 Thank you for having this paper on the program. It's a great pleasure to be a part of this terrific conference And as Matiu said, this is doing work with Bernardo and Oli and in this paper we are very much motivated by Policy discussions and we want to make academic research useful for central banks and Let me explain in a bit why we think it's it's a useful piece of research First we know when we think about monetary policy a lot of action involves changes in the real interest rate Right and so the conventional policy is kind of very straightforward You incur inflation expectations at some number no two percent three percent It depends on the country and then you vary the nominal interest rate and by changing the nominal rate You're going to change the real rate and so that to accelerate or decelerate the economy So it's kind of very straightforward Now obviously we don't have a lot of capacity to do this because the nominal rate is stuck at zero But it doesn't mean we we can't have powers to help the economy and Specifically what we can do is to use unconventional policy tools where this in here is stuck at zero more or less But we can still change inflation Expectations for forward guidance or quantitative easing through policy communication and other tools Hopefully through that change we can and hopefully through that change we can Help the economy when other tools are not available. There is clearly a strong appreciation of this idea not only in academics, but also in central in the central banking community Mario Gragi When he was describing the workings of quantitative easing he said looking away going to raise inflation expectations This is going to push the real rates down and this is going to stimulate firms to invest and stimulate economic activity Now so in Syria, it's working very nicely and that's a very powerful policy tool but reality obviously is more complicated and We have to think about how inflation expectations are responding to policy communication and in general, you know What the influence is the formation of inflation expectations? To give you a sense of, you know, what we know about inflation expectations You know once and I can do is to cite Jeremy Rott's paper, but instead I will give you three quotes from former Fed chairs This is from Alan Greenspan who is saying here that inflation expectations I important He doesn't know what it is exactly, but it doesn't mean it's not real So he wants to know more about expected inflation Some years later Ben Bernanke gave a major speech again about inflation dynamics inflation expectations and he again Emphasized that inflation expectations are very important. We know relatively little they are great practical importance And then he went on and said we know particularly little about Price expectations of businesses who are after all the price efforts in the first instance And this goes back to Philippe's point that, you know, we want to see the the wage expectations the wage bargaining You know, it's another form of price setting wage saving Then some years later again, Janet Yellen is saying, you know, most importantly, we need to know About inflation expectations and how they formed and how we can use them for policy Recently Jay Powell was saying that, you know inflation expectations are terribly important for him and he is watching them all the time So I think, you know, this brief review tells you that there is a lot of interest in understanding inflation expectations and using them as a policy tool To manage inflation expectations and through that help the economy Now we have been very attentive to this please from the central bankers to do something about this and help us Better understand inflation expectations specifically were particularly sensitive to this point And made by Ben Bernanke that we need to do something about measurement of inflation expectations for price setters Businesses, CEOs And so what we're doing this paper is introduce a new survey of CEOs and try to document some basic properties of inflation expectations for these economic players So that's our objective Unlike, you know, standard service where we have households or financial market participants, our subjects are going to be C level employees or CFOs, CEOs, business owners Usually it's very hard to get full of those people, you know, their time is very precious Access to them is protected by small armies of assistants Secretaries and all sorts of other filters. So it's very hard to talk to those people directly And as a result, what we did was to team up with a very prominent survey firm which, you know, talks to the CEOs as a part of other survey exercises that they do And have a few add-on questions to their existing service. So we kind of piggyback on what these guys are doing and try to have a direct connection to CEOs So bypass all the secretaries, assistants and so on. I get some information directly from chief executives Now this is going to be relatively a short survey. We started this only a little over three years ago Fortunately, or unfortunately, we had a lot of variation over the three years. So this is going to be a very informative survey despite the very short time series dimension We have a relatively large cross-section of firms participating in the survey, roughly 300 in every way wave And, you know, we would like to have more, but as I told you, these people are super busy and it's very hard to have very large service for these people And that would be very expensive. Also, what's great about the survey is that it has a very large panel component so that people repeatedly participate in the surveys And as a result, we can track expectations over time and see how people respond to changes in macroeconomic conditions or in their kind of idiosyncratic firm specific circumstances So that's useful. We also cover not standard industries such as manufacturing, but also services. It's a smaller part of the sample which reflects the kind of history of the survey But roughly half of the respondents are going to be from services and also we have a collection of small, medium and large firms And that's very important because we often have very small businesses, sometimes mostly households that are employed But we have very large businesses that participate, for example, in the Livingston survey, but we don't have everything in the same survey very often So what I want to tell you here in this slide is that the sample is going to be highly heterogeneous, roughly representative of the US population of firms And it has a number of desirable elements such as relatively large cross-section and a panel dimension. And as I said, we have a lot of variation Now what I will do next is to present you a series of facts and try to connect these facts to how incurred inflation expectations are for the chief executives But before we do this, let me briefly describe the questions that we have in the survey We're going to have only two questions in this add-on module. It doesn't sound like a lot, but we managed to squeeze actually five questions into two And we have been very creative and we're very grateful to the survey firm that allowed us to do this The first question is going to be asked in every way and we basically elicit a numeric inflation forecast from the CEOs And it may seem like a very simple question, but there is a lot of sort that went into this We wanted to minimize the prime in the fact so we have an open-ended question asked about this inflation rather than a change in the general level of prices It's about specific price index. So it may seem very simple, but in fact, this is a very good question. A lot of sort went into this Now then we have a second question and this second question is going to be different across waves and we're going to have a rotation across waves In the in the first version, say, you know, it's April wave We're going to ask people to tell us about what they think is the inflation target of the Fed And this is useful just to get a sense of how much people know about monetary policy objectives of the central bank How much attention do they pay to monetary policy? The second question is about what they think inflation has been Okay, so we want to look at perceptions and the reason why it's important is because we know perceptions are extremely strong predictors of future inflation And it also can tell us something about, you know, why we have disagreement in inflation forecast And what kind of model we should use when we think about inflation expectations Next, we ask people about longer run inflation expectations. What will happen over the next five years? Again, this is very important If we think about if we think about how incorrect inflation expectations are Because, you know, we don't want to just look at current business conditions. We also want to look at longer term outlook And presumably this number should be very close to the 2% inflation target in the US if inflation expectations are incurred Because whatever happens today probably has very little bearing on what is going to happen with inflation in 2026 or 2027 Finally, we ask people to give us a probability A measure of uncertainty that inflation is going to exceed 5% over the next 12 months And again, this is very useful because it tells us how much confidence people have in their forecasts It's also related to how anchored inflation expectations are For example, if inflation expectations are not particularly anchored, we should see a lot of uncertainty about future inflation And so what I'll do next, as I said, is go basically over each of these questions and sometimes relate one to another And see what we can learn from that about how anchored inflation expectations are And also some basic properties of inflation expectations for the CEOs Here is the first fact. This is the time series of average inflation expectations made by the financial markets This is coming