 Good morning everybody happy to open the second day of our conference. I hope you're all rested after a beautiful dinner I don't know how many of you went for post dinner drinks. So Be awake by the time it's time to ask questions. We have here a session on price dispersion and inflation with the Francisca from the Federal Reserve Board We have Gaetano from the coldest attitude the commercial in Paris has shoes in Paris Henning from the Dutch a Bundesbank and Slava also from Federal Reserve of Boston and Gaetano I hope you feel very safe among all these central bankers We start with You are even one of us. So Welcome back So we start from Francisca. You have 25 minutes one thing order of the day We don't end at 1145 for the posters, but at noon. So just that you know those of you who has posters we start at noon with that Okay, good morning everyone and thank you for having me here today In this paper, so sorry, how do I Where is Thank you first Let me just mention that all the views that I will present here today are solely mine my own and Not the ones from the Federal Reserve Board or the Nielsen IQ that is the company that provides the data The key question that I want to address in this paper is what are the welfare effects of steady-state inflation? In the standard sticky price models, which are the models that I will be addressing today Inflation decreases welfare You probably know why it is the case, but just to recap If nominal prices are fixed for any reason inflation is going to erode real prices So if we have two identical firms, so firms with the same Costs of production and they change their prices at different times The real prices are going to be different So we will have that the relative prices are not going to reflect the relative costs of production so when we observe Price dispersion this means that the This price dispersion is not going to be reflecting the relative costs of the firms and this will be generating inefficiencies so in these kind of models there is a very tight link between prices Persian and the costs of inflation and Even though the relationship between Inflation and prices Persian is crucial for welfare in this type of models We don't know much about this relationship in the data What I will do in this paper is first to try to estimate the relationship between prices Persian and inflation For several reasons that I will talk about later. I will focus in product-level relationships instead of aggregate level relationships And I am going to uncover a new fact that is that the relationship between Product-level prices Persian and inflation has a Upsilon shape around zero What do I mean with these? Well that around zero product-level inflation prices Persian is going to jump and then this relationship will become flatter as absolute inflation increases now I After trying out different of the shelf models. I find that these Models that I addressed in the beginning of my presentation cannot account for this Relationship so I am going to take one of these models in particular a menu cost model and I am going to Extend it to account for this relationship between prices Persian inflation And to account for this relationship. I am going to Assume that consumers want to search for the lowest prices So this is the new element that I introduced in my model, and I am also going to provide supporting evidence on Shopping behavior that gives us an additional reason to think about consumer search and inflation Finally, I am going to take these product-level data so these Relationship that I find at the product level and I am going to also take a multi-sector version of my model and I am going to calibrate this Model to study the relationship between welfare and aggregate inflation And I will find that there are or there might be benefits of inflation that have been overlooked by previous literature Let's start with the empirical section We want to know what is the empirical relationship between Price dispersion and inflation The literature and also myself have fades phase two challenges The first one is that we want to measure price dispersion resulting solely from nominal rigidity so we want to control for product Triginality namely size and quality of the products the location of the stores and date of transactions to Overcome this challenge what I am going to do is to compare the prices of products that have the exact same barcode among sellers that Have these transactions at the same date I will talk more about this later The second talent is that we have We need sufficient statistical power to identify the relationship What I mean is that we need we need enough variation and also enough observations to carry out the estimation but The sample that I have to compute the price dispersion is only for a short sample period So between 2006 and 2017 Moreover aggregate inflation in this period was low and stable so this is not going to allow me to Estimate the relationship between prices per share inflation. I am going to overcome this challenge by Estimating the relationship between product level inflation and prices per share Let me tell you a little bit about the data The rates that I use is Nielsen's IQ Scanner data for the US retail and I already said that the period is between 2006 and 2017 so in this data set what we can observe is weekly prices at the barcode level This means that we can observe the price of a two liter bottle of diet coke And we can observe around three million barcode level items that can be classified into a thousand categories for example carbonated beverages in the case of diet coke and These three million barcodes Are sold by over 35,000 stores In more than 200 metropolitans statistical areas in the US And an example would be the Whole Foods store in Hyde Park, Chicago so just to Pin down ideas what I am going to do is to Take the prices of diet coke that this is going to be the item index by K across all the stores in Chicago which is going to be the Metropolitans statistical area index by M at a particular week index by T so I will take the set of stores selling the exact same item at the same date and Within this set of stores I am going to compute prices version as the standard deviation of the log prices and I am going to denote this by sigma sub KMT and Then within the same set I am going to compute the average price change Which I am going to come to call product level inflation and this will be denoted by P KMT So since I have all these weekly measures But I am interested in a comparative statics exercise I am going to take annual averages of these measures. So I will end up with This series of prices version and product annual inflation a product level inflation sorry at the annual level for a set of products and Metropolitans statistical areas The next thing that I do is to simply take all these observations and Compute these beans cutter plot What this means is that I just take all the observations of product level inflation at the product MSA and annual level and I divide them into a hundred equally sized beans Then for each bean that you can see on the x-axis I am going to compute average price dispersion and this is each dot that you observe in this figure What you can see is that around zero product level inflation Price dispersion is going to jump and then it will become flatter as absolute inflation increases And this is why I called this pattern as Upsilon shape as a robustness what I do is to Well, one of the robustness exercises that I carry out is to control for several sources of heterogeneity Among products and also metropolitan statistical areas simply by adding product near fixed effects and MSA year fixed effects and Even after controlling for all these sources at of heterogeneity You still get this pattern in the data so I carried out several Robustness checks and the figure is still there So as I mentioned in the beginning I I Try to explain this pattern with several of the shelf models and What you would find in these models is that the relationship is flat around zero and then it becomes increasing as absolute inflation increases So in the models that would typically use this relationship looks you shaped instead of Upsilon shape So This is the reason why I wrote a model because I wanted to explain this pattern using an extension of Standard city price model in particular in this case a menu cost model So I am not going to show you the details of the model today. I will just explain In a very general level the ingredients of the model and how it works so in This model I I just start Working at the product level because that is how I I Those are the units in my data. So I will Show you how everything works at the product level and in the end I will talk about how we can aggregate all the the product level markets to say something about aggregate inflation So at the product level market, there is going to be a continuum of heterogeneous retailers selling an homogeneous product K and there is also be will be a Continuum of heterogeneous shoppers searching a retailer to purchase the product K so Going