The Granular Instrumental Variables (GIV) methodology uses idiosyncratic shocks to large firms, industries, or countries as primitive instruments to estimate causal linkages and general equilibrium effects in macroeconomics. This approach addresses the missing intercept problems that plague traditional shift-share models, which only capture partial equilibrium effects. The framework models how outcomes (such as TFP growth) depend on other units through network matrices parameterized by influence parameters, allowing researchers to trace how productivity shocks propagate through the economy. In applications to US industry data, researchers found that a 1% decrease in average TFP across all industries leads to only 2.7% average TFP growth, representing a multiplier effect of approximately 2.7, with about 70% of externalities flowing upstream to suppliers and 30% downstream to customers.
Macroeconomics and Productivity, NBER Summer Institute
Added:I'll give you a 10, five, and one.
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>> No water.
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>> Okay, great. Go ahead. Okay, great. Uh, welcome back. Um, so this is John with Gabe who's here and David Day who's uh who's who's online somewhere. Um, okay.
The pointer see it's working. Okay. So the goal is to estimate causal linkages and think about and sorry and estimate also all the general effects. Okay. So uh and for that we're going to use idiosyncratic shocks to large firms, large industries, large countries. It's a general purpose econometric methodology. We hope that maybe in the future I don't know a third of the papers can use that methodology to estimate their thing as a central tool or maybe as a partial tool for um and I had a discussion with John about that but his paper and you can calculate GFX.
So there's a background paper which is a paper I wrote with Ralph Coyan a few years ago the network GV uh there we had just one little market the market for I know phones and you can use this shocks to supply and demand to look at elasticities the demand supply for phones but here we're going to we attacking the whole macroeconomy uh and you can trace out you can have end markets linked with demand supply and other linkages and there are lots of applications potentially uh I work out one for you link to productivity uh macro network of firms, industries, countries in finance, supply and demand across different you know bonds versus stocks versus potentially general economics. Um and and again the key is this network GV granular instrumental variables. Uh it it estimates G effects.
So it solves the missing intercept problems and while shift share models for instance get only or techniques get only the partial equilibrium effect. So and so background uh the economy is very very concentrated okay and so part of the aggregate volatility and with uh it's you have incompressible grains of volatility coming from shocks maybe TFP shocks to large firms that maybe you can trace to CO has an idea or something.
some some data to see why what was going to talk about finding new uh work top firms in Japan but 45% of the exports in Korea top two firms 35% of the export of sales top 25 firms 50% of aggregate earnings uh and there are number of estimates in the literature about how those firm shocks or sectoral shocks can explain maybe a third of fluctuations and lots of fun anecdotes so the philosophy is to use those idiosync shocks to large sectors or large firms to uh as primitive instruments and first you have to see how to measure them and then we see how they in fact affect the general equilibrium and this way this is how you can get elasticities and actually calculate GE uh effects okay so um you know lots of we link to quite a bit of literature and I'll go more to the link with the um productivity so uh I'm going to spend the first uh 20. So I have how much? Actually 40 minutes.
Okay, great. So I'm going to spend the first uh maybe uh 15 minutes on uh general methodology and then we'll see how it applies to uh concrete economics.
So suppose you have a vector of outcomes YT it could be for instance the leading application for us it will be uh we have 16 65 industries and their TFP growth.
Okay. But later we can extend to their also their production and their sales and their etc etc. Uh so um my so the vector of outcomes depend on the vector of outcomes of the other firm so to speak via some thing maybe linked to input output productions or influences and it's parameterized by some vector gamma thing it's a low dimensional parameter maybe dimension 1 2 3 10 something like that okay uh and B is like a big matrix you know uh you know a lot of it structure maybe it's linked to input output but there's some elasticities inside that also matter and that's which they parameterized with this gamma and so potentially it depends on the past that's not very important in theory but it's important in particular applications and very importantly there are idiosyncratic shocks UTS so UITS it's an idioc if YT was TFP growth uh YIT to firm I or industry I UIT would be idiocyotic productivity shock we're going to try to extract it and there could be a vector of Igate shock U a T uh okay And so that's the structure and you want to estimate the gamma. That's the big uh that's the big uh thing u just notation suppose you didn't have a past that did in the past then if you have shock it's not going to affect the yt via this kind of style uh you know effect and so that's how we're going to that's what we're going to use. So let me give you three examples.
>> Yeah. So there's no there's no I subscript on the Y here.
>> Oh no no no it's a ve this is a big vector of dimension M. Okay this all vectors and B is a matrix. So let me just add some subs which maybe is a better way to communicate that exactly.
So YT maybe should be there for the internet world. Anyway uh Y here uh I think it's the TFP growth of industry that will be our application. It depends on uh the TFP growth of the other industries. Okay. Uh and times uh there's some strength of the network. It could be like input or output leakages.
Much more on that later. Times some parameter gamma. And gamma is this influence parameter. How influence you have. Each child has a positive GP shot.
How you know where child depending on some we want to estimate this gamma and there will be also secretive quality shock in industry. high and also maybe some loading on some aggregate factors.
Okay. Um and once you see that you can generalize to n kinds of networks for instance input output going from suppliers to customers or going to the other way or train networks and things like that. Uh another one it's just supply and demand. So you have Q the change in log demand in quantity depends on the price in some elasticity five we'd like to measure and the aggregate price depend on the aggregate demand times some elastic inverse elasticity of of of supply okay so it's a classic supply and demand uh problem and then it follow it works also in that general framework and then we use inducatic charts to for instance demand to estimate both SC of supply and demand That's what we do in the paper with Raj and here we we we generalize that uh and then there will be later so a strength of the framework is to do macro is the coefficient B of gamma can depend very nonlinearly on gamma you know most general effects it's you know ratios of elasticities elasticities sum of elasticities and stuff so it depend nonlinearly and so we work out a whole macro network and you can identify demand for steel versus for oil versus for stuff okay again with the causal framework using idioyncratic shock.
That's why we think it's a general purpose kind of methodology. So how does it work? So let's go back to the uh so if you have that you you be ded for at least two seconds to regress this on the the right hand side you cannot because everything is indogenous. So uh what you do is we will say there there are truly idioatic shots. as an issue of how we're going to be able to recover them. But we will we will under some conditions on the flame and we do recover them correctly. Uh they're uncorrelated across units and they're uncorrelated with this uh factor structure. In practice we we do always you know one or two factors I factors and you you can do more PCAS with three factors for factors and you see how the estimates are stable. Okay. uh there are some regular easy regularity conditions again you know the structure of this B matrix but you don't know the value gamma that's uh that modulates it for the inference so how do we do that right I show you the algorithm at a high level and we have econometric theorems and stuff okay at a high level so um so here's how it works so this is the structure of world well world lag uh the lag again doesn't matter but you practice is there so doesn't matter conceptually but it's there So you said imagine we have a guess gamma hat that's our guess I imagine it's correct but uh so we can always even if it's not correct you can always form with a data yt minus that form and so at the correct gamma which we call gamma star this residual should be exactly idiocratic shocks again this is a vector just this is u this a vector of nd uh shock of n and then lambda I * A T loading lambda of industry I on the common factor of it. Okay. So if at the correct gamma this this should satisfy that. Okay. Good an observation. So we hope again there will be a mixer but I give you the intuition here. Okay. We hope that we're close to if we hope to be basically at the correct gamma. If we have the correct gamma then we run a factor model a lot of knowledge on how to run factor models number of factors and stuff and we uh recover idio UIs. Okay. What do we do with them?
Uh I want to explain why it so the TFT growth of uh of industry I and u mostly this one. Uh so what what I'm going to use is the new jetties. So the idiosyncratic shocks of all the other industries but not industry high. I'm going to uh put them in some optimal way that I'll explain. Okay. Full way uh to best instrument the YTS and the YITS.
Okay. So we find the optimal way to instrument use those industry shocks to see how much is the productivity of industry I affected by all the productive shock of all the other industries.
Okay. And given that I need to with those instruments I can estimate a new gamma hat. Okay. And there new gamma hats I go there and and I and I circle until converges. Okay. Um that's that's how it works in the intuitive. Okay. Uh now a little being a little more uh specific uh the actual uh optimal instrument we use is that so it's you found you have all your radio shocks you you get the gamma you found your shock.
This is the value of a generic equival.
Okay, you should set the shock to industry at zero. This is the surrogate value of what the general should look like if you had all the old equi and you use this is directly respect to gamma to be a vector. is multi-dimensional z and that's some in the precise sense the optimal instrument you want to uh you want to use okay and so what we do is you form you you form this residual here and you regress your form residual on that instrument and you have a slope which is delta gamma okay call it gamma at convergence UI should be uncorrelated with this is made of industrial electro to the other industries and at convergence this this delta gamma should be zero. So you you youerate up to the point where delta gamma is statistically you know not different from zero but otherwise there's something really nice which is eometrically ideally uh the all gamma you have plus this delta gamma. Delta gamma is exactly an estimate of how much you should iterate and it's like Newton convergence. You do one step of estimation boom you go if you're close to the exact thing. In practice you're not always close so you iterate a few times but that's what you do. Okay. So you do this uh you do this iteration.
Okay. Um okay and we have again echometric theorem is the right thing to do in some some sense etc. Okay. So how many parameters do we estimate? Uh if we have n uh firms or sorry n industries we can estimate basically we have we use the variance matrix. So the factor we can use basically n square two parameters. So if you have 100 industry you have 5,000 parameters. Of course, we won't go there, but potentially is very very uh you know powerful. Uh it relies a lot. Um uh let me give you a little bit of intuition that there are some theories uh that uh uh and there's some intuition for why this is exactly the right thing to do but let me not uh I think let me not go uh let me not go there. How precise is uh the estimator?
So we have a proposition on that and uh the proport I give you the highlights the precision is proportional. So if you have n industries and t periods there's also the uh h which is the herindal or the square root of the hindal index. So uh how how many you know in terms of industry sizes u again it's very precisely defined on the paper but basically the standard error of the estimator is proportional to one of the squ of n * t * h so it means first in general to have a big precision you need or it's useful to have a few big big sectors big industries and the factor is mostly very sharp you see how the rest of the economy reacts to them that drives the identification but also if you have large t of course of t also if you have large n it converges one / square root of n * t so that's a message of hope because many panels we have in the past and also coming online you have fair a fairly small t okay but a very large cross-section of firms are panels of you know European firm lots of European firms but for past 10 years or so okay and so using this granular network g you can potentially have a very small stand error so high precision okay >> of course of course sure >> right so there >> that's right so the UI that's very very important so let me just go back to this is totally crucial so when we write the model where where is it uh so yeah so when we said you have a good enough factor model such that after removing one two three four five factors or whatever the residual UIs they are they are uncorrelated to each other we say independent but it's really uncorrelated >> across uh no across it turns out just across eyes so UI T and UJS are uncorrelated >> but the UI itself could be uh correlated temporarily that could be and ically there will be an autocorrelation there.
Okay. Likewise, this guy can be autocorrelated with itself but not with the UI. Okay. Yes. Direct.
>> Finance. We wow our students by saying that we only need five factors. How many do you need?
>> Oh, uh two. [laughter] No, we do two. We'll see. Or maybe three. It depend. And then you add some more factors and you see nothing really changes. But uh okay let's me um no there's no fixed uh the rule it's at some point just all within standard refinements within the standards of the parameters. Okay. So let me uh uh let me uh anyway so uh no more more generally if you have a very very general network you can calculate those kind of sum statistic and this is the whole thing that I was talking about and you get those you know rigorous theorem about the about the size of those errors. So this is a basic um uh paper algorithm. So we extend it in lots of ways. The most obvious exception is just having factor models.
Here I just show you no factor models. You can have more L of course more difficult but we did it. Uh uh you can have incomplete data. So you have some panels where some concrete didn't exist. You had no data suddenly you have data that comes online. So you can do it. So you can do missing observations. Uh you can have mismeasured data. You can calculate. We have a in the TF patient I show you. you can say well maybe this TFP is kind of bad partially badly measured with error and then you can correct for that with some scheme uh and you could also have completely nonlinear models here we we decided to show the linear version because that's easier to understand but you cleans saying okay here's my first order conditions whatever it's all very nonlinear but the the same ideas apply once you have the idea use shock see how they affect the aggregate doesn't matter if the aggregate depend linearly and nonlinearly in those things you can still uh you can still do it. Okay. Uh threats to identification the biggest is you have a misspecified model. Okay. You have this B of gamma matrix but correct it's it's more difficult there's extra it's not a homogeneous elasticity different kinds of elasticities. Uh so what we do is uh we say okay let's add some more richer specification with other kinds of influences at some point it stops or you have an incomplete factor model instead of having like taken two factors maybe it's four factors so you add more factors and you make sure it doesn't really change the estimate uh much at all you can do other identification tests you can classic test of the number of factors and and when you have high frequency data you can do a narrative check look at the what were the biggest events what they look like Okay. Uh link with MLE if you have zero factors what we are doing network G it's exactly the M okay uh and no L however once you have more aggregate factors it turns out the M become extraordinary awkward it's called the incidental problem I didn't know of it but it's a big deal apparently David tells us in in econometrics and also What's nice particularly nice about the defog JV is you see it's much more transparent you see okay those are the shock you use you can look at them in the eyes you can do various plots to see the accent I will show you such plots so it's much more transparent control much much blackboxy than much less blackboxy than m okay so now applications for here tics than it is for now in the US and I'll talk about in the whole world so here's the question. Suppose a sector has a 1% TFP growth. How does that affect the general equibium TFP in in the economy? Okay, so we did some future review but not exactly.