from the Cleveland FAD. Thank you for doing this public service, Cleveland FAD We have professional forecasters. This is the green line. This is coming from the Thiele FAD game Thank you again, Thiele FAD Michigan serve consumers. This is households, the blue line, and then we have firms. This is our survey Survey of firms inflation expectations, Sophie And what you should see here is that historically expectations were more or less the same across various economic players when inflation was high But since sometime in the 90s, we see a divergence. Professionals and financial markets think inflation is 2%, households think it's much higher And what is interesting is that firms are somewhere in between You know, when we started the survey, managers looked like households, then they started to look more like professional forecasters And in recent months, this is what I was mentioning in my question to Thielepa and Loretta, that we see this great divergence Professionals and financial markets don't see a lot of inflation on the horizon Managers and households see a lot more inflation. This number here, this is for July 2021. This is the last reading of our survey So what this tells you is that you can't use households or professionals as a substitute for a survey for CEOs It seems they have a different behavior and so it kind of justifies why we want to have a survey of price setters because they have different properties This also goes back to Ben Bernanke's point that we need a survey of price setters When you look at disagreement, how much in the cross-section you have a lot of variation in what people expect inflation to be This is professionals, very little disagreement, relatively little disagreement. This is households in order of magnitude disagreement And you know, again, firms are somewhere here in between. Again, this underscores that CEOs behave differently from professional forecasters in the households Now the reason why these two facts are important is because if you have incurred inflation expectations, everybody should be more or less agree in agreement about where inflation is going to be And you can see something like this for professional forecasters. They basically give you small variations around 2% inflation target These guys have a lot more disagreement and this is a sign that these people don't have incurred expectations The managers are somewhere in between. There is less disagreement than households, but still very, very high level The same is true here. You look at the levels, they are way higher than 2% inflation target And so this tells us that their expectations are not necessarily incorrect Now the next fact I want to present to you is the amount of uncertainty in inflation forecasts And here we have three agents. This is firms predicting, giving us a probability that inflation is going to be greater than 5% This is households, this is professional forecasters Professional forecasters, and this is for a specific day, 2019 first quarter So nobody knows that we're going to have COVID or anything like this Professional forecasters basically assign very, very little probability that inflation will exceed 4% You look at households and firms and you see this massive tail Massive tail. So these people are thinking it's entirely possible to have inflation more than 4% or more than 5% And again, this is not a sign of incorrect inflation expectations. People should not be thinking that this was possible At least this time. It should be super likely that we're going to have inflation this high Now exposed doesn't seem that crazy that these people thought this kind of inflation can happen because we see this kind of inflation now But at that time it was something pretty unreasonable to think that inflation maybe this high with this high probability So again, this is a sign of an incorrect inflation expectations Now we have a lot of disagreement about future and maybe this is not surprising people have different interpretations Of what is happening. Maybe they have different models But if you believe in full information, rational expectations, this is something that Jeremy Rudd was, I think, you know, critical of At least people should agree on the current conditions on past inflation So everybody can go to the BLS website and see what inflation has been or what inflation is You asked managers what inflation is now and this is the actual numbers, this vertical bars And you see that there is a lot of disagreement about what is happening in the direct one And again, this should not happen in the full information, rational expectations Now why would we see this dispersion? Well, you know, part of this may be an attention to aggregate statistics If inflation is not very high, you know, you can try to get your inferences about inflation from personal shopping experience Or from gas prices or from some other salient prices But in any case, it tells us that there is a lot of disagreement here And we know this stuff here, these perceptions are going to be very strong predictors of inflation expectations So again, this is telling us that, you know, this incurriness of inflation expectations is, you know, to some extent is there These people don't predict or perceive astronomical inflation rates But it's not as incurred as, I guess, one would like it to be Another thing you can do is look at how people realize their inflation expectations Alright, so we have, as I said, uncommon macroeconomic data or microeconomic data And if you have incurred inflation expectations, your expectations should not be sensitive to the shocks You shouldn't realize this numbers much when you go from one quarter to another You should expect inflation to be 2% more or less next year all the time And something like this is true for professional forecasters The size of revisions at the short end, this is field bars or loan and longer-run inflation expectations, empty bars Is very small, you know, the standard deviation of these revisions is very small You look at households and again, this is an order of magnitude bigger in terms of revisions It's not unusual to see people revising their inflation expectations by 5% up or 5% down In the short end and in the longer end, firm managers, again, somewhere in between Again, this tells us that we need to have a separate survey of firms, very bigger revisions Somewhere between households and professional forecasters And again, it tells us something about that, you know, these expectations are not particularly incorrect People are revising these numbers by big magnitudes And that's inconsistent with incurred inflation expectations Now we can move this a little further and say, you know, what is the connection between the revisions and short-run inflation expectations and long-run inflation expectations And if you really have incurred inflation expectations Then what you should see is that whatever happens today in terms of revisions for short-term inflation expectations Should be basically uncorrelated with what you think inflation revisions, expectations, revisions for expected inflation at longer horizons Because as I said, you know, what happens now with inflation is not going to tell us much about inflation in 2026 or 2030 We can do this formally by basically running a regression where you have one year ahead inflation forecasts, revisions for them on the horizontal axis This is five year ahead revisions and this is a bin scatter plot So you kind of reduce a lot of noise in the data by using the bin scatter But what this bin scatter shows to you is that there is a very strong, very clear positive relationship The R square is very high 0.6, the slope is very high close to 1 And so this tells us that households and firms, it's also true for households, that households and firms taking inflation is much more persistent than we actually have in the data We have a lot of meaner version in inflation and you also see a lot of meaner version in the forecasts, in the projections of professional forecasters And so here we have this remarkable persistence, a lot of correlation And again, this is not a sign of incorrect inflation expectations Now finally, we ask people, remember a question about the perceived inflation target of the Fed Remember this is CEO's, those people set prices, or at least according to our models, they set prices And so they should be very sensitive to monetary policy in general Again, if you believe in full information or rational expectations We ask these people to tell us what is the inflation target of the Fed 30% basically said I don't know Another 20 basically gave us a response which we can't use It's not interpretable And only 20-25% of people gave us a number which is close to 2% Now this may be a sign of success Remember Keynes once said that he wants to make economic policy as boring as dentistry And maybe we're at that stage, inflation has been low and stable for such a long time that most people don't care if inflation is 2.1% or 1.9% or 2% But it is important if you use management of inflation expectations to try to convince these people that inflation is going to be higher Above average for a little bit, but that it will be back to normal or now inflation is doing something But we convince you that this is going to be okay in the longer run This is going to be more challenging because if you see something like this, then it means that you have to penetrate through this wall of inattention on the part of managers And this may be a problem for policy in this dimension So we have these dimensions of incurredness from surveys and none of them seems to be satisfied, at least in the US Where does this leave us? Well for me, I guess for all of us, for all of us are some of this paper Management of expectations is a very powerful tool, at least in theory Maybe not as powerful as predicted by full information or rational expectations models, but it can still be very, very