 Manova, who is now at UCL. Thank you. It's an absolute pleasure to be here, really looking forward to your feedback. This is joint work with Andy Bernard, Emmanuel Dinh, Glenn Maguiman, and Andreas Moxnes. And this being the European Central Bank, I am especially obliged to say that this is part of a European Research Council consolidated a grant for both me and Andreas. And also a shout out to Emmanuel Dinh, who's been the gatekeeper, or should I say the door opener, to find fantastic data at the National Bank of Belgium. So this is sort of a shout out to other central banks to make such rich data available. There is vast heterogeneity in firm size. In any economy or slice of economies you look at. So even within industries, some of the biggest firms are forwarders of magnitude as big as some of the smallest ones. We'll be focusing on Belgium in our context. The inter-quantile range between the firms at the 90th and the 10th percentile exceeds 34. So the starting question in our paper is trying to understand why some firms are big while others are small. And we think this is a really important question because the firm size dispersion has important implications for various economic outcomes that we care about, both at the micro and at the macro level. So at the micro level, we know that bigger firms are much more likely to survive, they perform much better, and they also contribute significantly to total innovation activity. In the trade context, we know that bigger firms, more productive firms, participate much more actively in international trade, both in terms of importing and exporting. And moreover, real locations across heterogeneous firms are quite important for the aggregate gains from trade. At a macro level, there's more and more interest in the role of this underlying form heterogeneity for understanding aggregate outcomes. And there's been particular focus recently on granularity, not just extreme dispersion, and the extent to which this dispersion in turn contributes to aggregate productivity, but also shock transmission. And whether it is in cratic shocks hitting certain parts of the economy or specific firms will propagate up and trigger aggregate volatility. So what are we going to do in this paper? Well, in the literature, traditionally, there has been a focus on one side that sources a firm heterogeneity. This has been mostly on the supply side, so thinking about productivity, for example, determining firm outcomes. Recently, there's also been interest in demand heterogeneity based on consumer preferences. To the extent that the literature has thought about firm interactions with their input suppliers or downstream buyers, we've taken an anonymous view to that. And in particular, the assumption is that it doesn't really matter who sources from whom, because we all source inputs from everybody in the network. In practice, of course, firms are part of buyer supply production networks, which feature important two side of heterogeneity. Firm source inputs from other suppliers in the network combine with some labor, and what they produce in turn, they sell not just to final consumers, but also to other firms in this network. So these are the questions that we want to bring to the study of firm size dispersion. We want to understand what is the role of the production network in contributing to this firm size heterogeneity. And in doing so, we think there's several dimensions of the production network that we need to take into account. At the extensive margin, how many input suppliers or downstream buyers do you have? Who are these buyers and suppliers? What are the characteristics of your network partners? And at the intensive margin, how much do you sell to individual buyers? How much do you source from individual suppliers? What is the role of buyer supplier match heterogeneity? So what are we going to do in this paper? Roughly speaking, there are four pieces to the study. We start out by documenting some new stylized facts about a complete domestic production network. And this is only possible because of the VAT records that Belgium made available to researchers. So in principle, any country that has the VAT system has that underlying data. And in particular, we observe all firm to firm sales in the economy, all the links and the value of those transactions. In addition to documenting stylized facts, we can also do a very agnostic decomposition of firm size into three components that I'll be calling upstream, downstream, and final demand. So final demand is clear. Upstream, think of that as supply characteristics, which determine your average market share among your buyers. And the downstream is characteristics of the firms you're selling to. But we start out with a completely assumption-free, reduced-form decomposition into these three components. So motivated by this decomposition of the stylized facts, we're then going to write down a model which features two-sided firm heterogeneity in a biosupplier production network. And this model will allow us to express the firm size as a function of both own-firm characteristics. We're used to thinking of that as being your own productivity, but also characteristics of how you participate in the network. So characteristics of your suppliers and your buyers. The purpose of this model is two-fold. First of all, it's going to give us a structural interpretation of the reduced-form decomposition we start out with. So now we know what those upstream and downstream components actually capture. This is important because the upstream component contains information about your own productivity, but also productivity and characteristics of your suppliers. This is a classic reflection problem. And sort of as an aside, the methodological contribution of what we do is that we can back out these underlying firm primitives like productivity from the data only because we have that network data. So that allows us to overcome this reflection problem. So that's the first purpose, give a structural interpretation of that assumption-free decomposition. The second purpose of the model is to allow us to decompose those upstream and downstream pieces further. So that's what we do in the third part of the paper. We're going to implement this model-based decomposition of the firm size. Very intuitively, the upstream side is going to contain an element about my own productivity and then several features of my suppliers. How many? How good are they on average? How do I allocate purchases across them? On the downstream side, symmetrically, we're going to have number of your buyers. How good are they on average? How do you allocate sales among them? At the end, we're going to do some counterfactual analysis. This is where we need a few more assumptions. The base model is actually a very minimal assumptions only on the production function. No more structure is needed on pricing. So in other words, the demand structure or the market structure. For the G, we would need that. And the purpose of that is to say something about the role of the network in amplifying