It's a very important question. This is at the heart of all the you know Roma style externality models. Uh and uh but a lot of it is just completely OS no causal schema. Okay. And now it's just some wild. There are a few papers with IV uh IV design and actually the without flattering anyone intentionally uh the nicest one in this bloom than readen paper uh and using tax changes. Okay.
And here we have a general purpose methodology to get causal identification via text and I hope I'm happy to discuss validity of that. And so we do both causal design and G impact. That's the that's the where always we want to be some notations. So Y here will be TFT growth industry I uh we have the sales of the industry in dollar in dollar terms. How much you buy from and then you can form the input output matrix the classic one. how much I spend on J divided by I sales and the omega up which is quasi transpose which is a fraction of J cells that come from industry I so um reduce both so here's a basic specification uh with no l so my TP growth uh in industry I will depend on my should I here my shock and my loading and the shock but also I see how all other industries their TFP growth and if I'm one of their um um customers this is my input output strength of leg linkages there will be some impact on my productivity estimating that is gamma down that we need to estimate but likewise here you have a gamma up and omega up omega up is the input matrix going the other way from customer to supplier if my customers have a TF growth How much does that affect the suppliers? Okay, by this influence parameter gamma gamma and you can enrich the framework with other linkages, geographical linkages. We didn't do it but we know we could in principle. Uh okay so that's the identifying assumptions. Uh the UIs are uncorrelated with each other across time and injit could be autocorrelated with itself and the are factors uncorrelated with the V.
Uh great. Now this is with either zero lags. If you have h lags in practice we have two uh uh you get exactly the same thing and you have gamma down gamma up the influences have different lags okay so that's what we estimate and we run that in the basic basic j so I show you estimates of gamma but let's think before about interesting summary statistics um um the long run impact of tf epsilon j will be on industry I will be some influence I J and what's the I you want to form this uh those were the matrices of influences B 0 B1 B lambda B2 sorry and you want to form this uh this cumulative long-term impact matrix so this is the cumulative long-term impact of a shock J on firm district J TFP on industry I TFP and we estimate all that so we want to estimate both a little gamas but interesting summary statistics and the the main one is this aggregate multiplier. So it's this fourth experiment. Suppose each all sectors have a 1 percentage point increase in productivity growth before any linkages here. What will be the aggregate productivity growth? So what will be the average productive growth of all the sectors? When you think about it, it's just accounting. You want to do the weighted sum of those influences like long run influences. Now on top of that for the GDP TF based TFP it's all multiplied with the Hton uh Hton parameter if all average TFP at the industry level is 1% the GDP net TFP is 1% times this Hton the result is in all metro models not specific to us what's specific to us is this M dot how before any Hton effect um you know one industry affects the uh the others so the data is BN data 65 5 industries uh for this period annual we have lots of data and for now I'm just using the TFP uh data uh and uh we estimate you know zero lag one lag two lags and then it's after it's kind of like little zeros let me show you how to we want to interpret that so here's the headline the most important numbers for this TFP business so if you have a 1% decrease in the average TF primitive TFP across of all industries the average uh the average growth of TFP across all industries will be 2.7%. Okay. So that's like a multiply TFP multiplier r whatever like maybe externality of a factor of 2.7. Okay.
And if you add the just multiply by the whole factor uh you get to uh oops sorry you get to what is going on you get to uh five uh 5%. Okay. So like one to five the original one is 1 to 2.7 okay do they go up and it turns out 70% of the externalities they go upstream so Apple has a productivity shock and that makes it suppliers better okay and the rest 30% goes downstream so it's kind of interesting you could think about different models of influences that and here I show you the you know where the numbers are come from okay with standard errors and those magnitude of reasonable typically R&D type externalities typically an externality factor of maybe two three something like that. So it's in the it's the ballpark and here's the dynamics on impact meaning this is in years on impact you have a multiplier maybe 1.4 four or so in the long run the multiplier goes to this one 2.7 so you can have a dynamics as well okay some validation part of the chart you can hear this is the actual productive growth of uh industry and this is the instrumented productive growth mean the part of it that comes from the induc shots to all the other uh industries okay and ideally flow should be exactly one and it's you know within the standard of one so That's that's pretty nice. Uh and so this is the instrument we use. Another little validation again this is the productive growth industry I instrumented by the uh shocks of other industries. And this is the price change in industry I uh and if your the other industries have a positive TFP growth your TFP will be will fall will grow itself. So your price should fall and indeed you see a you know decent uh slope of minus 0.6. So it's a consistent we do lots of variance with time extract for factors. What about measurement errors? What of different matrices that are so it's a slew of number this is the mart. So yeah I just show you uh we get the baseline is 2.7 the average across all those 12 or so specifications 2.5.
So kind of the same thing. Okay. And the idea that it's mostly a bit up it goes up rather than down is quite robust across the specification. Okay. So basically what we have let me show you a few more more things we do. Uh we have in the workware what propagation TFP propagation in the world economy. So we are trying to get clean data for all the sectors and all the countries etc etc and so it's really in progress and that's part of why we develop a method to have missing missing data and stuff like that. Uh okay this is totally just it looks like the mart again it will transport shortly uh is less is less 1.5 and the externality is less good if uh it is larger within your own country than cross countries but something kind of interesting that's robust is that globalization is definitely good for emerging economies very civil but for developed economy it means you have fewer good externalities because if you rely on foreigners to to supply your inputs and sell to them, you get less externalities. So potentially there are less externalities in the world this way and and maybe that's that accounts for a fall in the TFP. They speculated but interesting. Okay. In three flag we have some questions. So okay uh we also have a what about an aggregate macro dynamic model with quantities and prices and stuff. So we do it and but we do a new somewhat new model with general CS where the demand for good eye could have an sigma eye supposed to be the same for everybody but allows you to say the demand for oil is less elastic the demand for uh strawberries or things like that. Okay and uh so we implement that using uh uh using the general methodology and some something in the appendics to do it. So what we use is TFP and also prices change in prices change in production and change in absorption by absorption by final demand. And what you get uh you can get elasticity of demand uh by final consumer so maybe 0.35 elic by uh for it inputs. So maybe on average you want 0.2 to lower but then it's mostly energy has very small elasticity of demand whereas for other materials it's a higher elasticity of demand so what you can do you can do much more is with that you can estimate loss of elasticity of demand again using a clear causal scheme which is idiose TFP shocks or demand shocks by other industries and it's you know previously consistent with other uh other papers anyway conclusion we hope the network I will be useful to do lots of things because again you can estimate lots of things. Uh you can get the generic effects. It's a fairly transparent estimation. You collect mods shocks. You see how they affect the aggregate. Uh it lowers or eliminates many the need to find unique one-off events like there's a tax reform one type reform China shock. In your paper you have many tax reforms you could do it. you have other effect restrictions and we have those two and 2.1 or so applications this one being in the works there will be platform package so uh we we're happy to provide free consulting services [laughter] network GI but in the meantime uh still a very early working paper if you have any criticisms fundamental or not we're very happy to listen to that to try to improve it and we try to make it very usable with again um accounting for measurement error, missing data and stuff. So we want this to be a robust machine you can use fairly easily to do macro causal identification.
>> Thank you.
Okay. Grab the money. Yeah. If you want to come >> I don't think it's okay. Now it's working. Okay. Um so even if you don't need the oneoff shocks, >> have you thought about using them to kind of validate the methodology?
>> It's a good idea. But say for for TFP we you know we don't quite I mean there's there a very very different design but somewhat similar in that sense validates we did that um uh he didn't survive the refrain just the printage of the paper in the the paper with right we had done that for oil using pl for oil comparing that to estimates by kon and bar hington was very similar but s one validation Yeah. So great. Um I I guess just I I think really important thing about this which I think is great is the idea about having to say what is the network? What is the structure of the network? I think that's an important think about that and I think it matters because I think as Nick hinted at one of the the threats to using this method >> goes back to general econometric techniques. you know this the correlation of the user across space if you're not controlling for that >> right >> that is potentially an effective identification it's analogous to the old geomet using lags instruments >> right >> and in that you have to rule out long quarter correlation so I think that's the main potential threat to what you're doing um and you know I think it's just you know can you be robust about using diagnostic >> the worry about older literature the instruments are just you know not very strongly you have to go further and further back the length of the network to go further and further away with your peers right that reduces the power but you know it's an empirical issue >> it's an empirical so one way to do it if we had like fine geographical uh you know we could do it we didn't do it but you know geographical where those industries how close are they if you have firm data to be even better establishment data you could have some you know the influence could depend also So on some measure proximity for instance that would be way to do it. Uh so that would be one way to do it. You can imagine more the short data depend where you are located or when when one could do it too. Absolutely. Now you might say well maybe the model is a little mis okay it's all continuous. So if the model is a little misspecified the error will be small. If the model is grossly misspecified the error will be enormous. So there's an issue of judgment of how you know how many extra leakages maybe did we miss on.
>> So have you thought about sort of diagnostic tests that you >> Yeah. So we have we have of some other speaking restrictions and stuff like that. Exactly. Yeah.
>> We haven't been super systematic about the I think directed the question.
>> So I I'm not sure if it's maybe the same question. So like so so so in finance language uh so the way that I explain to students whether you tell whether the factor model is working or not >> is I take all of my UITS >> and I take a large number of them and I sum over them and it's supposed to be zero exactly >> okay >> right that's that's the di that's that's the diagnostic for whether or not the factor model is working and what your what your model is doing is it's it's basically splitting systematic and idiosyncratic variation Now you're taking pieces of this idiosyncratic variation and showing it's reflecting materially on other stuff >> and I'm trying to understand is the other stuff is that the other UIs in which case I'm worried about my factor model assumption from the very beginning or are these UIs reflecting on other productivities. Is that what the factors are?
>> So what what are the factors?
What what are the factors? What's the relationship between the identifying variation and the factors?
>> Right? Well, normally there's no link sorry in theory inside the econometric framework. Uh there's no link zero correlation between this edit and the all the UI it's something we can check but it's going to be true mechanically because we do a principal component analysis. So mechanically it's going to be true. So we need some other other uh substantive test and what we do is okay you have all those residual UIs do they still have one more or two more principal components so they're not triggered that's what that's what we we would do >> I don't know if this helpful but the UIs if you don't size or network weight they're going to be mean zero the identification is coming because we have some units that are either big or really important in the network. And the difference from Zeb's earlier paper with Ralph is it's not just big here. It could be that you're some central in the network. And so then shocks are those units are going to propagate and that's what's driving uh that's what's driving the identification.
>> So you mean what's film? Yeah. Does that need to >> Okay, so I guess I need to know the gamut to know the fact.
>> Yeah. Yeah. Let me I want this to be very clear. So now let me go back to basics. Let me just show you the I said it but it went very fast. So let me just show again the very high level and we have few and stuff. Okay. So here here's what you do. You guess a gamma. You're right. Sorry. So but but but we solve a problem.
You guess the gamma and then you do left hand side minus the right hand the right hand side the factor the you know network part of the right hand side. So if gamma was correct it should just be a factor model. Okay. So then you can test is it a good factor model? Did you indeed have the maximum right dimension for the and stuff like that? And then once we have that we we have a UATS and then we estimate [snorts] uh should you change your estimate gamma half from gamma half plus delta gamma via uh via regression. Again the regression is very simple. You take the left hand side we just calculated yt minus the be yt minus one etc. and you regress on the instrument at conversion it should be zero the slope just you do little OS should be zero if it's not zero you take your old gamma and you add slope delta gamma and then you you get the new gamma prime and then you iterate until it converges of the estimation it's a structural estimation but with I mean sometimes called an internal instrument and for some people that's bad some people that's totally fine it's it's a bit of a structural estim But then you can look back and that's what we did in the oil example. Can look back what were those mysterious supply oil shops say oh there was a war Iraq etc. You can look at them in the eyes and say was there really a big show in that industry at RT does it make sense.
So you're not completely the model is you at the end. Yeah. And and just what lead to what you guys are already doing. First ask John after his presentation. Okay. What about the GE effect? So what you couldn't do I haven't put it through completely is you had all those uh innovations sorry extra subsidies to solar panels in region IT okay and you could say let's say you you run the model on them and you see you get the t part somehow okay and then you do some size weighted sum of the university shops to what extent do they affect the aggregate and then the stroke would be the aggregate multiplier uh of those secretic subs for instance could be greater than one less than one depending on the on economics of problem. So you know once you have a model with structure you can believe you have little G like I like test you can do to to get at the GE framework it's better to do that because then it's completely internally consistent but in the meantime this is what I described this for John's paper would be a good first first approximation >> um so without the fact is does it is it the same thing as a GMM and or more broadly Can you restate this as a GMM?