powerful It also tells us that if you want to manage expectations, and specifically price setters, we have to have a way to measure their expectations Because you can't have management without measurement It also tells us that there are massive departures from fire So some of the criticism from Jeremy is probably valid, but it's not as hopeless as he suggests I think we still have a lot of potential there, and maybe it's a sign of success rather than a sign of some deep trouble in our models We just need to think in terms of different models where expectations can have a separate life And finally, we obviously need to invest more resources into building infrastructure for measurement and management of inflation expectations This is why this kind of story should be run by a statistical agency or by a central bank rather than academics But for us, it's very clear for academics that we should really focus on building frameworks, theoretical frameworks So they can explicitly model information and rigidity and attention and so on that can rationalize the facts that we see in the data And hopefully inform policy about the optimal course of action I'll stop here, thank you Thanks, Juri, and very interesting So remember that you can leave your question in the chatroom or at the end we can also put your name and your affiliation And we can have a discussion at the end So now, Michael Werber, I don't know if you can share your screen Not yet actually And you now? Yes Just a minute Great So you have again between 20 and 22 minutes, so let's take it Okay, perfect Well, thanks a lot for including our paper and the program It's done with Francesca da Punto at Boston College Daniel Hoang and Karlsruhe And Marietta Palerita at the Bank of Finland I think actually I should have maybe compared notes with Juri beforehand because like first of all I brought some three quotes here At least they have different ones, but then the motivation is very similar I want to start out with a quote by Karl Brunner who at some point actually made a point that you know Central banking is kind of esoteric which is just reflected in the fact that you know whatever you hear is kind of Intelligible words and hard to make sense of which in a couple of years later Adam Greenspan kind of confirmed in the sense that saying that No, if you thought you understood what I was trying to convey clearly you misunderstood me And now if you move forward like two decades or so you step see that this is just I guess representative of the broader View of many many central banks that you know now actually on the one hand central banks Explicitly try to manage expectations of households and firms But crucially also like they make an active effort of trying to be understood by ordinary people Who central banks ultimately serve as Christine Lagarde said in 2019 and So here we are and so the reason why actually we want to understand and study like how central banks can potentially manage subjective expectations Because at the end of the day as Juri was also alluding to you know subjective expectations are potentially a very powerful tool to actually See a good demand. So like for example, so a subjective Fisher equation I feel like if you are able to move around Procedural interest rates has the power to in fact and we see that in micro data I think that's the key key innovation that it's not and tell me what's paper if you look at the bibliography I think the only paper that was cited in the last 10 years must not move his own work There's no host of micro evidence In which we do see that firms and households actually do adjust their consumption savings investment and weight-setting And price-setting decisions to inflation expectations. So I think we are now have a very powerful evidence And so like it's I think very urioli and co-authors at some point also highlight and some previous work Especially in times when policy rates are low and you can as a central bank not move around normal interest rates Still you could potentially stick to that demand through the management of subjective inflation expectations So what we understand in this paper is like if you look at ordinary households How can potentially central banks reach out and manage the expectations of households You know oftentimes the conventional policy narrative is inflation expectations are well anchored Households then actually make decisions on the normal rates are moved around which then translates into a moving Real interest rates And yet in some previous work we've actually shown that this narrative doesn't seem to really work out for the overall population So here we just actually plot the policy rate by the ECP over time and then we want to understand through surveys How to actually households adjust their propensity to take out debts to movements and interest rates We do that for Finland where you observe at the individual level measures of cognitive abilities You just simply split the sample in two and we show that you know if you look at the top part of the distribution by IQ They behave pretty much as we the policy narrative would say policy rates go down Propensity to take out debt go up Policy rates go up again Instead if we look at the bottom part of the bottom 50% of the Finnish population whom we observe by Q They barely reacted also like this first conventional narrative blocked off Then let's actually look at the second one like you know maybe a name of communication instead of directly managing expectations It's directly just to focus on whether we can actually anchor the expectations of households For firms you already saw it doesn't seem actually that expectations are well anchored For households similarly we see this unconditionally large upward bias Loretta alluded to large heterogeneity also in this upward bias in the cross section And just also very little knowledge of basic pillars of policy making So here what I'm plotting is which actually came out in the first time really about 20 years ago From a Cleveland spread discussion paper that there is a cross survey samples in countries this unconditional upward bias Of women relative to men so everyone is biased upwards However women even have higher average inflation expectations But these are two of the table years to show that actually this upward bias is actually also to within households Rather than across households Yes with men and women within the same household And what you however also see if you then just do a simple split of all households into two parts Those in which they have a male household had a class of not doing cross reshopping at all This panel here versus actually households in which a man and woman share the shopping You see that this gender difference increases by 50% in households where you've led traditional gender norms Versus like in households in which everyone at least partially participates in cross reshopping And therefore exposed to the volatile price changes in daily shopping You see that the gender bias disappears and it disappears because also like men have now even larger upward bias in inflation expectations So like as Loretta was saying exposure to frequent salient price changes is actually indeed a potential determinant for this upward bias in inflation expectations This now just comes up with all the jury like you know also that people have very little knowledge about basic pillars of policy making We run the server in households, 20,000 households in the US What do you think is the average inflation rate the Federal Reserve tries to achieve over longer periods of time And you see that actually it's about you know almost 40% of households of 20,000 You represent a few as American households that think actually the inflation target is higher than 10% So it looks like you know this idea that the expectations are well anchored doesn't pan out in the data So as Loretta was saying well it could be a sign of success inflation has been so low and stable So households don't really have actually strong incentives to gather and acquire information about inflation potentially But of course this is not an innocuous interpretation of the data because if that's the case Then of course communication has a really hard battle to fight to actually pierce the veil of ignorance and trying to actually get through the attention of households And so that's pretty much the backtalk against which we actually want to understand which type of communication potentially is effective in moving expectations And to do so we went out in the spring of last year to decide together with Statistics Finland, a large scale survey Which we fielded on the population of Finnish men in the spring of last year And the crucial part was that for those men that only do we observe like survey answers but also measures of IQ from the military But also like all type of franchise data And then what we did we went out and randomized different pieces of information that we provided through what we call like this You know, randomized controlled trial approach to those households that participate in Specifically we were to look at messages that were kind of imitated what the theoretical which is called like target versus instrument communications The target communication, you know, you just say what is the aim you want to achieve with a certain policy And I come back to which message we use in a second versus an instrument communication just tells us exactly what is now actually the instrument the central bank is using To actually reach the specified target you want to understand whether one or the others potentially a better able of moving expectations And just to give you some, you know, overview of the results, you know, and this is just a very simple way of seeing how households perceive those communication tools In a way that you don't really have to specify, you know, numerical answers or you don't really have to think too hard about scenarios