 Welcome to the second day of the second ECB annual research conference that we're organizing. So as Luke just told me, it's a bit of a novelty that we have a kind of trade session in this conference, but it's of course a very highly, I would say highly relevant topic these days. So we're looking forward to the presentation by Paul Antras of his paper this morning. Paul Antras is his Robert Ory Professor of Economics at Harvard after having obtained this MIT, at his PhD at MIT. So I don't have to introduce him further. I think he's well known in international economics. And after that, Professor Samuel Kortrum, who is teaching at Yale, and after having been professor also at Chicago, and Minnesota will be the discussant for this paper. So Paul, for the show. I don't have to explain the rules of the game, they're well known. Thanks a lot. Thanks for the kind presentation, Frank, and thanks to the organizers for having me. It's not often that I get to hang out with macroeconomists. So it's a pleasure to be here. Now I should say this is a present paper which is joined work with Adonso de Gortari, who's a star PhD student at Harvard. He's going to be on the market, so keep an eye on him. And with Oleg Izzoki, who used to be a star PhD student at Harvard, and is now teaching at Princeton University. So let me begin with a statement that might sound a bit provocative, but I think it sort of reflects the consensus in the international trade field, which is there are gains from trade in the sense that if you look at episodes of trade integration, there's widespread consensus that these episodes are associated with real income growth. That is, trade tends to grow the size of the pie. At the same time, a variety of pieces of evidence suggests that these episodes of trade integration are often, if not always, associated with increased income inequality. Okay, so again, I could refer you to a large literature on this, but if you just want to read one paper, one survey, maybe you want to look at Dina Paphnik's overview of the topic in the recent Jackson Hall conference, where she presented a paper on precisely this topic. Now, I would argue, and I think most if not all trade economists would agree, maybe we'll see what Sam has to say about this, that when trade economists think about quantifying, demonstrating, and quantifying the gains from trade integration, we largely ignore trading this inequality. Now to be clear, I'm not saying a trade economist ignoring equality, we have powerful theorems with each undergrads about how trade affects the income distribution and generates winners and losers, but when we're asked what are going to be the implications of this trade agreement of that trade agreement, we tend to provide one number, which is a number that ignores the effect of trade on inequality. And the reason for that is because the field has very much adopted the Calder-Hicks compensation principle, which doesn't have much to say about the effect of shocks, policies on higher moments of the income distribution, and I'll review that in a second. Now, obviously, there's good reasons why people are using the Calder-Hicks compensation principle. It's a great tool, but it has certain shortcomings. On the one hand, you might want to know just how much compensation there is, a principle that is based on the idea that the losers could potentially be compensated as to be measured against the extent to which actually that redistribution, that compensation actually happens. And second, even if you admit that there is redistribution, that we have a safety net that compensates or partly compensates the losers from these policies, like a trade liberalization, a key question to ask is to what extent that redistribution is costless, like the principle assumes, and if it's not costless, how costly it is, and how do we measure that? So, to be clear, this is what I'm going to present as a trade paper in the sense that I'm going to be focusing largely on trade shocks, but everything that I have to say, obviously, would apply to any policy that has redistributive effects. But what I'm going to do today with a paper that I'm going to talk about, basically what it does is it studies the welfare implications of trade liberalization in a model in which trade affects aggregate income, but it also affects higher moments of the income distribution, and in which society doesn't have access to this sort of lump-sum non-distortionary taxes that are implicitly invoked when applying the Higgs-Cowder criterion. And in particular, we're going to be looking at a situation in which redistribution, a compensation from trade shocks has to happen through an income tax transfer system. When developing a model with these features, we're basically going to isolate two adjustments to standard welfare measures of trade liberalization. We're going to say, rather than just looking at mean income growth, you might want to take into account something we're going to call a welfareist correction, which basically reflects preferences of an inequality averse social planner. So the idea being that if we know that compensation is not full and we know that trade is not only affecting the distribution of market income, but the distribution of disposable income as well, there might be good reasons to care about second moments of the income distribution, and that's going to connect to Atkinson's celebrated work. And then we're also going to emphasize something we're going to call a costly redistribution correction, which is going to capture behavioral responses of agents to trade-induced shifts across marginal tax rates. Anytime you are redistributing using an income tax transfer system in which marginal tax rates vary by income, if trade is affecting the positioning of agents in the income distribution, that's going to lead to kind of behavioral responses that might affect the size of the pie, okay? Now, how are we going to show all this? Let me just give you the building blocks. I'm not going to spend much time on the literature, but there are some key papers we build on. So that when we get to the trade model, and I'm going to get there pretty late, I'm not going to be able to tell you much about that. Essentially, there's going to be a mallet-style model, and mallet-style models is our models with intra-industry heterogeneity and firm, and we have firms that flourish, that grow with trade liberalization, they expand and export to world markets. We have other domestically oriented firms that are shrinking and are facing increased import competition from foreign sources, and that generates a widening of