back to Diet Coke We will have a continuum of shoppers that want to purchase Diet Coke And there is also a continuum of sellers that have Diet Coke So the shoppers each one of them are interested in Brutasing Diet Coke from only one of the retailers Okay, so Let's start with The retailers price strategies. So the first block there on your left So This is pretty much the same as a standard menu cost model We will have that the retailers Set nominal prices and to adjust they have to pay a menu cost They will also face Eosyncratic menu cost shocks and the product level inflation So these are the two reasons why these retailers would pay the menu cost and adjust So nothing new there for the moment after we aggregate the the retailers price strategies that is That is going to give us the real price distribution that I am going to denote by f of K so this Real price distribution is what The shoppers are going to take into account when they compute their optimal search strategies. So From the point of view of the shoppers they want to purchase Diet Coke and they know that there is a continuum of retailers out there, but they Don't know the prices that each retailer is charting. The only thing that they know is that The real price distribution has a particular shape in this case, they know the shape of fk of p so I am going to assume that Shoppers can search sequentially for the lowest price this means that they are going to start with a particular draw of this distribution and Depending on their search cost that is heterogeneous. They can decide whether to keep That price draw that can simply be the price that the store crossing the street is charging Or they can continue searching So what we will have is that there are some shoppers that have a very low search cost So they will continue searching and searching on until they find very very low offer so These shoppers are going to accept an offer if it's lower than the reservation price and there are other shoppers that have a very high search cost that Might be willing to accept a very very high offer So in the end we will have a distribution of search cost that is going to determine the distribution of the reservation price and this will mean that Shoppers who will be willing to accept different offers depending on the level of the search cost Sorry, okay Now we will have the distribution of reservation prices given by the distribution of certain search costs so We can aggregate the optimal search strategies of all of these shoppers and That is going to give us a demand function that is going to depend on the optimal search strategies of the of the shoppers so Then this demand function will affect the profit function and both of them will be affected by the Search strategies with in turn will be affected by the real price distribution Which in turn is going to affected by inflation so the only way in which inflation affects the optimal search strategies and also the demand function is through prices revision and Well, finally this demand function is going to Affect the retailer price strategies closing the the circle now I will Explain you the overall intuition about why this model reproduces this Upsilon shape relationship between price dispersion and product level inflation So as I mentioned in the beginning search cost is going to be Ethere genius and it's going to range between gamma lower bar and gamma upper bar Meaning that the consumers that have a very low search cost This is gamma lower bar are the ones that are going to search the most and we have the lowest reservation price So now let's go to the case in which Product level inflation is equal to zero So we want to understand why in the data we we would observe a Very low point in the relationship between product level inflation and price dispersion Before it becomes very steep as absolute inflation increases So in an equilibrium with zero product level inflation Search is not going to be profitable for shoppers that have a search cost that is very very high So the ones that are going to be searching are the shoppers that have a very low search cost These shoppers that have a low search cost will all have a Reservation price that is very similar and that I am going to denote by rk of gamma lower bar so these shoppers that have a very low search cost and that are a relatively high density in the market will Shop will search until they find a very very low price author Now the retailers that are very productive Internalized that these shoppers will be searching until they find this particular price So if I am a very productive retailer, I will be charging this very low Price only to serve searchers Because if I said a slightly higher price, I am going to lose all of these customers that are only willing to pay a low price and if I said a price that is slightly lower I am not going to be attracting more More shoppers. Yes. Ah, ten minutes. Okay. I thought you had a question five. Okay, okay Then we will have that All the productive retailers bunch around these very low reservation price That is we observing this real price distribution plot and this is what generates low-priced dispersion around zero product level inflation Then suppose we increase product level inflation by a little bit just by an epsilon In the previous case we had zero product level inflation So real prices were equal to nominal prices, but now that we have inflation Real prices will be eroding every period. So if the retailers wanted to stay They wanted to keep charging this very low Reservation price this very low price equal to the reservation price They would have to pay the menu cost every period So the the retailers only to save on menu cost. They allow low prices And this is going to increase prices version. So in this plot what you can see is that the the blue bars represent the equilibrium at zero product level inflation and the red bars are the Same equilibrium, but when we only allow retailers to Reoptimize as inflation increases. So when Search behavior stays fixed at zero, but inflation increases a little bit We will we will observe that prices person also increases a bit Now if we only we if we also allow shoppers to reoptimize We will observe that this little bit of prices person arising for from a little bit higher inflation Is also going to increase the incentives to search for lower prices. So what happens in this case is that? there is also feedback to the Behavior of the more productive retailers because they see that some consumers are searching more and Some retailers especially the more productive will have more incentives to decrease their prices and attract more searchers and this is why we observe that the Lower end of this distribution is also expanding But on the other hand, we will have that the least productive retailers Which are mostly serving non-searchers don't have incentives to decrease their prices so As the price gap by productivity increases Inflation is going to increase a lot and this is why we observe a jump around zero product level inflation now just to mention very quickly that What I do when I have this model is just to calibrate it to match this Upsilon shape Pattern also the frequency and the size of price changes as in the rest of the literature and then I compare my model with Two models so the goal of seven Lucas model that in both figures is the blue line And then the Venom model that is my model, but without the asyncratic shocks So the left-hand side figure shows a relationship between product level inflation and prices person and the right-hand side figure shows a relationship between absolute size of price changes and product level inflation and the The dots in each figure shows data. So the main takeaway is that my figure is the my sorry My model is the only one able to reproduce the relationship between price inflation and Product level inflation and prices person and also other relationships that can be matched by other models Well, finally, let me mention very quickly There is also shopping behavior evidence supporting this The mechanism in this model. So a prediction of my model is that shop shoppers that are searching more So shoppers that visit more retailers are going to pay the lowest prices in the market and this is going to be a Stronger mechanism when absolute inflation and the product level is higher so I go to the consumer panel data of Nielsen that is the sister data set of the Of the one that I used to compute the the Upsilon shape and I When I put in the x-axis is the number of distinct retailers that a household visited and on the y-axis the Log of the relative price that the household paid for a particular bundle so the blue line shows that the more Distinct retailers you visit the lower the prices that you pay and this relationship is going to be steeper as absolute product level inflation increases and When I take simulated data from my model and plot the same relationship you can see that the data matches the The model matches the data even though I didn't target this relationship And just to final finalize Well as Policemakers