and future outcomes You just simply ask, you know, those two type of communications to which extent do you think actually they will benefit households in Finland Seven means they will benefit a lot. One means they will benefit a little and so here you just see the full distribution for those men in Finland That receive the target communication versus the instrument communication and here you see that the full distribution is shifted to the right for target communication Indicating that it's perceived at least by our sample of Finnish men is being more beneficial to talking about the target rather than actually providing the details of the instruments Why which you want to achieve these targets. Now let me tell you a little bit about the sector survey we designed and the questions we asked So, like, as I mentioned, we did that in the spring of last year I just, I always see messages popping up, but I think it's just some chat between Peter and your result for being distracted And so, like, it's a sample of all men in Finland for whom we observe IQ data and then given that we cannot really directly use IQ for certification but only merge it in afterwards We actually just stratified for all men that have a certain age range for which we have IQ data but also like then by education because there is some correlation between IQ and education And then we fielded it in the tune of last year and the overall survey had three big parts. So the first part, you know, we first elicit some basic demographic financial constraints, financial portfolios The actual income in 2019. Then we elicit a prior income expectations or expectations on the expected change in monthly cross income in 2020 Then the second part was experimental stage so they'll detail in the next slide and subsequently, you know, we have the same questions for everyone again elicit again income change expectations But this time in a slightly different wording to just make sure that people actually don't get survey fatigue and still actually answer truthfully and then we also apply, you know, financial literacy question shopping duties and things like that Now what we did in the information profession experiment part of the survey we wanted to get an idea whether it is notion of target versus instrument communication Indeed, my two different three pan out and moving expectations. And so the way we did that was trying to imitate an ideal set up from the laboratory in which we keep constant the center of the message only in our case in which we kept constant the And the medium which wire which this message was communicated with us Twitter in our case. And then of course, you know, given that we are in the midst of a crisis period. We also wanted to make sure that the control group that doesn't get any relevant information about Monetary policy but also had like a tweet from a crisis period and the same type of amount of text to read just to make sure that everyone has like similar cognitive burden of going through the survey Now, this is the official tweets that we actually got from only rain's Twitter account, the president of the Bank of Finland. So here we didn't show actually this text here or like the picture instead, it just directly provided the finished version of this one sentence in the survey. And so the English translation weeks at the European Central Bank will do whatever is necessary to minimize the financial damage to citizens caused by the corona crisis, you know, it's not specific numbers. No instrument no charge and just literally what the aim of the policy is. And in the words of uncle letters when he discussed all in Yuri a checks know last year, you know, it's a simple crisp and constructively imprecise message. And as I said, like, you know, this last sentence was not part of the survey. The second treatment then was the instrument communication where we just provided the truthful fact that, you know, which came from only rain's Twitter account, the new 750 billion pandemic emergency program was launched by the European Central Bank. No reason why it's implemented. And this letter said, well, this potential is really crucial explaining to ourselves and firms where you do certain policies only like the actual policy instrument, no target a larger amount which personally likely is considered large for both experts and non experts. And again, we didn't have the last sentence. And then, you know, the control group also received a treat about period of crisis in Finland. However, no direct mention to any monetary policy action and you know, it is within individual posterior relative to prior design relative to control group allows us to purchase any potential crisis. Then a crucial ingredient of course for us is merging in IQ data. This is similar to what we've done in previous work we get from the military aggregate measure that is the outcome of about 120 questions with people in Finland take around the age of 19 and then you can think of it like the measure of IQ following a discretized normal distribution between one and nine, nine is the top 9% within the court, one is the bottom 4% within cohort in terms of cognitive abilities. As I said, you know, nice part of a minority country can merge in pretty much whatever you can imagine. And so like in terms of now the sample we've about 2600 survey participants that we can match to all the other type of data. We actually drop about 140 participants because there was a discrepancy with our survey elicited annual income and actual registry income was likely because people mixed up annual and monthly income of more than $100,000. And then it was equally split roughly across targets and instrument communication arms and the control group and based on observable because it was all well balanced. In terms of now average monthly income with about 5000 euros, people have expected a drop in monthly income in 2020 about 90 euros, people run average 40% 40 years old, a little bit less than 50% college educated, you know, of course, if everyone knew already that, you know, the PPP was launched the easy way to do whatever it takes, we wouldn't expect any treatment effects, but you see, you know, we listed it directly to which extent where you're aware of these policy measures that only about a quarter of our survey participants had actually heard of these policies. Economically, what are we doing, we just look at the change in individuals expected change in monthly income in 2020 after our policy treatment relative to before on treatment indicators and the host of observables. So, you know, eight, eight squared mental status income and all those type of things, which are listed below. Now let's just simply let's look at the data. So let's, you know, compare the effect on changes in income exchange expectations for target communication versus instrument communication raw data in one and three conditional observables in two and four. And so what you see is like, you know, remember, on average, people expected a drop in monthly income of about 90 euros, pretty much completely offset this drop in income change expectations prior to the intervention. If you hear only in telling us that the ECB does whatever it takes, instead actually for the instrument communication, you know, the point estimate is smaller by about half and also it's not statistically significant. Of course, you know, there could be and this is the main reason by which it's in Finland, lots of heterogeneity by the degree of cognitive abilities we know from some prior work that on average low IQ men in Finland have more pessimistic expectations. They have a lower level of informness and tend to actually on average react less to a policy interventions like cash for clunkers programs. And so now let's actually see whether the reaction differs by IQ. So here we just now focus on target communication. The ECB does whatever it takes, men below the median IQ and men above the median IQ. And you see that it is especially men with the lower cognitive abilities now a sample that actually update upwards. This is the area income expectations between 100 and 160 euros once they hear this target communication instead actually above median IQ men in Finland don't react statistically. So like especially those that typically have more pessimistic expectations are hard to reach and barely react to policy intervention that actually simple Chris communication about targets seems to be actually most responsible. Now we already talked about briefly about the fact that you know maybe there was a differential awareness to the two policies you know the PPP is a really big number maybe it was heavily covered in the media. Everyone knew about it and that's actually why we don't see any average effect. Let's actually see let's only focus on those several participants that stated within the survey after the intervention that they were not aware of it. And you see that you know if you look at the half of the sample that were unaware of the policy target communication strong significant reaction of 100 euros monthly income updating upwards for target communication again no reaction to instrument communication. And it's again even you know I'm aware below median IQ survey participants that strongly react to target communication don't react at all to instrument communication. And so the last thing before wrapping up on time I hope is that the you know when I also split based on prior expectations. So oftentimes you know if you look at the times of crisis and you want to actually raise the overall level of optimism in the economy try to actually see the outlook of those that have the most negative priors. And so on the one hand we might actually want to see whether the scope of deed reaching out to those who was actually the most negative priors and then you know if on the flip side we of course also don't want to make want to make sure that we don't put off those that actually had