the underlying firm size heterogeneity. So I should say that we are interested in an agnostic decomposition of the firm size dispersion and assessing, essentially, the contribution of the production network in explaining that firm size dispersion. In that sense, we don't need to model much formation in the production network. The actual observed network is a sufficient statistic, if you will, for our purposes. And so the decomposition analysis is valid and feasible under very many different matching models that generate the actual network. So it's sort of saying, I started out with some underlying firm heterogeneity. How much does the network amplify that to produce the observed firm size dispersion? So what do we find? Top tier result, the downstream factors explain the vast majority of the firm size dispersion, over 80%. The upstream component contributes significantly less. And a couple of points to emphasize here, when you think about the upstream as being linked to productivity, these results don't mean that firm attributes don't matter for the downstream component. In fact, one of our conclusions will be that in order to rationalize the results, you need several different firm attributes to match our patterns. So we are just thinking of productivity of being a primitive. In our case, that's going to be important for your average market share among your customers. But the results will suggest that there may be a second firm characteristic that matters with how you match with all downstream buyers. So that's one way to think about that. And a second point to make here is that we're focusing on the firm size distribution and the sources that generate that dispersion. This is different, obviously, from talking about value added, productivity growth, or profits. And it's entirely possible that firm productivity plays a much bigger role in explaining those outcomes. So then through the lens of the model, we can do a further decomposition of these upstream and downstream components. We find some interesting patterns here that also signal a symmetry between how you match with suppliers and with buyers. So the downstream component is dominated by sales to others in the network. So of those 82%, just 1% is sales to final demand. The rest is how you sell to other firms in the network. So this is not to say that sales to final consumers are not important. They may be very big for certain firms. But as a share of total sales, they're not what explain the heterogeneity in total firm size. In terms of sales to others in the network, the most important factor is how many firms you sell to, how many buyers you have. It turns out that on average, bigger firms don't match with better or worse buyers, bigger or smaller buyers. It's just that they have a lot of buyers. They also better allocate their sales towards buyers that they're really well matched with. So there is a role for buyer-supplier match characteristics. The big firms are not just selling lots to really good guys, but they're selling more to the firms that are really well matched with them. MyWidget is really good fit with your production function. OK, upstream looks quite different. So on the upstream or supply side, if you will, almost all the variation comes from my own production capability rather than characteristics of my input suppliers. To the extent that my input sourcing matters, we see this as symmetry with respect to the downstream side. Now, there's actually very little variation in number of suppliers among firms. On the other hand, the bigger firms are sourcing inputs on average from better suppliers. And once again, they're allocating their purchases very cleverly towards the suppliers that are really well matched with. So without modeling the match formation process, we're not going to put any structure on this. But I think what this implies is that there are different fixed costs or asymmetric information stories involved in matching with buyers and suppliers. Finally, what do we learn from the count of actual analysis? We conclude that the production network amplifies the underlying firm size dispersion, surprise, surprise. But in terms of an accounting exercise, over half of that overall firm size dispersion can be attributed to the network. So in other words, when we completely shut down from heterogeneity in productivity on characteristics and we allow firms just to match differently with other buyers and suppliers, we're going to keep more than half of the overall dispersion. So I'll have to be very brief on the literature. So let me jump straight to telling you more about the data and the stylized facts. I will walk you through the reduced form completely assumption-free decomposition. When I turn to the model, I'll try to emphasize the simple assumptions we make on the production function and spare you some of the technicalities. Instead, I'll prioritize the model-based decomposition. On the counterfactuals, I'll try to just show you the results, keeping all the G algebra. OK, so data, sorry that the top line's cut off. We have two sources of data, which are easy to merge. They're both at the firm level and have a unique form ID. One standard database is the balance sheets of these firms. That's where we obtain classic information on total sales. They're firms' total input purchases, employment, labor costs, industry affiliation. So later, when I talk about labor shares and so on, that's where it's going to come from. The novel database is the so-called B2B business to business transaction database. This contains the universe of all firm-to-firm transactions in Belgium, among all VAT registered enterprises establishments. As long as two firms trade it more than 250 euro within a year, we'll see that. So it really offers us pretty much comprehensive coverage. What we observe is the value of sales from firm I to firm J. So later, when we think about final demand versus downstream sales to others in the network, what is that for our purposes? Well, we have total sales from the balance sheets. We have total observed sales of the network. We'll take the difference between the two and call that final demand. I should mention that this actually has two components. One component is sales to final consumers in Belgium. One component will be exports. We do have information from the customs record, so we do observe exports. We could, in principle, decompose that further. But given that final demand overall is going to play such a small share, we don't learn much by doing that. Conversely, how do we think about inputs? From the balance sheets, we have total input purchases at the firm level. From the VAT data, we see all the firm-to-firm input purchases. And so we're going to take the difference between the two. And what's absent is going to be imported input. So again, we're going to be able to take that into account in our production function. It's not going to play a big role. OK, so three stylized facts. I'll be very brief about the first one. Lots of dispersion and heterogeneity in terms of firm size, the number