we care about aggregate inflation So aggregate inflation in this case is going to be the average of product level inflation In this economy and that can be decomposed into a common component That is in this case going to be the rate at which wages increases minus the average of The rate at which sectoral components increase and I am going to take that from the data So I will have in this exercise in which I vary only the common component That as inflation increases the average adjustment cost increase and also the resources that consumers spent on search increase But there is also a benefit of inflation and that is that search increases competition So in this case market concentration increases and also the average markup decreases So if we compare my model with other models that miss the Upsilon shape Relationship we will find that my model predicts that welfare is maximized at a positive rate of inflation while the other models predict that welfare is maximized at zero Inflation and that is everything that I have for you today So first of all, thank you very much for having me here I mean has been great pleasure to to read this paper That I think is a it's really a fantastic paper. So what I'm going to do is to talk a little bit about where This literature is and why is so important for monetary Economists, so this literature has noble tradition in days back to part of the job among others and Emphasize that the presence of search costs produce market power in the in the economy then in the 90s They were like models trying to understand how consumer search and firms price friction will deliver some realistic business cycle facts and They emphasize that among them Ben Abo is one of the leader of this literature They emphasize that more inflation volatility can be good Why because it generates price dispersion that the incentivized search that decrease the market power So it has a good effect on on the on the markups That is the other way around Reason for which we usually think inflation is bad So Francisco's paper contributes to this line of literature by providing three main contribution I mean, this is the way I see it. So the first is provide convincing evidence robust evidence I cannot find better Qualifier that price dispersion is oops long shaped inflation. So the introduction of oops long is also like a contribution I get at the item level. Okay, so when you think about the picture that she has shown each point Is an item? So he's a market for one item. Okay, so annual inflation is annual inflation on the item level It's not that inflation this will be important for something I will say later and then build a model of search menu cost and firms heterogeneity that replicates the fat and the Contribution is on stressing how important these firms heterogeneity and then among others There is something that attract my attention is that inflation she shows inflation has also bad welfare effects So she emphasized the good welfare effect, but the picture is you shape it comes back and there is like This effect that if there are more people that search There are some that stay with the with the firms are the ones that are less elastic So for them the markup increase and this is a welfare loss. Okay, this was absent in other in other papers Okay, let me try to give you a summary of the mechanism as I see it so Suppose there is a guy that can have consumption of price pH and there are firms that produce the The same good with different productivity and this guy has a search cost So he's going to accept only prices that are below that otherwise is going to consume this so what is happening that the optimal pricing is to price exactly at the reservation price and And there will be no dispersion in prices in this case So the heterogeneity in productivity is shut down by this kind of search mechanism So you have heterogeneity markups, but not any longer in prices. Okay So imagine that there is another guy that has different search costs still this can be optimal if If it's more important to try to attract two people Then try to make a larger markup on one of these guys and this is one of the future of the model Okay, so there is no price dispersion because these heterogeneity in productivity vanishes through this this mechanism And now I want to introduce menu costs So suppose that you have to fix the price one period and then there is a second period in which you cannot move The price okay extreme menu cost infinite menu cost. Okay, and there is inflation So what happens with inflation is that if you fix the price here? Then inflation is going to move your price your real price here right in this region And this can be good for the green firm But it's not any longer good for the red one because it deteriorates so much it goes below the cost Okay, so now the firm have to think again what would be the optimal price in the first period and Actually the red now may have an incentive to put a higher price Because inflation then will deteriorate the price But still you will be able to attract one guy and so you see heterogeneity matters again and shows up in prices through inflation Okay, and it matters not only the heterogeneity of productivity, but also the heterogeneity on the on the consumer side So this is how inflation Generate dispersion in a case in which without inflation you will you will have zero deflation Okay, and then if you understand this mechanism, you also understand that if you reverse The the inflation direction then it's completely symmetric So this is where the model is able to explain this symmetric behavior. Okay, so this is my Recollection of the mechanism and how is able to match the data But I want to do a further step So there is another reason why we should care about consumer search So there is a more recent literature that has showed that you can think about consumer search as a micro foundation For why firms are sticking their price? Why because if people run away from you, maybe you don't want to raise the price You want to retain your customer and so this is a micro foundation for price rigidity so in one of my recent work, I'm thinking about something else that Consumer search can be a micro foundation for paid price rigidity that is supposed that the firms are completely elastic Okay, but it's your action of searching for a lower mock-up that makes the price that you pay Less rigid with the with inflationary shock. Okay, so price go up one percent But when you are it by this you put more effort and search for something Lower markup. And so this is how you the price that you pay doesn't increase one percent Even if they are posting one percent more. Okay, so why I think that this is important to deserve attention because When we talk about Newken Asia Phillips curve all these things so we have in mind Posted price inflation. Why because we refer to the new kinesia and typically in which there is no difference between posted and paid price inflation Okay, in fact what matters is the paid by the inflation but in the new kinesia. There is no difference and What I want to and then this is why we we pay so much attention on pricing Okay, but there is another half of the world in which there are households and that choose where to go That is equally interesting and What what I what why my interest in reading this paper is trying to understand how this model may reach My view about this difference between paid and possible prices. Okay, so let me explain you why in the new kinesia We have no difference. Okay, so here in this graph. You have paid inflation posted inflation So suppose there is some posted inflation so firms raise one percent your the price but if you are if you are Attached to a firm that is raising the price. So it's optimized. You have an incentive to shift to the sticky prices, right? So then the the the the paid price is lower than the possible price. What happens with deflation when You are attached to a firm that is not revising your price Then you have an incentive to go to the flexible ones. So you are still lower Okay, so posted paid prices is lower than posted price. So this is the relation in the new kinesia and in the first order Approximation is equal. This is why we don't care about what households do. Okay, but you can have a different story What is the different story? The different story is that? When people buy stuff, they don't know what are the other prices? Okay, so I see my price going up the price of the Shopping enabled going up. I don't know if this is local or global But they give a chance that this is local. So my relative price is getting worse and this make me search So if inflation goes up in post inflation I Search more and my paid inflation goes down as in the new kinesia But the thing is different when we go on the other side When there is negative inflation Then I I give a chance to the price to my relative price to be better And so I have less incentive to search I'm more willing to stay and so the paid price may be higher than the Postal price. Okay. I experience less deflation and so this is a model in which