>> Uh it turns out GMM handles those lambda. It has quite with quite difficulty. Okay. And the enormous black box and then it tells you you have all okay you have always 65 perod instrument or 64 instruments how to weigh in optimally whereas here on okay if there are no factors what we're doing it's exactly the optimum GMM instrument. Exactly. But otherwise for instance what what we did you can say let's estimate uh this elasticity using uh when we do the the macro model elasticity of supply let's see demand just using TFP shocks you get an estimate and you can do another one that estimated just using demand shocks and we can get another G hopefully that they're you know they're consistent uh so you it's just much much more transparent than the big blocks back black box GMM. So it's not exactly GMM except in those very simple cases in the more complicated cases. It's less exactly perfect than GMM but infinitely more transparent and to the extent we want to understand what we're doing it's probably better and if it's more transparent it's more robust by the way and we have some theories of that.
>> Okay we've we're out of time. I actually have a question about demonstrated leadership.
Great. Thank you. Uh I'm really grateful uh and excited about this opportunity to present this work uh which is joint with Enanguli who's here with Talia Marcelo and Nick Reynolds. The usual disclaimer applies. These are our views and not those of the Federal Reserve. Okay.
Uh on February 14th, 1876, there was a collision in idea space. Uh two inventors, Alexander Rambell and Elisha Gray, by some accounts had independently arrived at the same new idea and showed up at the patent office with applications for the telephone patent.
As was the policy at the time, the patent office organized an administrative proceeding that was known as a patent interference that they held every time there were two inventors who showed up to the patent office claiming the same invention.
What this paper asks you to do is to think about this choice that inventors make in terms of what project to work on as akin to choosing a location but not in geographic space instead in the more conceptual space of ideas.
So if every invention can be characterized as a location in idea space then evidently what bell and gray had done was chosen the same location.
Okay, so this is not a mere these kinds of collisions were not a mere historical curiosity. They were pretty common. In the 1870s when Bell and Gray collided up to one in 20 US issu patents issued uh were involved in a patent interference and over the next 150 years that rate dropped steadily and significantly. So by 2014 uh that rate was less than 1 in 10,000 issue patents. uh and by the way the Dudna uh crisper interference is at the end of this this series.
So the claim that we're going to develop in this paper is that this decline reflects not just your head-on collisions but a more general spreading out of inventors across this expanding idea space and where inventors stand in the space of ideas matters for growth.
We're going to establish this claim using three questions along three routes.
One, are inventions indeed spreading out? Two, if they are, why? And three, what are the consequences of spreading out?
We're going to get you the answer.
First, we're going to build and validate a map of idea space. Then, we're going to develop a theory that explains spreading.
Finally, we're going to take the model back to the data to understand the consequences of spreading out at the potential cost to growth. So, we're going to map the pattern. We're going to explain the mechanism and then we're going to test the consequences are inventions spreading out. So, the strategy of this paper is we're going to take the text of patents to tell us about the uh colllocation of inventors in it space. So, we're going to take for every one of the 11 million plus issued patents from 1836 to 2024, we're going to take the text of that patent and we're going to represent the text as a highdimensional vector.
Then, for all patents issued in a given year, we're going to compute the average pair-wise similarity of patents issued in that year by computing the cosine similarity of their corresponding vectors.
So the figure that you see on this slide is that calculation standardized average pair wise cosine similarity using a representation model called TF. TF is a classic word counting uh way of representing patents as as as vectors.
And what this uh what this graph shows is that according to TF representations inventions are becoming more similar over time.
In other words, idea space is becoming more crowded contra the interference record.
It turns out this conclusion depends critically on the representation model that you choose. So when we look at TF representations, contemporaneously issued patents are becoming more similar. Idea space is getting more crowded. When we look at other representations of patent text, other embedding models or ways of transforming text into vectors, we get the opposite conclusion. Similarity is rising or similar is falling, i.e. idea space is becoming less crowded.
So the natural question here is what map of idea space should we trust?
So to answer this question, we're going to develop three complimentary validation benchmarks to evaluate a bunch of different representation models. We're going to see uh we're use examiner declared interferences, lay judgments of historical patents and USPTO classifications. And our thinking here is that a useful map of idea space should be able to capture multiple notions of similarity, should be able to uh uh uh uh uh span multiple historical time periods uh and and and and recover a a variety of opinions on what makes two inventions similar.
The results of this validation exercise suggest that we can safely discard the map that TF drew for us. While TF beats chance across all of our validation exercises, it ranks last on every benchmark. Therefore, we say it produces the wrong map. Instead, we're going to select a different representation, GTE, which performs most consistently and nearly the best across all of these benchmarks.
Our best map of idea space suggests that inventions are becoming less similar over time.
Over nearly 200 years, that decline is one to one and a half standardized units of similarity. And all three of our best validated maps agree on the general direction and quantitative size of this change.
We're also we also provide a complimentary evidence in the form of trying to measure or estimate how fast the size of that embedding space is is growing and we find that that's also growing. So inventions are spreading out across an expanding idea space.
To explain this finding we're going to develop a very simple spatial model of of of invention. So in the model idea space is going to be represented as a circle with circumference of size capital H.
Positioning in the circle is going to correspond to the idea that similar idea similar problems are going to have similar solutions. Okay.
Idea producers are going to develop new ideas. These ideas are going to be nonrivival and they're going to sell these ideas as non-exclusive licenses to use for downstream firms to improve their TFP. Okay. Idea producers are going to choose whether or not to enter.
Entry is going to be governed by a fixed cost F.
We're going to be analyzing symmetric equilibria. So the entry decision turns into a positioning decision. Okay. So we're going to describe the So in a symmetric equilibrium, all inventors are going to make identical decisions and be spaced equally apart, equally far apart.
That distance between neighboring inventors is going to be described by D.
C condition on entry. Inventors are going to choose how much R&D to put in their project, which is going to be determine the quality of their idea.
Small Q. And they're going to choose a price to charge idea users P.
Idea users are going to use these idea licenses to improve their own TFP.
There's a mass H of them. They're distributed uniformly on the circle. An idea users endowed location represents its preferred idea variety and it's going to have to pay some adaptation cost to h in order to adapt the idea license that it's purchasing to their own preferred to their own production process. And so that's going to depend on that distance small h that that user is from their purchased idea producer.
So, put yourselves in the shoes of an inventor. Where do you stand? Do you stand close to your neighboring competitor, perhaps taking advantage of positive knowledge spillovers, or do you locate as far away as you can uh from your competitors? And the way we've set this things up in this model, the answer is you want to be as far away as possible. And the reason is because these isolated idea users have few nearby alternatives. So isolation gives you as an inventor market power.
This is a really important feature of this model and that wider spacing raises equilibrium quality. Okay. So in the symmetric equilibrium inventors are spaced d units apart. That means the marginal user is halfway in between d over2. Okay, when inventors are really spread out, that marginal user is farther away. And it's going to have two effects.
The farther your marginal user is from you as the inventor, the more pricing power you have because idea users don't have any uh nearby alternatives and the bigger you have to build in order for it to be worth it for that marginal user to pay the adaptation cost to buy your idea.
So the spatial structure of this model couples together in a super tight way horizontal positioning and vertical investment decisions.
The spatial equilibrium turns that intuition into three compact equations.
Okay. So isolation sets your markup.
Quality expands your territory and territory revenue must cover your R&D costs and entry costs. Okay. So pricing is proportional to spacing. Quality or R&D investment is proportional to spacing and spacing is determined by free entry and the zero profit condition. Okay? So you need enough revenue to pay for your costs.
In other words, geometry bins pins where you stand, what you charge, and how big you build.
Two equations take this static equilibrium into a self-reinforcing growth loop. Okay. So innovation expands the frontier of what's possible to invent in the next period. The growth rate of the idea circle depends on prior uh the prior round of inventions.
The second equation is the key maintained assumption in this model and the engine of all the results. As the knowledge frontier expands, the burden of knowledge grows. So by this what we have in mind is that to even get to the starting line you have to invest more to even before you start inventing anything you have to get more education more training you have to assemble a larger team you have to buy more sophisticated equipment we think the best evidence comes from the Ben Jones paper of about the growing burden of knowledge with these two equations written down the dynamics follow from that the static equilibria follows from that so as these entry costs rise inventors optimally spread out in order to capture more revenue and recoup those rise those those greater entry costs.
So think about the uh uh the the dynamic uh spatial structure of this model as ripples emanating across the surface of a pond. Okay. Innovation expands a frontier. The expanding frontier raises the burden of knowledge and in response inventors uh uh spread out and build bigger thus expanding the frontier once again.
This ripple has a built-in break though I haven't told you about knowledge spillovers I'm telling you about them on this slide. So when an idea user purchases an idea, they get the quality of that idea that the the the the inventor invested, but they also get these uh hard to exclude spillovers from the density of their local knowledge environment. Okay. And so you can see from this term that as spacing increases, as D increases, TFP growth slows down.
inventors spread out, build bigger, and in some sense they borrow less from others. Okay, it turns out aside from slowing TFP growth, the model has a distinct spatial force that drives down research productivity.
So, I'm going to start that argument by showing you this expression for research productivity.
This is from the uh ideas getting harder to find paper. So this is the growth rate of TFP divided by aggregate R&D inputs.
You see in the numerator that attenuating knowledge spillovers slow the numerator down. So that's one source we've already talked about. But the other important source here in this model is that TFP gains are local. A new tractor is helpful to a farmer, but it doesn't really improve the TFP of a management consultant.
Meanwhile, R&D costs are aggregated across every project. So we have to pay for the new tractor and we have to pay for the new powerpoint. Okay. So the localess of ideas in this in this model mean that aggreate TFP growth is the average local gain across all of these projects while R&D is the sum of all the projects. Okay. And so this is a distinct spatial force that drives down research productivity in this model alongside what we already talked about we can explan that are also included in our model that capture fishing out and the burden of knowledge.
Okay, frontier growth in this model is pinned by cost and spillover parameters. So if you lower entry costs, if you lower R&D costs, if you lower adaptation costs or you strengthen spillovers, all of those are going to raise the growth rate in this economy. And the contrast here is that prior uh prior uh models are are omit uh uh [laughter] a role for spacing here where invention standard idea space matters for growth.
So the last thing to notice about this model is that the spatial geometry uh uh endogenizes parts of core growth concepts that are often treated as primitives. And so spillovers in this in our model are governed by spacing which is indogenous. The step size is is is is is also related to the indogenous spacing.
research productivity uh uh is related to indogous spacing and uh and the scale of research inputs is determined indogenously by the spatial equilibrium.
Okay, so this model explains spreading out through the rising bird of knowledge for this to be like a really useful framework. It would be nice if it could explain some other stuff too and maybe if there was something in the data that was a distinct prediction. So I'm going to show you these things next. Okay, so it turns out that the model uh unifies many facts with a single spatial geometry. So, and some of these facts have not been previously connected together in quite this way. So, I showed you evidence uh for some of these horizontal facts. So, inventions are spreading out. That was part one.
There's a few recent papers that suggest that spillovers in the aggregate of the economy are attenuating or weakening uh in in the economy. Of course, there's a lot of literature on the art and deep productivity decline. And then we have some good evidence that varieties are increasing over time. So there's the Hershey at all paper from 2012 that says that on the extensive margins more and more firms are doing R&D. And then just from armchair observation, there's more varieties of new ideas being produced today than there were 100 years ago.
The model also gets at this increasing step size over time. And we have accumulating evidence that this might be true. So again from the Hershey paper within a firm R&D intensity increases over time. And then we have this aggregate evidence that the rate of breakthrough patents seems to be increasing over time. And then we have evidence from citations from patent rents from stock market reactions that the values of patents seem to be increasing over time. So one geometry seems to unify a lot of these facts together.
We also find evidence for the model's most distinctive prediction, which is that spacing couples with quality. And so we find that more isolated inventions in idea space tend to use larger teams, are more often assigned to firms rather than not assigned to firms. That's an indicator of perhaps resources that go into invention. They're more often cited, and they have a higher market value, at least according to the estimates of the KPss paper. Okay, the last thing we're going to do in the paper is we're going to provide you a decomposition of the overall decline in research productivity. Uh uh the long run decline in research productivity. So this exercise is going to be conditioned on the RAS getting harder to find data.
So this is from 1948 to 2015. And the decline in research productivity is the difference between the slowdown in TFP growth and the increase in R&D. And so that's minus 1.6%.
And 4% the difference is 5 a.5% per year. Okay. Our strategy is basically we're going to decompose each arm separately, add the spatial contributions together and divide by 5.6.
This type of decomposition is based on two moments in the data. Okay. So on the TFP on the on the left side of this graph on the left side of the slide you see the co-movement in the time series between TFP growth and spacing. Okay the horizontal axis actually shows similarity so similarity is the inverse of spacing. So going left means more spreading out is associated with slower TFP growth.
On the right you see the time series co- movement of R&D and spacing. So again going left is more spreading out and that's associated with faster aggregate R&D growth. Okay. So in both of these graphs what we've done is we approximated the growth rate of spacing with the ch change in observed embedding space distance. And then next we're going to use the model to interpret these co- movements.