the most positive priors here what I show is that if you look at those low below median IQ man with ex ante priors below the media and you see they strongly realize upwards the expectations and set those with the below median income priors actually they slightly realize downward but it's not statistically significant and it's unlikely power issue because the samples are roughly equal size. So now let me wrap up so like we do know at least in theory that you know forward guidance or communication with households and firms can have pretty large effects. And I will now actually show in the paper that indeed conditional on being successful in reaching out. It's of course a big big condition. You know there is a type of communication that is really crucial and successful in in reaching households are moving forward in terms of communications which is communication about where targets and aims of policies no simple quiz and just constructively emphasize communication and especially successful in reaching those that potentially at least sophisticated unconditionally hard to reach actually the potential of communication I think we still actually have to find you know what are the channels actually for which central banks should communicate to reach ordinary households and I think what generally like you know better understanding the styles and with all to use actually to communicate with households. Thanks a lot. Hey Michael. So now turn to Hassan. You know, Hassan can you share the screen. Yes. So yeah, and again. You have like 20, around 20 minutes for your presentation and then after this we're going to have the Q&A. Perfect. Can you confirm that you can see my slides and I can see. Perfect. Thank you. Thank you so much for putting the paper on the program and for inviting us. This is such a great opportunity for us. Today I will be talking about selection and information acquisition and monitoring and neutrality, which is joined with the term you're going to listen to the audience so hopefully he'll take questions in the chat. So the motivation for this project needs no motivating to this audience. We know from even from the talks from today that there's a lot of uncertainty among firms about economic outcomes. The average firm in the survey data is highly uncertain about their own prices and their own future prices and as well as was about aggregate inflation. Today I want to focus though on the heterogeneity that we observe among firms about their expectations on different outcomes. In particular, one of the things that I'll show you and you should have seen from Yuri's graph a few minutes ago is that there is a high degree of heterogeneity and subjective uncertainty. And I will dig in deeper exactly what I mean by subjective uncertainty in a little bit. But taking this heterogeneity across firms about economic outcomes, a natural question that follows is that whose expectations matter for macroeconomic outcomes. In particular, if some firms are really informed and some firms are not, then should we think about the average firm as the average firm's expectations is the object that matters for our models or should we think about some kind of selection in a particular way. What I'm going to do today is to show you that the precision of firms expectations in particular measured by the subjective uncertainty is going to be positively correlated with time since last price change for firms, indicating that there is indeed some type of selection in the formation of expectations and information acquisition. To understand how this selection translates into aggregate outcomes, then we need a model. So we're going to write a model with a state-dependent information acquisition that's going to be a combination of rational and attention with nominal rigidities to first explain this selection to kind of get a prediction out of the model that is consistent with what we see in the data. And then we're going to use the model as a vehicle to drive the implications for aggregate outcomes. In particular, in this paper, we're going to focus on monitoring the neutrality and the response of output to monetary shocks. And we're going to show in a sufficient statistic framework that only the most informed firms expectations are going to matter for output response and the model that we're going to write, indicating that indeed we need to take the selection into account and the fact that the average firm is really uncertain about aggregate outcomes might not necessarily imply as worst outcomes as we would have imagined. So what do we mean by subjective uncertainty? I'm going to take some data off the shelf from Ali and Yuri's survey in New Zealand. In that survey, one of the questions that they have asked firms is about firms' own prices. In particular, there's a question that asks if this firm was able to freely change their prices at this moment by how much would they change their price? And instead of asking for a point estimate, firms are asked to deliver a distribution over that object. So the object that is being asked of firms in this question is something that in the menu cost models we would call the price gap. And here firms are reporting their belief distribution over their price gaps. So not only we know how far they think they are from their optimal price, but we also see the distribution and the percentage probabilities that they put on different price gaps over the horizon. We can take those distributions and we can calculate the uncertainty of every firm about their own price gap. This should say something about information acquisition. As a firm, I can go out and acquire information and be very certain about what my price should be, or I can delay that decision for when the time comes that I think is the right time to change my price. This figure here is showing a distribution of that object across firms. And what I want you to take away from this is that there is a tremendous amount of heterogeneity on how uncertain firms are about what their prices should be. There's almost no massive firms that are absolutely certain about what their prices should be. The largest mass happens around 1% standard deviation, which is like the standard deviation of inflation in New Zealand, just in case if you want to use it as a reference. And then this distribution has a fat tail that goes up to very large values. To two, three standard deviations away, even four standard deviations away, there's a positive mass there. So that's an unconditional moment. I just want you to keep this picture in mind, which is very robust to also looking at across industries. So not only we show in black the distribution for all firms, but we have done it for within industry and we want to convey the message that this doesn't really come from a particular industry. It's an economy wide object. So that was an unconditional object. We can also look at the conditional object. We can ask conditional on changing the price, how uncertain a firm is about their future prices. There's a question in the survey that asks about the last time the firm has changed their price. So I'm going to take that dummy question for a second and I'm going to say, among the firms that have changed their prices recently, relative to the firms that haven't changed their prices recently, possibly being measured by the last 12 months, how does subjective uncertainty differ? And what I want to take away from this is that firms that have changed their prices more recently tend to be more certain about what their prices should be, even if they could change it now as well. This is a very robust pattern that happens with industry fixed effects or even controlling for the perceived frequency of price changes at the firm level. But it's coming from this dummy variable. So one other thing that we can do is to, instead of regressing it on this dummy, we can actually regress the subjective uncertainty of firms on time elapsed since their last price change, which is a more continuous measure of how long it's been since their price changes. And firms that are farther away from their last price change tend to be more uncertain about economic outcomes and their own prices. With that, this is almost significant at two percent, at two standard deviation level, it barely fails to be a two star. But I also want to draw your attention that this is a very small sample because we need this very rich data about firms expectations and their beliefs about their own price gaps, which ensures us that we're not picking up just noise. So that's my motivation. I'm going to take those two observations and I'm going to try to write a model that makes sense of that. The model needs to have at least two ingredients and we're going to put only these two ingredients. We want to understand how expectations are formed. So information acquisition has to be endogenous. That's going to be the rational attention component. The other component that's really important is that we don't see firms changing their prices all the time in the survey and actually our measure of how certain firms are was correlated with the time since last price change. So we're going to add some type of nominal rigidity, which we're going to start with just Calvo, which is the simplest way of doing that. So the environment is going to be as follows. We're going to take a continuous time environment. There's going to be a measure of price setting firms that are going to be indexed by this I sub index and firms eyes instantaneous profit is just going to be a quadratic function. And it's going to be decreasing in the distance of the firm's price from an ideal price. That's going to be an exogenous process for the firm. And in particular, it's just going to be a Brownian motion. This is an assumption that shows up in analytical models of monitoring and neutrality, and it can be thought of as a second order approximation to a more micro founded profit function, where