dispersion across firms in an industry. Our model is going to be much simpler, it's not going to have firms, but we're going to capture the same ideas in a model in which we have heterogeneous worker entrepreneurs that are supplying labor, okay? So there's going to be a model where the highest ability individuals are going to be able to export their services, their output worldwide, and they're going to benefit disproportionately from trade, whereas the less able agents are going to just not be able to do that and face increasing import competition, and that's going to generate an increase in dispersion, not in the size distribution of firms, but in the income distribution, okay? And we're going to see how that plays out in the model. It's going to be a rather sparse model. The advantage of it, I'm going to try to highlight, is that it's a fairly easy model to calibrate, okay? Then we're going to not just compute aggregate income growth in the model, we're going to be thinking about social preferences that contain some amount of inequality aversion, you can reinterpret that as risk aversion, we're going to introduce costly redistribution, and in that sense, we could have done the full release and look for optimal income taxation in the model, and Oleg, my co-author has done that in his in prior work of his, we're actually going to do something simpler, which is we're just going to look at a particular log linear function of, log linear function that characterizes the income tax transfer system that I'll argue fits the data rather well, and we got really excited when we saw this in the data, we later realized as a recent paper by Heathcote, stores Latin and violante that actually use the same tax rule, so this is essentially what we're using here, and in terms of the application, we're going to be looking at US data, and we're going to be revisiting the issue of how trade integration in the US in the period 79 to 2007, we're also going to look at a starker counterfactual and where we go back to autarchy, we're going to see how the income distribution and the shape of the income distribution is affected by trade opening. Okay, I'm going to skip the related letter, try my come back to some of the key papers. Now what I'm going to do, there's only limited time, what I want to do is I'm going to walk you through a motivating example. There's not going to be much trade, but it's going to kind of make it clear exactly what we're doing in the paper, then I'm going to tell you that even though I'm going to be waving my hand for about five, 10 minutes, there's a well-specified model that basically delivers the same answers, and then I'm going to tell you how do we go to the data on how we look at trade opening through the lens of the model. So the motivating example, we're going to think about a hypothetical situation in which you have a society, let's think of us being a society, that is composed of a measure one of individuals that differ by ability, I'm going to index ability by fee, and associated with that ability, there's some possibility to generate some real earnings. Now obviously you might want to know what defines the mapping between ability and earnings, I'm going to come back to a model that actually lays that out. Let's just take it as given for now. And preferences are defined over consumption, which are equal to the market income you generate, which is our fee, but then you get tax as a non-linear income tax as a function of income, and for the time being I'm going to allow for some transfers that are a function of fee, therefore they're lump sum non-distortionary transfers. Later I'll argue that we don't see much of that, so I'm going to shut them down, but let me be fully flexible for the time being. Now there's going to be a distribution of ability, age of fee, and an associated distribution of real earnings, some of us have higher or lower ability and that generates different levels of income. And essentially what we're trying to figure out is if we're told that there's a possibility of trading with a different society that has a different distribution of income, a distribution of ability, we're asked how do we feel about that, and essentially what we're going to be doing is comparing a distribution of income, maybe a distribution of consumption, and figuring out whether this is something we want to do, do we want to trade with that other society, and if we do, how much are we going to gain according to some well-defined metric? Okay, so it's a fairly simple situation we're envisioning. Now what do trade economies do? They say, okay, we're going to invoke the color hex principle, where we realize that this trade opening might not benefit everybody. We know that maybe because of some features of our ability distribution or the foreign ability distribution, some agents are going to be suffering from this, but we can go ahead and compute for each individual something we call the compensating variation. You can do the equivalent variation, and with a couple of simple steps of math, you can show that if we compute this amount of money that you need to provide to the losers that are losing from trade, if you compensate those agents and make sure that they're at least as well-off as they were before trade opening, even after that compensation, there's still money on the table. That is, the size of the pie has grown enough such that the net gain of the winners is going to be larger than the net cost of the loser. Now, I'm basically speaking as if it's clear that there are net gains. What I should be saying more properly is that with the color hex criterion basically tells you is that if you want to look at what's the net effect, what is the sum of this compensating variations that's actually identical to aggregate income. Is this R prime and is R? Okay, so if aggregate income grows as a result of the policy, we can compensate the losers if not, we cannot. Okay, and a standard measure of the gains from trade or the gains of any given policy is going to be basically associated with this cap Rs and it's the growth that say the gross or the net growth in income associated with a policy. If a policy raises aggregate income by 10%, we say that the gains from that policy are 10%. Now, why do we do this? There's a variety of reasons for that. There's historical reasons that have to do with people being uncomfortable with interpersonal comparisons of utility. So in some sense, it's sort of a concept that is void of value judgments, but there are also kind of natural causes or natural limitations of this. So you might say it's good to kind of have