So on the TFP side, uh we're going to run this regression and this regression has an interaction term and that's because there's a corresponding structural equation which says that the effect of spreading out on TFP growth depends on the level of spacing and that's a spillover base effect. So when uh ideas are higher quality, the spillover drag is larger. Okay. And so that's why there's interaction term. So that's where we have to evaluate the spillover drag conditioned on observed spacing. So for the 1981 to 2000 period, we find that spreading out drags TFP growth down by 16 basis points a year.
Over the larger 48 to 15 period, uh spreading out drags TFP growth by about 11 basis points a year. So that's going to go directly into the decomposition.
On the R&D side, we're going to do something different. We're going to run this regression. Again, there's a corresponding structural equation here.
And what that structural equation says is that the growth in R&D or the the co-movement between R&D and spacing is largely about rising quality per invention. And so the um the uh the slope of this regression is going to help us pin down the variable cost share of producing that quality. And so based on that regression, we estimate that the variable cost here in R&D is 70%.
The constant or the intercept ter intercept term in this regression, the model tells us that it primarily reflects more inventions and rising entry costs. And both of those things in the model are mapped to the growth rate of the knowledge frontier itself. And so based on this regression, we can back out that the frontier growth rate is about 2.7% per year. Okay, so we're going to use these parameters to discipline the decomposition. But now you're saying this is crazy, Jeff. You ran two time series regressions of 70 70 observations each. How can we have any confidence that this is this is reasonable? Well, this is the answer.
This is our answer to that question. We do four quantitative checks to support the decomposition. So the first row here shows the spillover drag that I showed you from the last slide. So that was 16 basis points per year. We're going to benchmark that against an external estimate which comes from Bloom Shankerman Van Reina 2013. What they do is they have an estimated spillover elasticity. We're going to standardize that and they will multiply that by our observed rate of standardized spreading.
And so that is a cross-sectionally identified uh TFP spillover elasticity.
And that that exercise suggests that the TFP drad from observed spreading would be about 15 basis points a year. So these are completely separately identified quantities that are nearly exactly the same.
A second external benchmark, we identify the variable cost share in R&D at about 70%. If you look at the NSF bird survey data, the labor share of R&D is 69%. This is not quite apples to apples because some labor costs are fixed and some non- labor costs are variable. But we think that this is in the ballpark and it indicates to us that there's some you know there's there's some signal here.
The model also uh survives two internal consistency checks. So we identified the growth rate of idea space from the regression. It turns out this is overidentified. The model provides an alternative route to estimate this. The model says that the growth rate of idea space should be 2/3 that of the growth rate of R&D. So 2/3 of 4% is also 2.7%.
And the model also uh implies that the growth rate of spacing should be one-third that of the growth rate of R&D. And in the data that appears to check out as well. Okay.
So this is the decomposition at work. So on the TFP slide, we're going to we're going to take that 11 basis points a year directly from the regression.
Remember that's for the larger 1948 to 2015 sample.
And then know having pinned down the variable cost share and the growth rate of idea space that's going to allow us to to partition R&D growth into four distinct channels that the model describes. Entry expansion, so more varieties of inventions over time.
quality scaling. So inventors in investing more in quality in order to cover more territory.
Fishing out is the convexity of the cost curve, the R&D cost curve. And the burden of knowledge is that fixed cost of entry. And so the first two things we classify as spatial as as existing in in the spatial uh uh part of this model.
And together these these these these these account for 2.25 percentage points. So 0.11 plus 2.25 divided by 5.6 six is 42%.
So spatial forces account for around 40% of declining R&D productivity.
This comp this this this this decomposition is conditioned on linear burden of knowledge and con uh quadratic costs. If we do some sensitivity analysis right that around that and in particular if we pick some better identified numbers we get an even higher share of the R&D productivity decline that's attributable to spatial forces in the model up to up to 58%.
Okay. So uh three takeaways from this paper. Inventions are spreading out. We documented this with validated NLP measures over 200 years and declining interference rates. An interfer expanding idea of frontier uh makes it optimal for inventions to spread apart and this mechanism both unifies empirical patterns and indogenizes core growth primitives.
And lastly, where inventors stand in the space of ideas matters for growth. Thank you.
uh very cool paper. So uh I was I was wondering um could it be that maybe the um the narrowness of patents is increasing. So I guess that happens also when we are writing papers the first paper in a literature is claiming something very broad and then over time people are refining and they're kind of trying to take smaller and smaller chunks of that space. Yeah, >> great. And one comment is related to an it would be interesting to look at um I al I wonder a slightly different angle which is lawyers trying because then lawyers are increasingly involved in writing patents and whether they're trying to make them write written in a way that looks different from others or something. So I one thought I know you know I think you've looked at this but the Microsoft academic graph looks at like academic papers that should be interesting to see academic papers where the incentives there's some similarities with some very different ones um and see how those overlap the other question was conceptual one which is I think you have in your mind like a 2D model you know there's these things like Tim Brosahan coined this term general purpose technologies that boost everyone and you know they're rare but is that conceptual like putting another level above it. So I think everything's on this space and they're all far away. If I can bring computers or AI, it kind of touches everything as close by. Is that something that gets you out of this?
Because I can see your you're kind of diminishing. But by the way, just Thomas Philippon has this really nice paper I think on like linear growth rather than constant proportional growth. Do you end up with something like that? I don't know if you've seen the Philip on it.
There's some coers and I'm just remember talking to Tom about it but the I can't remember his coers statistically the linear >> it looks quite linear. I would be interesting if you get it out of that looks a much better fit to be quite honest.
>> No, I I think it's a it's a very nice idea. I think it would be nice to but your model is very qualitative. It would be nice to think more systematically if you have a bandwidth to do that. But what is the right topology? Maybe it's not a one-dimensional you know two dimensional space but it's a or even one dimensional if it's a line it's a circle uh it's a n dimensional you know and taking the functional form seriously here is all very qualitative like the world book or something was a quadic there and we and it's nice but to go towards maybe like a ch what does you know with functional forms you can believe for the distance and it should be important weighted etc etc I think that would be a a great plus for the paper.
>> Yeah, thanks. So, um it would be good to kind of I mean I my my reaction was a little bit like the Anna's first questions. I wonder whether it's the kind of the importance of innovations is declining and you're you're getting some of the results from that that dimension.
So, it's you know it's filling up more of the product space but each one is less important. you know when we think about me too drugs for example we think there's a more of those coming along which are not not so important so I was wondering whether you know somehow getting some way to tackle that you know um I think that that is my my main another thought I had I mean maybe this was in the model but you know your your motivating example you know two people coming along with exactly the same invention at the same the same time um and now we we do a lot less of that. I mean, there's an advantage to doing less of that because you're not doing duplicative R&D. So, that's that's a benefit from, if you're right, from the current regime to the early regime. And that was seemed to be something which should be reflected in more welfare rather than less welfare from the lack of duplication.
>> Oh, there's one in the back.
I think Ena was over in the other room when Enrico presented this lovely paper on using language and um how people use language to communicate well with specialists. Uh but it's at the burden of not communicating well with generalists. And so I'm kind of curious a how that interplays with what you're finding here because I think you mentioned burden of knowledge, right?
And so there's this question of like depth of knowledge before you can invent. And that's going to likely embed you in a community of specialists who are using specialist language that if properly embedded is going to look more dissimilar to to other language. And so I'm sort of I don't know. I'm curious what the interplay is with that. And maybe that's just something for you guys to think about as you're thinking about how to write this up.
Yeah, there's >> okay I've got two things on the model and then you'll have a couple minutes to respond to all this.
>> Um, one's an esoteric question, the other is a pedantic point. So the esoteric question, how's the entry process work? Is it sequential >> simult?
>> What's the equ So you're computing the number of entrance according to the free entry condition then plop them down and impose equal spaces like salad. The pedantic one then is you've got uh linear adaptation cost. You have this backyard demand thing. How do you handle that?
>> You mean like the the form the form of of how we specify demand or >> No. So in with linear with linear transport costs or that if I invest in in the context of your model if I invest enough so that the that the adopter who's located at my nearest competitor wants to adopt for me rather than them I don't just get them I get everyone on the other side of that nearest competitor to discontinuously adopt for me. So you have a discontinuity in the production in the profit function which can create uh >> so what we do there is we verify a no no spatial deviation condition. So nobody's nobody's um better off by deviating. No no inventor is better off by deviating.
>> Okay.
>> All right. Well anyway you should answer respond to the other questions.
>> Okay. Um well thank you thank you for from so much for the questions. Um there's a couple questions about you know like what are patents measuring and how narrow they are. So let me say a couple things about that. So the first thing is like we know like you know um uh one issue with patents is like we don't know like if that corresponds to an idea you know this is the idea counting problem. Uh and in fact in the quantitative exercise n is a free parameter here. We're not pinning that down. Um if we pin that down at say like the rate of growth in unique uh inventors uh then actually we can estimate like how uh how the how the the growth rate in the number of ideas per patent and we find that that's slightly negative over time. A second question is about like independence of like you know like there might be like these like fence uh uh like innovation fences or like one idea spread across a number of of patents. One thing that we do there is we uh look at uh patents issued to independent inventors and we analyze the changes in similarity uh conditioned on only independent inventor comparisons. And what we find there is if anything the decline in similarity is even steeper uh compared with what you saw on the screen. We also look at different spatial scales. So not just the global average of similarity but close like nearest neighbor similarity uh all the way up to all the way up to uh uh uh different quantiles.
Um the the I think there's a lot of things to think about in terms of like how patents are generated uh and lawyers are involved in patenting. the the compounds that you should be worried about are things that are happening within a year because that's uh uh uh uh that's that that that's that's what the the the object that we're estimating is within year similarity.
Um a couple questions about topology. So I agree right the the circle is an abstraction. It's a tractable abstraction. Uh a couple things on this.
So one um you know we we chose it because it's easy and it results in like really nice functional forms. That said, uh, you know, in a super highdimensional space, which we kind of imagine idea space is super high dimensional space, that space is likely to be very sparse.
And so it may be that competition in idea space is governed by, you know, one or two or maybe three closest neighbors.
Uh, and in that case, maybe the the the one-dimensional salup approximation is is not doing too much harm. Um, thank you for the suggestion on the Thomas Philippon paper. Um G last last comment GPTs. So there's a couple ways to think about GPTs in this model. One is a GPT could be uh uh an invention that everybody wants to buy. So it has like a huge spatial reach. But I can also imagine in this model thinking about it in terms of the costs. So you know AI lowers R&D costs, AI lowers entry costs, AI lowers adaptation costs. And so it can enter in that it can enter into this model in that in that way too. uh and so I think it'll be interesting in future work to see like what is the best way to think about you know GPTs like AI uh in in the spatial context. Thank you.
and our next presenter. Take it away.
>> Amazing. Um well, thanks a lot for having our paper in the program. This is joint work with Victoria Basi Razul and Otavia Veru. I'm going to take you from a very different cont to a very very different context from the one that we saw so far which is Uganda and the starting point of this paper is the growing evidence that labor idleness is really pervasive among small businesses in low-inccome countries and what I mean by labor idleness is workers spend long hours on the firm premises but they spend the majority of this time completely idle now when we think about idle resources we typically think about productivity losses But there is obviously a long-standing literature macro that shows that these type of idle resources can be actually a key input for firms to be able to respond to idiosyncratic demand shocks. And this is particularly important in environments that are characterized by two features.
High levels of demand uncertainty and high input adjustment costs. The idea being that if it's very hard for firms to predict uh future demand and it's very costly to adjust inputs, these idle resources can help ramp up or ramp down production.
Now there are good reasons to believe that these type of features are particularly salient in low-inccome settings. On the one hand because we have one uh some evidence that firms face higher levels of uncertainty and on the other hand because frictional labor frictional markets are likely to make uh input adjustment costs particularly high.
However, this type of second has be second best behavior also has implications for firm's decision to invest in inputs. And in particular, we're going to show that it can reduce firms investment in inputs that require fixed upfront costs. And the idea here is pretty simple. If inputs only pay off when they get utilized, lower expected utilization rates lower the expected returns from these inputs which reduce firms investment to invest in them.
Okay. The input that we're going to focus on in this paper is on the job training. And the reason why we focus on this uh type of input is that it is it is a key channel of human capital accumulation and therefore productivity in low-inccome settings and therefore understand what affects this type of investment can help us understand productivity differences across countries. So what we're going to do in this paper is really think about what are the causes of the high level of labor idleness we see in low-inccome countries and what are their consequences in terms of training and more generally effective effectiveness of labor market of of policies targetingmemes in these contexts we're going to do that by combining a panel data set a model and an RCT let me start by talking about uh the data that we collected so we have about five years of data uh that we collected on an annual basis of from more than a thousand small firms in Uganda. We use this data to document a key a few key facts about the causes and the consequences of labor utilization. First, I'm going to show you that indeed firms in our setting face very low levels of labor utilization. They have demand that is highly unpredictable and they face high input adjustment costs. I'm then going to show you some semicausal evidence that firms facing higher levels of demand uncertainty do indeed utilize labor as intensively and invest less in training their workers.
I'm going to build on this task uh to uh sort of motivate a model in which firms make input choices under demand uncertainty and costly input adjustment.
And the purpose of the model the model is going to be to uh sort of formally tie the causes of idleness to its consequences in terms of investment in training.