you can have That paid price inflation is different from posted even at the first order Okay, and this is the effect of search In the paper we show with eye our eye data that 1% posted inflation Equals to 0.3 paid inflation. So this relation exists in the data and This is just to advertise that I I have a ERC Consolidator grant that is going to build on this. This is one of the legs so a part of for advertising this Why I Introduced this discussion because I thought oh, but we have a model of search incentives So I want to think about the same picture with the model of francesca. Okay, so the first thing is search incentive Symmetric as in the new kinesian case So I was expecting maybe this evidence will point me out that new kinesian is the right one But it's discontinuous. So first of all, I don't know what happens in first-order terms But then I also realized that this is not so simple because the distribution of post it Changes with a with a realization. So in practice one of the advantage of the model is that the distribution of post it It's a function of the shock and the shock is also moving the distribution of the paid Okay, how people choose to move and so it's a very complicated thing and Actually, I I would suggest to explore this because there could be a contribution in that in that dimension. Okay But I'm thinking a bit more. I also realize that where the moment is not obvious that search incentive are Symmetric in this model in the sense like they push me to the new kinesian case And I show you this picture is the last thing that I'm going to show to to motivate that So this is a picture for the for the European data showing the dispersion of Inflation at the item level. Okay, so for each period you have the dispersion at the item level And you can see that as the average increase so more inflation Means also more cross-section of dispersion across items. Okay, so it means that if my incentive to search is inflation it means also that Francisco will find in the data that I'm searching more at the item and item level when the This this at the item level. I have much more dispersed inflation rates. Okay, so this is a very interesting relation that I think deserves more Investigation and I think Francisco has something in the model that can explain that because If you interpret different varieties of different items. Yes, you have that. Okay, so my recollection of the paper I think this is a fantastic paper. It's really I mean very interesting for me. So I never think enough for What do you mean here? I think It's a fantastic quantitative micro data paper What still I don't see very well is how aggregate inflation can feedback especially for the fact that people Search for bundle of goods doesn't search for each item separately And so I think this is the maybe the margin of improvement for the for the research Thanks, sorry for thinking long Thank you We still have five minutes for discussion are there questions from the audience before Francisco gets a chance to answer also to the Yeah, Peter Thank You Peter karate from a CB. So so one question is is in the data We see a lot of sales which is kind of these temporary cuts Which are kind of it's it and and there are models with kind of dynamic pricing when Then firms are kind of using this this kind of dynamic Distermination so have have searchers kind of come for the search price and and try to get Others who are kind of not searchers kind of keep paying the high price and and and basically my question is Is how do you kind of first treat in the data these these kind of behavior? I guess you don't have this in in your model and and the other is is how do you think this kind of mechanism would change Some of your conclusions. So if you kind of take take this kind of possibility of firms into account Okay, so first Let me think Got a ton of for the discussion most of what we discussed in dinner yesterday so I do think that it is relevant to introduce consumer search in inflation models especially for central banking because We do observe that so as I I just show you that as inflation increases We have consumers searching for the lowest prices as And that's guide Hano Noted there might be differences between how posted and Effective price inflation react to the to the Business cycles so consumer search might have a crucial role in this so of course I take his comments and I do think that We should continue doing more research into these areas Then to address Peter's question so the first step that I took to address that question was to Filter my data to remove all the temporary price cuts. So these data has Doesn't have sales blacks. So you have to make several assumptions in order to remove sales So I started applying sales filters that are Typically Algorithms that allow you to remove Be shaped patterns in the price series and There are also filters That take a reference price From the price series so I Thought That it would be very hard to do it, but it was Easier than I thought so it took me a month instead of you know, like six months and What I find is that after Removing these temporary price cuts and focusing on Series that show you regular prices. You still have this pattern. In fact in a Newer version of the paper that I am working on I am just focusing on regular prices since I Don't have any sales in my model And the overall conclusions don't change And then Regarding sales, I think that that is also a very interesting mechanism that could be added in the paper because I So the way in which they fit into my model is that by charging Low prices, you know, the the retailers are attracting more searchers So I don't think that the main mechanism would change much You would still have these micro price setting behavior that in the end would have Irrigate implications But of course if you were to think of Sales as a Mechanism that retailers use just to To Just on the retailer side without any consequence on the consumer side, so if You do not include consumer search. I mean you would be reaching the same conclusions as the previous literature So we have no question from Webex. So I've been now Hennington can bring us to the other side of the moon on the heterogeneity of productivity and firms Good So I really enjoy the conference. I have to say and that this thanks to a number of people so that is Sarah Ina Elena Peter Edward Micaela, it's also Jean-Paul Chiara Mathieu and Richard. Okay. Thanks to all of you Good now to confuse you a bit more. I have two co-authors. This is Klaus Adam University of Mannheim and Andrea Alexandrov from Rome and There's a disclaimer That's the usual one so This paper is About inflation distorts relative prices. So this is our main finding and I'm going to take you through a little bit of theory and evidence Now in case you missed Francesca's introduction, I'm using the same So there are monetary models and these monetary models have a feature So so quite many of them have this feature and that is that inflation distorts relative prices If nominal prices are sticky So how does it work? Suppose you are a firm and operating in a high inflation environment Now you set your price, you know that price is gonna stay for some time and you know that inflation is gonna erode that price over time so you Understand this and you know, there's a target price that you want to hit so you're gonna Set your price above the target price initially understanding that in expectations You're gonna end below the target price eventually Okay, now that gives inefficient trifts and relative prices during these non-adjustment periods and these trifts generate Inefficient fluctuation and relative prices right and those inefficient fluctuations they generate misallocation and that that is where things get Not so nice, right? Now this mechanism Which is in many of these models is also key for many of the well-known predictions of these models And I put just two here so permanently high inflation reduces economic welfare and Another one would be low and stable inflation is desirable, right? You've you've seen these predictions frequently Now as Francesca emphasized as I'm also emphasizing structural evidence supporting this mechanism is Largely absent and the emphasis here is on structural now Why is this there's a relatively straightforward reason for this? So identification of price distortions in fact is difficult Now look at this decomposition over there, which has to observe relative price So that's the sticky price that the firm sets and you can decompose it in the flexible relative price So that's the that's the price that the firm would like to set ups and pricing frictions Plus the price gap, which is just the gap between the sticky and the flex price And that price gap is the distortion Which depends on inflation, idiosyncratic shocks, the degree of suboptimality of inflation, what have you, right? Now the thing is we don't observe this flexible relative price That's a counterfactual price, right? We don't see that and hence we don't see the price gap Now that's that's a problem because that's the object