B just captures the curvature of the profit function around the optimal price of the firm. Given this profit function and this environment price change opportunities are going to arrive at plus on rate data, which is just the Calvo assumption is completely endogenous to the firm. They just get a plus on draw once in a while and they change their prices when they get that. Now that was the nominal rigidity part on the information acquisition part. We're going to assume that firms do not observe their ideal prices directly, but they can design a signal process that informs them about that price. So the story behind this is that I don't know what my optimal price should be, but I can hire a bunch of researchers that can tell me what my price should be, or I can spend time myself and try to figure out what that price should be. But it's not something that I can do for free. I am not informed about it without doing any without exerting any type of effort. So the way that we're going to model this process is that I can receive signals of what this ideal price is at any point in time, but I get to decide what the precision of that signal is going to be, which is the Sigma SIT. The Sigma SIT is basically the noise in the signal that I'm receiving. I can reduce that noise, but reducing that noise is going to be costly, which is the information acquisition cost. Now, given these signals at any point in time, I have a history of these observations. They form my information set. It's going to be this big SIT. It's the sequence of all the signals that I've seen since the beginning of time. And over time, I'm going to choose these precisions or the variances of the noise. How are we going to measure the cost of information acquisition following the rational attention literature? I'm just going to assume that this cost is going to be increasing and potentially convex in the mutual information that the firm increases over time. So look, the firm requires information. Information is measured by mutual information. And that's going to give me a measure of how much information a firm requires at an instant. The cost is just going to be a convex in that instant information acquisition. That's what this DI implies. What's the problem? So the firm is just going to minimize their lifetime losses. There are two types of losses. The first loss is that if I choose a price that's away from my optimal price that's going to create losses and profits for me. The second type of cost is just going to be the cost of information acquisition. The story is that information acquisition allows me to have a better estimate of this. And a better estimate reduces these losses, but I also don't want to be too precise because the cost of information can be large. So what is the firm choosing? They're going to choose these precisions or the variances of the noise that I mentioned. But there's also the Calvo friction. I don't get to reset my price all the time. But I get to have planned prices, which we're going to call Ptilda. Every instant I'm going to have a planned price. If the Calvo shock arrives, the planned price is going to be my actual price. That's this equation here that at the menopuasan shock arrives, my price resets to this planned price. And then the planned price is going to be chosen according to my information set at a given time, which is going to evolve based on my choice for information acquisition. Today, I'm going to consider two types of convexities for this cost, which is going to be very important for the results that we're going to drive. The first is just going to be no convexity at all in the sense that the cost of information is just going to be proportional to mutual information. The other one is an extremely complex function, which means that information acquisition is free until a constant rate, lambda bar, and anything beyond lambda bar is just going to be extremely expensive. So I get to acquire information at the constant rate rather than deciding how much information I want to acquire at any time. I'm casting this in terms of convexity because there's going to be a very nice interpretation for how much firms want to smooth their information acquisition over time. Now, before going into the results of the model, I want to briefly mention that how this model is going to be mapped to the data that I showed you in the beginning. So there's going to be the object of a true price gap. The true price gap is how much the firm's price is actually in reality away from their ideal price. This is something that is neither observable to us as econometricians nor something that is observable to the firm under the assumption of rational attention. This is what firms are trying to learn. But we can decompose that into two components. One is going to be the perceived price gap. This is something that we can ask the firm about. But in the survey, when we ask how much do you think you are away from your ideal price, the firm is just giving us the expectation of this object given their information set. And we can also think about the variance of this object, which is from the perspective of the firm, how uncertain are they about their estimate. And this is what those subjective uncertainties were that we were calculating in the data. So I observed this as the mean of the distributions that firms report. And I observed this as the variance of the distributions that the firms report. And that's how we can map this model to the data, even though we don't observe what the true price gap is. So in terms of the results, I showed you two different information acquisition technologies, one linear, one convex. And I'm going to tell you how information acquisition looks like under each of them. So under the linear cost, there's going to be no smoothing in information acquisition. Firms have no control over their price changes, which means that in between price changes, firms are not going to pay any attention to what their prices should be. The linear cost implies that I can always postpone information acquisition to the moment that I like and pay no penalty for adopting a lumpy information acquisition technology. So firms are not going to change their, acquire any information in between price changes. But when the opportunity of a price change arrives, they're always going to acquire enough information to reset their uncertainty to a baseline level Z star, which is going to be characterized implicitly by this equation. Now this equation doesn't need to make any sense to you on this slide. But the goal is to show you that this Z star, this optimal reset uncertainty depends on the curvature of the profit function, on the cost of information, and on the frequency of price changes, as you would expect from the incentives of these firms. So that's the strategy for information acquisition under linear cost of information. But this doesn't have to be the model. We can also think about a model where firms do a lot of precautionary information acquisition. And that's the case when the cost of information acquisition is extremely convex. In that case, firms are always going to acquire information at a constant rate, independent of whether this is the time for a price change or not. Because they want to be prepared for the time for when the time comes and lumpy information acquisition is extremely costly. So they do it at a constant rate. So what are the predictions for the graphs that I showed you under the two models? We can derive the time and variant distribution of uncertainty across firms in the model and see which one looks like the data that we started with. So with the convex cost, the distribution of uncertainty is just going to be a univariate degenerate distribution because everyone is acquiring information at a constant rate. Everyone will have the same uncertainty about their prices. However, with the linear cost firms that don't change their prices for a while, they also don't acquire any information. So uncertainty is going to be linearly related to time since last price change, which is the regression that I was showing you in the third slide. The implication of that is going to be that uncertainty inherits the exponential distribution between price changes, the time between price changes. And it itself has shifted exponential distribution like this. There are a lot of firms that for low levels of uncertainty, there are no firms. But at an interim level, there's a mass and then there's a long tail that follows from that, which is very similar to the second slide that I was showing you. So the data seems to be very close to this idea of lumpy information acquisition in the sense that firms don't acquire information until they need it. And when they do, they acquire enough information to go back to the baseline uncertainty. So now that we know which model fits the data better, what are the implications for macroeconomic outcomes? We're going to do this in the case of implications for monitoring on neutrality. So I'm going to follow the always leapy-la-behan approach of driving a sufficient statistic for monitoring on neutrality. The idea is that we can take a firm and at time zero, we can look at their expected contribution to the impulse response of output. Given that we have moved their initial output by a shock of size delta. So this is like something like we shocked the ideal prices of the firms and that's what a monetary policy shock is. And then we look at the expected contribution of a firm to the impulse response of output over their lifetime. There are two state variables to take into account for firms. Their initial gap, so firms can be very far away from their ideal prices in the beginning when the shock happens. That has to have an impact on the impulse response of output. There's also the uncertainty of the firm, which here is going to be endogenously determined by the information acquisition strategy of the firm. And that's