of buyer and supplier connections at the firm level, and also the value of firm to firm sales. So some stylized facts, but I don't want to be labor at this point. Some stylized facts, too, is where we start looking at the relationship between firm size and the number of links they have in the network. So on the left side, you have firm sales on the vertical access and the number of downstream customers in the network on the horizontal access after demeaning by industry. So obviously, a very sharp upstream slope. Bigger firms have more downstream buyers. And likewise, on the right side, bigger firms source inputs from more upstream suppliers. Our third stylized fact thinks about the relationship between the extensive and the intensive margin of your participation in the production network. So let me digest this for you. Take a firm which has 10 suppliers. Look at the input purchases across those 10 suppliers. Take the input purchases at the median, the 10th percentile, the 90th percentile. This gives you a sense of the spread of input purchases across your suppliers. So I just did that for a firm with 10 suppliers. I can do this for a firm with 100 or 1,000 suppliers. And plot that spread of input sourcing across suppliers. That's the right graph. So what you see is that the firms that are sourcing from more suppliers end up varying those input purchases more across suppliers. So to us, these sort of signals, there's an important role for much specific quality in input purchasing. And this is going to jive with some evidence later. I'll show you in the decomposition that how you allocate purchases across suppliers matters. On the left side, I'm doing the same exercise, but now looking at your downstream buyers. Do you sell more to your 90th percentile versus 10th percentile buyer, depending on the number of buyers you have? And the answer is no. So the dispersion of your downstream sales doesn't actually vary very much with your number of buyers. So again, this is going to jive with the decomposition later, where we're going to see that there isn't much action there. OK, so these are the stylized facts. So let me then turn to a very agnostic decomposition of the firm size into upstream, downstream, and final demand. We'll start with looking at from-to-from sales. So sales from I to J, from me to you, can be expressed as, I sell a lot to you because I'm great, because you're big and you buy a lot from everyone, or because we're really well-footed to each other. Essentially, I can run that regression and I can identify my average market share among suppliers with a seller-fixed effect. And I can identify your average purchases from all of your suppliers with a buyer-fixed effect. And the residual is going to tell me something about the match quality, which is specific to this buyer-seller transaction. So essentially, the seller effect is giving me an average market share, controlling for my buyer characteristics. And that's why this is going to be related to supply factors. Essentially, through the lens of the model, this is going to be my marginal cost, which depends on my productivity and my supplier's productivity. Whereas the buyer effect is going to be much more closely related to buyer characteristics. Bigger buyers are going to be sourcing more. I'll spare you the technicalities on identification. Let me walk you through a thought experiment. So imagine that all the variation in firm to firm sales comes from the seller effect. What that means is that who I am is the only thing that matters. So big firms are big because they're really capable and they have a big market share among all their buyers, but all buyers purchase the same from a given seller. The flip scenario is that who you are doesn't matter at all. The only thing that matters is who you meet, who you match with. And so the only reason some firms are big is because they happen to match with really big buyers. So these are the thought experiments. So I can run this regression and obtain those seller and buyer effects. What is that good for? Well, think about aggregate firm sales. Just as an accounting identity, it's just the sum of all your sales to others in the network plus final demand. So now we arrive at this completely agnostic decomposition of total firm sales into an upstream component, my average market share among my buyers, a downstream component which aggregates up information on my buyers and their buyer characteristics but also our match characteristics and then this final demand piece. So the final demand I'm gonna absorb directly from the data, the other things I can estimate in my first stage regression. What is this good for? Well, by the properties of OLS, I can take each of those three components, the upstream, the downstream, the final demand, regress them on total sales and the three coefficients I get, first of all, are gonna sum to one and they will tell me how much each of those margins contributes to the overall variation in the firm size. So that's the exercise. These are the results and these are the takeaway numbers are started with. The vast majority of the firm size dispersion comes from the downstream side, over 80%. Final demand plays a much smaller role, upstream 80%. And again, to remind you, these upstream supply factors may just be different from the kind of firm attributes that determine how successfully you match with buyers downstream and also we're looking at size rather than profits, you know, from productivity, from attributes may matter much more for profits. Okay, so I'll skip this actually. Now I'll go straight to the model and ask, okay, how can we rationalize these facts? How can we put together a model that has decided from heterogeneity in a production network and allows us to link the firm size to this participation in the production network? So the purpose of the model in the first instance is to allow us to interpret that agnostic decomposition I just showed, you give us a structural interpretation of those components and as the output of that, we'll also be able to back out primitives of the firms from the observed components. So with those primitives, we can then implement a final decomposition of the firm size margins that is model-based. We'll have very minimal assumptions on the economic environment, right? So here are the key ingredients. Firms are gonna be heterogeneous in what we'll call production capability. This can be productivity in the efficiency sense or it can be quality. And in firm to firm matches, we're gonna allow for there to be a much quality component. Okay, as you'll see in a moment, this much specific component will actually combine both demand and supply shifters. So it's very, very flexible. We're gonna assume a CS production function, which I'll show you in a moment, and condition on the observed equilibrium network. We don't need to model the match formation to implement a decomposition. Okay, so this is the first assumption on the production function. So it's actually a very standard one in the trade literature. In some sense, we're going