We're going to exploit an RCT where we provide firms with a subsidy to hire and train new workers for a period of six months for two things. We're going to use the RCT to estimate some key model parameters which I'm going to come back to and then we're going to replicate our RCT in the model and compare our estimated results to the data uh that we the the results that we observe in the data for model validation. Finally, the meat of the paper and the key takeaways is going to come from the counterfactuals where we try to understand what is the role of demand uncertainty for firm level outcomes. And there are three takeaway from this paper. First, I'm going to show you that demand uncertainty is as an important driver of low levels of training in low-inccome settings as more classic channels that have been studied in the literature such as high training costs or high worker turnover.
And then I'm going to show you that there is uh a sort of complimentarity between demand uncertainty and policy effectiveness. And in particular, I'm going to show you that the returns to standard firm policies that are targeted at enhancing firm growth, such as credit management or market access, are indeed less effective in environments where uncertainty uh is high. Final thing I'm going to do is consider policies that are directly targeted at reducing demand uncertainty. Particular, I'm going to focusing on policies incentivizing demand sharing among firms operating within the same cluster. And I'm going to show you that these policies have a strong potential for enhancing firm growth in our setting.
Okay, let me just spend a few words on this thing because I think a lot of people are less familiar with it uh than my usual development crowd. So um our data comes from an initial census of over a thousand firms uh across 15 urban areas in Uganda. To be eligible eligible for our study, firms had to satisfy two criteria. First they had to operate in one of these eight sectors. These are sectors that span both service and manufacturing. They are uh motor mechanics, plumbing, electrical wiring, construction, welding, tailoring, cutting and hairdressing.
Just to give you a sense of how important these are, they employ about 30% of the non agricultural labor force in Uganda. Okay. Second eligibility criteria was that these firms had to employ between one and 15 works workers excluding the firm owners at baseline.
What this means is that the average size of the firms in our sample is three. So firms have three workers. Again to put this in perspective, this puts our firm at the 93rd percentile of the firm size distribution in Uganda and then the 59th percentile of the employment distribution. So these are the firms that are the key uh kind of sources of labor creation and training provision in this setting. The majority of these firms employ skill labor and the primary sources of the primary source of these skills is on the job training. This type of training however is quite costly. So it requires firms to train workers for about 10 months. And this type of training typically takes place at the beginning of the job spell and it's carried out by the firm owner. So it requires a very uh large upfront time cost investment.
We follow this trend for a period of five years as I said earlier and a nice feature of our data is that we have monthly data on both expected and realized output as well as inputs which allow us to sort of document the extent of demand uncertainty that these firms face as well as think about how that affects investment in inputs.
Okay, now let me jump into our stylist facts. As I said, uh labor idloness is really pervasive among firms in our setting. The way in which we measure labor utilization in our data is by is as the number of uh hours that workers spend actually doing production tasks relative to the time that they spend in the firm premises. Okay. And this graph shows the distribution of both of those margins. So in dark blue you have the distribution of the monthly hours workers spend on the premises. In light blue you have the number of hours actually spent in production. Takeaway is the utilization rate in our firm is about 30%. Now this doesn't take into account time spent on non-production tasks such as you know looking for suppliers, customers and so on and so forth. We know from other studies that that's about 20% of the worker's time which brings utilization rate up to 50%.
meaning half of the time that they are at the premises workers are still completely idle. Okay.
What are some of the causes of these high levels of idleness? So I'm going to try to convince you that one of the leading causes is the high levels of demand uncertainty faced by our firms together that we collected data on owners expectations about their future sales and their future number of customers. And so here I'm showing you the distribution of uh both of those variables. Let me just point out a couple of numbers. So what these two numbers show you that over a six months period, the monthly revenues that owners expect to have in their worst month, uh which is this 239 are about a third of the monthly revenues that owners expect in their best month. Okay, we see a similar patterns over much shorter horizons. So in terms of the expected customers over a 7 days period and again a similar patterns when we see uh when we look at realized revenues rather than expected revenues. Now obviously you might tell me well but this tells us nothing about whether this predict this is predictable or it's unpredictable. So what we do next is a decomposition exercise. So what we do is essentially we take uh our u monthly data on sales and we deco compose how much of the variation that we see in the data is due to sort of uh location specific and sector specific time trends and time invariant firm characteristics and we do that by regressing our monthly revenues on these fixed effects. So you have firm fixed effects, location by time fixed effects and sector by time fixed effects. Location is a 2 kilometer radius. So it's really really granular.
What we see is that even after controlling for all of these fixed effects about 42% of the variance in sales remains unexplained which suggests that a lot of the variation in sales is completely idiosyncratic and it's very hard for firms to predict. When we do the same exercise for inputs we see that a much larger share particularly for capital is predictable by these fix effects.
So what are some of the consequences of these high levels of demand uncertainty?
Uh I'm going to show you that higher demand uncertainty leads to lower utilization rates and lowers investment in training. [gasps] To get that we need a measure of demand uncertainty because there's different way of doing that.
What we use is the coefficient of variation of uh actual monthly revenues within the firm. So we have monthly data on the firm uh at the firm level. we can construct the coefficient of variation of monthly revenues over a three-month period. And to uh to isolate the exogenous part of these uh uh uh these uh changes in demand volatility, what we do is to you use a leave one out instrument where we instrument for the coefficient of variation of monthly revenues of a given firm with the coefficient of variation of sales of firms in the same sector location and a same at the same time period same follow-up. And what we see is that um on average a one standard deviation increase in demand uncertainty is associated with an 18% decrease in utilization. Okay. When we do the same exercise using the number of hours the owner spends uh training its workers uh uh in a given uh at a given follow-up we see that a one standard deviation increase in demand uncertainty is associated with the 12% decrease in the number of hours one spent training. So this is kind of uh providing empirical evidence that demand uncertainty indeed has the consequences that we would expect.
So this is a summary of the stylus fact.
One thing that I want to mention because I didn't show it uh due to time constraint is that in the paper we provide quite a bit of evidence that firms face high adjustment costs and that where the evidence comes from is from the fact that we see that firms respond to unexpected demand shock. So increases or decreases in demand primarily by adjusting utilization and we don't see any changes in inputs capital and labor. So what I'm going to do next is to build a model that really tries to tie the causes to the consequences of labor idleness and use it for counterfactual analysis. So let me just uh uh describe the setup of the model. This is uh a model that features homogeneous riskneutral firms and workers. Importantly the demand function of the firm is given by these the demand of the firm is given by this expression.
So it's a function of the prices which are endogenous and an idiosyncratic demand shocks which which is drawn from the distribution f that is known to the firm. This is a two period model. So in the first period firms know the distribution of the demand shock but they don't know its realization. So based on their information, they choose how much to invest in capital, how many workers to hire, how much training to provide to their workers, at what price to charge for their for their output.
At the same time, we let workers choose how much time to supply to the firm. So you think about this as workers deciding how much time to spend on the firm premises. Okay? And this is also chosen before the realization of the demand shock. In the second period, the idiosyncratic demand realizes and firms just choose how much to utilize their labor.
The production function of the firm is the following. So when operating a capacity, capac output is a pretty simple uh CRS cop Douglas production function where the only thing I want to point out is that the labor input is sort of the product of three things.
It's a product of the number of workers that the firms hires, the training that it provides them, and the amount of hours that labor the workers supply to the firm.
When operating below capacity, we assume that output scales linearly with utilization. So output is simply equal to the capacity of the firm times the utilization rate L over B, which I'm going to denote by U. What this implicitly implies is that all inputs are idled in the same proportions. So there is no separate choice of how much to utilize labor versus capital. Okay, this we think this is a reasonable assumption in our setting given that most of the machines are manual machines. [sighs] So what is the realized output which is clearly a a a function of the realized demand shock. In the paper we show that optimal price charged by the firm is above marginal cost. So it's always optimal for the firm to choose utilization rates that allow them to meet the demand. So when firms face a very low demand shock and in particular a demand shock that is below the shock that equalizes demand and capacity output is just equal to demand and scales linearly with the cap with the demand with the demand shock V. When the firm faces a high demand shock the firm is going to be constrained and therefore output is just going to be equal to capacity. Okay, pretty simple.
So how do firms decide how much training to provide to their workers? firms choose training to maximize their expected profits given that they don't they choose this uh uh input before observing the demand shock and the only thing I want to point out about uh this expression is that on the one hand you have variable costs which are essentially the workers wages which are a function of expected utilization and the reason for that is that the vast majority of the workers in our setting are paid peace rate so they are only paid when they get utilized okay on the On the other hand, both training cost and capital rental costs are fixed costs, meaning they they don't depend on how much the these inputs get utilized.
Okay.
So when deciding how much training to provide to their workers, firms as usual equalize marginal benefit to marginal cost. And I want to sh uh draw your attention to this expression for the marginal benefit. So the marginal benefit of extra training is obviously the productivity gain from the training from training workers which has two uh sort of benefits. The first one is the decrease in marginal costs of the firm but importantly these saving these cost savings are only realized when the inputs are actually utilized. Okay. So that's why we have a marginal benefit which are a function of the expected utilization. A second benefit of the extra uh training is that it produces extra capacity for the firm. Okay. So the firm uh uh capacity overall goes up.
However, how important this capacity is depends on the extent to which the firm is constrained which is this one minus f and to the uh depends on the markup that is charged by the firm. Obviously the higher the markup the higher the price at which the firm can sells this extra capacity and therefore the more the more valuable the training is.
So this is the setup of the model. What is the role of demand uncertainty? Okay, first thing you will show in the paper is that holding inputs and prices fixed a mean preserving increase in demand uncertainty decreases expected utilization and this is the cause of luck in our setting. What is the intuition here? Well, because of the capacity constraint at the firm, essentially the output function and the utilization function as are kinkedked function of the demand shock. So below the threshold that equalizes uh demand and capacity. Essentially utilization and output scale linearly with the demand shock above the uh cutoff. What happens is that uh the exact size of the demand shock doesn't affect utilization rate and doesn't affect uh output because the firm is operating at capacity. So this is essentially creating a concavity in output relative to the demand shock without necessarily imposing uh uh sort of uh risk aversion.
What this means is that there is an asymmetric impact of low and high demand shocks. Okay, with low demand shocks decreasing demand more decreasing output more than high demand chocks increasing.
Okay, this is the the b the basic intuition. So what happens when uh uh you have when we have a mean preserving increase in uh demand uncertainty here I'm showing you a log normal distribution in the paper we show these holds for any distribution. So a mean preserving increase in volatility shifts mass both towards the lower end and towards the upper end of the distribution. But because of the asymmetry that I just discussed, the mass that is shifted towards the lower end of the distribution matter more than the mass that is shifted towards the low the uh upper end of the distribution and therefore on average the utiliz the expected utilization rate decreases.
Okay.
So what does this mean in terms of investment in training? In the paper, we show that a mean preserving increase in demand uncertainty decreases training if the derivative of this term with respect to sigma is weekly negative. What is this term? This is the term that we had in the first order condition for training before. Let me give you again a graphic intuition for this. So on the one hand, so this an increase in in in volatility does two things as I just told you first thing it does it decreasing it's decreasing expected utilization because the cost savings that are generated by additional training only pay off when inputs are utilized. This decreases the expected uh benefits from training. But the second thing that happens when we change demand uh volatility is a shift in the probability that the firm is constrained. Okay. And this which is the probability one minus f. And this probability can either increase or decrease in response to uh a shift in demand uncertainty depending on where exactly this vt is. Now a sufficient condition for training to decrease with the uh with demand uncertainty is that this probability goes down meaning that firms become less constrained as uh demand volatility increases. What is the intuition here? Well, if firms are less likely to be constrained then the extra capacity from the gen that is generated by training is also less valuable. So firms have less incentive to train also via this second margin.
Okay, this is it. This is the model.
It's pretty transparent I would say. So happy to hear to to have feedback on what we uh uh you would like to you would like us to change. Now let me use the last 10 minutes to talk about the estimation and the counterfactual. Okay.
Not going to spend too much time on on uh the estimation but what I want to mention is how we use our experiment to recover some of the parameters of the model. So our experiment is uh a training subsidy which we provided to a random s set sub subset of firms in our sample. The training subsidy consisted in a subsidy provided to work conditional on them hiring and training a new worker for six months. Um we didn't provide firms with the training curriculum but we monitored them to make sure that indeed the worker was at the firm. But what this means in practice is that owners could decide how much training to provide to our firm to our workers. The size of the subsidy was pretty generous and therefore the take up rate was above uh 70%.
How do we use the training subsidy? We use it for two purposes. The first one is estimation. So we use it to estimate two key parameters in our model. The first one is the returns to training for which you know we need some kind of exogenous variation and the second one is the opportunity cost of workers time.
So I didn't have time to go through the details of the workers problem but the intuition here is that workers labor supply also responds to utilization. The reason for that is that workers are paid when only when utilized and so lower expected utilization rates decreases the labor supply to the firm and the extent to which [snorts] this uh the labor supply responds to changes in utilization is is captured by these gamma parameters. And we have an a an a interesting uh result from the uh RCT which I'm going to come back to which disciplines this parameter. The second purpose of the model is to validate uh sorry the second purpose of the RCT is to validate our model. So what we do is essentially extend our framework to replicate our uh wage subsidy uh training subsidy intervention in the model and compare the estimated to the uh sort of uh the uh results that we get in the data.