a criterion that is not based on preferences and to be clear, the reason we can say that is because I've assumed the utility function you hear, but anything that you say about the measurement of the gains from trade is independent of the actual utility function that agents might have, but there's good reasons why we might care about cardinal issues associated with utility. For instance, if we think about a situation in which there's no redistribution and we know that after trade, we're gonna be, the income distribution is gonna be affected, it's sort of natural to think that if agents are risk averse or the social planner is inequality averse, it's gonna care about the distribution of income in the same manner that in situations with risk, we care about higher moments of the income distribution in situations where we have risk aversion. So it's an argument that goes back to Vickery and Harsani and was sort of fuel to this well first approach that became mainstream in public finance in which we think about policies that maximize some social welfare function that features some inequality aversion. There's also issues of redistribution, which is all this is sort of based on the notion that we can give to the losers at no cost, but obviously in practice, we don't have access to the lump sum transfers and that generates costs that we might wanna take into account, okay? So to a side note, this Dixit and Norman paper is a classical paper in the trade field that says, if you thought that Calder Higgs is crazy because we don't have access to lump sum transfers, here's a simple mechanism by which you can engineer Pareto gains from trade by using commodity taxation, factor and commodity taxation is a beautiful paper, but if you look at the mechanism, they used to show that result as a mechanism that basically kills most of the gains from trade. So that's telling you, yes, you can compensate the losers, but if the compensation is very costly, don't use this R prime over R as your measure of the gains from trade because you actually realize gains from trade might be much, much lower, okay? So how do we think about correcting for this risk aversion, say, or correcting for this cost of redistribution? Let me give you a nutshell of what we do in the paper and then I'll illustrate it with a model. So in terms of the welfare's correction, it's all about specifying a social welfare function in which you have agents that direct utility from consumption, this is a static model, so they consume their disposable income, R, D, of E, and then you think about aggregating that utility across agents. Now, obviously you need to take a stance on what that utility function is and how it is for different individuals. Here I'm gonna focus on a situation in which it is common for all agents and it's actually given by this constant inequality or sort of constant risk aversion function where Rho governs the degree of inequality aversion or the degree of risk aversion if you interpret that concavity as reflecting risk aversion. What's cool about this preference is that, again, this is something that because of our ignorance of the literature we got kind of excited about, through a simple transformation that allows us to think about welfare in terms of consumption equivalent terms, you can decompose welfare, okay, the sum of these utilities multiplicatively into a term that reflects aggregate income and a term that reflects the cost of inequality, okay, this term delta, okay, so this term delta, which is a function of meaning disposable income and some higher moments of the income distribution turns out to be related to this Atkinson measure of inequality, something that we didn't sort of realize, but it's basically this term, big delta is one minus the Atkinson measure of inequality. So this decomposition basically tells you if you wanna think about how a policy, say trade opening is affecting aggregate income, sorry, aggregate welfare, then you're gonna care about how it affects mean income but you need to also track how it affects the higher moments of the income distribution through this term delta. Now we're gonna be looking at the data fairly non-parametrically, but if you put some structure into the income distribution, if you have a Pareto distribution or log normal distribution, notice that you have, these are not just higher moments of the income distribution, they're power functions of income. So if you have distributions of income that are closed under power transformations, that Pareto, log normal, you're gonna get like very neat expressions for welfare as a function of say, meaning come and say the genie coefficient or other things like that, okay. And what we're essentially saying is then, if you're evaluating the welfare consequences of trade, you're gonna wanna know what mu is, remember mu is the growth in aggregate income, but you're also gonna care about how the term delta is moving with trade and if trade increases income inequality, delta will naturally go down. If the genie coefficient goes up, delta will go down, okay. So that's a first simple reason why you might care about inequality in situations in which the distribution of disposable income might widen as a result of trade and you have inequality aversion and this is a simple kind of way to kind of capture that. The second correction has to do with class delivery distribution and for that I'm gonna think about a situation in which we don't have access to lambson transfers and we're moving income across individuals through the income tax transfer system that function tau I introduced before and as I mentioned before, I'm we're using this formulation that Heathcote stores let an ambulance to use as well in which the tax system takes this particular power function. Okay, so the idea here is that the extent to which an individual with income or pays taxes is governed by this equation one. This is an equation in which you see that marginal tax rates are gonna be increasing in income but at a constant power rate and it has the benefit of having a tax system that is governed by two parameters. The parameter K is a level effect and you can sort of we're gonna pin it down to ensure that we have balanced budget. The key parameter is the parameter fee and that governs the degree of tax progressivity. If he is very large, the tax system is very progressive. Marginal tax rates increase with income very steeply. If he is very low, goes to zero, then you go back to a proportional tax system in which all taxes are the same proportionally for all individuals. What's interesting about this tax system, we'll see is