after a rather macro question by thinking about the firm size dispersion, but we're utilizing some of the trade tools or techniques for aggregating up from heterogeneity to speak to aggregate outcomes. Okay, so this is a CS production function. Your output depends on some normalization context as constant, your own productivity, Z, a labor input with a corresponding labor share and sort of an aggregate intermediate input. So it's cop Douglas across the labor input and the intermediate input. The intermediate input itself has two components. V is the one that's relevant to us. These are your input source from the network. U is the imported ones. They'll end up playing a very minimal role. How will your source inputs from the network is gonna be a CS aggregate of individual input purchases from different suppliers, right? And so the quantity that you purchase from an individual supplier is gonna be this little new KI, but for each supplier, you're gonna have a demand shifter. So one which is maybe especially well suited to my own production function, but less so to someone else. So we're gonna allow for match quality to enter in the production function. That's our demand shifter. This assumption is actually sufficient for us to characterize from smart general production cost. That's a function of your wages, your own productivity and the input price index across your input suppliers. And this input price index in turn depends on the prices of your input suppliers adjusted for the match quality. We don't need to make assumptions on pricing. So in other words, the demand structure, the market computation structure, we can allow those bilateral prices to be fully flexible. So you might say, look, they depend on the marginal cost of the supplier and a match specific supply shifter. So that's tau for our purposes that could be match specific trade costs, markets, we don't need to specify that. We can now express firm to firm sales just as a function of seller, buyer and match characteristics. So that's what we get out of the model. And this is the expression that you see. It's exactly the same as what I showed you before in our agnostic decomposition, but now we actually have a structural interpretation to all these components. So I will skip this and go straight to some correlations. So now that we have given the agnostic components some structural interpretation, what do we learn from them? Well, the first point is perhaps not surprising. Larger firms have lower input prices, more customers and a higher market share among their customers. And low input prices are associated with sourcing for more suppliers and from really high capability suppliers. What perhaps is a bit more surprising is how productivity, on firm productivity correlates with outcomes of interest. It is true that more productive firms have a higher market share among their customers. However, at the same time, they actually have a higher input price index and fewer customers. So as a result of that, more productive firms have unconditionally lower sales. If you were to condition on the input price index, they would have higher sales. So this is sort of a surprising finding that you cannot easily rationalize with existing canonical models. And to us, it suggests that there are several formatual fields that matter for how you match with suppliers, with buyers, and ultimately size. We can do a further decomposition of the upstream and downstream components that's model-based, but actually quite intuitive. So this downstream decomposition, we don't even need the model for. I can express a downstream component just as, well, the number of buyers, average buyer capability, and a covariance term. Do I sell more to the buyers that are objectively good and subjectively well-matched to me? I can estimate all those moments either based on observed data or what I did before with the seller and buyer effects, and again, run these all less regression so to the decomposition. Upstream looks similar. The upstream component contains my own productivity and then characteristics of my sourcing behavior in the network. Number of suppliers, average supplier capability, and this covariance term. Do I source more from the guys that are objectively good and subjectively well-matched to me? Okay, so I've given you everything, and I can just show you the results, ignore the pictures. So this is the downstream decomposition. So 70% of that component is driven by the number of customers. For the reason big firms are big is because they have many buyers. They don't on average match with bigger or better buyers. They do to some extent allocate sales more towards their well-matched buyers. So there is some kick there. The upstream margin looks quite different in that my own firm characteristics dominate. So the supply side factors are really driven by who I am. To the extent that different firms sourcing puts differently from the network, this time it's not about the number of suppliers. It's actually now about matching with better suppliers on average and sourcing inputs from the ones that are really, really well suited to your production function. Okay, for the GE, only thing I should warn you is that here we need to make some additional assumptions in order to close the model. For example, on markups, labor shares being constant so far they could fully flexibly vary across firm source sectors. Okay. What do we get out of this exercise? We're going to look at two counterfactuals. First, we're going to kill any heterogeneity in the underlying firm productivity. And say, given the structure of the production network, given the fact that some firms are matched with more suppliers and more buyers than others, how much residual firm size distribution do we observe? Okay, this would be sort of a way to assess the contribution of the network. The alternative is to say, keep the underlying firm heterogeneity. Only so far, we allow the input share to be estimated from the data as a share of your total production cost. Make inputs more important relative to the labor share, what happens? So if you make the network more important, how much more does it amplify the underlying firm size dispersion? So these are the two thought experiments. What do we find before I conclude? If you shut down any heterogeneity in all firm characteristics in productivity, you're still gonna keep more than half of the firm size dispersion you started out with. So in the economy, we start out with a standard deviation of 1.4. When you shut down the firm heterogeneity and you only have network, so heterogeneity and how firms plug into the network, you end up with 0.8, okay? The second counterfactual tells us that if we make sourcing from the network more important in firms production process, we're going to amplify the firm size dispersion. Intuitively, two things are happening and they kind of reinforce each other. So to start out with big firms have lower input prices. So if you make inputs more important relative to labor, you're gonna make them even more competitive. They'll capture