So what is the impact of the RCT? Let me first look at the data. So here I'm showing you percentage changes in the data for all of these outcomes. Uh nothing too surprising. We find an increase in number of workers reassuring this is coming from an increase in skilled workers meaning that these workers indeed receive some training. We find some effect on sales and some sort of uh positive but imprecisely estimated uh effects on profits. The most novel results is the impact on the time the workers supply to the firm. Okay. So what we see here is the an 11% an 11% decrease in the hours that the workers spend at the premises. And the intuition is what I just described. So in because of the additional worker being hired by the firm, the average utilization rate of each worker decreases. And so if these workers are responding to the intervention by decreasing their labor supply to the firm. So it's more of a change or a response on the intensive margin rather than the standard extensive margin uh that we think about.
When we replicate our model uh uh our um intervention in the model, we find uh results that are quantitatively in line with what we see in the data which is uh sort of a validation.
Okay. So we use our estimated uh model to run three sets of counterfactuals.
The first one is a counterfactual in which we run a horse race between sort of frictions that have been studied and proposed in the literature as being drivers of low levels of training.
Namely high training costs uh high workers outside option. So the fact that the worker can leave the firm or supply less labor to the firm, low levels of demand and our novel channel of demand uncertainty. Okay. The way in which we do this or phrase is by simulated changes in parameters that generate a 10% increase in firm sales. And here I'm showing you what is uh what is the impact of those changes in parameters on number of trained workers and effective labor where effective labor is just number of trained workers times utilization times supply uh labor supply. take away from this uh graph is classic channels uh of uh the classic channels that the literature have has studied as drivers of training are indeed important but our novel channel of demand uncertainty is quantitatively as important as those additional channels. Okay, next counterfactual is uh a counterfactual that is more policy oriented. So what we do is to estimate sort of policies that have been widely studied in development to try and uh enhance the growth of small businesses in in these type of economies and simulate them across environments that are characterized by different levels of demand uncertainty. Okay. Particular we simulate uh training and rental subsidy management training intervention and market access intervention. Let me focus on management intervention obviously given the crowd uh and the way in which we simulate this intervention is through changes in a change in TFP that again generates a 10% increase in sales and we simulate these policy in our baseline environment in yellow uh a um an environment that has 5% low lower volatility in blue and an environment that has 5% higher volatility in in dark green and what I'm showing you on this graph is essentially the treatment effect. So the change between treatment and control. Again take away from this this graph is that uh these type of policies are uh substantially more effective in environments where firms face lowers level lower levels of uncertainty. And the intuition here is that uh firm uh investment in uh inputs in response to these policies are much more responsive when firms face low levels of demand uncertainty. We do uh the same exercise for other policy and we see a very similar pattern which is kind of indicative of this very strong complimentarity between policy effectiveness and demand uncertainty.
Last thing we do is to think about what are the policies that we can implement to reduce demand uncertainty. This is very imperfect and it's next on our agenda to do it more concretely. But the policy that we have in mind is a policy that facilitates uh sharing of demand among firms that operate within again the 2 kilometer radius and same sector.
Okay. And we simulate it by essentially reducing the demand volatility faced by the firm to the level of demand volatility that we observe for aggregate sales of firms within the same sector and location. Okay. So here I'm showing you in dark blue what is the uh volatility of individual sales and in light blue I'm showing you what is the volatility of aggregate sales of firms within a cluster. This there is a big change there is a big decrease in volatility when we aggregate sales which is in line with what I told you earlier that a lot of the dispersion in sales and a lot of the hetrogenity in sales is purely idiosyncratic and uncorrelated even within very closely located firms.
Okay. So what would happen if firms uh aggregated demand and face these lower levels of demand uncertainty? We would see large effects on a bunch of firm outcomes ranging from labor, capital, increase uh profits and effective labor.
Meaning that there are large untapped gains from sharing demand that these firms are are not getting. Okay. [gasps] So let me conclude here. If you want to remember anything from this paper, there's three takeaways. uh demand uncertainty is a critical channel for human capital accumulation in low-inccome countries firms. Firm growth policies are less effective when firms face high levels of demand uncertainty and there is a promising avenue for uh policies targeting demand stabilization rather than just increase in demand or market access. There is a couple of implications that the paper has for uh productivity for for understanding productivity dispersion both within and across countries. The first one is obviously that uh the high levels of demand uncertainty faced by firms in low-inccome settings can suppress training and can explain some of the lower lower levels of human capital and lower levels of productivity than we see in this setting. The first one is a more uh kind of measurement point which is part of the higher marginal revenue product sorry part of the higher dispersion in marginal revenue product of inputs that we see in firms in low- income countries could be driven by a trogenity in utilization. So potentially because of this feature firms might less appear might appear less productive than they actually are. Let me just conclude here. Thank you and I'm happy to answer questions.
So one question is uh what what is demand and certainty? Um and in a sense you know to me this is also you can make choices as a manager as an own as an owner to position yourself in a product space that is less uncertain or more uncertain. The fact that it's idiosyncratic across firms tells me that there might be you know it's not like an act of god but it's maybe something it's a policy the lack of taking some policies that might reduce that uncertainty. So from that perspective I wonder whether the issue here is you've captured one other dimension of managerial incomp incompetence or you know um that might be correlated with human capital investments and I think that that changes uh the interpretation of the policy interventions as well but I don't know may you you you've thought deeply about what demand uncertainty is but I'd love to hear more.
So I have a couple of related questions about uh you know what is the training on offer. So I you know could say a bit more about what it is and I was trying to think you know is it to what extent is it general uh training or is it specific to the firm? So you know if it's general then you think you know there could be market failures because the poaching exterality. If it's more specific maybe that's not there. you seem to be finding effects of sales which suggests that you know maybe there's an ine inefficient investment in training. So that would be good. And then a related question is um you know often when we think about things like uh training or other kinds of investments the things that kind of uh you know you might want to do when there's a negative demand shock because if you've got idle workers then why not do a bit of you know informal training on them if they're not actually serving customers.
I guess you don't have that in your model because everything is peacework pay. So it seems a little bit surprising because you think some workers might be on more salary especially maybe it's you know you know developing countries that's less the case but I think in you know in a in a more advanced country you might well think that the way you overcome utilization is that you can just reallocate activity towards things which kind of you know um you know don't cost much money when you haven't got much demand but you know reallocate time So I I was going in sort of the direction Raphael was pointing but maybe thinking slightly differently. Um which is to say that your stabilization experiment suggests that the market structure is inefficient in the sense that a smaller number of larger firms would have more stable demand. And I was wondering if that points to the ideas that Nick and John have have proposed about uh uh the management uh difficulties or fictions uh that that maybe in order to have these larger firms you would need to have more layers of management and you really can't have the owner sort of trust the the managers. Um so everybody is a owner manager but maybe the that's the true friction.
So when I think of the demand uncertainty, I know you have like the labor utilization as the margin, but I would think price and giving for these small develop like there's a lot of bargaining. Why can't couldn't they just like lower price instead of 180 and then in terms of the training I was following up on John in table two it seems like a majority of the employees don't pay for it or actually pay the owner roughly around 80%. So it or maybe I misread the table but it seemed like they were doing most of the payment. So, and it seemed like the cost was really the owner time, the number of hours, and then how do you think about when there's like low demand, like is it cheaper to train versus so the cyclicality of that?
>> Great. Super interesting. I I was going to follow up. I agree that thing was like the market solution would be to merge. I was also thinking very much as Raphael said, you think of Starbucks in the US, they face a similar problem and how or a lot of services they get around it. I think partly by better forecasting but maybe this is impossible but they you know partly this is law of large numbers they have thousands of stores and they can forecast also they often adjust their prices like you know Starbucks doesn't many places have happy hours or reduced prices to try and shift demand so I don't know that would flip it slightly more towards management question I think it's a really great topic and I can see why merging may not work but just there's other ways the firms it may just be they're badly managed at predicting or manipulating demand but maybe it's hard it's Someone walks by and wants their bike repaired and it's just unpredictable.
>> Yes, I agree.
>> How much is sheer density and maybe a planner would create would accept the same amount of slack? I don't know. So if you went to say India which is extremely poor but much more dense is what's the what's the equivalent of slack? Maybe it's very zero. They're all super active or with extremely low productivity. I don't know the facts.
>> Question four minutes.
>> Okay. Uh well, I'll try. Uh so what is demand uncertainty? Um that's a great question. In the paper, what we the best we can do is sort of a uh regression of like the coefficient of variation of monthly sales on a bunch of firm characteristics. The two things that uh sort of stand out are the number of customers of the firms, firm size to some extent and like the nature of the network. So whether they have um networks that are more like family based versus like uh non-family based and where I think fundamentally the demand the demand um uh uncertainty comes from is is the fact that most of these firms are serving individual households. Okay, individual households have very unpredictable income. A lot of them work in agriculture and so it's very hard for everyone to predict when when a customer is going to walk in. And this reinforces itself because workers are paid peace rate. So they're also exposed to the same level of uncertainty and they are also consumers. Uh so that's that's kind of where uh everything is is coming from and that's why I think it's very hard for for these firms to uh try to better predict um the the you know when demand is going to come in on managerial incompetence actually I I didn't mention it but the regression that we run are with firm fixed effects so even within the firm we see that higher uncertainty decreases training okay and this also connects me to the point of um owners opportunity cost of time uh I think that force might be a play. Unfortunately, we don't have uh any data on uh owner's idleness. But you know, the fact that you know we see a negative uh correlation between uncertainty and utilization and training even within the firm suggests that you know our force if anything outweighs the you know opport the opportunity the lower opportunity cost of of of the owner's time. Um training tends to be fairly general. So there is a lot of um ch turn churn and turnover that happens and we try to capture that to some extent via this uh sort of uh opportunity cost of the workers time.
It's imperfect but um there is this uh inefficiency within uh within the model.
Um what else did I have?
Density and slack. I am not uh sure uh how those two correlates. Uh I think Dennis Edgar presented simon's lack last year and what he finds is that there is more lack in less dense area uh which is what you would expect. I think we tried to check whether so a lot of firm all of our firms are in urban areas so they're all in relatively dense areas. We see in campala they are slightly less slack but there is not huge heterogenity. Um, okay. I'm sure I forgot something, but uh happy to talk about it offline. Okay.
All right. Uh, perfect. All right.
Great. Well, thanks so much um uh for sticking around to the end. Um uh this is concentrating on customers. Um it's joint work with Alex Blumenfeld who's um a graduate student at UC Berkeley um and Joe Babra.
So there's a large literature that's documented kind of an increase in concentration and the rise of superstar firms across an array of industries. And this has led to kind of many concerns about a potential rise of market power stemming from this increase in firm size. But a firm size overall and their market share in general doesn't tell you how important a firm is to its customers. So consider kind of an example um here with two different firms. They each have a 10% aggregate market share. One could get 100% of the spending from 10% of the customers.
another could get 10% of spending from 100% of the customers. They both have the same market share and yet it feels like they have quite a different relationship with their customers. So to give you another example, a little more concrete, consider kind of your favorite uh local coffee shop. This here is a picture of Plain Air. Um it's the coffee shop across the street from the department of economics um at University of Chicago. If you visited, somebody probably brought you there. um it has um about a zero market share nationally. It has a very tiny market share of Chicago.
It even has a pretty small market share in Hyde Park. And yet to the students and faculty who go there, it makes up quite a large share of, you know, their coffee shop spending. Why? Well, because it's good and because it's one of the few options in walking distance. And so even though this is a small firm, it actually kind of looms large in the basket of its customers. And so this divergence between a firm's overall size and its importance to its customers is going to be kind of the starting point of this paper. We're going to use linked customer firm transaction data to try to measure kind of how important these firms are to the customers they serve and how that changes as firms grow. So to do so, we're going to construct um what we're going to term here a firm's effective market share. And that's going to be how much of their customers category spending they receive. So a conventional market share, which would be the share of market sales that they get, is going to combine two dimensions.
It's going to combine customer reach, that's how many customers you're serving, and customer depth, which is kind of how much of those customers sales you're getting. And the effective share is going to distinguish between these two and sort of focus on the latter here in terms of depth. AND WE'RE GOING TO SHOW THAT this distinction uh matters um when viewed through the lens of these kind of benchmark variable markup models um that have been the foundation of many of these concerns um where uh a rise of firm size could lead to an increase um in uh market power.
And so in these benchmark models with a representative customer you get that the firm's elasticity of demand is a function of their overall market share.
But when you introduce kind of dur uh persistent customer heterogeneity that role is instead played by this effective market share. And so understanding how this effective market share is distributed and how it changes over time is sort of important for understanding um the potential for this sizebased market power within this class of models which has been the foundation of a lot of the kind of quantitative work in macro um on misallocation and market power.
But this is mostly an empirical paper.
And so we're going to focus on organizing our findings um into four kind of overall overall findings here.
So I'll just preview them before I jump in. We're first going to find that these effective shares are only weakly correlated to a firm's conventional market share. So huge differences in market shares actually correspond to relatively small differences in effective shares across firms.