that it's gonna deliver a very, there's two good features about it. First is in terms of analytics is gonna deliver a very neat representation of the cost of inequality. Also, it's gonna turn out to be the case that empirically it fits the data remarkably well which is what we noticed and then found that paper where they show it even more convincingly. Now, in order to generate some cost of taxation, we're gonna obviously need the fact that marginal tax rates vary by income to matter and we introduce a sort of constant elasticity of income to marginal tax rate. So where is that elasticity coming from? Again, I'm gonna have to bring in a model in which sort of that mapping is made explicit but for now allow me to just assume that if you're facing a higher marginal tax rate, your reported income is gonna go down presumably because you generate less income and that elasticity is constant. If you put these things together, then you can show that aggregate income in the economy is a function that you can decompose into a term that reflects potential income that is the income that the society would generate in a world in which there were no costs of a distortionary cost of redistribution times a term theta that governs the cost of redistribution. Now that equation is a bit ugly but it is a very simple function you can compute if you have access to an income distribution, okay? And again, it's a function of higher moments of power functions of the income distribution and invoking holders inequality. It's simple to show that theta is reduced by mean preserving multiplicative spreads of the income distribution and theta is also decreasing in a degree of tax progressivity. So if you have more inequality or more progressive tax system, the society is generating disproportionately less income than it would in an economy in which there were no such distortions, okay? What that basically tells you is, well, you can compute it for certain income distributions and again, there's all power functions. So if you choose the right distribution to get like neat expressions that decompose this thing into the gene coefficient and aggregate income but more generally the point here is that if you're thinking about policies that are gonna affect the whole income distribution, if you wanna compute this counterfactual income growth following say a potential trade liberalization, you again are gonna wanna think about how that's gonna affect the whole income distribution and how that's gonna affect the extent to which agents are moving across marginal tax rates and that's exactly captured by this expression here. Now the next thing to do is to say, okay, that's all fine but where is this elasticity epsilon coming from? How do we think about the mapping between ability and income distribution? So the next thing to do is to kind of put that in a well-specified model and the model I'm gonna describe is actually gonna be super close to what I just showed you. It's just making a couple of things more explicit. So again, we're gonna think about this society with a distribution of ability fee but now we're gonna think about these agents as being workers that can produce goods that are differentiated relative to the other goods produced by other agents in society. The technology is gonna be a simple linear function in ability fee and labor supply, L fee and if you couple this technology with a standard constant elasticity aggregator of the output of all agents in society, you're gonna get a nice concave function, revenue function that is the income of individual fee as a function of their output which is linear in their labor supply fee, okay? Where beta is the first parameter that governs how marginal revenue falls without it. It's governed by this differentiation. On the preference side, we're gonna think about utility as being defined over consumption and leisure is the same function that Laura was using yesterday where gamma is associated with labor supply elasticity and then consumption again is equal to market revenue minus taxes and we're invoking this tax rule that I mentioned before which leads to a disposable income being concave in market revenue with tax progressivity fee governing the concavity of that mapping, okay? As a result of this, if you kind of put all these things together, this is what we call a constant elasticity model. Everything sort of has all this power function floating around. You end up with a distribution of consumption in society in the closed economy that is power transformation of the distribution of ability where parameters of the model are not gonna go over it sort of affect that mapping in intuitive manners, okay? And then if you kind of filter that through a social welfare function of the type that I mentioned before, this Atkinson constant elasticity inequality aversion function, you're gonna end up with social welfare function being decomposed in three terms. W tilde is what we call a color Higgs welfare. It'd be the social welfare or the aggregate income of a hypothetical economy that did not care about inequality and in which there were no cost of redistribution. And then, but you need to also take into account this terms delta. Delta is one minus the Atkinson index as I mentioned before and this term theta hat which is associated with the cost of redistribution. And that essentially is the same thing we had before except for the red terms which reflect on the one hand a lot for variety effect that emerges and when you lay down, you know, when you kind of have a model in which there's agents producing differentiated varieties and the first term here in red which reflects the fact that before we didn't take into account that in order to kind of get income agents need to work and work creates this utility. So that's the term that kind of goes against what we had before but overall you can show that the same comparative aesthetics emerge. That is other things equal societies that have higher inequality are gonna have lower welfare societies with higher tax progressivity are gonna have higher distortions coming from redistribution and social welfare functions with higher values of row are gonna penalize inequality more. Okay, now with this social welfare function you can do one of many things. You know, if you were a macro economist you might say, okay, I might get data for all these things and I can pick natural parameters for these values and I can pick values for these parameters and I can compare income growth in the last few years and see to the extent that income inequality has been changing not just mean income but higher moments