bigger market share, they'll get bigger. The second effect is really because the first one kind of fits through the network. Because you amplified the size and the competitiveness of some big firms, everybody else was buying from them benefits and this thing kind of reinforces each other. So essentially bigger firms also expect bigger declines in their input price index. Okay, so to wrap up, we've taken a very agnostic approach to decomposing the firm size dispersion into upstream and downstream components. What we've learned is that downstream matters the most, especially the number of buyers you match with. We've also learned that it's important to overcome this reflection problem and carefully separate your own productivity from characteristics of your suppliers. Because when you do that, you find all of a sudden that firm productivity is negatively correlated with sales unless you condition on input prices. What I wanna leave you with is some open questions. So what are these multiple firm attributes that determine firm sales, right? So one of our conclusions is that one attribute like productivity is not enough. So in my mind, it's possible that production capabilities what pins down your market share among your customers but other characteristics like management practices something that I'm working on in other work or marketing effectiveness is important for drumming up business, for establishing your customer base. Another conclusion is that there is some asymmetry in the way you interact with suppliers and buyers. So the nature of the asymmetric information that you're overcoming may be different. So just to speculate, for example, the way you match with buyers, maybe you just need to pay more fixed costs to match with many, many buyers and you end up selling to all of them even if they're smaller big, you just kind of adjust your sales accordingly. Whereas on the sourcing site upstream, it's different because you gotta work with those inputs. It can't be just anything, okay? So maybe they're the screening of match specificities more important. And finally, just to kind of emphasize what I mentioned earlier, we're focusing on the firm size, okay? I think it will be super interesting to think about firm performance measures such as profits in the short term or growth long run and try to understand how the network contributes to those. Thank you. Many thanks, Kalina. The paper will be discussed by Julian DiGiovanni, who's at the UPF at the moment. Great, well thank you for having me here, for inviting me to discuss this interesting paper. Okay, so just to repeat something, I think Kalina explained very nicely to begin. She's studying a big topic, firm heterogeneity and we care about this for many reasons and I tend to focus more on macro, macro trade, but you can think of many different topics where firm heterogeneity plays a role, agri-productivity, fluctuations, a lot of recent discussion and markups pricing the superstar firms, for example, in the literature, as well trade, I mean the new trade theory of malice at all focuses on firm heterogeneity. So traditionally, to try to better understand why some firms are big, why some firms are small, we either focus on the supply side, firm productivity, cheaper sourcing, especially internationally with the global value chain, or via the demand side, just consumers have different preferences. This paper tries to think a little differently and they wanna look at both sides and ask how the firm production networks influence both through upstream and downstream linkages, the steady-state size firm distribution. I've steady-state in bold, partly because of what I'm gonna discuss in my comments and as a macro guy, what we might be more interested in thinking about and what this paper can tell us. Okay, so the approach, we're not dealing with big data, we're dealing with huge data, okay? So we have every firm to firm sale within Belgium, granted a pretty small economy, but I imagine quite a few sales going on. Where the author is used a high-dimensional fixed-effect regression analysis that's becoming more and more common in this literature. You can find it also in the labor literature as well as looking to give bank credit shocks, for example, all right, so it's all over the place. What's very nice though, and what kind of a major contribution of this paper is to then take a model, like a very parsimonious model, also a very big model that fortunately I saw on a footnote requires only 20 minutes to solve, given some clever Python programming, to really discipline what these regressions can tell us about the structure of the economy, okay? So what is the one regression we care about? Okay, so it's simply this bilateral fixed-effect regression where you have the sales from firm I to firm J, we can break it down between a seller effect, a customer effect and this matching effect. It's the error term, which they're assuming is uncorrelated with the seller and customer effect, they have some robustness checks on it. Within the model, it's still kind of floating around being some individual preference shock. We can get into this, but I'll leave that alone for the purpose of this talk. What's crucial though is that we can take the upstream effect with the model, map it to the quality of inputs that the firm is using as well their own inherent production capabilities. High productivity, good marketing skills, et cetera, good quality goods that they're selling. Whereas the downstream effect, which accounts for the majority of the fit of the model of the regression maps into the number of customers, the fixed effect, as well as the matching term, the errors. Okay, so maybe it's not so shocking that downstream shows up so hard given it's so highly in the regressions in terms of explaining the variation in the data given that I believe the R-square is roughly 40%, which is quite high, but then of course, everything else is going into the error term. So maybe no shock there. So the key findings are indeed the downstream factors really explains the majority of the dispersion across the industries. Using this model-based decompositions, the authors show that it's extensive margin of customers that matter, not how big they are necessarily, but how many there are. And that the upstream component is driven by the seller-specific production capabilities. So kind of using capability as a catch-all for how good firms are. Okay, and finally, their counterfactual, one very nice result. They can show, well, what happens if you kind of kill the network effect or kill the labor share effect. So just everything seemed to matter with networks. And you can explain me about 56% of the observed Tetris day and 80. Okay, so I'm going to also say what the paper does not do or some of the things that they can't do, and it's just asking too much in this paper, but I think it's also important to think about given that the word origins is in the paper title. So first, they do not provide an explanation what drives from heterogeneity over time. So there's nothing about