also a potential variable for this. But for every firm with a particular gap and a particular uncertainty, I can calculate their expected contribution to the response of output. And then I can take all of these and integrate it with respect to the stationary distribution of price gaps and uncertainty in the equilibrium. And that should give me the area under the aggregate impulse response of output to a monetary policy shock. Of side delta. Now, what is this object look like for a shock of size one, let's normalize the size of the shock to one. This is going to be a sum of two components. The first component is going to be what we know about these models is going to be related to the frequency of price changes. So this is like the famous kurtosis over six times the frequency of price changes, sufficient statistic, which in a very simple Calvo model that we have. This component just boils down to being one over theta, because the kurtosis of a Laplace distribution is just six cancels with the six in the bottom goes away and we're just left with one over theta, which is the one over the frequency of price changes. What is new here is there's an extra term that comes from the fact that whenever these firms get to change their prices, they don't reset their prices, their gaps to zero, because there's uncertainty on their part about what their prices should be. So in the language of these models, this is a model with random re injection whenever the firm gets to change their prices, they go back to a place where their contribution is not going to be zero going forward, what's going to be something smaller. That should depend on how uncertain firms are and how close firms get to their optimal prices when they get to reset their prices. So it should intuitively have something to do with subjective uncertainty. If it's zero, we should be back to if subjective uncertainty is zero, we should be back to just like sufficient statistic being one over theta. But in this model, uncertainty is never zero for no one. And there's a lot of heterogeneity in an uncertainty of firms. So the question is that whose uncertainty shows up in the sufficient statistic. And it turns out that the only uncertainty that shows up here is the uncertainty of the most important firms in the economy, which is in the exponential distribution that I was showing you the minimum uncertainty that firms have in that distribution. So even though that there's a long tail of uncertain firms, when we think about the contribution of those firms to the impulse response of output, that long tail does not matter. And the firm that shows up in the sufficient statistic is the firm that has the lowest subjective uncertainty. So my main takeaway from this. We don't want out of time. Sorry. I am almost concluding. Thank you. So the main takeaway is that even though that there's a lot of heterogeneity and there are a lot of firms that are uninformed, only the most informed firms matter for monitoring and neutrality. So to conclude, we show suggestive evidence that there's selection and information acquisition. We show that this is consistent with the state dependent information acquisition model with selection and information acquisition. And we show that as macro economic implication, this implies that the only most only the most informed firms expectations matter for the response of output to a monetary policy shock. Thank you very much. And I'll stop there. Thanks. Thanks a lot for your presentation. That's very interesting. So now, let's move to the Q&A. And actually, Emmanuel has a question for you in the chat. Hi, Hassan. You find a positive relationship between uncertainty and the time and time since the last price adjustment, does that suggest that the firm that face more volatile shock, which may take them, may be more uncertain, repress less frequency and so that the implication for many goes more and increasing the volatile shock implies more frequent press adjustment. Okay, so I can divide it to two questions because I think I'm sympathetic with one implication, but not sure about the other implications. So the positive correlation between uncertainty and time since the last price change at price adjustment is robust to controlling for the frequency of price changes. So one of the things that I didn't show you and one of the controls that we had in that regression is there's a question that firms asks how frequently do you change or review your prices. And there's a lot of heterogeneity in that object, as there is a lot of heterogeneity in the underlying uncertainty, underlying volatility of the shocks for these firms. But when we control for that frequency, this relationship between time and uncertainty gets even larger. And that is very consistent with this idea of adding this new mechanism that firms don't acquire information between price changes. But I'm not sure if it's going against the predictions of many cost models because that is not a margin that we are modeling. And I think that's a margin that has its own implication for how frequently firms are changing their prices. We just fixed that frequency and we said, okay, conditional on the frequency that firms have, what is the relationship between time since last price change and their subjective uncertainty, which is a different object now because we're not assuming that firms fully know what their prices should see. I hope that answers the question, but I'm happy to discuss it first. And I have a follow up question on that line. So basically from your regression, we can also think about the opposite relationship that basically when firms receive information, they tend to change their prices. And actually, like I think in the US and so I think the fine evidence of, for example, when a firm have to renegotiate the accelerates, for example, they actually like basically have better estimation of inflation expectations. And also, I think that most of the RCDs related with server inflation expectations should assume that actually actually give them information can change basically the pricing decision. And in your model, I guess that basically because of Calvo rising, that's not present there, but do you have any thought about how that opposite implication from your regression, what would be the implication for your model? Absolutely, I think you put your finger on the most important question, I think, which is the idea that I didn't say anything about reverse causality, which is exactly what you're saying. Like in the model, I'm assuming that firms have no control over when they change their prices, which eliminates one reason that firms might want to acquire information. One of the firms can go out and hire researchers to see, okay, tell me when is a good time for me to change my price, which is nothing in the, nothing captured in the model. So I have two ways of approaching that question empirically, it's a really hard question to answer because we would need some kind of an instrument that affects inflation expectations without changing firms desire to change their prices. Even this data was very kind of like detailed and unique in the sense that it's asking about distributions. I have run some experiments, exactly trying to disentangle this where in an experimental environment, we can give control to agents to decide whether they want to change their prices or make it completely exogenous in its calval model. And in that experiment, we do find evidence for this channel. Now, whether the other channel that you're mentioning dampens or amplifies this effect, that's a theoretical question. And we have started working on a menu cost model where we implement the same mechanism in a menu cost model where there's also benefits for firms information acquisition in terms of when they want to change their prices. It does dampen the results a little bit, because now even firms that are not changing their prices acquire information, but that should show itself in the variance of the distribution of subjective uncertainty that I showed you. And when I was presenting, I saw that Yuri was like talking about New Zealand might be a unique case. I think it's important for us to actually go and look at the distribution of subjective uncertainty. And each of these models will show themselves in a very particular distribution of subjective uncertainty. If all firms are like continuously acquiring information, then I should see a lower variance for that distribution, which is not something that we see for New Zealand, but we might see for other countries. Thanks. So Peter has a question for Michael. So maybe we can turn to Michael. So it says, how much do you worry that low IQ participant overestimate the effect of monetary policy during the COVID crisis and that is why the responder responded more possibly to that target announcement. Those that have higher IQ might have understood that this policy will have a small impact on their income in Finland. Would you think that in case of the other shop where monetary policy is more effective instrument communication to higher IQ participant might be more effective to target communication in more detail in what exactly is going to be done. So Michael, maybe you can give us a little bit of this. And maybe you can also answer like part of the of the of the discussion. Yes, so like, Peter, thanks a lot for the question. That's that's great. So like, you know, now I'm stepping obviously a little bit outside of the didn't pay off in the paper because like, you know, and I'm not sure how people might react if eventually another economic environment. I think the COVID pandemic and the situation last soon is nice because it is a time where potentially, you know, you might want to find ways to reach out to people that had very depressed beliefs where you saw lots of dispersion in beliefs and in that that situation like this. And I talked about targets was very successful, especially