not going to necessarily be getting immediate adjustment. You're going to be taking some time to analyze and that's gonna take some time to pass through to prices. So there's always going to be this timing aspect to prices. It's not going to immediate. And once you get that timing and you get the supply chain mechanism, things then gradually work their way through if they're big enough shocks. And that does make it complicated. I do think the downside though is going to be a very challenging case. As mentioned, some input costs are falling, but at the same time as wage pressures may be going up. And trying to figure out what may dominate whether they're going to balance or whether the overall state of demand is sufficiently relevant to change that dynamic I think is going to be really critical. Okay, so very quickly again on the asymmetries. Look, I'm not, I don't have any particular expertise on wage settings symmetry or asymmetry. That's a bit outside of my area. But as I mentioned before, and this also relates to Isabel's question. My view of what is likely to happen. I understand your point. Of course, frequency is going down, which maybe we would like it to go up again and see a lot of price reductions, which of course come manifest themselves through an increasing frequency. I think what's more likely to happen given the stickiness we observe is that those prices are just gonna have very long durations. And there will be a convergence to the trends without much further ado. Because remember in this model, I mean the truth is I haven't worked out the exercise, but you have so many good economists working close to you that I'm sure this will be like a fun exercise for a central bank and we'll be honored to interact. But it's kind of a simple exercise. Once you have the model, you can answer that question in the model and see what comes out. And my guess is just a guess. I guess an educated one, but is that what's gonna happen is a reversal to the trend that was there before the shock with a period of below average price revision. Now, Silvana, the model again, it's very simple. So I just have one sector. In fact, I know it's embarrassingly simple, but again, it's very easy to kind of do the analysis. Well, maybe we did it. We did calibrations for food and beverages, then for the whole CPI, then Peter Karadi gave us some supermarket data. So it's not completely true what I'm telling you. In the paper, there are estimates for different vendors, but it's very easy to extend and to improve the analysis. Now, finally, Harold, I totally agree with you. I mean, one beauty of the model is that you see everything. So if you hit it with a huge shock, everyone will change prices. So you can get price flexibility.  So it's a quantitative question, whether or not this person goes up or not. What you're conjecturing in theory can indeed happen. A shock big enough such that for a moment we all go to the flexible price. It's very costly because everyone is going to pay the cost. But that's not what happens. It's a quantitative question and a good one. But I guess more generally, the philosophy is to understand that persistent is an endogenous object. It's not this one parameter that we pick from the shelf. We plug it in there. It worked between 2010 and 2019. Why should it change? It's not a deep parameter. These firms are doing stuff because they want to and when there is a big benefit of adjusting, they will adjust. Also, let me conclude by saying, I focus today on an energy price shock. It's not because I believe inflation comes from energy price shocks.  I mean, I'm a monetarist. I believe that long-run inflation cannot occur without sustained monetary growth. And indeed, the fiscal and monetary premises of the environment are fundamental to understand inflation over the long run.  Thank you. Thank you very much. Let me wrap up by saying the following. You referred, Francesco, to this moment of beauty when the unobservable becomes observable. But you didn't just refer to this. You created the moment of beauty when you illuminated us on a number of things. And I will not repeat all of those, but some of them will echo. Large shocks are different. Large shocks travel fast. I think that you used the metaphor of a plane, a little bit more sustainably, I would suggest as of now, you speak of high-speed trains, but that is maybe the only thing I wanted to say there. And you reminded us that this might have policy implications. Sharon, you took us to supermarkets, but also to many people that use vouchers and have to spend their time and maybe waste their time on finding the bargains to make and meet. And I thought that was a point in the reminder of what I said at the very beginning that high inflation is very painful. And Gita yesterday told us that we are all waiting for our good friend, but for many people, stable prices are not just a good friend, but they are their best friend. And the only way to make sure, to ensure that that best friend comes back is that we in an unwavering way, as the president said this morning, and doggedly pursue our mandate. With that, I close this session.