that depends on inflation and that we would like to know, right? So then We would like to know say the price gap ideally directly or moments of the distribution of the price gap But we don't see it so price distortions Generally are not identified if we just observe the sticky relative prices alone Okay, that's that's the problem and of course you could you could adopt special assumptions like the the flexible price follows a random walk Or you suppose you have quite informative data about this flexible price Then of course you could overcome that problem, but this in general is not is not what we what we have Now the insight that we exploit in this paper is that in fact We don't have to Directly identify the price distortions if we want to test whether or not inflation distorts relative prices You know this main mechanism that is there in theories The only thing that we need to identify is the marginal effect of inflation on these price distortions And that's something different and it turns out that this can be done and we show how we do this in this paper Now we derive a structural empirical approach So we go back to the theories and derive our estimation equations directly from the theories to estimate Exactly this marginal effect, right? And it turns out that approach that we're going to derive works for both time and state-dependent pricing frictions So this paper is really not about whether one of the other one or the other is more plausible in light of the micro data because the mechanism is in both of these types of models and That's what we are interested in to see whether the mechanism is really there now once we have this empirical approach We're gonna implement it using the UK micro price data, which you can find on the website of the Office of National Statistics So three main findings in the cross-section of products Suboptimal inflation and I have to explain to you how we get to the suboptimal part of inflation is strongly associated with price distortions So that is confirming that this mechanism is there in the data now in the aggregate UK economy Going from the product to the aggregate level these price distortions happen to co-vary with Aggregate inflation, which is a prediction of very basic models and that prediction is going to be borne out in our data also However, most of observed price dispersion so remember my my little decomposition That's dispersion of the left-hand side the observed price in fact is unrelated to price distortions Okay, and the reason is pretty simple this flex price is just so variable that it's going to dominate most of most of the observed price dispersion Okay So I'm going to show you this even though we cannot directly identify price distortions, okay Good now here's a little preview about the Empirical approach. It's a two-stage approach and we're going to go and start out with Detrending the relative price of an individual product and here you have to be careful now my Labeling here or my word use is different than Francesca's so product for me is a physical good at a particular place Okay, it could could also be a service But the point is it's not the UPC a barcode that you can buy at different stores or a different region It's really a barcode in a store. Okay, so it's a finer definition of a product Now we take this product and we're going to follow it over the lifetime of this product and We see the relative price of that product and that relative price over the lifetime. We're going to detrend this gives us a residual and We compute the variance of this residual so residual dispersion. That's the first stage now in the second stage we take this variance for different type of products and generate a cross-section and Then we're going to relate that cross-section to product specific measures of suboptimal inflation Okay, now We do that regression We get a coefficient and that coefficient is the object of interest That's the marginal effect of suboptimal inflation on price dispersion And I show you here that the marginal effect that we estimate so you see the distributions of this coefficient That is quite positive. So we estimate this coefficient in each of the thousand Roughly a thousand expenditure items so an item would be a collection of similar products in each of these items in the UK CPI and That's the distribution we get it's fairly positive and fairly significant also Good now related literature Let me reiterate. So what we do is go back to the theories and derive our estimation equations directly there And these equations suggest that we look at a very specific type of price dispersion measure namely the one over the product life cycle and That you should relate to the product suboptimal inflation rate Now what existing work has done is something a bit different Existing work had has looked at at a given point in time at The cross-section of dispersion and prices across different products. Okay, that's also what Francesca did and then Existing work took this measure of price dispersion and related it to actual inflation. So we would relate it to suboptimal inflation So with this let's let's jump into the general setup, it's relatively simple aggregate consumption is contactless composite of item level consumption Item level consumption is a CES composite of all products in the item Now that that demand structure is just to replicate our data structure now a product in an item as I said is really a physically good It could be a service also in a particular location. Okay Same degree of price for the DD for all the products in the item and you could have product turnover in the item Now how about the pricing we use a quadratic approximation of the firm objective So firm J which produces product J and item Z is going to set the price to minimize the period loss function over the expected price Bell and that loss function is in fact quite quite simple It's just the squared deviation between The the sticky price of the firm relative to the item level price level. So that's the PJ over the PZ Minus the flex price. That's the P star right and the only interesting object here is really the flex price So let's let's look at this Now we assume this flex price has three components and now the first one is Blue so that's a product fixed effect that is drawn from some arbitrary Distribution at the time when the product enters the market And it could be a lot of stuff It could be on some quality service model across markup all the stuff That's kind of constant over the product lifecycle, but specific to the product and location of that product Now the second component, that's the red one That's a product specific trend again. It's drawn upon entry of the product and that's a marginal cost trend in terms of structural Structural bits So you could think the the firm comes into the market starts producing its its product And but gets more for more productive in the course of time of producing that product So it learns how to produce that product better and that gives a trend in the marginal cost of the product Now it turns out that that this trend is in fact the optimal inflation rate of this specific product and It's quite easy. So post this trend is 2% now The firm sets its price at some point its sticky price now its flex price is gonna decline over time, right? So ideally its sticky relative price also should decline at the same rate Now if the flex price trend is 2% you want to have the price level also trending up At 2% because that's going to reduce the the sticky relative price of the firm Okay, that's the sense in which this trend here is really capturing the optimal inflation rate for this specific particular product now the last component of this Dynamic this flexible price is the idiosyncratic shocks and again, this could be cost productivity or demand shocks We don't really take a stand here. The important thing is that these shocks that come from a Stationary process which is the same for all the products and item, right? So realizations of the product process, of course are different across the products But the process the process itself is really the same for all the products Now before I really jump into the empirical approach Let me be very clear about how we achieve identification and there are two things to this The identifying assumptions and identifying variation Now the identifying assumptions. I told you already, right? So we can assume that products face the same degree of price rigidity in the item and they have the same process for idiosyncratic shocks Now of course to satisfy this we cannot look at the entire economy at once at all the product But instead we really implement this empirical approach separately for the expenditure items for each of the expenditure items that we see Now the identifying is some variation that we use that is really Variation across products in the product specific optimal inflation rate Okay, so that's that's variation in the trend that is specific to the flex price of the product Now this means that we do not exploit time series variation in actual inflation So in inflation