in for the parts of the population that typically is not reactive at all. And so we do have like the survey data from the Commission for Finland, where we like run in the past like quasi or like equations of like, do you think it's a good time to purchase larger ticket items on people's inflation expectations. And so typically you see, like, pretty precisely estimated zero for the bottom part of the IQ distribution and strong intertemporal substitution effects for high IQ man in Finland. And it was also still true last year. So like, even during the COVID pandemic, you still didn't see any intertemporal substitution. At least as the list is it through the European Commission survey for the bottom part of the IQ distributions like at least, you know, unconditionally during the times of crisis, there was no specific change on like let's call it a lack of reaction typically observed for the bottom IQ distribution was only that this specific target communication was really effective. And whether it's also different whether instrument communication would be more effective than normal times. You know, I'm, I can only guess but I can see that it might be effective for the top part of IQ distribution. I just think that the bottom part is just no idea even, you know, we're talking about specific policy instruments would mean for the actually day to day life and unless it's actually specified with the implications I think will could never be be effective in managing the expectations of the bottom part of IQ distribution. Thanks Michael and I think there is a couple of questions but maybe like there was before we can as you read that there was a question that was mentioned before about the how basically communication should target household some firms and basically the different style of that and also like kind of that relates with this question about whether like firms are looking at particular prices. And in particular, for example, like last year, there was a huge kind of changing policy in the case of the US that was the average price of time. Basically, if you saw something around those events, and then like what what you think about how central bank should communicate with household and it should be different type of film as Christian was asking for. Yeah, maybe actually just a few thoughts and then I think you can discuss on the change of policy framework and the evidence there's like no channel. We found in some work with all in Yuri that you know simple relatable statistics can be very powerful in moving the expectations but this communication cannot be let's quite outsource to the media. Because at least for the case of US consumers, we saw a systematic discounting on the side of households for anything that was transmitted through traditional print media. And we asked them why that is the case and it just actually the very low level of trust and credibility as a source of information about monetary policy. Instead, maybe some were surprisingly and this is how again I have to specify this was evidence for the US that social media had the highest degree of credibility when it comes as a source of information about monetary policy. Now, what does this means like, you know, think about you might want to think of him what you want but about our former president, Trump, you know, he had just a personal Twitter account I used to have it for which he was actually had a direct line of communication communication to many many households. Like, you know, at some point made a statement before and was actually at I think in December 2019 at the ECB in a research seminar with someone from the communications department said well we also have this at ECB Twitter account through which we communicate but you know people don't follow institutions people follow people's like to the extent that the ECB maybe wants to communicate your ordinary households via Twitter I think it would have to be president like art so the person in charge of on top of the institution to actually actively use Twitter and I guess, you know, that's I'm not saying she should do it but at least in our setting we saw that this kind of could be quite, quite successful and I guess I'm handing it over now to who you are to talk about his evidence on AIT. A very brief, you know, we'll hear more about AIT tomorrow in the keynote, but you know, I would like to echo what Loretta said that communication is a journey. You are never there but you can always do better and as Michael said you can always use different channels of communication learn from politicians, hire professional PR firms to make sure that monetary policy communication is reaching out to different parts of the population. I don't think we need to rethink the framework that we have, but we just need to understand the limitations and we shouldn't expect miracles from forward guidance so average inflation target and just even how people form expectations. Thanks a lot, Mike and Yuri for the question and now we have like some questions from Hazan and maybe you can fully give your answer as you get out of time. So one is from Kia says, hi Hazan, I read the question, how would you think about low and high inflation environment to your model just be a higher frequency or price change. And I think that Javier today and also has a question. And does the one say something about a time varying question since the update in his exogenous event Palbo, the state of the economy is independent in the center to acquire information. Can we stand this. And I think it was answered that finally like Christian also has a question. What is the role, the role of the firm size, and learn to be better in acquiring information about the state of the economy. Okay, so regarding Kira's question, I think, yes, like, so I'm speculating beyond the model and I just want to make that clear because like none of this is in the model but yes the first place that it would show up is by changing the frequency of price changes. And that is going to higher inflation will make firms. Change their prices more frequently if that was endogenized in the model, which would shrink the variance of the distribution of subjective uncertainty so that's a direct channel that it could affect that, but there's also an indirect channel which is in, in other work with true real we have shown that changes in the variance of the shocks in the economy can affect the slope of the Phillips curve and have non trivial effects on how inflation response to an output respond to shocks. And we know that level of inflation and volatility of inflation are correlated. When we have higher inflation, it tends to be more volatile. And in the model, if that that is the case that having higher inflation also implies higher volatility it would also affect firms information acquisition. In particular, it'll make them more attentive to the economy and reduce the effects that expectations have on on macroeconomic outcomes. Again, these are speculations I haven't done this but I expect these channels to emerge. And that's why we're not endogenized in the model for how years question very interesting question again, nothing that we have in the in the model. But we could instead of like assuming these shocks are ID across firms. Think about an aggregate monetary shock and and shock the volatility of that, which would affect information acquisition beyond what's the, what we discussed in the paper. The question that I have tried to work on in the past doesn't have like all these nice analytical results flowing out of it maybe I'll have a breakthrough. But yeah, definitely I think it's a very interesting question that follows up we didn't have aggregate shocks here. We're just MIT shocks, and I think it's very interesting to think about the implications of making firms endogenize the volatility of these the fact that time. And finally, regarding the question about firm size. I have, I have done some work earlier in a different paper, which was about oligopolistic competition and rational attention. And what I learned from that work was that firm size definitely increases firms incentives, larger firms have higher incentives to pay attention to monetary shocks, or aggregate shocks but that's not the only effect. So that's one effect that increases attention. There is a counter effect, which is the, the role of pastoral we know that larger firms also have lower pastoral so they have lowered incentive to pay attention to shocks to begin with. Because they're not going to utilize that information, even if they know what their marginal costs are going to be in the future, with which shock dominates which force dominates I think needs more work. So for example, in New Zealand, larger firms tend to be less attentive, which seems that the second chat theoretical channel might be a work, more than the first channel that larger firms. So I think that's the intention to aggregate shocks. Thanks. There is a last question for Michael maybe maybe after you guys like it has a question. It really takes a form of either or why not with them with both of the things that they have. I think you're muted. Completely like the question was whether we don't actually provide both treatments to households like just a little bit restricted by power considerations and so like, I'm thinking back if we had a few more people that would have been indeed like, you know, a nice exercise of having like a fourth pool that would have received actually both treatments at the same time to see if there was potentially an interaction effect. And whether it actually would have maybe increased also like providing some context to the instrument communication would have actually potentially even increased effectiveness but unfortunately I can we can go back in time to change but definitely think it would be quite interesting whether providing context to these treatments potentially would actually increase the effectiveness of the.