dynamics. This is fine, it's about a paper about the steady state. They take the linkage patterns, the network as given. Again, there's a lot of active research on trying to understand and dodge this network formation, but for tractability, they don't try to explain these patterns. They just take them as given the data. And further, and something that's, I guess, from a policy perspective, which would be nice, that they don't do in the paper, I'm not sure if it's tractable, that's some questions about this after. So they do not relate it in their estimated parameters to any potential market frictions, for example, cost access to market. So as the last slide pointed out in the presentation, this seems to be something where the research is going. So my main comments are going to be basically, based on questions on the data and interpretation of the model and some questions on model fit and some potential applications or why we might care about this kind of from a more macro-y perspective, okay? So to start though, I thought it'd be useful to actually think what are the large firms are in Belgium, okay? And I didn't have the data, so I just looked at Forbes 2018 global 2000 ranking, okay? Of firms. Beers number one, as I pointed out. Okay, so the rankings on the right hand side, it's actually based on market capitalization and I just kind of flipped it to at least have sales and it more or less matches up, so it's ranked by sales. And a few facts you might want to take away from this. So besides beer being really important, okay? A lot of these firms are global firms, okay? And this is a point I'm going to take about the data, okay? Number one, number two, you do see them across a bunch of different industries and they make a, you know, it's all firms in the economy in this paper and they do show that you have this skew distribution across all industries, that's great. But, you know, you also see that there's lots of like diversified chemicals, diversified insurance. These firms sell a lot of different products. And number three, a lot of these firms are quite old, in fact. And this is kind of going back to the dynamics and some questions I'm curious about, you know, back in the 1824 for a kind of insurance company, et cetera. So there's kind of some facts to think about, okay? So my first data question is, you know, I was somewhat surprised to find that neither final demand nor exports matter, okay? Or play an important role in explaining the size distribution. Well, when you step back, maybe this isn't so shocking because you think firms don't literally go to your door and try to sell you a product, rather they go through some intermediate, right? It could be a wholesaler, retailer, et cetera. So how key are these players in the downstream component? Moreover, what about the trade and intermediaries, both domestically and internationally? In fact, one of your co-authors has a forthcoming paper in the restart about carry-along trade, think also using Belgium data. So it's just more about interpretation. How do we think about these types of firms in the model itself? And then also, you know, if shock, you know, if I think about shock propagation, why, you know, how does it actually pass through the network, okay? Second, you know, how does the existing multi-product firms impact interpretation of the fixed-effect regressions? So I imagine you could probably rewrite this model or this paper pretty easily with a multi-product firm, but then, you know, I start thinking about, well, not low-average market share, but the contribution of a low-average market share, given the seller fixed-effect is quite small, explaining the variability. But then if you think of, you know, one seller with many customers, they might be selling differential products and this might kind of lead naturally to this kind of lower estimate of the fixed-effect, okay? And then, of course, why you have so many more customers. Okay. Number three, and something which, again, it's more about dynamic, but if you look at the information of the Forbes list, it points to kind of a natural correlation between age and size. And this comes to this notion of why are firms big or why are they gonna be able to grow and therefore have more customers? So maybe you're in your garage, you're in a Harvard dorm and you have a really good idea and you're gonna be really productive, you know, and you're gonna be able to access the market. So Mark Zuckerberg, Facebook, et cetera. All right, great idea, initial idea, super productive, super innovation, successful entry, and then over time, you're gonna grow almost, you know, just definitionally, I mean, by a growing customer base, right? So it's almost a little tautological or mechanical that we should see that downstream component matter so much. Of course, the relative size, you know, kind of the extensive or the incentive margin, of course, is important to think about, but also consumers also like diversified consumption. So maybe not so shocking then that you have just the only way we're gonna grow is by getting more and more customers over time. And of course, you can think about this in an open economy context as well, where again, kind of going back, why firms are entering in the first place is super important. Okay, so maybe, and this is maybe too much for this paper, maybe not, but, you know, some statistics based on the firm age, just even in the cross-section, I think would be super useful, right? Has someone give you some ideas, potential dynamics, but more importantly, it maybe might help us interpret a bit more about the importance of adding one more seller with good inputs or not so good inputs, versus just kind of having one more customer, right? Because they're gonna be giving, you know, customers just give you some demand, this is pretty linear, whereas if you just get a much better input or cost saving coming in, this might have a big kick on your productivity, and therefore let you access markets more easily or more attractive to many more customers. Okay, so model fit and counterfactuals, and here I kind of hope you could have done a bit more. So the main kind of figures you have for model fit are based on the aggregate price level, which, if I understand, I mean, if you look at the model, it basically will fit perfectly by construction. Okay, and the other fit that they look at is total sales of a firm, and again, it's a good fit, but again, I'm not shocked about this, given the degrees of freedom afforded with the model, you're basically just trying to fit all the fixed effects, plus the residual. So, and that final goods don't matter very much in your data to explain total sales. Again, it's not so surprising I'm a good model fit. So what more can you do? Well, I think some of the, you know, what you might wanna explain in other models that you mentioned at the end would also be good to just even check whether this model works well. So your firm profit rates, how does, you know, how does the distribution of firm profit rates predicted by the model compared to the actual