of income distribution have been changing to what extent these terms have been changing. Okay, so you can do that. I'm not sure I'll have time to kind of tell you much about that. The other thing you can do is sort of envision an open economy version of this model and sort of compare a closed economy versus an open economy. You can look at different degrees of trade openness and see how welfare is changing as a function of how welfare would change in an economy with no distortions or in an economy in which inequality didn't matter. Okay, so in terms of sort of looking at the data essentially what you need to kind of measure these things while you obviously need an income distribution. Okay, so if you're looking at evolution over time you can look at you rely on past income distribution. We have a lot of data on that. We rely on IRS data that is publicly available from the NBR. And then you have to choose parameter values for the free labor supply elasticity for the degree of tax progressivity, beta and row. Okay, and it's not a lot of parameters to take into account but also we feel like there's kind of natural ways to calibrate them. So the income distribution we're simply gonna look at data and see how it looks like. For epsilon we're gonna rely on Raj Chetty sort of picks a value of 0.5 it's a sort of a focal one parameter beta pick a parameter that it's about 0.8 which sort of generates markups in line with the data. And then for row we're gonna play with different parameter values but log utility is sort of a natural benchmark. Okay, now this raises the issue of fee how do we measure tax progressivity but here's where the data really helps us. If you look at the implied log linear relationship between disposable income and market income this is a relationship that fits the data remarkably well. And that's kind of surprising because we know that the access system in the US is very complex and you'd think that there'd be all sorts of funny things but arguably part of it is because we rely on just a few moments of the income distribution but you see that the log linear fit maps the data very well. And this has been shown to be more broadly true with richer data sets. Okay, that allows us to kind of back out fee. You can see how fee varies over time because in Democrats, Republicans coming in and out. And then with this you can basically compare mean income growth in the US in recent years which is about 1.3% a year. And then you see that it doesn't take much inequality aversion to kind of back out much, much lower welfare growth. So from 1.31 to 1 from 2.24 reflecting this sort of the fact that the income distribution mean income has grown but the dispersion in income has grown. So let me not say more about this and let me spend four or five minutes on the trade side of the model. So what we do on the trade side is essentially we're gonna take that closed economy in which there were all individuals providing differentiated goods and contributing to society. And now we're gonna envision an open economy version of it in which there's N economies out there that are symmetric in every respect to that economy. There's some cause of doing that. We're just trying to kind of build some tools to think about the effects of trade. We're gonna allow agents in any economy to market their goods locally and in foreign markets but we're gonna introduce costs of doing so. We're gonna have the standard iceberg trade costs which are proportional costs associated with shipping goods across borders. And we're also gonna have fixed costs of exporting that are gonna be key to generate selection into exporting. The fact that yes, we might have a situation where we can now sell abroad as well as domestically but the amount of revenue I'm gonna get abroad is gonna matter for whether I do that or not. And that's gonna generate selection into exporting by which only the most able individuals in society are actually gonna go export and gain from this policy. And we have this parameter FX that governs the size of fixed costs and a parameter alpha that basically tells you how quickly fixed costs grow with the rise of markets and that's gonna generate a more continuous selection by which it's not just that you have individuals that export to all markets and agents that do not, you're gonna have a smooth selection by which as ability grows and grows, individuals are gonna be selecting into more and more markets. So that's gonna generate a more smooth effect of trade on the income distribution. The type of results that come out of the framework are not super surprising relative to autarchy. We have that trade increases inequality in revenues and utilities. And as a result of that when you compare welfare under autarchy with say the current trade opening, you're gonna this sort of corrections that I introduced before are gonna matter in the sense that as inequality grows, yes, there's gonna be some redistribution through the progressive tax system, but it's not gonna fully compensate the losers. The distribution of disposable income is gonna get wider as well and that's gonna generate lower welfare gains that we would infer from aggregate income at the same time the fact that the distribution of income is becoming wider, meaning that rich individuals are transitioning towards higher marginal tax rates, which is gonna lead to labor supply decisions and a generation of income that differs from the one that you'd get in a model in which you didn't have those distortions. So to show exactly how that plays out quantitatively, we calibrate the US economy to 2007. We do so in a manner analogous and I went very quickly, but in a manner analogous to what we did in the closed economy, which we use the distribution of income from the data, we use parameters that are sensible that have been sort of widely used in the literature and then we compare the implications of a move to autarchy or a move to 1979 trade levels in terms of aggregate income and inequality and we use this formula to kind of do that. And the key things is how does social welfare, the social welfare implications of trade vary with different degrees of inequality aversion and how large would welfare have been in the absence of cost of redistribution. Okay, so this is some details on the calibration. I'm gonna skip that if that's okay and then just show you some results. What we get is this is a move, we have a move to 1979 trade cost. We have a move back to autarchy. It generates fairly moderate consumption gains and income gains. You might be surprised about that if you've been following trade literature. This is not