Second, we're going to show some uh pieces of evidence that effective shares predict customer behavior in response um uh to shocks and in particular can inform future uh customer shopping behavior. And we're going to take this as evidence that these effective shares are kind of capturing something meaningful about this customer firm relationship that's missed by these conventional market shares.
We're then going to focus on thinking about how firms grow and show that effective shares grow slowly um as firms gather more sales. And we'll argue that this is because a lot of uh uh growth uh comes from the acquisition of new customers and those new customers tend to be much less attached to their firms than the existing customers. And then putting all of this together um we're going to show that since 2014 um the sales concentration of the largest firms has risen a lot more than their effective shares. And so these big firms um have become come to dominate more of the overall market but they haven't had a commenurate rise in their kind of dominance of their customers uh baskets.
Okay. So with that overview, let me jump in and go a little bit more into detail about what these effective shares are.
So for customer I and firm J, um a customer's share is going to be their share of spending within a category that goes to that firm. So for example, if 40% of my grocery shopping is at Trader Joe's, my customer share here at Trader Joe's is going to be 04. Now the firm's effective share is then just going to be the sales weighted average of those customer level shares. And this alpha here, the sales weight is the um share of that uh firm sales that comes from the given customer. And this is important. If one customer spends $1,000 at a firm, another customer spends $10, the first customer is kind of more important to that firm.
Okay. So this statistic um uh can as I previewed can be interpreted through the lens of this kind of st standard variable benchmark model. So in this variable um markup model um as long as the elasticity of uh substitution across firms within a category is greater than the elasticity of substitution across categories. you get the result um that the elasticity of demands declines with a measure of firm size and so with a representative customer um that size is the conventional market share as in the standard Atinson and Burstein framework and so just to review the intuition here what's going on well if a firm's a small share of the market then a lot of the substitution away from that firm is going to happen to other firms in the same category and that's going to have a relatively low elasticity if instead Instead, the firm is a much larger share of the market. Substitution away from that firm is going to be across categories and that's going to have a lower elasticity.
Now, if you instead of having a representative customer, you have kind of persistent heterogeneity across customers and their relative demand, maybe coming from preferences, maybe coming from geography. Um, the size that's relevant here is going to be this effective share. It's going to be the same intuition, but now it's going to operate customer by customer. And so the customers that are spending a larger fraction of their spending in that category on the firm are going to have this lower elasticity of demand. So what's the implication of this? Well, one, it's that it's effective shares instead of market shares um that in this uh extension of the model can be interpreted as some kind of measure of the size-based market power.
Second, I want to say we're not proposing that this is kind of an alternative to doing kind of careful demand estimation um in particular industries. Rather, it's a simple statistic that we can calculate across, you know, an array of industries and locations and years. And so for questions that are related to kind of thinking about macro trends in firm size and market power, we think of it as an alternative um to uh the kind of widely used measures of market shares and concentration. And so in that spirit and what's going to follow here, we're going to focus on the empirical distinction between the effective shares and market shares rather than kind of on the specific structural mapping that comes out of this uh interpretation of it.
Okay, so let me talk to you about the data we're going to use uh to be able to construct this new measure here. So our data is going to be the universe of US data from a large card payment network.
We're going to have data from 2018 to 2025. The data is large. There's about 600 million deidentified uh cards in the data set per year on which there are 70 billion transactions totaling $4 trillion of spending. So that's about 20% uh of PCE. Within this data set, we're going to observe several things about the transactions.
Many of them are things you would see if you looked really carefully at your credit card statement, but just to name a few of the important ones here. We're going to observe a firm identifier that's constructed by our data provider here. So to borrow the language of marketing, we're going to generally capture the banner company, not kind of the parent company. So, for example, in our data set, Whole Foods is separate from Amazon. We're going to observe the um merchant classification code of the firm. That's going to be kind of our category or industry.
We're going to observe the mode of transaction um uh for that transaction.
So, whether the card was present or whether the card was not present for the transaction. Sometimes we have further information on why the card wasn't present, but we're going to go ahead and treat all of this as sort of online spending.
For the transactions that are done in person, we're going to have the location information for where that transaction took place. Often the exact address of the establishment, um, but at least the zip code. And then I just want to flag here again, think about what you observe on your credit card statement. you observe the total spending of what you did at the store, not what you purchased without that store. So, we're going to be um our kind of our unit of observation here is going to be kind of the retailer um uh as opposed to the item. So, you should think of this as the share spent um on Trader Joe's and not the share spent on say pasta.
Okay. For much of what I'm going to show you today, I'm going to focus on a subset of this, which is a subset of credit cards that we can link to TransUnion credit records. This linkage began in 2021 and includes about 100 million individuals. And the advantage to doing this, uh, this yields kind of two advantages. So, the first big one is that it allows us to link cards that belong to the same person. So, most people probably don't have as many cards as people in this room do. um but um they are about 1.6 cards per person on average. And so this gives us a more complete uh vision of uh a person's spending. And we also observe several additional things about these uh the the owners of these cards. Um their home address, their age, their estimated income. Um and we'll use this at various points as well.
And then lastly, I'll mention a couple sample restrictions that are important to kind of keep our focus on these kind of customer firm relationships. One thing I'll just flag is that we're able to keep transactions that happen through Apple Pay or Google Pay. That's because that's about the mode of transaction, but it doesn't obscure who the merchant is. But we have to drop some payment intermediaries. Think PayPal or Toast.
Uh because we don't observe kind of where uh what merchant uh that spending was actually from. We're going to focus on spending that's within a 100 miles of the home zip code or online to kind of abstract from um things that happen when you're kind of on vacation. And we're going to focus our attention on 33 categories um that are in both services and retail. And these are the places where we think this credit card spending has a pretty good coverage across firms.
So these are a lot of categories you would think about. They're kind of big retail categories like grocery stores, general merchandise, as well as some service categories like restaurants, barber shops, nail salons, and things like that.
Okay. So our goal here, as I said, was to measure these firms effective market shares. And I've kind of reproduced um that uh equation right there for you.
Now the challenge here is that customers make a finite number of purchases and so purchases at any one point in time may not capture a meaningful relationship between the customer and the firm. So where I chose to do grocery shopping today might not really be informed that informative of my underlying preferences. And so my main approach here is going to be to pull all transactions for a person within a year.
And so the idea being that the distribution of my grocery store spending over the course of a year is going to kind of um reveal my underlying preferences across uh grocery stores.
It's going to kind of be a large enough that the law of large number is going to kick in to kind of diminish the importance of kind of just idiosyncratic realizations and yet it's going to preserve the sort of idiosyncrat the kind of individual preferences or the individual variation that is the key distinction. between these effective shares um and these market shares. Now, for grocery stores, that seems pretty good. There are some categories, say furniture, um where even a year of spending uh seems uh like it's kind of not going to be quite enough to reveal your underlying preferences. And so there we're going to do an alternative kind of robustness specification where we're going to consider we're going to pull all of the shoppers who live in the same kind of census block and have the same demographics with the idea being that they're subject to the same kind of micro geographic constraints and maybe they have some correlated preferences.
And so the results, all of the results I'm going to show you uh look very very similar uh if we use that kind of synthetic customer as opposed to the year. But my main our main spec will be pulled over the year. And then I want to just make one note before I move on here which is that while we have to take this care to kind of think about um constructing these effective shares, it buys us one really uh uh uh big thing which is that we don't have to make any assumptions about the geographic scope of these firms. And this has been a big issue in the literature and kind of how you calculate market shares. Is the market national? Is it local? Is it a zip code? You know, we don't have to take a stand on that. Instead, it's going to be revealed by who the firm's customers are. Whoever is shopping there, um, and wherever else those customers are shopping is going to define kind of the geographic scope of that firm.
Okay, so let me go ahead and then jump right in and show you what this looks like in the data. So, we'll get to our first uh finding here, which is that these effective shares have a relatively weak relationship with the conventional market shares. So this here is a picture just to give you you know closest to the raw data um that I can show you here on the y ais we have the effective share um of each firm. So each dot here is a firm in our data and on the x-axis we have the firm's national market share and I think there are several things that you can see in this picture. The first is that by construction the firm's effective share is going to be at least as large as their market share. That's because in a closed economy, you have to have at least as much of your customers spending as you do of the market as a whole. But there are some firms for which this gap is really substantial.
The second observation is that there's a relatively weak correlation between these two measures. There are some firms kind of all the way over to the left that are basically 0% of the national market and yet on average they're getting around 60% of their customers spending within that category.
And then lastly and relatedly the firms that look like these kind of huge outliers in this market share space look a lot less like outliers in this effective share space.
Now, this is helpful for kind of just seeing the raw data, but most of the mass of firms is clumped at zero. So, in the next figure, we're going to kind of try to show you this these same patterns, but kind of spreading them out. So, what we're going to do is we're going to rank firms by their um uh market share within their category. And we're going to plot here for each percentile of that distribution their market share relative to the average market share in their category. So this blue dot, these blue lines are increasing by construction. That's how we constructed the percentiles. And you can see here that this is very skewed.
Most firms say like 90% um have market shares very close to basically zero or their their uh category mean. And then the biggest firms in these categories have a market share that's about 50 times bigger than the average firm in their category. And you can compare that to this red line here, which is the effective share of those firms at each point in this distribution. And you can see here it is increasing, right? Bigger firms on average do have higher effective shares here. Bigger firms by market share. um but it's increasing m it falling much much much more slowly throughout the distribution and note here that the effective shares are plotted on the the left axis uh which has a much uh uh uh smaller spread.
Okay. Now, one explanation you might have in mind while you're sitting there looking at this is that maybe one of the reasons that these two measures don't line up is because most markets aren't national, right? I'm not doing my grocery shopping in California. what happens in California is not that relevant um uh for me. And so what we're showing you here in this picture is instead what happens when we look at it um at the effective shares relative to a local establishment share. I've chosen here the three-digit zip code. Um uh the blue dots are all of the underlying establishments. Um and the blank is a bin scatter of the relationship uh where each bin has an equal amount of sales.
And you can see here that this sort of attenuated relationship um persists even when we look at this local market. Now of course I had to define some measure of the local market. That was one of the issues with market shares in the first place. But we find that this kind of distinction between effective shares and market shares and in particular the sort of attenuation this sort of flattening um of the slope persists whether you go smaller and you look at you know five-digit zip codes or you look at the state level. Um either way um uh they're kind of distinct cate distinct measures.
Okay. So that first fact was showing you that these effective shares and conventional market shares look different. Our second is about telling you that the effective shares kind of are containing useful information about the nature of customer firm relationships.
So to do that we're going to first look at the the relationship between these and retention. So a customer is retained if they shop at an establishment J in the previous year and they shop at it in the next year. And we're going to ask whether um there's a relationship between customer retention and either a firm's effect a customer's effective share or the firm's market share. And this effective share captures how important that firm was in the customer's spending basket. And the market share is how large that firm is in the local market overall. We're going to standardize uh these two measures so we can kind of directly compare the beta coefficients here. And we include these marketby-year fixed effects. So we're comparing two customers who are shopping in the same industry or in the same category in the same local market and in the same year. And I'll note here that these are lagged effective shares and market shares. And they're asking about what you're doing in the future. So there's no kind of mechanical relationship here um uh between how we've constructed the effective share and the outcome. Now our prediction is that if these effective shares are capturing some kind of durable heterogeneity in these customer firm relationships then these effective shares should predict uh future retention at the firm. If instead they're mostly dominated by these kind of idiosyncratic realizations um then we wouldn't see such a relationship. And we can see here that they do contain this information. So the first column shows that a one standard deviation increase in uh effective share is associated with an 18 percentage point increase um in retention. Column two shows you do still see a positive relationship um between retention and uh a firm's overall share.
But when we column three when we add them both you can see kind of the predictive power really loads on the effective share. We also find a similar result um when we add establishment byear fixed effects essentially comparing two customers say two people who shopped at Walmart. One customer had a large concentration of their spending at Walmart. One shopped there kind of occasionally. And what we find is that it's the customer who shopped a lot at Walmart who's more likely to shop there in the future. And we also find this holds at longer time horizons. So the effective share kind of predicts customer potention even several years out in the future.
Now, you may think that there are reasons why you would persistently shop at one place, even if you weren't particularly attached to them. Maybe you're close to indifferent, they have the lowest price, they haven't changed their price in a while, but if they did, you would actually switch. And so, I don't have time to show you the details here, but what we show is that we find the same patterns u when we look at um retention um specifically in response um to a new entrant entering the local market. And so what we we take this as evidence that these effective shares are capturing something meaningful about these customer firm relationships.
All right, our third finding is going to be about thinking about firm growth. And so so far I've shown you these relationships in levels, but the same sort of weak relationship holds in growth rates. So this figure shows you that on the x-axis is the change in the log of the market share of a firm between 2021 and 2025 and on the y-axis is the change in the log of their effective share over that same period.
And you can see we have it for national firms in for national markets in blue and local markets in yellow or orange.
Um and you can see here that there's a a positive relationship but it's somewhat attenuated.