at the item level or inflation in the at the aggregate economy level And the reason is that both of these variables are relatively stable in our sample And that's that's not gonna give a lot of identifying variation Now with this let's look at the at a little example in order to illustrate what in fact we do Sorry, I just stopped my time Now this example Has a deterministic flex price to keep things simple and of course that's a special case in which the idiosyncratic shock process is The same for all the products it has the same price adjustment calvo probability for all the products in the item. So that's 1-alpha and then it has the item level inflation rate. That's the pie is that being positive say 2% to keep it Specific and importantly, it's gonna be constant over time. Okay Now then you see the figure over there two things are there the sticky relative price That's the gray line and the flexible relative price. That's the blue dotted line and we follow a specific product product one over time and you see that these two things perfectly overlay Which tells you that the 2% is in fact optimal for the product one Okay, so the relative price stand of that product is exactly equal to the inflation rate in the item Now that's that's kind of a nice case. Let's look at product two Now for product two it turns out that the flex price trend is steeper than the inflation rate so The product at the firm sets the price Knowing that this price is eroded too slowly Relative to what the flex price of the firm is doing So the firm starts below the flex price knowing it's ending up in expectation Above the flex price at the point in time when it can change the price again Now there is now a gap between the flex and the sticky price and that gap is the price distortions We're gonna be interested in okay Now look at the product to prime to just see that this is symmetric argument Now inflation is too high because the flex price trend is equal to zero okay Again, you get the price distortions But instead of starting below the flex price the firm is now going to start above the flex price Okay, but apart from this it's it's fully symmetric Now let's look at product three here That's the situation in which the flex price is even steeper. So The inflation rate and the item is even more suboptimal and of course what's gonna result is more price distortions Okay, now you take the Mechanics of all the products together you get the equation down there that says that the variance of the Residual that you get after detraining the flex the the flexible sticky price. So that's the gray lines That's our data after detraining this data We can compute the variance of the residual variance of you and that's gonna be related to the product specific measure of suboptimal inflation Pi minus pi star squared because this is a symmetric argument and then that's gonna depend on the coefficient C That's the marginal effect. We are interested in okay, and in the theory this marginal effect is just driven by the degree of stickiness in the economy Now this of course was a simple example without the shocks So let's get a bit more serious here adding shocks. The first stage is still the same. We're gonna be trend the sticky relative price of the firm and That is gonna give us an estimate for the a that's the the intercept coefficient and an estimate for the B That's the slope coefficient now. We can show in the theory that these two things converge to The respective moments in the flex price, right? So the a converges to the p star and the B converges to our product level of the manipulation Which is what gives us an estimate of that object now? Then we go into the second stage as I said we take the variance of the residual from the first stage Put this together for many different products Which gives us a cross-section and then we got to relate this in a linear fashion to the suboptimal matter squared of inflation We get our marginal with marginal effect. That's the C again of suboptimal inflation on price distortions And now because we have idiosyncratic shocks. We also get this constant V Now this constant V captures two things Elements from the flex price and elements from the sticky price economy. Okay, so that's the identification problem These two things we cannot tell apart But luckily these two things do not depend on the degree of suboptimality and inflation, okay? So it's fine. We still get our marginal effect but I mean we as everybody else in the literature are subject to the Identification difficulty that we cannot tell apart the sticky and the flex price elements in the constant Now I said this works for both Calvo and menu costs So for Calvo the coefficient we looked at already For menu costs, so that is a continuous time result. That is one over the adjustment frequency squared the coefficient the marginal effect and Importantly in the menu cost model the second stage holds Approximately to the second order right so this is to say that more stuff is going on in the menu cost model But to second order our second stage is going to be valid Now it is true that our estimate of the marginal effect is going to be biased towards zero in small sample In small samples and this is because of estimation error We make this argument in the paper. I'm not gonna go through this here now with this Look at the theory. Let's look at the evidence. I told you about the data. It's the official UK micro price data So We prepared a little bit we get rid of sales, but our results are robust to including them So we have about 800 products in the average typical item and we have about 15,000 price quotes in the average item And we have about a thousand expenditure items So we get a thousand estimates of this combination here of the slope and the intercept And of course our question is this is this slope coefficient Positive right and you know the answer already I showed this at the beginning so this here is our coefficient estimate the distribution of this and It's clearly very positive here's the t statistics Which are informative under the null that this coefficient is equal to zero that also looks kind of convincing to me now We get estimates for for the intercept also, but those remember we cannot really disentangle into inefficient and efficient variation Now that's that's the evidence of course, I Showed you that the theories imply an Interpretation of these coefficients the marginal effects that the estimate in Terms of the adjustment rate and this adjustment rate is observed in the micro price data Right so we can go and compute it and compare it to our estimated coefficients Which is what this figure does here? So you get the estimation implied the adjustment rate that's down here and then The adjustment rate that you can straight compute in the micro price data. You see that they are correlated It's a point. It's a point six correlation but you also see a quite the downward bias regression slope which is the downward bias that we get in our Marginal effect estimates, okay now about the identifying variation. Let's take away in our second stage The optimal inflation remember he was the pie star in my original baseline Specification and instead replace it by the inflation rate of the item And this now is the average inflation rate of the item Over the lifetime of the product that that we look at in this specific case And you see if we do this we take out our identifying variation We don't get any indication of a significantly positive marginal estimate, okay? So this coefficient is now completely centered at zero and that's also what the T statistics tell you, okay? So the point is if you relate our measure of price dispersion To actual inflation, which is what the previous literature has done. We don't find anything, okay? Good now we do a few further robustness checks one of them is allowing for non-linear relative price trends I guess that's something that's that's kind of important I don't want to spend more time on this Except you asked me especially for one of them So we also include sales prices and do a couple of other things I mean, I think this evidence is actually fairly robust Now let's let's go back to our little decomposition of surf prices flex price plus price gap On the left hand side, we can just compute the cross-sectional dispersion of the observed price Which is what the literature has done before now we can do this also in our framework In order to speak a little bit about this aggregate decomposition And show what this would be in in our case, right? So on the left hand side, this is now The cross-sectional price dispersion of the observed relative price in an item set at a given point in time So that's a given month and we can decompose it into Part that we can safely attribute to the flex price dispersion So this is the component of the flex price the deterministic component So the intercept and the slope coefficient and the variance of all that in the cross-section at a given point in time Plus a residual component and that residual component again has has our difficulty here and that started