that surprising. Our models of trade tend to generate relatively small income implications of trade opening. What I wanna highlight however, is that the effects on inequality are not small. That is percentually you get income growth, say of going to autarchy of like two, three, maybe 6% of you assume a higher free slave or supply elasticity but the effects on the genetic coefficients are not trivial, okay? So that's gonna tell you that these inequality corrections may have some bite. How exactly? Well, that's gonna be a function of the degree of inequality aversion if you're in a situation in which, think about first about the welfare's correction. This is essentially one minus the Atkinson index. If you don't have any inequality aversion, obviously you don't discount against from trade. You're at one up here. But as you start increasing the degree of inequality aversion, obviously the welfare implications of trade or the percentage growth in social welfare are gonna be lower than the percentage growth in min income by how much lower it's this blue line and you see that it depends on really what row you pick. If you pick a row of one, you get something between 20 and 25% lower welfare against from trade than you would without inequality aversion, okay? You can play around with numbers. You get smaller, bigger numbers but it's all, you know, it's not minuscule but it's not saying that all the gains from trade are gone. You can look at the costly redistribution correction. Now that one is naturally gonna be shaped by the elasticity of taxable income. We pick 0.5 as a focal parameter value and what we see is that the auto counterfactual would kill about 15% of the gains from trade and whereas the 79 counterfactual is a little bit less like 10%, okay? So overall, you know, we do a lot of robustness on how different parameter values affect this numbers but something along 20% reductions and welfare gains from trade seems to kind of be a good sort of summary of the results. So let me, I think I'm basically out of time so I'm just gonna conclude. What I've argued is that trade in those inequality, yes, it's partly mitigated by the tax system but it's not fully mitigated and because compensation is not full, one might argue whether the Calder-Hicks principle is really free of value judgments. If we know that compensation is actually not taking place and we know that the distribution of disposable income is becoming more dispersed as a result of trade, should we not take that into account when we measure the gains from trade? I would argue that we should and if we know that income taxation is not distortionary, that it induces behavioral responses that affect aggregate income when trade opens up, shouldn't we take that into account? I would argue that we should and we're developing tools to kind of deal with that and that's essentially what this paper does. It's sort of develop a welfare system because of the distribution corrections to standard measures of the gains from trade. So I'll pass here and I will leave you with Hicks. Thank you, Paul. And I immediately give the floor to which will be done automatically now. I'm gonna play by with the. Yeah, you need to close that. Okay, it was a real pleasure to be asked to discuss this paper because it's the kind of paper that really educates you. I felt like I have kind of a hole in my knowledge about welfare economics. It was partially filled as I read this and you could even tell from the Paul's presentation that you can see some of that. But let me kind of emphasize different things in this talk. Let's start with a picture. They have right at the beginning of the paper which looks at the US from 1979 to 2007. So almost a 30 year period and it looks at two things. It looks at trade to gross output which is the blue line that's growing from 5% to almost 8%. And those numbers seem very small but that is done over. We often look at say the manufacturing sector. This is just looking at the whole economy. So those numbers look sort of small and then it's also looking at the Gini coefficient of market income. So let's first think about the blue line and then we'll bring in the red line later. So in the trade literature, we've been calculating gains from trade using quantitative models that fit bilateral trade data so we feel like they're based on something. So let me give you a little sense of how those work. Well, we start by measuring a country's distance from autarky by looking at basically one minus the blue line. So how far are you from just buying everything locally? So the XNN is what you buy from yourself, XN is what you buy in total. Okay, then we observe that we can see this thing changing over time. I mean, just a profound trend in the data is that Lambda is falling over time although it's kind of leveled off in the last few years. So if we have two values of Lambda, we can take the ratio, raise it to the minus one over theta power where theta is a trade elasticity and we get a measure of the proportional gains from trade. So if we put in theta four, which actually very nicely matches the value, one of the parameters in close paper, we get a welfare gain of about three-fourths of a percent. Now, that's modest, that's just, I mean, that's kind of in the ballpark of what you get. Those numbers can get bigger when you have multiple industries or input-output relationships, but in a big country like the United States, you don't get giant numbers for such in such calculations. Okay, now, where is that coming from? What are the kind of pros and cons of that approach? Well, it's theoretically sounding. Actually, Jonathan Eaton and I kind of came upon it. Randomly in working on a model of trade and we thought, oh, wow, that's a real, we were doing these complicated simulations on the computer and then we realized, oh, actually, we could just do this back in the envelope calculation. At least we were thinking of it as going all the way from autarky where the Lambda equals one to our present situation where Lambda is less than one, but not all that much less than one for the United States. And then, Dave Donaldson used it in the way that I just used it where it's sort of how much gains you've gotten by moving from some level of trade to some higher level of trade, so Lambda declining, and then Archelacus Costano and Rodriguez-Claris show that it actually is a statistic that's kind of theoretically motivated by a bunch of the models we've been using to fit bilateral trade and to fit firm level data and so on. So that was kind of attractive. And back to Donaldson, I think his use of it in his paper, Railroads