And what we're going to argue is that this arises due to the nature of firm growth. So a bunch of recent literature has demonstrated that firms primarily gain market share by reaching new customers. And we find that in our data as well about um for the average firm um for about 80% of the growth between 2021 and 2025 in terms of their sales comes from the acquisition of new customers.
But firms gain effective shares these things the the by deepening their relationships within existing customers or among their customers. And so then the question becomes what are the kind of effective shares of these new customers as opposed to the existing customers. And we find evidence in our data that new customers have lower effective shares than incumbent customers. And in particular, we find that the median firm, the new customers, have about a 40% lower effective share than the firm's incumbent customers.
Now, maybe that's not that surprising, right? The people who have the highest taste for the firm, they shop there both first and most intensively. Um, we also find that this gap shrinks after customer acquisition, but relatively slowly. And even several years later, there's still a gap in the effective share between kind of the newer cohorts and those who have been shopping there uh over the entire period. Okay, so that's not the only thing that's going on though, right? Because if we were just acquiring new customers as you grew, this would suggest that that slope should be negative, right? And we find it's a small positive. So this is basically the small positive relationship is a balance of two forces.
expanding reach by adding these new customers lowers your effective shares, but increasing depth among your incumbent customers raises effective shares. And growing firms typically do both. And so overall, we find that these two forces are kind of competing and we end up with this attenuated slope. So just to show you that kind of more concretely here we have that same kind of log log figure from before but now we've split firms into tersiles based on kind of how um uh much their growth came on the extensive margin. So in red are the firms that grew most through the acquisition of customers. In blue are those that grew least through acquisition of customers and most through sales per customer. And you can see here that the elast the rise in the effective share for a given change in their market share was about five times larger for the firms that grew most on the intensive margin as opposed to the extensive margin.
Okay. And in the last couple of minutes we'll kind of build um to our last result which is to kind of think about the kind of recent trends in superstar firms and concentration.
So I'll start by showing that kind of two particularly prominent sources of growth for these superstar firms in recent years are particularly associated with the expanding reach across customers and thus particularly small increases in effective shares. So these two are first the growth through geographic expansion. So we know that a lot of these big firms from previous literature where we know that they've grown by kind of expanding um uh locations either within markets or across markets and this is particularly you know associated with new customer acquisition. So just to show you that here in purple we've put the firms um that had a change in the number of zip threes in which they operated over this period and in green we have those who had no change in their kind of geographic footprint over this period.
And you can see here um that for the same increase in market share, those that achieved it by growth within uh a market as opposed to growing across markets um had a much bigger increase in their effective share. The second key margin of growth um that's kind of uh uh been important for these supertore firms over the past several uh decades has been this growth in e-commerce. Um and a rise of online spending um expands the number of opportunities available to customers that uh both expands customers options and it expands firms access to more customers. And so we find at the customer level that customers that shop online are more weakly attached to the firms they shop at than those that shop in person. And this means that firms that grew predominantly through the acquisition of online sales would saw kind of smaller increases um in their effective shares. And that's in fact what we see here. In blue are those firms that grew predominantly online. In blue are those that grew predominantly in person. And you can see here um that we find um that the uh uh the growth in effective shares was lower for the high online growth group.
Okay. So these trends are going to suggest that there's going to be a divergence between the growth of top firm sales and their average effective share shares over this period. And so we can look at that directly by calculating the top the share of total sales for these top four firms in each category.
That would be the CR4. And compare that to the average effective shares of those same top four firms. We're going to do this using a kind of historical um uh version of our data set that goes back to 2014. It has less detail um across firms and customers than our u more recent sample, but it allows us to calculate these top four shares um going back in time. And when we do this, we get the following patterns here. On the left are the levels um of this CR4 and the average effective share of those firms. And on the right um we have uh the log growth since 2014. And you can see here consistent with kind of the large literature we see a big increase um in uh the CR4 so the market concentration of these largest firms and a much smaller increase in the average effective share of those same firms. Now this is across all industries. I don't have time to go into it but there are some coverage issues um in different industries in this historical sample. So you can see here um just another version of this which is if we restrict um to the um um uh biggest uh sector in our our data set that has the best coverage over time which is general merchandise stores. And you can see here um that the um the this uh industry be had a huge rise in concentration and almost no increase in the average effective share of those same large firms.
Um that would include Amazon. Um it would include uh yeah it would include Amazon. Um all right so with that let me conclude. Um we started in this paper to show that kind of there's a difference between firm size and kind of the customer importance of these firms. A firm can be large in the aggregate without being particularly important to its customers. and a small firm like this local coffee shop could be very important to its customers even though it's relatively small in the aggregate.
We proposed this kind of effective share as a scalable um customer-based empirical measure that captures this distinction. We showed three or things about this which is that the conventional market shares are much less skewed um or much more skewed than the effective shares. um that growth that comes through customer reach or customer acquisition attenuates um this growth in effective shares as firms grow. And we put these together to demonstrate that sales concentration has risen much more over the last uh decade um than uh effective shares. So these superstar firms, they're serving more markets, they're serving more customers, but they don't seem to be having a commenuratement rise um in their importance in their customers shopping baskets. And if you interpreted this through the lens of the variable markup uh framework that we talked about at the beginning, um you would conclude that rising sales concentration has kind of not produced a comparable rise in this size-based product market power. And I'll I'll leave it there for questions.
Yeah, that's super interesting. So, I had a question. It seems so you're interpreting this effective market share through a like a as a measure of supplier power, but it seems that buyer power is also varying with it. And I'm thinking about the University of Chicago example like that's a effectively a bilateral monopoly. And I don't think there's a clear prediction that that the pri equilibrium price on the bilateral monopoly is lower or higher than the perfect equilibrium. It depends on bargaining power and outside options.
Um, and then I think then you need to think about like outside options and like maybe the reason why plane air can squeeze us is that we're like we have no outside options in in hide park. But then you need to measure who else is selling coffee in hide park and then you're back to this like the same same issues of like measuring like local market power. So yeah, I was just like question about like buyer power. Yeah.
>> Um really interesting. I was going to follow on from Anders. So it looks like market shares of you know again it's is a bad measure particularly even if you can go locally partly because just the local definition is too broad. One question is from your own data you could generate a putitive. So take plane air.
You look at everyone that you have a prediction of shopping at plane air and what's that going to load and it's going to load on ICU shopping in other stores nearby and then that's going to be a much better way to predict if I look at a pet store in Philadelphia. Are you buying prep products but probably across the entire Philadelphia? Your own data will give you I don't maybe you're doing this already but it seems like I totally get market share is not good. You could create from your data I presume just a much better definition of the market then is that effectively because you you've gone all the way towards effective share you could go something which is a better market definition does that beat effective share effective share maybe 90% of the way there but not all the way >> this is maybe an extension of of Nick's comment but if you think of taking the effective shares and putting a logit shock you're basically getting demand at the individual level and then you could take that so for any a and B you could get individual level diversion ratios based off of that then get the aggregate diversion ratio and sort of get a measure of how close competitors A and B are and compare that to just using market shares. So it's something we the FTC do with hospitals where we have all discharges uh but it's a lot harder to do in other markets. So, but I think you could do it with your data >> just there's an old literature in marketing about this like share of the wallet which does basically your whole and I just didn't see a lot of sites on that and you I think it's cool how you bring it to the aggregate but just kind of making sure that literature has kind of been cited in there someone took a microphone don't use it in the shower uh I'm sort of interested in a a decomposition of this effective uh market share to um something that's about the features of the good like the trade ability to do over time for space versus like theatic firm level uh things that a firm can do to increase That's great. Um I what one thing it would be kind of cool kind of cool to do would be to see you know linking it up with the more general just literature.
So you know one thing that we like to do sometimes is look at kind of openings of new stores or entry and how much that affects the incumbents how much behavior there is. So it' be good to see you know if you looked at those type of events and looked at the kind of loyalty or lack of loyalty with the switching handbooks how how well does that match up with your you know effective market shares relative to the overall market share I mean that'll be a nice kind of validation of the method I guess price is harder because you only have per prices but the kind of entry thing you could do I think more straightforward Thank you. Fascinating uh data and study. Looks to me and you get this when you were explaining that you are overestimating the market share of retailers and you're sort of diffusing the market power of CPGs through their retail network. So would you be able to kind of understand a bit how big this bias is by looking at services versus retailers because the services the service providers sell directly to customers while your whole foods is capturing the Pepsis the world share and so on. So there you have an overestimation of both foods is capturing versus the underlying producer systems.
>> Okay, five minutes. All right.
>> You have a high effect to share with this group.
>> All right. Let's see. Um, okay. I'll take the first step and then um I want to I open it to my co-authors if um they have things to jump in on. So, let me start honors with your um your uh idea.
You know, I think you know, in some sense that's precisely what our effective share is sort of trying to capture, right? So, why does plain air have a much higher effective share? Um, not that we've, but anyways, it it coffee shops like that have a much higher effective share than they have as a share of Hyde Park. Um, it's it's meant to capture some combination of preferences. Maybe I just really love this local coffee shop and outside options, which is that I might have a high share here because I have nowhere else to go. Um and so that is precisely you know it's not a perfect estimation of this but it's precisely the forces that are going to be captured in um this this heterogeneity across customers. And so we don't take a stand on exactly where that heterogeneity might come from. It can come from a variety of sources. Some of which could be just you know I just love you know the particular brand Lululemon and so I only buy from Lululemon. Or it could be that there aren't other options that are good substitutes and therefore um uh I'm kind of stuck. I I I reveal that this is my only option by spending a huge fraction of my spending there. So maybe we can talk a little bit more about the distinction, but I think that's exactly what we're kind of trying to capture.
>> Yeah. the synthetic um consumption zones. Um you know, I think that's to your question of could you kind of come up with a better um alternative to a kind of local market. Um you know, uh you know, certainly you can do better than just kind of a looking at kind of a a generic five-digit zip. We've tried to do a bunch of things here. And one thing that we see in the data um uh you know, and maybe it's a worthwhile exercise to say, can we get 80% of the way there?
Can we get 70% of the way there? But that two firms that are kind of close to each other seem to have a very different geographic catchment area. So if you think about like there's a little, you know, grocery market that's right next to me, but it doesn't have parking and then the Trader Joe's kind of just down the street does. Um they look, you know, they're in the same market. So for each firm, I think you could do a really good job of kind of defining their geography, but you know, at any boundary uh of those things, you're you're going to get it wrong. Now, how wrong is the empirical question. And so I think that that's we have it. Yeah.
>> Used customers. I see.
>> I told you customers if someone shops >> fashion drivers are >> Yeah.
>> You know, you know the bid market size than anyone who ever bought anything.
>> Exactly. Right. Right. Exactly. I think that relates a little bit.
>> Why is that? Why is that better? That's what I'm confused on. Like I think we're sort of already measuring in some sense.
I think what you would want to measure too small.
>> So the effective share captures exactly that as you said. Yeah, exactly. And now you're saying can is there a poor man's version of that that you could kind of approximate is what I understood your question to be. Um and uh uh yeah, fair enough. Um the question about the diversion uh indices I think that's uh you know that's super interesting.
There's a paper um that um is by Lauron and Pete Cleow and others um that tries to do something similar even within a similar data set of kind of you know that's a pair-wise uh uh statistic. Um this is kind of you know in some sense it's not exactly it but it's kind of languaging that across all potential pairs to kind of get something that approximates your share. Um and so you could we could think about kind of connecting um more directly with that.
Um uh the entry example I was way too quick here but um one of the exercises we do um is to look at whether the effective we look at kind of new entrance to a market um and we ask whether uh the customers you lose uh who leave you and start shopping at the new entrant um are the high effective share customers or the low effective share customers. and we find that it's kind of these low effective share customers who are much more likely to switch um to the new firm that enters. Um so I don't think that you know that helps us connect to that.
Of course if we had variation in prices uh we we could kind of do even better.
Um but certainly we've been thinking in that direction. Um one minute. Okay. Um the question of the decomposition and sort of what drives it. Um we have some results in the paper that sort of try to look at this whether it looks like you can look within a market and how much of it you know part of this is just market segmentation right so I look within a market either I've drawn the wrong geography and actually like right next to the University of Chicago is one tiny market and other parts of hide park are another market and there's a segmentation or you know different types of people just buy different types of things and that's some within market segmentation that is a force that always pushes effective shares up relative to the market share.
And then you're exactly right, things like online shopping, travel, moving, you know, are are forces that kind of uh sort of pull it down for kind of the big uh retail establishments. Um so we can talk more about that. Joe, I took the minute I think, but go ahead.
>> Yeah. Um the one other thing related to that and then like the last question that was also asked too you were like pretty quick on kind of going through the categories that are in the data but you know a big chunk of the data is in service related stuff and like you know for those like durability is not going to be relevant. You don't have this issue of like mixing like product stuff as much with like you know the retailer aspect of things and all the patterns look very similar when you restrict to service related things you So you see these patterns for restaurants, you see them for barbers, you see them for you know a bunch of different consumerf facing services.
>> Thank you very much productivity for 2026. Thanks for coming everyone. We had 90 subs. Fantastic.
Thanks for the interest that you showed any of your papers and being here today sections of >> Yeah. Other tower >> of the tower. Safe travels and thanks for coming.
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