data? So you're assuming average kind of constant markups as well as the elasticity of substitution being constant throughout the demand elasticity in the model. So I guess this is just gonna give you, it's not gonna give you a distribution of markups, but I'm still trying to figure out is there some way you could tease out some information, maybe across industries, et cetera, and see how this maps to the data, but also whether there's, you know, how this might be correlated with the residual in your fixed effect regression. So basically, is all this markup actually might be missing, just getting sucked up in there. Moreover, can you map, you know, can you actually match the input cost shares that we observe in the data? As a side note, I didn't know what happened to capital in the data. So it's only, you have only labor in the model intermediate goods, but then where did capital go? Is it included intermediates in the data, or is this kind of an equipped labor measure that one uses in the trade literature like Alvarez and Lucas? I wasn't clear on this. As a side note, you have a footnote somewhere in, so the production function is very standard and you have a footnote somewhere saying, kind of, you know, our model solution doesn't matter the elasticity, whether you're substitutes, whether you're complements. I got a little lost there wondering, you know, let's say you go dramatically to Leontief or something, you know, how Leontief production or some complementarities, you know, what does that have a sizable quantitative impact on kind of the importance of input suppliers, you know, and kind of the overall impact on kind of production capabilities that you're estimating. Kind of what's, you know, does this do a lot to change a lot in the model and what means for your quantitative results. Okay, so some potential applications, just trying to think, you know, what could we, you know, how could we kind of take this to some macro models or kind of some questions we would like to ask about it. I mean, you know, there's a lot of recent research thinking about the change in market structures and implications for policies, thinking about firm concentration, markups, more work on fluctuations. So what might the paper's results in particular in the downstream imply or what can we maybe use with them? Is it possible, for example, to back out, you know, from the model estimates of trade costs from markups is how IJ that captures everything and some relate them to observables such as distance, customer size. Maybe there's some, I don't know if you also have, you know, quantities in the data but perhaps back out some measure of prices or, you know, and relate these to prices, market segmentation. What I thought would also be interesting is, you know, again, thinking about different competition structures, now this paper seems to point that all the action is going on between intermediates. So maybe we should really be thinking about writing down models where we're having different markups, kind of actions going through the production change and also much on the final goods market. Okay, and finally just work I've done, kind of a bit of work, you know, quite a bit of thinking about kind of the propagation of shocks, especially at the granular level. Well, I guess one open question, the diversification of customer base helped dampen shock transmission. It's not clear, so for example, some work my co-author, Isabelle Benjamin-Jean, has shows that this need not be the case. You might be trading with a lot more partners but you might still have a very skewed distribution. So again, this is just why we find this, you know, why I find this quite interesting and why there's a growing literature thinking about the distribution and shock propagation. Okay, so I think I'm almost done so just to conclude, as I said, very interesting paper, lots of new facts to understand. I think the current paper kind of thinks a bit more as a very static exercise, trying to explain these rich data patterns. Personally, I'd like to see a bit more work, trying to understand the model fit and what's the right structure, you know, to really impose the discipline to fixed effect regressions. And of course, this opens up a lot of very nice, you know, questions to answer and to exploit this data with if I guess we get to know the gatekeeper better. You know, there's lots to do on dynamics, network formation, I know people are working on this already actively and then there's some interesting aggregate and policy implications that hopefully we can take this type of underlying microstructure and apply it to these types of questions. Thank you. All right. Thank you, Julian. Time for a few questions. Shepnam, behind you is a mic, yes. Very nice paper. I'm a little bit puzzled by one thing that actually Julian already raised, but maybe I can put another perspective on it. So the two big facts in firm dynamics literature is small firms grow fast, but they're also more volatile. They also exit quicker. And then this research is based on US and this research also showed that this fact is purely driven by age. So this goes back actually, you know, making very similar points as Julian did. That fixed effect doesn't have any role, right? But that's because, you know, you're assuming they're independent. And in fact, if they are, then age is going to play a big role. And maybe for this paper, it's okay because you assume it's orthogonal but the minute you start looking at the performance indicators, as you said, investment, employment growth and all that. So because age single-ended explains that fact that small firms create more businesses, you know, and all that in the US firm dynamics literature. Okay, next question. Yes, Mark. Actually, I think this paper provides some insight into this sort of lifecycle behavior of firms, the fact that firms start out small and then grow. And I guess the important extra dimension that you add is the relevance of establishing a number of buyers that is expanding the customer base. And that's been absent from the existing literature. And the sort of natural reason that's important is because of diversification. If you just have a few buyers, it's risky to grow large because the demand of those buyers can drop. So what this is suggesting is part of the growth process as a development of the customer base, which is allows for diversification. I think you won't disagree with that last one. It's one of the reasons to have it on the program. Okay, Kalina. Well, thank you, Julian. This is fantastic, extremely thorough and it's given us lots of food for thought and also comments that Chevna and Mark made. So I won't be able to touch upon everything. So I'll prioritize, but let me group things around three or four things. Some things we have done, some are definitely planned for future research and some we just haven't thought about. So one thing to start with, network formation. The way we identify everything, that's sort of a starting point for us. It is okay if firms match based on seller or buyer characteristics. So