of the Raj, was particularly compelling because then he shows that in looking at the gains from railroads, it kind of beat out a direct measure of railroads as a way to capture the real income gains brought about by the railroads. So it was sort of this sufficient statistic. Who cares about the railroad data? You can just look at how much more India traded and that itself would be a better measure of how the railroads raised income. Okay, what's the major shortcoming? Well, this comes out of models where labor's mobile, so there's no income variation. For that matter, there's no taxes in most of our trade models. So it didn't really, we were kind of implicitly building in this Caldor-Hicks principle, and that's where this paper comes in, is what do you do if you don't want to build in such a principle? And the paper both gives good reasons why you wouldn't want to build in such a principle, and then what you do if you want to get around it, what else can you do? Okay, so it's a real, as I said, it's a real third of force. It's a very tight theory, careful calibration, and sometimes surprisingly, calibration that really fits the data nicely. And as I mentioned, a kind of clear connection to the past theory that it's very nice for just sort of understanding how all these things fit together. It really exploits these constant elasticity functional forms and makes it very parsimonious and clear, but one nice feature is that it leaves the income. By doing that, it can be very non-parametric about the income distribution itself, which is quite nice. So you can just kind of let that, the shifts in the income distribution kind of speak directly rather than having to parameterize them. So you get a formula like this where you start on the right side with something like I showed you, which is a calculation that's not taking into it. It doesn't have any distortions from taxation and labor supply elasticity and then takes account of how you lower the gains from trade because of such distortions and then how you further lower them if you're inequality averse and then gets you to an overall gains from trade. Now, it's not quite that general in the sense that the rightmost term, you can't just take the one I gave you before and stick it in there because you actually, I mean, this is a first shot at this. They have to make a kind of particular model of trade that integrates with the rest of the theory. So the W tilde prime over W tilde has to come out of a model of trade that integrates with this theory. And so that's what I wanna talk about for most of the rest of my discussion here. So let me, I think Paul did a great job of kind of describing the basic stuff. So let me skip over this and go right to the international trade part which he had to go over kind of quickly. So the way the international trade model works that does integrate with this theory and allows us to do this welfare correction to take into account both inequality aversion and the losses from the interaction of progressivity and a labor supply elasticity is a model with symmetric countries. There's preferences over the outputs of individual individuals in the economy, individual workers. It kind of has a feel of a Krugman monopolistic competition model except there are no firms and there's no monopolistic competition. The firms are replaced by just individuals who are just supplying their output to different countries. So workers have an incentive to try and sell their output in multiple countries because they escape kind of pushing down their demand curve for their special thing that they bring to the world. If you sell a little bit in the US and a little bit in Germany, you're not glutting the market in the US. But it's increasingly expensive to export to more countries and that's a kind of Melitz feature of the model that there's this fixed cost of entry into different export destinations. But again, it's individuals not firms. Now that seems like the kind of, when I first read the paper, I was like, great. And then I got to that and I thought, this isn't gonna cut it. This is such an abstraction as a way to think about firms. I don't really sell my, you know, the output of what I do internationally. Well, maybe we kind of do as academics. But anyway, it didn't seem like a good way to explain the whole economy. As I sort of lived with the paper over the last few weeks, sort of became more sympathetic for one, it wasn't easy to think of a better way to do it. And I think there is a way to think of this kind of connected to more classical models of trade. So that's what I want to do next. Okay, so this is an example actually, a numerical example that's very similar to one that Krugman had, which he said he himself borrowed from Lewis. So it has three sectors, sector one, two, and three. And I'm making two countries, the US and the EU, and I'm showing you there the productivities. Don't worry, I copy those into each subsequent slide because you kind of need them to figure out what happens. Okay, so each country is endowed with three workers and there's symmetric Cobb-Douglas preferences. So we spend one third on each of these goods. We want to spend a third of our income on each of these goods. Okay, so let's start with autarky. Now in autarky, because of Cobb-Douglas preferences, there's gonna be, the equilibrium will be one worker in each sector and that the labor theory of value will then give us relative prices. So that's kind of our baseline setting. Okay, so it's two under the anniversary of Ricardo's model of trade, so it's nice to talk about that today. In a model of trade, wages get equalized across countries, at least if the countries are similar enough and they're symmetric here. And that's because both countries continue to produce a sector too good and in the sector too good, they're equally productive so they have the same wage because they're competing head to head with the same productivity so they have to have the same wage. Now trade is disruptive as it typically is in the sense that workers abandon sector one in the US and workers abandon sector three in the EU. Then relative prices, you can think of the labor theory of value still holding within the two sectors that each country still has workers in because you gotta make them happy to work in either of those sectors and that gives us our relative prices two thirds one and two thirds and we can think about the gains from trade here in a kind of idiosyncratic way that I like which is that the US who's abandoned sector one has effectively a productivity of producing sector one goods that's improved and why is