edification problem containing flex and sticky price elements plus something a term that has All the effect of suboptimal inflation on price distortions And you see this thing is now a bit more complicated than what you get in the simple models It depends on inflation in the item But also at the entire distribution of optimal inflation rates across products at the given point in time Okay, so it could inflation actual inflation in fact could raise This thing here, but it could also reduce this thing here depending on what the distribution of the optimal inflation rates is So it's interesting to look at this in the data and that's what we do. So we aggregate across items using expenditure weights and The overall price dispersion. That's the red line and you see it has over our two decades sample a massive upward trend, right? which could be Product heterogeneity increasing over time. There's more products. What have you I mean lots of reasons for this to occur and our approach would say that most of this basically all the trend and most of the variation in overall price dispersion is What we would attribute to the identified part of flex price dispersion. Okay So that is not about inflation distorting relative prices. That's something else Um now what's left over that's the red line here and we plotted together with um the actual inflation rate in the uk And you see that these these two times here is kind of co-move quite strongly and uh, that is because of price distortions that result from some optimal inflation here Okay, so that's that's because of the last term that really we could identify because we could identify this marginal effect Now we still have our identification problem, which is about the level of that thing Right, so we can't really tell whether everything we see is inefficient or not But we can derive lower bounds on price distortions So so the the component of overall price dispersion that is due to suboptimal inflation And that is a standard deviation of the log relative price about four percent. Okay, so that is uh Not overwhelming, but it's also not negligible. Okay So that's that's basically it. Um, so what did we do? We derived a structural empirical approach to test a main mechanism in the sticky price models Whether or not suboptimal inflation distorts relative prices We find at the product level very strong evidence in favor for this At the aggregate level we get positive co-variation between price distortions and inflation Which is what a very simple model would predict in which optimal inflation for all the products in fact is equal to zero Right, so that's consistent. This evidence is consistent with even the simple model But of course most of the price dispersion that we observe Is not about suboptimal inflation is really what's going on in the flex price. Okay, let me stop you Well, first of all, let me thank the organizers for inviting me to discuss this very interesting paper and for organizing this great conference here in and here out I really enjoy being here Uh, the usual disclaimer applies. So I'll use on my own and not of any other person or institution um So I'm going to start by uh, quickly summarizing the uh, contributions of this paper and I think Kenyon did a great job Presenting it. It's a very long very dense very technical paper It takes time to read it. It takes time time to check the derivations and everything, but he did really wonderful job So I'll be very quick on this and I'll go very uh, quickly to the comments So what this paper does it proposes a novel approach to identify suboptimal price dispersion Why do we care about optimal versus suboptimal? Is because some of the price dispersion is due to heterogeneity So maybe there's the same product that you can buy in different stores But really like the amenities in store a more than you like it in store b So you buy that product in store a and you're willing to pay a higher price There is no problem with this kind of price dispersion because you just pay in for an extra service that you receive So the type of price dispersion that economists really worry about is the one that arrives due to the price distortions or price rigidity and so this is uh, exactly the price dispersion that this paper is identifying So what I particularly like about this paper is that its empirical strategy is based on standard models of price rigidity And they're going to unify different types of model They will look at both time dependent price rigidity models and state dependent models Now on the empirical side it documents large price distortions and a strong commovement with inflation in the UK CPI microdata, which confirms some of the evidence in the literature that that uh Hennan told us about earlier So let me itemize the key elements of this paper So the key challenge as I said is to separate the optimal price dispersion from suboptimal price dispersion What is their solution the solution is to exploit a variation in trend inflation across different products So they're going to go product by product at a very granular level different items in different stores estimate the average growth rate of prices for that product and then use the variation in this growth rate to Identify the uh the suboptimal dispersion Now nothing is free in economics that will come with the at a price That it requires some assumptions on on the fundamentals in the model and i'm going to talk about these assumptions later But before that let me quickly provide the motivation. This is also related to francisco's paper So in in our models and different classes of aggregate models, we can uh Approximate the welfare function In the following way, we will have a steady state component that depends on price dispersion And we will have a business cycle component that depends on the variation of the price dispersion From uh from the steady state level And so here you can see the theta naught in this approximation is a steady state channel and the theta two depends on the variation of inflation Over time, it's a business cycle channel Uh, what is interesting is that this approximation is not specific to a particular time a pricing assumption It just based on the on the utility function of consumers So whether you have time dependent price in a state dependent price, you know, you add search You're going to arrive to to an equation like that. So price dispersion is a fundamental issue in this type of model Now in different price and models, we would have very tight links between price dispersion and an inflation And of course the easiest model is the calva model because it gives you a close form solution In the calva model, we can actually write down the equation that will also show up and enhance paper In other models will also have this relationship. Uh, it tends to be positive, but it's more difficult to pin down So let me briefly go over the identification in a nutshell of this paper. So What what this paper does? It regresses individual prices on on time trend. It extracts product level Time trend inflation and then it uses the log deviation on the product's price from the trend to identify the dispersion Then in the second stage, you just take the variance of the product level Deviation and you regress it on the deviation of Trend inflation for a given product from the trend inflation in that category of products and the slope coefficient will give you exactly the marginal effect Now there are two key assumptions. So I think I didn't had more, but I'm going to simplify it. One is that you need to have a variation in trend inflation's Across products within a narrowly defined product category But at the same time you need idiosyncratic shocks to be homogenous across products So these assumptions need to work together to achieve identification So my first comment is exactly about that So I wonder if we can get more evidence more external validity for these assumptions That in fact, this is the case For instance, think about two products like take a category as flat screen TVs And the product here would be an LG TV versus a Samsung TV So the identification here assumes that LG TV would be growing at a 3% rate say and Samsung TV would be growing at a 4% rate But at the same time the shocks are exactly the same So I wonder if that assumption applies better for services So if it applies better to goods and any additional evidence will be welcome And of course, if we could relax the assumption of homogenous shocks That would make the identification even more powerful there A very quick comment that there could be an additional Additional analysis of time variant trends. So this paper uses linear trend and the use of quadratic trends is a robustness check But maybe we can use some filtering techniques to identify the strength of the product To identify the strength non-parametric My second comment is about distinguishing between time dependent and state dependent pricing models So the interesting result in this paper that up to some approximation and for a given value of parameter kappa We're going to get exactly the same slope