more productive firms always match with different people, that's fine. It is also okay if there is a pair specific matching cost which can be fixed across pairs or it could be completely variable across pairs, as long as this is not related to what happens conditional on the match. So the only thing that violates the exogenous mobility assumption is that you are matching based on the match quality term. So one way to think about that is, you know, think about the marriage market. It's easier to meet someone next doors than three villages over, but exactly you don't know if you're gonna be a good fit. And so even if the bilateral matching cost somehow isn't dodging as to who you are, where you're based and so on, it doesn't guarantee you're gonna get married. So for our purposes, that's what we require for that. We've done a series of exogenous mobility tests that are somewhat inspired by the labor literature. Okay, but that is a technicality, so I wanna now focus on the stuff that I find more interesting on the economic side. Several questions were about dynamics. Everything I showed you was done in a cross-sectional context for one year. One advantage of that is that we can do this exercise repeatedly for different years without imposing the seller effect, the buyer effect, and so on to be constant over time. So this actually helps going back to the earlier point, it actually helps with the exogenous mobility assumption. We have, however, done a different exercise trying to understand what generates not the firm size dispersion in the cross-section, but firm growth over time. We can do more on that. What we've done so far is focus on the firms that survived from the first year, 2002, to the last year in our panel, which is 2014. And for those survivors, you sort of do a decomposition at the start, do it at the end, and figure out what explains your growth. Bird's eye perspective, the decomposition looks similar, but there are some differences. So for example, in the top decomposition, downstream firms, downstream explains 80% of the variation, same for firm growth. However, in the cross-section distribution decomposition, the upstream factor is like 18%, final demand is only one. In fact, if you look at firm growth, they become 10 and 10. It turns out that over time, what explains firm growth more than firm size dispersion is actually final demand. For our purposes, that does include exporting. So sure enough, being a trade economist, presenting lots of trade conferences, we've often gotten this comment, how come exports don't matter much? It turns out they do, and they're certainly very large in value, but it's not what generates variation across firms. It does explain more firm growth dynamics. There were several questions that asked us to think about performance metrics out of the inside. This is something that I find extremely interesting. So in future work, one of the things I'd love to do is understand how firms position in value chains and production networks is associated with firm performance, which means profits in the short term and growth long run. So I'm doing some work on China, looking specifically at that question. We're hoping to do some more on that in Belgium as well. There were related questions about the role of market frictions, and I think Julian mentioned this, in terms of the specific estimation, but also what it implies from size dispersion or presumably firm growth. To answer the question very narrowly, you could map those kind of matching frictions into the towel, which is a supply shifter, conditional on a match, or you could say it is part of this match formation game that we're not modeling. In practice, I'm actually very interested in financial frictions and labor market rigidities. And so I'm doing some other work on Pakistan where we're looking at the response of Pakistani exports in response to several trade reforms. So you can think of the trade reform as being one shock, and you can think about different market frictions in Pakistan. So what we want to understand is how Pakistani firms responded to this trade shock by relocating activity across different buyers and suppliers and to what extent those underlying frictions actually played a role. But that's on the extended to-do list. Also for future work, and this is probably going to be one of my last points, very interesting point that Julian made about the role of concentration going up and what this implies for the micro-distribution. So as I mentioned, we don't need to put structure on the mark of dispersion. We can have that supply shifter very flexibly, but I find it very interesting. At a very deep level, this has to do with rent sharing along supply chains, which is something that policy makers, especially in developing countries, scared a lot about. And whether pricing of inputs upstream kind of has repercussions for what's happening further down the supply chain. So again, in other work, I'm starting to think about this question using some match-trade data for French firms importing from China and thinking about how the competitive environment in China affects how French firms are sourcing, the prices they're paying for different inputs and the such, okay? Very last point, which is kind of very broad stuff we haven't really thought about and we probably should. You had something about capital in the model. Yeah, where is that? I first got that comment last weekend. I was like, right, where is capital? So to the extent that it's an input, you bought a new equipment piece, right? Okay, that's part of our input production function. We could expand our production function to have the labor input, the capital input, and our intermediate inputs. And yeah, we might need to massage the data to estimate the capital share carefully, but we can do that. We probably should. At a minimum, what I think we should do is look at how our estimated productivity correlates with more standard measures that we have, even though they're admittedly TFPR. And to see, you know, does our productivity measure correlate positively or not? Is it because of this reflection problem that typically you face, where you cannot separate your productivity from your input suppliers? Okay, so I'll leave it there. There's several other really interesting points that Julian made, but I think it's time for lunch. Indeed, thank you, Karina. I just wanted to mention that one other reason to have this paper on the program and why we're so interested in how we can aggregate up from micro-data is that we're in the process together with all the other central banks in Europe to collect a lot of micro-data, including the kind of data that you are using in this paper with the emphasis is really on micro-price data to better understand inflation dynamics. And Luca Dederlau was sitting here next to Shepnam and Olivier, is actually running this program for us. So if you have any questions on that and just bug him over lunch. So lunch is a buffet lunch at the end of this floor. It's probably it's a call to go out, but there is also a bug.