that? Because they've pulled that guy from sector one who's moved over to sector three, he can produce three units of sector three good, trade them at a relative price of one to two thirds to get sector two goods, trade that to buy the sector one good and he ends up getting three of the sector one good so it's as if the US got a productivity gain from one to three in sector one but they're literally not producing any sector one goods they're trading for them, they're producing sector three goods and buying sector one goods from the EU and that gives the US and it would be symmetrically kind of a mirror image in the EU a welfare gain of 1.44 or 44% it's a little bigger than my 0.7% but anyway that's the idea. Okay now what if we go back to autarky and think about those workers there to distribute remember the Ricardian model the workers all abandoned sector one in the US and sector three in the EU now let's go back to these workers in these three sectors one worker in each sector and let's suppose that when we open up to trade they just can't move, they're stuck maybe that's just what they know how to do or maybe this is a kind of transitional situation where they haven't yet realized they need to it's costly for them to retrain for the other sectors. So in this situation we basically get an endowments model because why is that? Because there's these fixed workers in each sector one in each sector there's productivity that generates an output of each of these three goods in each of these three countries and then they start to trade well that's called the endowments model of trade you just got some stuff here you've got some stuff here you start to trade they're still gains from trade in that world because of the heterogeneity and productivity. So in fact the gains from trade are 1.1 the Caldor Hicks gains from trade are 1.1 so but it's incredibly unequally distributed so think about it I mean the way to think about it is that wages are just gonna suddenly be quite different across sectors but one way to think about it is just think about a worker who's still stuck in sector one that guy used to be able to buy three units of sector three output in autarky because then he was producing this thing with low productivity so the price was high now the price isn't high anymore it's not any higher because we're now trading with this symmetric mirror image of ourselves and so now he can only buy one unit of the sector one good so that's a huge loss to that guy and that generates a huge amount of dispersion in gains and I mean I think that's a reasonable way to think about a kind of populist backlash against trade is that you got those sector one guys are the ones who are they're gonna like what Trump has to say so okay so what did I wanna go? Okay so now what happens how do I tie this together with the model in polls paper? Well before I abandon this do I have five minutes left? Okay let me say one more thing about this model which is this is not the source of the changes in the income distribution in the model in polls model. I think this is a good way of thinking about it but it's not what they do they mentioned that this is not what they do because they sort of think of this kind of effect as being more of a show run effect about workers not moving now of course because if the workers just moved to where the high wages were we'd be back in the Ricardian thing and everybody would gain and then you'd have the Caldor Hicks. So what do they do? Well they do something slightly different basically eliminate the head to head competition in international trade by just saying well actually they're just six goods there's the good one produced in Europe and that's not the same as the good one produced in the US. So now they're six goods makes symmetric CES preferences across those six goods. Productivity's unchanged from my example and now you can just think of some workers having high productivity and some workers having low productivity. We've kind of eliminated this idea that a sector really means anything it's just you this is just you and how much stuff can you produce and these goods are all symmetrically entering people's utility function. Now you can see that the workers with the you know now it's really high productivity workers because they're just producing the same it's not the same stuff but it's symmetric and it's those high productivity workers who are gonna be more willing to overcome the fixed cost of selling abroad and in fact that's crucial for this widening of the income distribution in their model is that some people decide to sell in both countries and some people don't find it worthwhile to pay that fixed cost. They're stuck just producing locally and now they're facing the increased competition from abroad so you widen the income distribution and that's the model of this paper. Okay to just give you a little taste for results remember I came up with like a three-fourth percent gain Caldor-Hicks gain in their calibration give something slightly different but it's the same ballpark around one percent. Now let's get back to the red curve the genie coefficient so in the data it went up 23% in their model calibration of this sort of inequality generating mechanism of trade they capture about a one percent change so it's five percent of the actual inequality can be captured by this mechanism but that doesn't do trivial things it's even though there's a lot of inequality increased still to be explained their correction for inequality that the social planner doesn't like has them down weight that one percent Caldor-Hicks gain by a factor of 0.8 and then the inefficiency of kind of generating more inequality having that taxed higher at the high end and then that leads that guy to work less that's the kind of theta effect that has you reduce welfare by another factor of 0.9 so these are adjustments that aren't overwhelming on the other hand they're not trivial and I think that's about all you can hope for in this kind of first cut so I think we do need a better understanding of the distributional consequences of trade this paper takes a big step in the right direction by kind of developing a very nice tool for doing that and I guess my main comment would be going ahead with this research agenda to try and get this kind of tool to interact with more standard models of trade one that I really like that has this heterogeneity is by Kali Endo, Dworkin and Perot that kind of speaks to some of the issues that Autodorn and Hansen have uncovered about distributional consequences of trade. Thank you sir. We have some minutes left for questions from the floor.