here Now this works for kappas in a range from zero completely flexible prices to some kappa Bar kappa here is the menu cost That is positive And my question is how large is that kappa that approximation holds Usually the movement of price dispersion inflation is much stronger in the calva model Because there's no selection effect than in the menu cost model because menu cost models the selection effect is strong And so It's important to know that this kappa is smaller kappa bar is small enough or whether it can be large enough to get this approximation And I want to show Some result on this from a paper that I particularly like mostly because they wrote it In this paper, I I I wasn't as good at math as handing on co-authors So I just asked computer to solve this for me. I didn't do the closed form solution But I had a model that nests A time dependent and a state dependent model given the parameter xi And so when xi is zero you get a calva model and when xi increases you get closer to the fixed menu cost model And I simulated the model and computed the Com movement of price dispersion and inflation and compared to that in the microdata And I found that there is much more state dependence In the model uh in the data that that we would observe in the benchmark model So in the paper, uh, that Henning the co-authors write, uh, you would actually have exactly the same Com movement between the two but up to some values of parameters and and some shocks So I wonder how to reconcile this simulation results and the closed form solution results here So let me skip this and go straight to my third comment. Sorry So I think I think this paper makes a lot of progress and understanding granular level price dispersion But it requires granular level data that doesn't come at high frequencies And I think practitioners would really appreciate some measure That is available in real time or at least monthly or quarterly And so I try to see whether we can learn something from relative price variability from sectoral inflation rates and how strongly income moves With inflation So this chart plots two series one is 12 months headline pc inflation And the other is the relative price variability, which is standard deviation of sectoral inflation rates And it measures the correlation between the deviation of inflation from trend Although I was lazy and assumed the 2% trend, which is clearly not the case in the 70s and 80s But it applies now And the price dispersion and the correlation aggregate data is fairly strong So that there's some reason to look at the aggregate data as well And if we fix the sample to start from 2012 when the target was announced So we can be confident that the trend was 2% the correlation is spoiled in 94 So even though we all appreciate very much the the granular level evidence This movement is actually strong at the aggregate level in the u.s price data And let me briefly show you a recent result obtained From recent work with my colleagues at the boston fat We tried to analyze the recent post covered inflation run up And see what the price dispersion increased when inflation went up So this is the benchmark distribution of a desegregated inflation rates before the pandemic as you see It's very unimodal bell shaped fix dispersion But inflation was a 2% or slightly below during that time As we moved to the high inflation environment, not only the distribution moves to the right It also becomes wider Exactly as the models predict and in 2022 when inflation was particularly high Not only it was wide but the shape changed completely. It become multimodal as well So now it starts moving back as trend inflation goes down And it sort of converges back to a unimodal Distribution so there is quite a lot that we can learn from the aggregate distribution of sectoral inflation rates And with more granular data becoming available We can also use the decomposition that Hanyan Carter proposed to refine this results and also track the distortions at the granular So with this I'll conclude This is an excellent paper. It's very timely because the question of the cost of inflation is very important when inflation is high There's a lot of progress in this paper both in theoretical and empirical sites And I look forward to future work. I think it's more of a research agenda They just want paper and I think one of the Innovations in the in this literature would be to relax this assumptions of homogeneous shocks and solve the model for more complex shock process Thank you very much Still have five minutes any questions from the floor before I give the word back to Henning Yeah Hi, Lorena master from the Cleveland fence. So Henning I was wondering in your paper Can you say anything about the optimal pie star in case you further questions for the question? Let me start with this one The optimal pie star is a complicated object in this world, right? It is Average of all the product level optimal inflation rates But the difficulty is in the weights So how you would aggregate them up and it's not just expenditure waiting But you want to make sure you wait the products with the most sticky prices higher So that's kind of the the classical stickiness principle, right and Probably also relative sectoral trends and productivity or what have you gonna play a role for these weights? so It is there in the in the background this object But it's kind of difficult to compute and we looked a little bit at this in previous work But in this work we kind of tried to stay away from this Yeah So Slavic thanks a lot for your discussion. I mean, this was extremely insightful to me You raised really a lot of points and I wonder whether I should talk about all of them probably not um Now you emphasize that we have to adopt the assumptions and yes, I agree We have to adopt assumptions. I think our assumptions are still a little bit less strong than what you often find in the field So often people in the field assume Random work shocks So the flex price follows random work idiosyncratic shocks And I think that is really a knife at knife edge assumption And we show in the paper that if you adopt that assumption in fact, you can go and identify the price gap distribution Right, that's also what other work shows But if you do not adopt this assumption, you cannot make this link and that's why we think that the Stochastic process which is stationary is in fact a good assumption to make because it's a more general assumption And it makes our life harder Now having said this, we do have to assume that in a given item All the idiosyncratic shock processes are the same across products And we have one robustness check Now why does this matter? Well, it implies that the constant that we get in the second stage Is the same for all the products in the item Okay Now we have looked at a robustness check where we get away Where we can do away with this assumption and it turns out to work right so empirically we could Abandon this assumption and I agree with you. I think that's a very important robustness check Now Linear trends, I mean you may think that's a bit of a crazy assumption You want to go more fancy less parametric in the theory we start from a quadratic loss function for the firm so I feel it's That suggests you want to have a linear trend in the in the flex price And also the effect of inflation on prices So price erosion turns out to be lock linear, right? So in that sense, I think the linear trend is a good thing But I mean, I understand the point and we do robustness checks and I think they pass Now you point out that Time and state dependent pricing models have different implications for this marginal effect and Say that the marginal effect should be considerably larger for the state dependent pricing pricing models than the time dependent pricing models Well, I guess my answer here is a bit hence off Fine You know, we don't want to take a stand what which of the two models have generated the data and Both is fine with us Now you could push us and go further To a higher order approximation of our second stage in order to Be a bit more decisive here, but I think At the current state I would like to stay away from this Relative price variability and sectorial inflation rates I have difficulty seeing how this measure maps into the price dispersion measure that we want to look at from the theory's Point of view, right? And I understand that there's a practical practical interest to have something like this I think that's a separate type of analysis to see how that kind of easily available measure is related to really the theory consistent measure and Yeah, that could be an interesting type of analysis pandemic and Price dispersion a super exciting topic. We haven't had time to do it The paper is not only not so easy to read. It was also not so easy to write which took us a little bit of time And I guess I I stop here in case down all further questions On this light or maybe heavy note depending on the eye of the be holder whether that's light or heavy So I invite you to the poster session and then lunch. Thank you very much